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Replacing hype about artificial intelligence with accurate measurements of success.
(Illustration credit: Kyle Palmer / PPPL Communications Department)
PPPL researchers find overoptimism in journal articles using machine learning to solve fluid-related partial differential equations
The hype surrounding machine learning, a form of artificial intelligence, can make it seem like it is only a matter of time before such techniques are used to solve all scientific problems. While impressive claims are often made, those claims do not always hold up under scrutiny. Machine learning may be useful for solving some problems but falls short for others.
In a new paper in Nature Machine Intelligence, researchers at the U.S. Department of Energy ’s Princeton Plasma Physics Laboratory (PPPL) and Princeton University performed a systematic review of research comparing machine learning to traditional methods for solving fluid-related partial differential equations (PDEs). Such equations are important in many scientific fields, including the plasma research that supports the development of fusion power for the electricity grid.
The researchers found that comparisons between machine learning methods for solving fluid-related PDEs and traditional methods are often biased in favor of machine learning methods. They also found that negative results were consistently underreported. They suggest rules for performing fair comparisons but argue that cultural changes are also needed to fix what appear to be systemic problems.
“Our research suggests that, though machine learning has great potential, the present literature paints an overly optimistic picture of how machine learning works to solve these particular types of equations,” said Ammar Hakim , PPPL’s deputy head of computational science and the principal investigator on the research.
PDEs are ubiquitous in physics and are particularly useful for explaining natural phenomena, such as heat, fluid flow and waves. For example, these kinds of equations can be used to figure out the temperatures along the length of a spoon placed in hot soup. Knowing the initial temperature of the soup and the spoon, as well as the type of metal in the spoon, a PDE could be used to determine the temperature at any point along the utensil at a given time after it was placed in the soup. Such equations are used in plasma physics, as many of the equations that govern plasmas are mathematically similar to those of fluids.
Scientists and engineers have developed various mathematical approaches to solving PDEs. One approach is known as numerical methods because it solves problems numerically, rather than analytically or symbolically, to find approximate solutions to problems that are difficult or impossible to solve exactly. Recently, researchers have explored whether machine learning can be used to solve these PDEs. The goal is to solve problems faster than they could with other methods.
The systematic review found that in most journal articles, machine learning hasn’t been as successful as advertised. “Our research indicates that there might be some cases where machine learning can be slightly faster for solving fluid-related PDEs, but in most cases, numerical methods are faster,” said Nick McGreivy . McGreivy is the lead author of the paper and recently completed his doctorate at the Princeton Program in Plasma Physics .
Numerical methods have a fundamental trade-off between accuracy and runtime. “If you spend more time to solve the problem, you’ll get a more accurate answer,” McGreivy said. “Many papers didn’t take that into account in their comparisons.”
Furthermore, there can be a dramatic difference in speed between numerical methods. In order to be useful, machine learning methods need to outperform the best numerical methods, McGreivy said. Yet his research found that comparisons were often being made to numerical methods that were much slower than the fastest methods.
Consequently, the paper proposes two rules to try to overcome these problems. The first rule is to only compare machine learning methods against numerical methods of either equal accuracy or equal runtime. The second is to compare machine learning methods to an efficient numerical method.
Of 82 journal articles studied, 76 claimed the machine learning method outperformed when compared to a numerical method. The researchers found that 79% of those articles touting a machine learning method as superior actually had a weak baseline, breaking at least one of those rules. Four of the journal articles claimed to underperform when compared to a numerical method, and two articles claimed to have similar or varied performance.
The researchers created the image above to convey the cumulative effects of weak baselines and reporting biases on samples. The circles or hexagons represent articles. Green indicates a positive result, for example, that the machine learning method was faster than the numerical method, while red represents a negative result. Column (a) shows what the system would likely look like if strong baselines were used and reporting bias was not an issue. Column (b) depicts the likely results without reporting bias. Column (c) shows the actual results seen in the published literature. (Image credit: Nick McGreivy / Princeton University)
“Very few articles reported worse performance with machine learning, not because machine learning almost always does better, but because researchers almost never publish articles where machine learning does worse,” McGreivy said.
McGreivy thinks low-bar comparisons are often driven by perverse incentives in academic publishing. “In order to get a paper accepted, it helps to have some impressive results. This incentivizes you to make your machine learning model work as well as possible, which is good. However, you can also get impressive results if the baseline method you’re comparing to doesn’t work very well. As a result, you aren’t incentivized to improve your baseline, which is bad,” he said. The net result is that researchers end up working hard on their models but not on finding the best possible numerical method as a baseline for comparison.
The researchers also found evidence of reporting biases, including publication bias and outcome reporting bias. Publication bias occurs when a researcher chooses not to publish their results after realizing that their machine learning model doesn’t perform better than a numerical method, while outcome reporting bias can involve discarding negative results from the analyses or using nonstandard measures of success that make machine learning models appear more successful. Collectively, reporting biases tend to suppress negative results and create an overall impression that machine learning is better at solving fluid-related PDEs than it is.
“There’s a lot of hype in the field. Hopefully, our work lays guidelines for principled approaches to use machine learning to improve the state of the art,” Hakim said.
To overcome these systemic, cultural issues, Hakim argues that agencies funding research and large conferences should adopt policies to prevent the use of weak baselines or require a more detailed description of the baseline used and the reasons it was selected. “They need to encourage their researchers to be skeptical of their own results,” Hakim said. “If I find results that seem too good to be true, they probably are.” This work was completed with funding from DOE grants DE-AC02-09CH11466 and DE-AC02-09CH11466.
PPPL is mastering the art of using plasma — the fourth state of matter — to solve some of the world's toughest science and technology challenges. Nestled on Princeton University’s Forrestal Campus in Plainsboro, New Jersey, our research ignites innovation in a range of applications including fusion energy, nanoscale fabrication, quantum materials and devices, and sustainability science. The University manages the Laboratory for the U.S. Department of Energy’s Office of Science, which is the nation’s single largest supporter of basic research in the physical sciences. Feel the heat at https://energy.gov/science and https://www.pppl.gov .
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Nature Machine Intelligence volume 5 , pages 1326–1335 ( 2023 ) Cite this article
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A tool that could suggest new personalized research directions and ideas by taking insights from the scientific literature could profoundly accelerate the progress of science. A field that might benefit from such an approach is artificial intelligence (AI) research, where the number of scientific publications has been growing exponentially over recent years, making it challenging for human researchers to keep track of the progress. Here we use AI techniques to predict the future research directions of AI itself. We introduce a graph-based benchmark based on real-world data—the Science4Cast benchmark, which aims to predict the future state of an evolving semantic network of AI. For that, we use more than 143,000 research papers and build up a knowledge network with more than 64,000 concept nodes. We then present ten diverse methods to tackle this task, ranging from pure statistical to pure learning methods. Surprisingly, the most powerful methods use a carefully curated set of network features, rather than an end-to-end AI approach. These results indicate a great potential that can be unleashed for purely ML approaches without human knowledge. Ultimately, better predictions of new future research directions will be a crucial component of more advanced research suggestion tools.
The corpus of scientific literature grows at an ever-increasing speed. Specifically, in the field of artificial intelligence (AI) and machine learning (ML), the number of papers every month is growing exponentially with a doubling rate of roughly 23 months (Fig. 1 ). Simultaneously, the AI community is embracing diverse ideas from many disciplines such as mathematics, statistics and physics, making it challenging to organize different ideas and uncover new scientific connections. We envision a computer program that can automatically read, comprehend and act on AI literature. It can predict and suggest meaningful research ideas that transcend individual knowledge and cross-domain boundaries. If successful, it could greatly improve the productivity of AI researchers, open up new avenues of research and help drive progress in the field.
The doubling rate of papers per month is roughly 23 months, which might lead to problems for publishing in these fields, at some point. The categories are cs.AI, cs.LG, cs.NE and stat.ML.
In this work, we address the ambitious vision of developing a data-driven approach to predict future research directions 1 . As new research ideas often emerge from connecting seemingly unrelated concepts 2 , 3 , 4 , we model the evolution of AI literature as a temporal network. We construct an evolving semantic network that encapsulates the content and development of AI research since 1994, with approximately 64,000 nodes (representing individual concepts) and 18 million edges (connecting jointly investigated concepts).
We use the semantic network as an input to ten diverse statistical and ML methods to predict the future evolution of the semantic network with high accuracy. That is, we can predict which combinations of concepts AI researchers will investigate in the future. Being able to predict what scientists will work on is a first crucial step for suggesting new topics that might have a high impact.
Several methods were contributions to the Science4Cast competition hosted by the 2021 IEEE International Conference on Big Data (IEEE BigData 2021). Broadly, we can divide the methods into two classes: methods that use hand-crafted network-theoretical features and those that automatically learn features. We found that models using carefully hand-crafted features outperform methods that attempt to learn features autonomously. This (somewhat surprising) finding indicates a great potential for improvements of models free of human priors.
Our paper introduces a real-world graph benchmark for AI, presents ten methods for solving it, and discusses how this task contributes to the larger goal of AI-driven research suggestions in AI and other disciplines. All methods are available at GitHub 5 .
The goal here is to extract knowledge from the scientific literature that can subsequently be processed by computer algorithms. At first glance, a natural first step would be to use large language model (such as GPT3 6 , Gopher 7 , MegaTron 8 or PaLM 9 ) on each article to extract concepts and their relations automatically. However, these methods still struggle in reasoning capabilities 10 , 11 ; thus, it is not yet directly clear how these models can be used for identifying and suggesting new ideas and concept combinations.
