💻 bioinformatics

Joint Variable Selection for Omic Biomarkers in Time-to-Event Data

The paper introduces vampW, a novel fully parametric Bayesian method based on Vector Approximate Message Passing and a Weibull model, which outperforms traditional marginal testing and other joint models by significantly reducing false discoveries and improving disease onset prediction through the effective joint modeling of correlated multi-omics biomarkers and time-to-event data.

Original authors: Bajzik, J., Depope, A., Zolfimoselo, Y., Sharipov, A., Lesayova, A., Klein, H., Richmond, A., Vernardis, S., Grauslys, A., Andrejev, S., Zelezniak, A., Ralser, M., Marioni, R., Mondelli, M., Robinson

Published 2026-10-14

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Bajzik, J., Depope, A., Zolfimoselo, Y., Sharipov, A., Lesayova, A., Klein, H., Richmond, A., Vernardis, S., Grauslys, A., Andrejev, S., Zelezniak, A., Ralser, M., Marioni, R., Mondelli, M., Robinson, M. R.

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed. It is not medical advice. Do not make health decisions based on this content. Read full disclaimer

As people grow older, their risk of developing many common diseases—such as heart conditions, cancer, and neurodegenerative disorders—rises sharply. This relationship is not a slow, steady climb but an exponential one, where the likelihood of illness accelerates rapidly with each passing year. Scientists have long sought to understand which specific biological markers, such as proteins floating in the blood, are responsible for driving this process. By linking the timing of disease diagnoses found in medical records with measurements of thousands of these biological markers, researchers hope to uncover the hidden genetic and molecular pathways that lead to illness. The goal is to identify reliable early warning signs that could help doctors predict when a person might get sick, allowing for earlier screening and prevention.

For decades, the standard way to find these connections has been to test one biological marker at a time. Researchers would look at a single protein and ask if its levels were linked to the age of disease onset, ignoring the fact that proteins often work together in complex, interdependent networks. This approach, while simple, has a major flaw: because it treats each marker in isolation, it frequently mistakes correlation for causation, leading to a high number of false alarms. To solve this, a team of researchers has developed a new computational tool called vampW. Instead of checking markers one by one, this method looks at thousands of proteins simultaneously, accounting for how they influence one another. By doing so, it can distinguish which proteins are truly driving the disease process and which are merely bystanders caught up in the same biological currents.

The researchers tested this new approach using data from the UK Biobank, a massive collection of health information from over 53,000 individuals. They paired blood protein measurements with electronic health records to track the age at which people were diagnosed with 24 different diseases, ranging from Alzheimer's and prostate cancer to hypertension and depression. When they applied their new method, the results were striking. The traditional approach of testing markers individually produced tens of thousands of associations, but the vast majority of these were likely false discoveries caused by the tangled web of correlations between proteins. In contrast, the new joint modeling method identified a much smaller, more precise set of 219 protein associations with disease onset when not adjusting for age, and 1,308 associations when accounting for the complex, non-linear ways age affects protein levels.

Crucially, the new method did not just find fewer results; it found better ones. Many of the proteins identified by the new tool were completely different from the top hits found by the old methods. For instance, while the traditional approach highlighted proteins that simply rose with age, the new method uncovered specific biological signals, such as a protein called CXCL17 linked to colorectal cancer and another called Tenascin-XB linked to depression, which had been missed or obscured by the older techniques. The researchers also confirmed that these findings were not just a fluke of the UK data; they successfully replicated the results in independent groups of people from Iceland and Scotland, using different technologies to measure the proteins. This replication suggests that the method is robust and capable of finding genuine biological signals across different populations and measurement systems.

Beyond simply identifying which proteins matter, the new tool also proved far superior at predicting exactly when a disease might strike. In tests across 14 different outcomes, the new method reduced the error in predicting the age of disease onset by more than 30% compared to the best existing statistical models and by 26% compared to advanced deep learning approaches. This improvement is significant because it means the tool can provide a much clearer timeline for disease risk, which is essential for planning medical interventions. Furthermore, the method maintained its accuracy even when applied to minority populations with different genetic backgrounds, a common challenge where other models often fail.

The study also highlighted the importance of how age is handled in these analyses. When the researchers adjusted for the fact that protein levels change exponentially with age, the list of important proteins shifted dramatically. Some proteins that seemed important under the old methods disappeared, while new, biologically relevant candidates emerged. This sensitivity shows that the way scientists correct for age can fundamentally alter what they discover about disease. By using a fully parametric model that respects the actual timing of events rather than just their order, the new approach offers a more accurate and interpretable map of the biological architecture behind complex diseases.

In the end, this work provides a powerful new way to sift through the noise of massive biological datasets. It moves the field away from the inefficient practice of testing one variable at a time and toward a holistic view that respects the interconnected nature of the human body. By reducing false discoveries and improving prediction accuracy, this method offers a clearer path to understanding the genomic roots of disease. As biobanks continue to grow and include more diverse populations, tools like this will be essential for turning vast amounts of data into actionable medical insights, potentially transforming how we screen for and prevent the diseases that affect us as we age.