Rzhetsky et al. 12 pioneered an alternative approach, creating semantic networks in biochemistry from co-occurring concepts in scientific papers. There, nodes represent scientific concepts, specifically biomolecules, and are linked when a paper mentions both in its title or abstract. This evolving network captures the field’s history and, using supercomputer simulations, provides insights into scientists’ collective behaviour and suggests more efficient research strategies 13 . Although creating semantic networks from concept co-occurrences extracts only a small amount of knowledge from each paper, it captures non-trivial and actionable content when applied to large datasets 2 , 4 , 13 , 14 , 15 . PaperRobot extends this approach by predicting new links from large medical knowledge graphs and formulating new ideas in human language as paper drafts 16 .
This approach was applied and extended to quantum physics 17 by building a semantic network of over 6,000 concepts. There, the authors (including one of us) formulated the prediction of new research trends and connections as an ML task, with the goal of identifying concept pairs not yet jointly discussed in the literature but likely to be investigated in the future. This prediction task was one component for personalized suggestions of new research ideas.
We formulate the prediction of future research topics as a link-prediction task in an exponentially growing semantic network in the AI field. The goal is to predict which unconnected nodes, representing scientific concepts not yet jointly researched, will be connected in the future.
Link prediction is a common problem in computer science, addressed with classical metrics and features, as well as ML techniques. Network theory-based methods include local motif-based approaches 18 , 19 , 20 , 21 , 22 , linear optimization 23 , global perturbations 24 and stochastic block models 25 . ML works optimized a combination of predictors 26 , with further discussion in a recent review 27 .
In ref. 17 , 17 hand-crafted features were used for this task. In the Science4Cast competition, the goal was to find more precise methods for link-prediction tasks in semantic networks (a semantic network of AI that is ten times larger than the one in ref. 17 ).
The long-term goal of predictions and suggestions in semantic networks is to provide new ideas to individual researchers. In a way, we hope to build a creative artificial muse in science 28 . We can bias or constrain the model to give topic suggestions that are related to the research interest of individual scientists, or a pair of scientists to suggest topics for collaborations in an interdisciplinary setting.
Dataset construction.
We create a dynamic semantic network using papers published on arXiv from 1992 to 2020 in the categories cs.AI, cs.LG, cs.NE and stat.ML. The 64,719 nodes represent AI concepts extracted from 143,000 paper titles and abstracts using Rapid Automatic Keyword Extraction (RAKE) and normalized via natural language processing (NLP) techniques and custom methods 29 . Although high-quality taxonomies such as the Computer Science Ontology (CSO) exist 30 , 31 , we choose not to use them for two reasons: the rapid growth of AI and ML may result in new concepts not yet in the CSO, and not all scientific domains have high-quality taxonomies like CSO. Our goal is to build a scalable approach applicable to any domain of science. However, future research could investigate merging these approaches (see ‘Extensions and future work’).
Concepts form the nodes of the semantic network, and edges are drawn when concepts co-appear in a paper title or abstract. Edges have time stamps based on the paper’s publication date, and multiple time-stamped edges between concepts are common. The network is edge-weighted, and the weight of an edge stands for the number of papers that connect two concepts. In total, this creates a time-evolving semantic network, depicted in Fig. 2 .
Utilizing 143,000 AI and ML papers on arXiv from 1992 to 2020, we create a list of concepts using RAKE and other NLP tools, which form nodes in a semantic network. Edges connect concepts that co-occur in titles or abstracts, resulting in an evolving network that expands as more concepts are jointly investigated. The task involves predicting which unconnected nodes (concepts not yet studied together) will connect within a few years. We present ten diverse statistical and ML methods to address this challenge.
The published semantic network has 64,719 nodes and 17,892,352 unique undirected edges, with a mean node degree of 553. Many hub nodes greatly exceed this mean degree, as shown in Fig. 3 , For example, the highest node degrees are 466,319 (neural network), 198,050 (deep learning), 195,345 (machine learning), 169,555 (convolutional neural network), 159,403 (real world), 150,227 (experimental result), 127,642 (deep neural network) and 115,334 (large scale). We fit a power-law curve to the degree distribution p ( k ) using ref. 32 and obtained p ( k ) ∝ k −2.28 for degree k ≥ 1,672. However, real complex network degree distributions often follow power laws with exponential cut-offs 33 . Recent work 34 has indicated that lognormal distributions fit most real-world networks better than power laws. Likelihood ratio tests from ref. 32 suggest truncated power law ( P = 0.0031), lognormal ( P = 0.0045) and lognormal positive ( P = 0.015) fit better than power law, while exponential ( P = 3 × 10 −10 ) and stretched exponential ( P = 6 × 10 −5 ) are worse. We couldn’t conclusively determine the best fit with P ≤ 0.1.
Nodes with the highest (466,319) and lowest (2) non-zero degrees are neural network and video compression technique, respectively. The most frequent non-zero degree is 64 (which occures 313 times). The plot, in log scale, omits 1,247 nodes with zero degrees.
We observe changes in network connectivity over time. Although degree distributions remained heavy-tailed, the ordering of nodes within the tail changed due to popularity trends. The most connected nodes and the years they became so include decision tree (1994), machine learning (1996), logic program (2000), neural network (2005), experimental result (2011), machine learning (2013, for a second time) and neural network (2015).
Connected component analysis in Fig. 4 reveals that the network grew more connected over time, with the largest group expanding and the number of connected components decreasing. Mid-sized connected components’ trajectories may expose trends, like image processing. A connected component with four nodes appeared in 1999 (brightness change, planar curve, local feature, differential invariant), and three more joined in 2000 (similarity transformation, template matching, invariant representation). In 2006, a paper discussing support vector machine and local feature merged this mid-sized group with the largest connected component.
Primary (left, blue) vertical axis: number of connected components with more than one node. Secondary (right, orange) vertical axis: number of nodes in the largest connected component. For example, the network in 2019 comprises of one large connected component with 63,472 nodes and 1,247 isolated nodes, that is, nodes with no edges. However, the 2001 network has 19 connected components with size greater than one, the largest of which has 2,733 nodes.
The semantic network reveals increasing centralization over time, with a smaller percentage of nodes (concepts) contributing to a larger fraction of edges (concept combinations). Figure 5 shows that the fraction of edges for high-degree nodes rises, while it decreases for low-degree nodes. The decreasing average clustering coefficient over time supports this trend, suggesting nodes are more likely to connect to high-degree central nodes. This could be due to the AI community’s focus on a few dominating methods or more consistent terminology use.
This cumulative histogram illustrates the fraction of nodes (concepts) corresponding to the fraction of edges (connections) for given years (1999, 2003, 2007, 2011, 2015 and 2019). The graph was generated by adding edges and nodes dated before each year. Nodes are sorted by increasing degrees. The y value at x = 80 represents the fraction of edges contributed by all nodes in and below the 80th percentile of degrees.
At the big picture, we aim to make predictions in an exponentially growing semantic network. The specific task involves predicting which two nodes v 1 and v 2 with degrees d ( v 1/ 2 ) ≥ c lacking an edge in the year (2021 − δ ) will have w edges in 2021. We use δ = 1, 3, 5, c = 0, 5, 25 and w = 1, 3, where c is a minimal degree. Note that c = 0 is an intriguing special case where the nodes may not have an associated edge in the initial year, requiring the model to predict which nodes will connect to entirely new edges. The task w = 3 goes beyond simple link prediction and seeks to identify uninvestigated concept pairs that will appear together in at least three papers. An interesting alternative task could be predicting the fastest-growing links, denoted as ‘trend’ prediction.
In this task, we provide a list of 10 million unconnected node pairs (each node having a degree ≥ c ) for the year (2021 − δ ), with the goal of sorting this list by descending probability that they will have at least w edges in 2021.
For evaluation, we employ the receiver operating characteristic (ROC) curve 35 , which plots the true-positive rate against the false-positive rate at various threshold settings. We use the area under the curve (AUC) of the ROC curve as our evaluation metric. The advantage of AUC over mean square error is its independence from the data distribution. Specifically, in our case, where the two classes have a highly asymmetric distribution (with only about 1–3% of newly connected edges) and the distribution changes over time, AUC offers meaningful interpretation. Perfect predictions yield AUC = 1, whereas random predictions result in AUC = 0.5. AUC represents the percentage that a random true element is ranked higher than a random false one. For other metrics, see ref. 36 .
To tackle this task, models can use the complete information of the semantic network from the year (2021 − δ ) in any way possible. In our case, all presented models generate a dataset for learning to make predictions from (2021 − 2 δ ) to (2021 − δ ). Once the models successfully complete this task, they are applied to the test dataset to make predictions from (2021 − δ ) to 2021. All reported AUCs are based on the test dataset. Note that solving the test dataset is especially challenging due to the δ -year shift, causing systematic changes such as the number of papers and density of the semantic network.
We demonstrate various methods to predict new links in a semantic network, ranging from pure statistical approaches and neural networks with hand-crafted features (NF) to ML models without NF. The results are shown in Fig. 6 , with the highest AUC scores achieved by methods using NF as ML model inputs. Pure network features without ML are competitive, while pure ML methods have yet to outperform those with NF. Predicting links generated at least three times can achieve a quasi-deterministic AUC > 99.5%, suggesting an interesting target for computational sociology and science of science research. We have performed numerous tests to exclude data leakage in the benchmark dataset, overfitting or data duplication both in the set of articles and the set of concepts. We rank methods based on their performance, with model M1 as the best performing and model M8 as the least effective (for the prediction of a new edge with δ = 3, c = 0). Models M4 and M7 are subdivided into M4A, M4B, M7A and M7B, differing in their focus on feature or embedding selection (more details in Methods ).
Here we show the AUC values for different models that use machine learning techniques (ML), hand-crafted network features (NF) or a combination thereof. The left plot shows results for the prediction of a single new link (that is, w = 1) and the right plot shows the results for the prediction of new triple links w = 3. The task is to predict δ = [1, 3, 5] years into the future, with cut-off values c = [0, 5, 25]. We sort the models by the the results for the task ( w = 1, δ = 3, c = 0), which was the task in the Science4Cast competition. Data points that are not shown have a AUC below 0.6 or are not computed due to computational costs. All AUC values reported are computed on a validation dataset δ years ahead of the training dataset that the models have never seen. Note that the prediction of new triple edges can be performed nearly deterministic. It will be interesting to understand the origin of this quasi-deterministic pattern in AI research, for example, by connecting it to the research interests of scientists 88 .
Model M1: NF + ML. This approach combines tree-based gradient boosting with graph neural networks, using extensive feature engineering to capture node centralities, proximity and temporal evolution 37 . The Light Gradient Boosting Machine (LightGBM) model 38 is employed with heavy regularization to combat overfitting due to the scarcity of positive examples, while a time-aware graph neural network learns dynamic node representations.
Model M2: NF + ML. This method utilizes node and edge features (as well as their first and second derivatives) to predict link formation probabilities 39 . Node features capture popularity, and edge features measure similarity. A multilayer perceptron with rectified linear unit (ReLU) activation is used for learning. Cold start issues are addressed with feature imputation.
Model M3: NF + ML. This method captures hand-crafted node features over multiple time snapshots and employs a long short-term memory (LSTM) to learn time dependencies 40 . The features were selected to be highly informative while having a low computational cost. The final configuration uses degree centrality, degree of neighbours and common neighbours as features. The LSTM outperforms fully connected neural networks.
Model M4: pure NF. Two purely statistical methods, preferential attachment 41 and common neighbours 27 , are used 42 . Preferential attachment is based on node degrees, while common neighbours relies on the number of shared neighbours. Both methods are computationally inexpensive and perform competitively with some learning-based models.
Model M5: NF + ML. Here, ten groups of first-order graph features are extracted to obtain neighbourhood and similarity properties, with principal component analysis 43 applied for dimensionality reduction 44 . A random forest classifier is trained on the balanced dataset to predict new links.
Model M6: NF + ML. The baseline solution uses 15 hand-crafted features as input to a four-layer neural network, predicting the probability of link formation between node pairs 17 .
Model M7: end-to-end ML (auto node embedding). The baseline solution is modified to use node2vec 45 and ProNE embeddings 46 instead of hand-crafted features. The embeddings are input to a neural network with two hidden layers for link prediction.
Model M8: end-to-end ML (transformers). This method learns features in an unsupervised manner using transformers 47 . Node2vec embeddings 45 , 48 are generated for various snapshots of the adjacency matrix, and a transformer model 49 is pre-trained as a feature extractor. A two-layer ReLU network is used for classification.
Developing an AI that suggests research topics to scientists is a complex task, and our link-prediction approach in temporal networks is just the beginning. We highlight key extensions and future work directly related to the ultimate goal of AI for AI.
High-quality predictions without feature engineering. Interestingly, the most effective methods utilized carefully crafted features on a graph with extracted concepts as nodes and edges representing their joint publication history. Investigating whether end-to-end deep learning can solve tasks without feature engineering will be a valuable next step.
Fully automated concept extraction. Current concept lists, generated by RAKE’s statistical text analysis, demand time-consuming code development to address irrelevant term extraction (for example, verbs, adjectives). A fully automated NLP technique that accurately extracts meaningful concepts without manual code intervention would greatly enhance the process.
Leveraging ontology taxonomies. Alongside fully automated concept extraction, utilizing established taxonomies such as the CSO 30 , 31 , Wikipedia-extracted concepts, book indices 17 or PhySH key phrases is crucial. Although not comprehensive for all domains, these curated datasets often contain hierarchical and relational concept information, greatly improving prediction tasks.
Incorporating relation extraction. Future work could explore relation extraction techniques for constructing more accurate, sparser semantic networks. By discerning and classifying meaningful concept relationships in abstracts 50 , 51 , a refined AI literature representation is attainable. Using NLP tools for entity recognition, relationship identification and classification, this approach may enhance prediction performance and novel research direction identification.
Generation of new concepts. Our work predicts links between known concepts, but generating new concepts using AI remains a challenge. This unsupervised task, as explored in refs. 52 , 53 , involves detecting concept clusters with dynamics that signal new concept formation. Incorporating emerging concepts into the current framework for suggesting research topics is an intriguing future direction.
Semantic information beyond concept pairs. Currently, abstracts and titles are compressed into concept pairs, but more comprehensive information extraction could yield meaningful predictions. Exploring complex data structures such as hypergraphs 54 may be computationally demanding, but clever tricks could reduce complexity, as shown in ref. 55 . Investigating sociological factors or drawing inspiration from material science approaches 56 may also improve prediction tasks. A recent dataset for the study of the science of science also includes more complex data structures than the ones used in our paper, including data from social networks such as Twitter 57 .
Predictions of scientific success. While predicting new links between concepts is valuable, assessing their potential impact is essential for high-quality suggestions. Introducing a metric of success, like estimated citation numbers or citation growth rate, can help gauge the importance of these connections. Adapting citation prediction techniques from the science of science 58 , 59 , 60 , 61 to semantic networks offers a promising research direction.
Anomaly detections. Predicting likely connections may not align with finding surprising research directions. One method for identifying surprising suggestions involves constraining cosine similarity between vertices 62 , which measures shared neighbours and can be associated with semantic (dis)similarity. Another approach is detecting anomalies in semantic networks, which are potential links with extreme properties 63 , 64 . While scientists often focus on familiar topics 3 , 4 , greater impact results from unexpected combinations of distant domains 12 , encouraging the search for surprising associations.
End-to-end formulation. Our method breaks down the goal of extracting knowledge from scientific literature into subtasks, contrasting with end-to-end deep learning that tackles problems directly without subproblems 65 , 66 . End-to-end approaches have shown great success in various domains 67 , 68 , 69 . Investigating whether such an end-to-end solution can achieve similar success in our context would be intriguing.
Our method represents a crucial step towards developing a tool that can assist scientists in uncovering novel avenues for exploration. We are confident that our outlined ideas and extensions pave the way for achieving practical, personalized, interdisciplinary AI-based suggestions for new impactful discoveries. We firmly believe that such a tool holds the potential to become a influential catalyst, transforming the way scientists approach research questions and collaborate in their respective fields.
In this section, we provide details on the generation of our list of 64,719 concepts. For more information, the code is accessible on GitHub . The entire approach is designed for immediate scalability to other domains.
Initially, we utilized approximately 143,000 arXiv papers from the categories cs.AI, cs.LG, cs.NE and stat.ML spanning 1992 to 2020. The omission of earlier data has a negligible effect on our research question, as we show below. We then iterated over each individual article, employing RAKE (with an extended stopword list) to suggest concept candidates, which were subsequently stored.
Following the iteration, we retained concepts composed of at least two words (for example, neural network) appearing in six or more articles, as well as concepts comprising a minimum of three words (for example, recurrent neural network) appearing in three or more articles. This initial filter substantially reduced noise generated by RAKE, resulting in a list of 104,948 concepts.
Lastly, we developed an automated filtering tool to further enhance the quality of the concept list. This tool identified common, domain-independent errors made by RAKE, which primarily included phrases that were not concepts (for example, dataset provided or discuss open challenge). We compiled a list of 543 words not part of meaningful concepts, including verbs, ordinal numbers, conjunctions and adverbials. Ultimately, this process produced our final list of 64,719 concepts employed in our study. No further semantic concept/entity linking is applied.
By this construction, the test sets with c = 0 could lead to very rare contamination of the dataset. That is because each concept will have at least one edge in the final dataset. The effects, however, are negligible.
The distribution of concepts in the articles can be seen in Extended Data Fig. 1 . As an example, we show the extraction of concepts from five randomly chosen papers:
Memristor hardware-friendly reinforcement learning 70 : ‘actor critic algorithm’, ‘neuromorphic hardware implementation’, ‘hardware neural network’, ‘neuromorphic hardware system’, ‘neural network’, ‘large number’, ‘reinforcement learning’, ‘case study’, ‘pre training’, ‘training procedure’, ‘complex task’, ‘high performance’, ‘classical problem’, ‘hardware implementation’, ‘synaptic weight’, ‘energy efficient’, ‘neuromorphic hardware’, ‘control theory’, ‘weight update’, ‘training technique’, ‘actor critic’, ‘nervous system’, ‘inverted pendulum’, ‘explicit supervision’, ‘hardware friendly’, ‘neuromorphic architecture’, ‘hardware system’.
Automated deep learning analysis of angiography video sequences for coronary artery disease 71 : ‘deep learning approach’, ‘coronary artery disease’, ‘deep learning analysis’, ‘traditional image processing’, ‘deep learning’, ‘image processing’, ‘f1 score’, ‘video sequence’, ‘error rate’, ‘automated analysis’, ‘coronary artery’, ‘vessel segmentation’, ‘key frame’, ‘visual assessment’, ‘analysis method’, ‘analysis pipeline’, ‘coronary angiography’, ‘geometrical analysis’.
Demographic influences on contemporary art with unsupervised style embeddings 72 : ‘classification task’, ‘social network’, ‘data source’, ‘visual content’, ‘graph network’, ‘demographic information’, ‘social connection’, ‘visual style’, ‘historical dataset’, ‘novel information’
The utility of general domain transfer learning for medical language tasks 73 : ‘natural language processing’, ‘long short term memory’, ‘logistic regression model’, ‘transfer learning technique’, ‘short term memory’, ‘average f1 score’, ‘class classification model’, ‘domain transfer learning’, ‘weighted average f1 score’, ‘medical natural language processing’, ‘natural language process’, ‘transfer learning’, ‘f1 score’, ’natural language’, ’deep model’, ’logistic regression’, ’model performance’, ’classification model’, ’text classification’, ’regression model’, ’nlp task’, ‘short term’, ‘medical domain’, ‘weighted average’, ‘class classification’, ‘bert model’, ‘language processing’, ‘biomedical domain’, ‘domain transfer’, ‘nlp model’, ‘main model’, ‘general domain’, ‘domain model’, ‘medical text’.
Fast neural architecture construction using envelopenets 74 : ‘neural network architecture’, ‘neural architecture search’, ‘deep network architecture’, ‘image classification problem’, ‘neural architecture search method’, ‘neural network’, ‘reinforcement learning’, ‘deep network’, ‘image classification’, ‘objective function’, ‘network architecture’, ‘classification problem’, ‘evolutionary algorithm’, ‘neural architecture’, ‘base network’, ‘architecture search’, ‘training epoch’, ‘search method’, ‘image class’, ‘full training’, ‘automated search’, ‘generated network’, ‘constructed network’, ‘gpu day’.
We use articles from arXiv, which only goes back to the year 1992. However, of course, the field of AI exists at least since the 1960s 75 . Thus, this raises the question whether the omission of the first 30–40 years of research has a crucial impact in the prediction task we formulate, specifically, whether edges that we consider as new might not be so new after all. Thus, in Extended Data Fig. 2 , we compute the time between the formation of edges between the same concepts, taking into account all or just the first edge. We see that the vast majority of edges are formed within short time periods, thus the effect of omission of early publication has a negligible effect for our question. Of course, different questions might be crucially impacted by the early data; thus, a careful choice of the data source is crucial 61 .
Table 1 shows the number of positive cases within the 10 million examples in the 18 test datasets that are used for evaluation.
Another field of research that gained a lot of attention in the recent years is quantum physics. This field is also a strong adopter of arXiv. Thus, we analyse in the same way as for AI in Fig. 1 . We find in Extended Data Fig. 3 no obvious exponential increase in papers per month. A detailed analysis of other domains is beyond the current scope. It will be interesting to investigate the growth rates in different scientific disciplines in more detail, especially given that exponential increase has been observed in several aspects of the science of science 3 , 76 .
What follows are more detailed explanations of the models presented in the main text. All codes are available at GitHub. The feature importance of the best model M1 is shown here, those of other models are analysed in the respective workshop contributions (cited in the subsections).
The best-performing solution is based on a blend of a tree-based gradient boosting approach and a graph neural network approach 37 . Extensive feature engineering was conducted to capture the centralities of the nodes, the proximity between node pairs and their evolution over time. The centrality of a node is captured by the number of neighbours and the PageRank score 77 , while the proximity between a node pair is derived using the Jaccard index. We refer the reader to ref. 37 for the list of all features and their feature importance.
The tree-based gradient boosting approach uses LightGBM 38 and applies heavy regularization to combat overfitting due to the scarcity of positive samples. The graph neural network approach employs a time-aware graph neural network to learn node representations on dynamic semantic networks. The feature importance of model M1, averaged over 18 datasets, is shown in Table 2 . It shows that the temporal features do contribute largely to the model performance, but the model remains strong even when they are removed. An example of the evolution of the training (from 2016 to 2019) and test set (2019 to 2021) for δ = 3, c = 25, ω = 1 is shown in Extended Data Fig. 4 .
The second method assumes that the probability that nodes u and v form an edge in the future is a function of the node features f ( u ), f ( v ) and some edge feature h ( u , v ). We chose node features f that capture popularity at the current time t 0 (such as degree, clustering coefficient 78 , 79 and PageRank 77 ). We also use these features’ first and second time derivatives to capture the evolution of the node’s popularity over time. After variable selection during training, we chose h to consist of the HOP-rec score (high-order proximity for implicit recommendation) 80 , 81 and a variation of the Dice similarity score 82 as a measure of similarity between nodes. In summary, we use 31 node features for each node, and two edge features, which gives 31 × 2 + 2 = 64 features in total. These features are then fed into a small multilayer perceptron (5 layers, each with 13 neurons) with ReLU activation.
Cold start is the problem that some nodes in the test set do not appear in the training set. Our strategy for a cold start is imputation. We say a node v is seen if it appeared in the training data, and unseen otherwise; similarly, we say that a node is born at time t if t is the first time stamp where an edge linking this node has appeared. The idea is that an unseen node is simply a node born in the future, so its features should look like a recently born node in the training set. If a node is unseen, then we impute its features as the average of the features of the nodes born recently. We found that with imputation during training, the test AUC scores across all models consistently increased by about 0.02. For a complete description of this method, we refer the reader to ref. 39 .
This approach, detailed in ref. 40 , uses hand-crafted node features that have been captured in multiple time snapshots (for example, every year) and then uses an LSTM to benefit from learning the time dependencies of these features. The final configuration uses two main types of feature: node features including degree and degree of neighbours, and edge features including common neighbours. In addition, to balance the training data, the same number of positive and negative instances have been randomly sampled and combined.
One of the goals was to identify features that are very informative with a very low computational cost. We found that the degree centrality of the nodes is the most important feature, and the degree centrality of the neighbouring nodes and the degree of mutual neighbours gave us the best trade-off. As all of the extracted features’ distributions are highly skewed to the right, meaning most of the features take near zero values, using a power transform such as Yeo–Johnson 83 helps to make the distributions more Gaussian, which boosts the learning. Finally, for the link-prediction task, we saw that LSTMs perform better than fully connected neural networks.
The following two methods are based on a purely statistical analysis of the test data and are explained in detail in ref. 42 .
Preferential attachment. In the network analysis, we concluded that the growth of this dataset tends to maintain a heavy-tailed degree distribution, often associated with scale-free networks. As mentioned before the γ value of the degree distribution is very close to 2, suggesting that preferential attachment 41 is probably the main organizational principle of the network. As such, we implemented a simple prediction model following this procedure. Preferential attachment scores in link prediction are often quantified as
with k i , j the degree of nodes i and j . However, this assumes the scoring of links between nodes that are already connected to the network, that is k i , j > 0, which is not the case for all the links we must score in the dataset. As a result, we define our preferential attachment model as
Using this simple model with no free parameters we could score new links and compare them with the other models. Immediately we note that preferential attachment outperforms some learning-based models, even if it never manages to reach the top AUC, but it is extremely simple and with negligible computational cost.
Common neighbours. We explore another network-based approach to score the links. Indeed, while the preferential attachment model we derived performed well, it uses no information about the distance between i and j , which is a popular feature used in link-prediction methods 27 . As such, we decided to test a method known as common neighbours 18 . We define Γ ( i ) as the set of neighbors of node i and Γ ( i ) ∩ Γ ( j ) as the set of common neighbours between nodes i and j . We can easily score the nodes with
the intuition being that nodes that share a larger number of neighbours are more likely to be connected than distant nodes that do not share any.
Evaluating this score for each pair ( i , j ) on the dataset of unconnected pairs, which can be computed as the second power of the adjacency matrix, A 2 , we obtained an AUC that is sometimes higher than preferential attachment and sometimes lower than it but is still consistently quite close with the best learning-based models.
This method is based on ref. 44 . First, ten groups of first-order graph features are extracted to get some neighbourhood and similarity properties from each pair of nodes: degree centrality of nodes, pair’s total number of neighbours, common neighbours index, Jaccard coefficient, Simpson coefficient, geometric coefficient, cosine coefficient, Adamic–Adar index, resource allocation index and preferential attachment index. They are obtained for three consecutive years to capture the temporal dynamics of the semantic network, leading to a total of 33 features. Second, principal component analysis 43 is applied to reduce the correlation between features, speed up the learning process and improve generalization, which results in a final set of seven latent variables. Lastly, a random forest classifier is trained (using a balanced dataset) to estimate the likelihood of new links between the AI concepts.
In this paper, a modification was performed in relation to the original formulation of the method 44 : two of the original features, average neighbour degree and clustering coefficient, were infeasible to extract for some of the tasks covered in this paper, as their computation can be heavy for such a very large network, and they were discarded. Due to some computational memory issues, it was not possible to run the model for some of the tasks covered in this study, and so those results are missing.
The baseline solution for the Science4Cast competition was closely related to the model presented in ref. 17 . It uses 15 hand-crafted features of a pair of nodes v 1 and v 2 . (Degrees of v 1 and v 2 in the current year and previous two years are six properties. The number of shared neighbours in total of v 1 and v 2 in the current year and previous two years are six properties. The number of shared neighbours between v 1 and v 2 in the current year and the previous two years are three properties). These 15 features are the input of a neural network with four layers (15, 100, 10 and 1 neurons), intending to predict whether the nodes v 1 and v 2 will have w edges in the future. After the training, the model computes the probability for all 10 million evaluation examples. This list is sorted and the AUC is computed.
The solution M7 was not part of the Science4Cast competition and therefore not described in the corresponding proceedings, thus we want to add more details.
The most immediate way one can apply ML to this problem is by automating the detection of features. Quite simply, the baseline solution M6 is modified such that instead of 15 hand-crafted features, the neural network is instead trained on features extracted from a graph embedding. We use two different embedding approaches. The first method is employs node2vec (M7A) 45 , for which we use the implementations provided in the nodevectors Python package 84 . The second one uses the ProNE embedding (M7B) 46 , which is based on sparse matrix factorizations modulated by the higher-order Cheeger inequality 85 .
The embeddings generate a 32-dimensional representation for each node, resulting in edge representations in [0, 1] 64 . These features are input into a neural network with two hidden layers of size 1,000 and 30. Like M6, the model computes the probability for evaluation examples to determine the ROC. We compare ProNE to node2vec, a common graph embedding method using a biased random walk procedure with return and in–out parameters, which greatly affect network encoding. Initial experiments used default values for a 64-dimensional encoding before inputting into the neural network. The higher variance in node2vec predictions is probably due to its sensitivity to hyperparameters. While ProNE is better suited for general multi-dataset link prediction, node2vec’s sensitivity may help identify crucial network features for predicting temporal evolution.
This model, which is detailed in ref. 47 , does not use any hand-crafted features but learns them in a completely unsupervised manner. To do so, we extract various snapshots of the adjacency matrix through time, capturing graphs in the form of A t for t = 1994, …, 2019. We then embed each of these graphs into 128-dimensional Euclidean space via node2vec 45 , 48 . For each node u in the semantic graph, we extract different 128-dimensional vector embeddings n u ( A 1994 ), …, n u ( A 2019 ).
Transformers have performed extremely well in NLP tasks 49 ; thus, we apply them to learn the dynamics of the embedding vectors. We pre-train a transformer to help classify node pairs. For the transformer, the encoder and decoder had 6 layers each; we used 128 as the embedding dimension, 2,048 as the feed-forward dimension and 8-headed attention. This transformer acts as our feature extractor. Once we pre-train our transformer, we add a two-layer ReLU network with hidden dimension 128 as a classifier on top.
All 18 datasets tested in this paper are available via Zenodo at https://doi.org/10.5281/zenodo.7882892 ref. 86 .
All of the models and codes described above can be found via GitHub at https://github.com/artificial-scientist-lab/FutureOfAIviaAI ref. 5 and a permanent Zenodo record at https://zenodo.org/record/8329701 ref. 87 .
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We thank IARAI Vienna and IEEE for supporting and hosting the IEEE BigData Competition Science4Cast. We are specifically grateful to D. Kreil, M. Neun, C. Eichenberger, M. Spanring, H. Martin, D. Geschke, D. Springer, P. Herruzo, M. McCutchan, A. Mihai, T. Furdui, G. Fratica, M. Vázquez, A. Gruca, J. Brandstetter and S. Hochreiter for helping to set up and successfully execute the competition and the corresponding workshop. We thank X. Gu for creating Fig. 2 , and M. Aghajohari and M. Sadegh Akhondzadeh for helpful comments on the paper. The work of H.L., R.S. and J.G.F. was supported by grant TWCF0333 from the Templeton World Charity Foundation. H.L. is additionally supported by NSF grant DMS-1952339. J.P.M. acknowledges the support of FCT (Portugal) through scholarship SFRH/BD/144151/2019. B.C. thanks the support from FCT/MCTES through national funds and when applicable co-funded EU funds under the project UIDB/50008/2020, and FCT through the project CEECINST/00117/2018/CP1495/CT0001. N.M.T. and Y.X. are supported by NSF grant DMS-2113468, the NSF IFML 2019844 award to the University of Texas at Austin, and the Good Systems Research Initiative, part of University of Texas at Austin Bridging Barriers.
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Max Planck Institute for the Science of Light (MPL), Erlangen, Germany
Mario Krenn
Instituto de Telecomunicações, Lisbon, Portugal
Lorenzo Buffoni, Bruno Coutinho & João P. Moutinho
University of Toronto, Toronto, Ontario, Canada
Sagi Eppel & Andrew Gritsevskiy
University of California Los Angeles, Los Angeles, CA, USA
Jacob Gates Foster, Harlin Lee & Rishi Sonthalia
Cavendish Laboratories, Cavendish, VT, USA
Andrew Gritsevskiy
Institute of Advanced Research in Artificial Intelligence (IARAI), Vienna, Austria
Andrew Gritsevskiy & Michael Kopp
Alpha 8 AI, Toronto, Ontario, Canada
Independent Researcher, Barcelona, Spain
Nima Sanjabi
University of Texas at Austin, Austin, TX, USA
Ngoc Mai Tran
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Francisco Valente
University of Pennsylvania, Philadelphia, PA, USA
Yangxinyu Xie
University of California, San Diego, CA, USA
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M. Krenn and R.Y. initiated the research. M. Krenn and M. Kopp organized the Science4Cast competition. M. Krenn generated the datasets and initial codes. S.E. and H.L. analysed the network-theoretical properties of the semantic network. M. Krenn, L.B., B.C., J.G.F., A.G, H.L., Y.L, J.P.M, N.S., R.S., N.M.T, F.V., Y.X and M. Kopp provided codes for the ten models. M. Krenn wrote the paper with input from all co-authors.
Correspondence to Mario Krenn .
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The authors declare no competing interests.
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Extended data fig. 1.
Number of concepts per article.
Time Gap between the generation of edges. Here, left shows the time it takes to create a new edge between two vertices and right shows the time between the first and the second edge.
Publications in Quantum Physics.
Evolution of the AUC during training for Model M1.
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Krenn, M., Buffoni, L., Coutinho, B. et al. Forecasting the future of artificial intelligence with machine learning-based link prediction in an exponentially growing knowledge network. Nat Mach Intell 5 , 1326–1335 (2023). https://doi.org/10.1038/s42256-023-00735-0
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Prostate cancer (PCa) is a prevalent malignancy among men, primarily originating from the prostate epithelium. It ranks first in global cancer incidence and second in mortality rates, with a rising trend in China. PCa's subtle initial symptoms, such as urinary issues, necessitate diagnostic measures like digital rectal examination, prostate-specific antigen (PSA) testing, and tissue biopsy. Advanced PCa management typically involves a multifaceted approach encompassing surgery, radiation, chemotherapy, and hormonal therapy. The involvement of aging genes in PCa development and progression, particularly through the mTOR pathway, has garnered increasing attention.
This study aimed to explore the association between aging genes and biochemical PCa recurrence and construct predictive models. Utilizing public gene expression datasets (GSE70768, GSE116918, and TCGA), we conducted extensive analyses, including Cox regression, functional enrichment, immune cell infiltration estimation, and drug sensitivity assessments. The constructed risk score model, based on aging-related genes (ARGs), demonstrated superior predictive capability for PCa prognosis compared to conventional clinical features. High-risk genes positively correlated with risk, while low-risk genes displayed a negative correlation.
An ARGs-based risk score model was developed and validated for predicting prognosis in prostate adenocarcinoma (PRAD) patients. LASSO regression analysis and cross-validation plots were employed to select ARGs with prognostic significance. The risk score outperformed traditional clinicopathological features in predicting PRAD prognosis, as evidenced by its high AUC (0.787). The model demonstrated good sensitivity and specificity, with AUC values of 0.67, 0.675, 0.696, and 0.696 at 1, 3, 5, and 8 years, respectively, in the GEO cohort. Similar AUC values were observed in the TCGA cohort at 1, 3, and 5 years (0.67, 0.659, 0.667, and 0.743). The model included 12 genes, with high-risk genes positively correlated with risk and low-risk genes negatively correlated.
This study presents a robust ARGs-based risk score model for predicting biochemical recurrence in PCa patients, highlighting the potential significance of aging genes in PCa prognosis and offering enhanced predictive accuracy compared to traditional clinical parameters. These findings open new avenues for research on PCa recurrence prediction and therapeutic strategies.
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PCa is one of the most common malignant tumors in men, mostly caused by malignant tumors of the prostate epithelium [ 1 ]. From the latest global cancer statistics in 2019, we know that the incidence of PCa is ranked first and the death rate is also ranked second, and the incidence of PCa in China has been rising in recent years[ 2 , 3 ]. Early symptoms are more insidious, such as urinary frequency, urgency, and reduced urinary flow, comparable to those of prostate enlargement[ 4 ]. PCa is not diagnosed accurately through symptoms but requires digital rectal examination, prostate-specific antigen (PSA) test to assist in the diagnosis, and tissue biopsy to confirm the diagnosis [ 5 , 6 ]. Patients with advanced disease usually require a combination of therapies including surgery, radiation, chemotherapy, and hormonal therapy [ 7 , 8 ].
The mechanisms and significance of aging are becoming increasingly important as the population ages. Aging genes are a group of genes involved in the aging process whose main role is to control a number of molecular biological processes of organismal aging (DNA damage response and cell cycle regulatory pathways, etc.) [ 9 , 10 ]. Aging genes may be involved in PCa development and progression by regulating cancer cell proliferation, cell cycle, and apoptosis [ 11 ]. Its involvement in the encoding of the mTOR protein and over-activation of the mTOR pathway, which activates Akt, can inhibit apoptosis in cancer cells28283069 [ 12 ]. These findings provide valuable insights into the relationship between the Aging gene and PCa.
The aim of this study was to construct a predictive model by exploring the association between senescence genes and biochemical recurrence in PCa. PCa remains a significant clinical challenge due to its high incidence and potential for recurrence after initial treatment. Despite advances in therapeutic strategies, predicting BCR remains difficult, which underscores the urgent need for reliable biomarkers. However, the specific contribution of these genes to PCa recurrence has not been fully elucidated. By utilizing two public gene expression profile datasets, GSE70768 and GSE116918, as training sets, and validating the findings with the TCGA dataset, this study aims to identify key genes that are strongly associated with the biochemical recurrence of PCa. Through rigorous statistical analyses, including analysis of variance, univariate analysis, and the application of lasso and stepwise multifactorial screening, a prognostic model was developed. The innovative aspect of this study lies in its focus on the integration of senescence-related gene expression profiles to predict BCR in PCa, an area that has been underexplored. This study includes data from a total of 323 patients, offering new theoretical insights that may inform future research on predicting and treating biochemical recurrence in PCa, thereby filling a critical gap in existing research.
We downloaded the PCa expression profile microarray from the public database Gene Expression Omnibus (GEO), which includes peripheral blood samples from PRAD patients and controls, containing GSE70769 [ 13 ] and GSE116918 [ 14 ] totaling 268 samples, and the TCGA database to do the validation group, containing 55 columns.
We conducted univariate and multivariate Cox regression analyses to determine if risk scores could serve as independent prognostic indicators. Utilizing the "rms" R package, we integrated these risk scores with clinicopathologic features to create histograms that predict patient survival at 1, 3, and 5 years within the TCGA-PRAD cohort.
CIBERSORT analysis ( https://cibersort.stanford.edu/ ) is a robust tool that leverages gene expression data to estimate the relative proportions of various immune cell types within complex tissue samples. To assess immune cell infiltration in cancer tissues, we utilized this method, allowing us to precisely quantify the relative abundance of different immune cells. This approach provides a detailed understanding of the immune landscape in heterogeneous samples, offering valuable insights into the tumor microenvironment.[ 15 ].
To evaluate the efficacy of treatments across different risk categories, we utilized the "pRRophetic" R package. This tool allowed us to analyze treatment responses in patients classified as either high-risk or low-risk based on their prognostic scores. We drew on data from the Genomics of Drug Sensitivity in Cancer (GDSC) database, which provides comprehensive information on drug responses. Specifically, we used the dataset to obtain half-maximal inhibitory concentration (IC50) values, which measure the concentration of a drug required to inhibit a biological process by 50%. This approach enabled us to assess how effectively various treatments could suppress cancer growth in PRAD patients, providing insights into potential therapeutic strategies [ 16 ].
GSCALite ( http://bioinfo.life.hust.edu.cn/web/GSCALite/ ) is a comprehensive online tool that integrates genomic data from 33 types of cancer available in The Cancer Genome Atlas (TCGA) with normal tissue data from the Genotype-Tissue Expression (GTEx) project. In our study, we utilized GSCALite to perform a detailed analysis of various genomic alterations, including copy number variations, DNA methylation patterns, and pathway activities related to ARGs in PRAD. This platform facilitated a thorough examination of how these genomic features influence the biological behaviors of ARGs in PRAD.
TISCH ( http://tisch.comp-genomics.org ) is a comprehensive database dedicated to single-cell RNA sequencing data specifically focused on the tumor microenvironment (TME) [ 17 ]. Utilizing this resource, we systematically investigated the heterogeneity of the tumor microenvironment across various cell types and datasets.
All statistical analyses were conducted using R software (V. 4.2.0). To evaluate the reliability of the diagnostic model, ROC curves were generated, with the area under the curve (AUC) used to determine predictive accuracy, applying a significance threshold of P < 0.05. Furthermore, the goodness-of-fit of the constructed nomograms was assessed using the Hosmer–Lemeshow test. This rigorous analysis ensured a thorough evaluation of the model's performance and fit.
A risk score model based on ARGs was developed to identify prognostic biomarkers for PRAD patients. LASSO regression analysis (Fig. 1 A) was utilized on DE-ARGs with prognostic significance, and cross-validation plots (Fig. 1 B) identified 12 key genes: HDAC3, IRS2, HIF1A, PRKCA, MSRA, APOE, HSPA9, CDKN2A, TP53BP1, CNR1, CDKN2B, and SERPINE1. High-risk genes were found to have a positive correlation with risk, whereas low-risk genes were negatively associated. The risk score model demonstrated strong predictive power for PRAD prognosis, with an AUC of 0.787, outperforming traditional clinicopathologic features (Fig. 1 C). In the GEO cohort, the model's predictive performance was further validated, showing high sensitivity and specificity with AUC values of 0.67, 0.675, 0.696, and 0.696 at 1, 3, 5, and 8 years, respectively (Fig. 1 D). Similarly, in the TCGA cohort, the AUC values were 0.67, 0.659, 0.667, and 0.743 at 1, 3, and 5 years (Fig. 1 E). Survival analysis in the GEO cohort revealed that patients with higher risk scores had significantly increased mortality, while those in the low-risk group demonstrated a better prognosis ( P < 0.001) (Fig. 1 F). This trend was consistent in the TCGA cohort, where a better prognosis was also observed in the low-risk group ( P = 0.003) (Fig. 1 G). Overall, this ARG-based risk score model offers superior predictive power and may serve as a valuable tool in identifying prognostic biomarkers and guiding clinical decisions for PRAD patients.
Construction and validation of ARGs signatures. A Ten-fold cross-validation used to adjust parameter selection in the LASSO model. B Lasso coefficient profiles. C Multi-exponential ROC analysis. D ROC profile analysis of the GEO cohort over time. E ROC profile analysis of the TCGA cohort over time. F KM curves comparing overall PRAD patients between low and high risk groups in the GEO cohort. G KM curves comparing overall PRAD patients between low and high risk groups in the TCGA cohort
We collected BCR profiles and time to recurrence (bcr time) of prostate patients and plotted a scatterplot with the prognostic model's scoring profiles (dataset), and from the plot, we clearly observed that with the rise in patients' RISK SCREEN, not only the number of recurrences in BCR of recurrence, the time to recurrence (bcr time) also increased from 0–6 years to a wide range of 0–8 years (Fig. 2 A, B ), which also suggests that our prognostic model can, to some extent, also predict the circumstances and timing of biochemical recurrence in prostate patients. We then categorized the patients into high and low risk groups based on the median value of the risk score (Fig. 2 C, D ), and viewed the expression of the modeled genes between the high and low risk groups through the limma package, and we could see that all modeled genes, except HSPA9, were actively expressed in the high risk group (Fig. 2 E, F ). By principal component analysis (PCA) of the patients we can clearly see that the high and low risk labels can classify and summarize the patients well and there is very little overlap of patients (Fig. 2 G, H ).
Exploring the relationship between the prognostic model's scoring profile of prostate patients and biochemical recurrence (BCR) in the clinic. A , B Scatterplot of the scoring profile of the prognostic model for prostate patients versus the time to clinical biochemical recurrence (BCR) recurrence (bcr time). C , D Scatterplot of the distribution of risk scores for prostate patients. E , F Heatmap of differential expression of modeled genes between high, and low risk groups. G , H Principal component analysis of prostate patients
To explore the relationship between risk factors such as prognostic model scores and clinical characteristics and BCR outcomes in prostate patients. We plotted forest plots by the results of univariate and multivariate COX regression analyses as well as Log Rank tests (Fig. 3 A, B ) in which the P value of T-stage and risk scores were < 0.05, the Hazard ratio (HR) of T-stage in one-way, multifactor COX regression was 0.569 as well as 0.585, and HR > 1 was a risk factor. Hazard ratio (HR) for multifactorial COX regression was 0.569 as well as 0.585, in addition to pvalue < 0.001 for both risk scores, and HR > 1 was a risk factor. Subsequently, we constructed a multi-indicator clinical prognostic model based on the results of the multifactorial COX analysis, and plotted the nomogram and the corrected curves (Fig. 3 C, D ). Based on the nomogram, each sample was scored by the COX analysis, and based on the Points, we predicted the patient's OS in the clinical diagnosis and treatment, and the results of the corrected curves showed the discrepancy between the predicted and actual results of COX model. The results of the correction curves show that the COX model has excellent predictive performance, as the difference between the predicted results and the actual situation is very small.
The construction of the nomogram. A Forest plot for a one-factor COX analysis. B Forest plot for multifactor COX analysis. C Nomogram of a multifactor COX analysis model. D Correction curve plot for a multifactor COX model
Given that BCR in the high-risk (HR) and low-risk (LR) populations differed dramatically in terms of individual clinical attributes. In order to study this difference in depth and compare it more precisely, we categorized patients diagnosed with PRAD into five different subgroups based on clinical parameters. These stratifications included age (≤ 65 and > 65 years), gleason (6–7 and 8–9), pca (10 > and < = 10), and T-stage (T1-2 and T3-4). Notably, in all subgroups, the survival of LR patients was significantly better than that of HR patients, which was characterized by a longer survival period (Fig. 4 A-H). Based on the analysis of the results, we further strengthened our confidence in the reliability of the ARGs profile as a clinical predictive tool.
Correlation between clinical characteristics and biochemical recurrence of ARGs in PRAD patients. A–H KM curves between different clinical features
Figure 5 highlights genomic alterations involving ARGs and hub genes across three domains: single-nucleotide variation (SNV) (Fig. 5 A-B, I ), copy-number variation (CNV) (Fig. 5 D, H ), and methylation (Fig. 5 F-G). ARGs did not show significant mutations in KIRP (Fig. 5 A).
Analysis of GSCALite and cBioPortal Data. A SNV of all mutated genes in the gene set in PRAD. B SNV classes of hub-gene set in PRAD, C Survival difference between high and low methylation in each cancer. D Survival difference between CNV groups. E Correlations between methylation and mRNA expression of ARGs in PRAD. F Correlation between methylation and mRNA expression; G Methylation differences among tumor and normal samples of SKA3 and top ten hub genes in PRAD; H Pie plot summarizing CNV of ARGs. I SNV of ARGs and hub genes in PRAD. J Correlation between CTRP drug sensitivity and mRNA expression
CNV in PRAD patients encompassed heterozygous, homozygous, amplifications, and deletions (Fig. 5 H). Importantly, no apparent correlation was observed between heterozygous or homozygous CNV. However, CNV in genes such as MSRA, TP53BP1, IRS2, HSPA9, and HDAC3 displayed significant associations with mRNA expression, with MSRA exhibiting a particularly strong correlation (F i g. 5 I). In PRAD patients, CNV groups, including CNR1, HSPA9, and TP53BP1, demonstrated a negative correlation with overall survival (OS) and progression-free survival (PFS), while others showed varying degrees of positive correlations (Fig. 5 D).
The analysis also unveiled differential methylation patterns in PRAD genes between tumor and normal samples (Fig. 5 G). Specifically, low methylation of APOE and CDKNA2 was associated with poorer overall survival (OS) in KIRP (Fig. 5 C). Furthermore, methylation of ARGs displayed a negative correlation with mRNA expression (Fig. 5 F). In the majority of genes, there was a positive correlation between CTRP drug sensitivity and mRNA expression. SERPINE1 exhibited a significant positive correlation, while a few genes, including CNR1, displayed negative correlations. This suggests a degree of specificity in the drug sensitivity experiment, providing valuable insights for future clinical research in developing treatment strategies.
In Fig. 6 A, our analysis revealed a notable influence of the ARGs on the distribution of specific four clinicopathological features within both high-risk and low-risk groups. It was obvious that patients aged 65 and older, those with pca more than 10, and individuals at gleason7 comprised a larger proportion of patients in the high-risk (HR) group. Furthermore, the heatmap illustrates various clinicopathological features, including T stage, age, gleason, pca, and risk scores across the entire cohort of TCGA-PRAD patients (Fig. 6 B). We extended our analysis to explore the relationship between risk scores and various clinicopathological factors, including tumor grade, disease stage, T stage, patient age, and gender. These correlations were systematically evaluated to understand how each factor interacts with the risk scores, as illustrated in Fig. 6 C to 6F. The analysis revealed significant variations in risk scores among patients with differing age, pca, gleason, and T stages, with patients in more advanced stages showing higher risk scores. Based on our findings, we concluded that a significant positive correlation exists between risk scores and various clinicopathological factors.
Distribution of risk scores in different clinical subtypes. A The proportion of patients with different clinical subtypes (Age, Pca, Gleason, T stage) in the HR group and LR group. B Heatmap of clinicopathological variables in HR group and LR group. The proportion of patients with different clinical subtypes (Age, Pca, Gleason, T stage) in the HR group and LR group. C-F Risk score distribution of different clinical subtypes
Immune cell infiltration represents a fundamental aspect of the TME. Utilizing the CIBERSORT algorithm for Spearman correlation analysis, we observed a notable association between risk scores and the abundance of immune cells in the PRAD TME. Specifically, CD8 + T cells were predominantly correlated with CD4 + T cells (Fig. 7 A). In the combined analysis of the 12 ARGs with immune cells, HSPA9 was found to be highly correlated with M1 macrophages (Fig. 7 B). To assess the distribution and correlation of the 22 tumor-infiltrating immune cells (TICs) in the GEO cohort, we utilized CIBERSORT as the immune analysis tool. The results indicated that BRC samples exhibited significantly higher levels of immune infiltration compared to non-BRC samples, particularly in B cells, plasma cells, and macrophages (Fig. 7 C). The ARG-based risk score model effectively differentiated between various immune subtypes, thereby influencing the response to immunotherapy. To further investigate changes in immune function, we conducted a comparison of single-sample GSEA (ssGSEA) scores, revealing a significant increase in scores for the high-risk group (Fig. 7 D). Additionally, we examined differences in the expression of immune checkpoint genes, which are critical for tumor immunotherapy. In the low-risk group, 13 immune checkpoint genes, including BTNL2, CD244, CD28, CD40LG, CTLA4, LAIR1, NRP1, PDCD1, TIGIT, TNFRSF25, TNFRSF8, TNFRSF9, and TNFSF9, were significantly upregulated. In contrast, the high-risk group showed upregulation of only TNFSF9 and TNFRSF25 (Fig. 7 E). The upregulation of immune checkpoints suggests the presence of inflammation within the TME [ 18 ], implying that low-risk patients may have an inflammatory microenvironment. Targeted therapies against these elevated immune checkpoints could potentially benefit this tumor subtype [ 19 ].
Immunoassays in patients with PRAD. A Histogram of immune cells. B Correlation of 12 genes with immune cells. C Differences in immune cell infiltration between high- and low-risk groups. D Immune function ssGSEA scores between high- and low-risk groups. E Differences in immune checkpoints between high- and low-risk groups
We scrutinized the expression of 12 ARGs in the immune microenvironment using the PRAD_GSE143791 single-cell dataset retrieved from the TISCH database.There are 15 different immune cell types in GSE143791 (Fig. 8 A). We used pie charts to represent the proportional composition of different immune cells and their distribution in the samples (Fig. 8 B). To deeply investigate the expression levels of individual ARGs in immune cells, we generated a downscaled distribution map of CCRGs in immune cells (Fig. 8 C-N). Our analysis showed that HDAC3, HIF1A, HSPA9, and TP53BP1 were widely expressed in a wide range of AML immune cells, whereas the expression of CNR1 and CDKN2B in the immune microenvironment was almost negligible. These findings based on the PRAD dataset validate the correlation studies between ARGs and the immune microenvironment, thus complementing and refining the clinical targeting of PRAD induced by the immune microenvironment.
Correlation study of ARGs with the immune microenvironment of PRAD. A Downscaled distribution of various immune cell subpopulations of PRAD_GSE143791. B Pie chart showing percentage of immune cells. C–N Distribution of 12-ARGs in PRAD_GSE143791
PCa is the most common malignancy among men, emphasizing the importance of effective screening and detection methods. PSA testing has proven valuable in identifying localized PCa. However, PSA testing is limited by its lack of sensitivity and specificity. While PSA screening has raised the lifetime risk of a PCa diagnosis to 16%, the mortality rate remains relatively low at 3.4% [ 20 ]. This discrepancy suggests that increased detection of slow-growing or relatively benign cancers, which do not necessarily require definitive treatment, has led to concerns about overdiagnosis and overtreatment, exposing patients to unnecessary risks and potential urinary and bowel dysfunction post-treatment [ 21 ]. Recent reports indicate that a significant proportion of men with low PSA levels still develop PCa, many of which are high-grade malignancies. Thus, PSA is less effective as a screening tool for differentiating between high and low-risk cases. Research is ongoing to identify other markers that could more accurately pinpoint malignancies that are clinical threats while avoiding interventions for inert diseases. Preventive strategies tailored to genetic or other risks may help reduce the incidence of PCa [ 22 ]. PCa incidence escalates markedly with age. Data from the US Surveillance, Epidemiology, and End Results Program (2000–2008) indicate that the rate of PCa is 9.2 per 100,000 men in the 40–44 age group. This incidence rises sharply to 984.8 per 100,000 men aged 70–74 years before experiencing a slight decline [ 20 ]. PCa often develops gradually, typically preceded by dysplastic lesions that may remain undetected for many years or even decades. Autopsy studies have indicated that if most men lived to 100 years old, they would likely develop PCa [ 23 ]. Macrophage-tumor cell interactions have been found to promote androgen resistance and increase PCa invasion through tissue factor expression. Studies by Parrinello et al. demonstrated that aged mice with increased macrophage infiltration in the prostate glands reflect the role of immune cells in aging and its association with PCa development [ 24 ]. Thus, prognostic models based on senescence-related biomarkers can complement PSA screening for early diagnosis and predict genetic risk related to senescence [ 25 ].
We merged two prostate tumor patient cohort transcript datasets, GSE70768 and GSE116918, collected from public databases, and extracted the aging-related differential genes that were differentially expressed in the patients after de-batching and normalization, and then the Aging-DEGs were analysed by one-way COX analysis, followed by a lasso machine learning approach and stepwise multifactorial COX analysis. analysis to screen the genes for constructing prognostic models (HDAC3,IRS2,HIF1A,PRKCA,MSRA, APOE, HSPA9, CDKN2A, TP53BP1, CNR1, CDKN2B, and SERPINE1), and finally a prognostic model was constructed by logistic regression algorithms in patients with 12-Agings prostate tumors, and additionally A nomogram of prostate tumor patients was depicted as well as the immune microenvironment, immune function, mutation load, pathway enrichment analysis, and clinical subgroup survival analysis of patients with high- and low-risk prostate tumors were explored using the CIBERSORT database.
Histone deacetylase 3 (HDAC3) is an enzyme with histone deacetylase activity that plays a critical role in transcription regulation. By binding to the promoter region, HDAC3 inhibits transcription. Additionally, it modulates gene expression through interaction with the zinc finger transcription factor YY1 and suppresses p53 activity, which is essential for regulating cell growth and apoptosis. HDAC3 is recognized as a potential tumor suppressor gene. It has been proposed that the corepressor SMRT, together with N-CoR and HDAC3, forms a complex that inhibits AR activity and interacts with AR nuclear steroid receptors to suppress specific protein expression in PCa cell lines [ 26 ].
Hypoxia-inducible factor 1 subunit alpha (HIF1A) is a crucial transcriptional regulator that enables cells to adapt to low oxygen environments. In hypoxic conditions, HIF1A drives the expression of over 40 genes that enhance oxygen delivery and support metabolic adaptation. These include genes for HILPDA, vascular endothelial growth factor, glycolytic enzymes, glucose transporters, and erythropoietin [ 27 , 28 ]. HIF1A plays a crucial role in embryonic and tumor angiogenesis, as well as in the pathophysiology of ischemic diseases, influencing both cell proliferation and survival [ 29 ]. Early prostatic intraepithelial neoplasia (PIN) is hypoxic, and HIF1A signaling in luminal cells enhances malignant progression by suppressing immune surveillance and promoting luminal plasticity, leading to the emergence of cells that impair androgen signaling [ 30 ].
Protein kinase C (PKC) encompasses a family of serine- and threonine-specific kinases that are activated by calcium and diacylglycerol. As key receptors for tumor-promoting phorbol esters, PKC family members display unique expression profiles and contribute to various cellular functions, including adhesion, transformation, cycle checkpoints, and volume regulation. Aberrant PKC expression is a well-recognized cancer hallmark, with elevated levels linked to enhanced cell proliferation and diminished apoptosis in several malignancies, such as bladder cancers [ 31 ], gliomas, and PCas [ 32 ]. Aggressive PCa cells with high PKCα expression require this for mitogenic activity [ 33 ].
Apolipoprotein E (APOE) is a protein-coding gene.APOE is a core component of plasma lipoproteins and is involved in their production, transformation, and clearance [ 34 ], Venanzoni MC et al. examined protein expression in 20 prostatectomy specimens by immunohistochemistry and determined the association between the Gleason score of each sample and ApoE expression. ApoE expression was positively associated with Gleason score, hormone independence, and both local and distant invasiveness in prostate tissue sections. In contrast, while ApoE was positive in prostate intraepithelial neoplasia (PIN) adjacent to clinically evident cancer, more distant PINs showed a negative expression for ApoE [ 35 ]. Additionally ApoE gene scores were performed by blood samples from patients with prostate tumors. The E3/E3 genotype was found at a significantly higher frequency in patients compared to controls ( P = 0.004). Carriers of the E3/E3 genotype had a 3.6-fold increased likelihood of being patients compared to controls (OR = 3.67, 95% CI = 1.451–9.155; p = 0.004). Moreover, patients with the E3/E3 genotype exhibited significantly higher Gleason scores (p = 0.017) and a greater prevalence of Gleason scores above 7 ( P = 0.007). In contrast, the E4 allele was more prevalent in the control group ( P = 0.006)(26,851,028).
Heat shock protein family A (Hsp70) member 9 (HSPA9) is a chaperone protein crucial for mitochondrial iron-sulfur cluster (ISC) biogenesis. HSPA9 interacts with and stabilizes ISC cluster assembly proteins, including FXN, NFU1, NFS1, and ISCU [ 36 ]. HSPA9 regulates erythropoiesis by stabilizing ISC assembly and may also play a role in controlling cell proliferation and cellular senescence [ 36 , 37 ]. It has been shown that JG-70, a variant inhibitor of HSP98, inhibits aerobic respiration by targeting mitochondrial HSP70 (HSPA9) and re-sensitizes desmoplasia-resistant PCas to androgen deprivation drugs in addition to Hirth CG et al. retrospectively reviewed the records of 636 patients who underwent radical prostatectomy and mounted paraffin embedded adenocarcinomatous and non-tumor tissues for microarrays. We evaluated the ability of HSPA9 to predict postoperative PSA outcome, response to adjuvant/rescue therapy and systemic disease. Results showed that HSPA9 was diffusely expressed in tumor cells and that diagnostic HSPA9 staining helped identify patients at increased risk of recurrence after salvage therapy [ 38 ].
Serpin family E member 1 (SERPINE1), also known as plasminogen activator inhibitor 1 (PAI-1), inhibits tissue-type plasminogen activator (tPA) and urokinase (uPA). These enzymes convert plasminogen into plasmin, which in turn activates matrix metalloproteinases (MMPs) to degrade the extracellular matrix (ECM), thereby promoting invasion and metastasis. SERPINE1 blocks cancer cell invasion by inhibiting uPA protease activity. Additionally, knocking down six transmembrane epithelial antigens (STEAP2) in PCa cells upregulates SERPINE1, reducing their invasive potential. This indicates that SERPINE1 may serve as a downstream effector of certain oncogenes to regulate prostate cancer cell migration [ 39 ].
Additionally epigenetic changes in the remaining biomarkers are thought to be associated with severe subtypes of prostate tumors and metastatic, invasive capacity. This includes mutations in CDKN2A [ 40 ] as well as large amounts of unclipped TP53BP1 [ 41 ] and hypermethylated CDKN2B [ 42 ].
In order to more systematically analyze the mutations in the genes of patients with prostate tumors and to explore their correlation with the prognostic models predicted by the 12-Agings Prostate Tumor Patient's Prognostic Model for high and low risk patients. We obtained patient mutation data from the TCGA database and conducted analyses across various omics levels, including genomic and copy number levels. The analysis revealed that single nucleotide variants (SNVs) were the most common mutations in the cohort, with single nucleotide polymorphisms (SNPs) being the predominant type. Additionally, we identified the genes with the highest mutation frequencies. Subsequently, we analyzed the proportion and type of homozygous versus heterozygous mutations among the copy number variants (CNVs) in the sample. We conducted Spearman correlation analysis to explore the relationship between CNVs and gene expression. Moreover, significant correlations were found between the expression of senescence biomarkers and drug sensitivity in the Cancer Treatment Response Portal (CTRP) and the Genomics of Cancer Drug Sensitivity (GDSC) databases. These results suggest that our risk markers could potentially serve as predictors of chemotherapy drug sensitivity or be targeted in future drug development efforts.
However, our prognostic model still has a lot of shortcomings, including the lack of real clinical cases and the lack of in vivo and ex vivo experiments to validate the expression and enrichment of the corresponding genes and pathways with the progression of the disease. These further experimental studies will be discussed in our subsequent papers.
In conclusion, our proposed 12-Agings signature is a novel biomarker with significant potential for predicting patient prognosis and serving as a therapeutic target in prostate tumor patients. The 12-Agings signature is capable of predicting clinical outcomes, thereby assisting physicians in identifying cases that are at risk of deterioration and recurrence. Moreover, it can characterize the immune environment of prostate tumors, enabling a more precise stratification of patients and the development of individualized treatment plans. Additionally, the signature facilitates the early identification of patient subgroups that may benefit from immunotherapy and chemotherapy based on mRNA expression profiles. These capabilities underscore the potential of the 12-Agings signature to improve clinical decision-making and patient management in prostate tumors.
In conclusion, our study presents a robust prognostic tool for PRAD utilizing ARGs. Validated through LASSO regression and cross-validation, the risk score model identified 12 pivotal genes that illuminate the molecular mechanisms underlying PRAD. High-risk genes were positively correlated with increased risk, whereas low-risk genes were negatively correlated. These findings are anticipated to enhance PRAD treatment and facilitate the development of more targeted therapeutic strategies.
Although the GEO and TCGA datasets have been meticulously curated in terms of scale and quality, the diversity of their origins may introduce sample heterogeneity, potentially affecting the generalizability of our findings. Additionally, since these datasets were generated by different research centers, variations in sample collection and processing methods might result in batch effects. Despite implementing appropriate bioinformatics techniques to mitigate these issues, some inherent variability may still influence the interpretation of the results.
Our study makes a significant contribution to PRAD research by introducing a novel prognostic model rooted in ARGs. Validated by rigorous statistical methods, the model outperforms traditional clinicopathologic factors and provides greater accuracy for PRAD prognosis. The identification of 12 key genes provided valuable insights into the molecular mechanisms that drive PRAD prognosis. By demonstrating the robustness and clinical relevance of the model, we facilitate more informed therapeutic decisions for patients with PRAD, potentially enabling personalized treatment. Furthermore, our work highlights the importance of exploring ARGs in cancer prognosis, paving the way for future research in this critical area of oncology.
The datasets employed in this study can be accessed through the GEO repository ( https://www.ncbi.nlm.nih.gov/geo/ ) and the TCGA portal ( https://portal.gdc.cancer.gov/ ). Additionally, the raw data files, code files, and images supporting this research are available for download via the following link: https://www.jianguoyun.com/p/DY7CFbEQkeKyCxiQvaAFIAA .
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Department of Oncology, Chongqing General Hospital, Chongqing University, Chongqing, 401147, China
Yuni Wu & Zhibin Luo
School of Clinical Medicine, North Sichuan Medical College, Nanchong, 637100, China
Department of Oncology, Chongqing Hospital of Traditional Chinese Medicine, Chongqing, 400021, China
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The study was conceptualized by YW, RX, and JW. ZL, YW and RX were responsible for drafting the manuscript. YW and ZL conducted the literature search and gathered the relevant data. Subsequently, YW and JW analyzed and presented the data in a visual format. The final version of the manuscript was reviewed by ZL and JW, and necessary revisions were made. All authors critically evaluated and provided their approval for the final version of the manuscript.
Correspondence to Jing Wang or Zhibin Luo .
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Wu, Y., Xu, R., Wang, J. et al. Precision molecular insights for prostate cancer prognosis: tumor immune microenvironment and cell death analysis of senescence-related genes by machine learning and single-cell analysis. Discov Onc 15 , 487 (2024). https://doi.org/10.1007/s12672-024-01277-6
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Published : 27 September 2024
DOI : https://doi.org/10.1007/s12672-024-01277-6
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