Technical Summary: Joint Variable Selection for Omic Biomarkers in Time-to-Event Data

Problem Statement
The incidence of neurodegenerative, cancer, and metabolic diseases increases exponentially with age. Identifying the genomic and biological pathways driving these diseases requires linking time-to-diagnosis data from electronic health records with multi-omics measures. Current standard practices rely on semiparametric Cox proportional hazards (CoxPH) models. However, these approaches face two primary limitations:

Marginal Testing: Most association studies test one genomic feature at a time, ignoring pervasive correlations among markers. This leads to inflated false discovery rates and difficulty in distinguishing which proteins are truly driving disease onset.
Prediction Limitations: While penalized CoxPH models allow for joint modeling, they rely on partial likelihoods that ignore the baseline hazard and exact event spacing. Consequently, they provide relative risk scores rather than direct predictions of absolute event times (age at onset) and lack a continuous survival curve.

Methodology: The vampW Framework
The authors introduce vampW, a fully parametric Bayesian computational method designed for joint variable selection and time-to-event prediction. The method integrates the Vector Approximate Message Passing (VAMP) framework with a Weibull survival model.

Model Formulation: The approach models the logarithm of time-to-event ( $y$ ) as a linear combination of biological markers ( $X$ ) and a Gumbel-distributed noise term, scaled by a Weibull shape parameter ( $\alpha$ ). This formulation allows for a flexible hazard structure that can increase, decrease, or remain constant over time.
Prior Structure: To handle high-dimensional data and sparsity, vampW employs an adaptive spike-and-slab prior on the marker effects ( $\beta$ ). This allows the model to adaptively estimate inclusion probabilities and mixture-specific variances.
Algorithmic Innovation:
- Weibull Channel Denoisers: The authors introduce novel denoisers specifically derived for the Weibull link function within the VAMP framework.
- Handling Censoring: A key contribution is the adaptation of VAMP to handle right-censored data. The algorithm incorporates the survival function of the Gumbel distribution into the optimization objective, effectively maximizing the probability that censored individuals survived longer than their censoring time.
- Estimation: Parameters are estimated via an Expectation-Maximization (EM) procedure. The algorithm utilizes the Hutchinson estimator for trace calculations and warm-started conjugate gradient solvers to ensure computational efficiency. Damping and damping autotuning are employed to stabilize convergence in the presence of non-rotational invariant data design matrices.
Output: The method yields Posterior Inclusion Probabilities (PIP) for variable selection and provides continuous survival curves for out-of-sample prediction of absolute event times.

Key Contributions

Novel Algorithm: vampW is the first method to apply the VAMP framework to Weibull survival models with right-censored data, enabling joint modeling of thousands of omics features.
Improved Variable Selection: By modeling features jointly, the method accounts for correlation structures, significantly reducing false discoveries compared to marginal testing and other joint CoxPH approaches.
Superior Prediction: Unlike CoxPH, which offers relative risk, vampW provides direct predictions of absolute age at onset with continuous survival curves.
Integration of Prior Knowledge: The Bayesian framework allows for the incorporation of prior knowledge and provides credible intervals for uncertainty quantification.

Results
The authors evaluated vampW through extensive simulations and real-world applications using the UK Biobank Pharma Proteomics Project (PPP) dataset ( $N=53,018$ , $P=2,924$ proteins).

Simulation Studies: Across 24 scenarios varying signal-to-noise ratios, censoring rates, and distributional assumptions, vampW demonstrated:
- Variable Selection: A calibrated false discovery rate (FDR) and a higher true positive rate (TPR) compared to marginal CoxPH, joint CoxPH, LASSO-penalized CoxPH, and DeepSurv. Marginal testing produced over 80% false positives in simulations.
- Prediction: vampW achieved higher concordance indices (C-index) and lower Root Mean Squared Error (RMSE) than all benchmarked methods, including DeepSurv.
- Robustness: The method remained competitive even under model misspecification (e.g., non-linear effects, interactions, and competing risks).
UK Biobank Application:
- Associations: Applied to 24 disease outcomes, vampW identified 219 protein associations (without exponential age correction) and 1,308 associations (with exponential age correction).
- Novelty: The majority of vampW discoveries were not among the top marginal discoveries. Notable findings included associations between CXCL17 and depression, TNXB and depression, and PARK7 and Parkinson's disease.
- Age Correction: The study highlighted the sensitivity of results to age-correction methodology. Without correcting for exponential age effects, many associations (e.g., CGA) were driven by age correlation; correcting for this revealed distinct biological pathways.
- Replication: Findings replicated in independent cohorts using different technologies: an Icelandic cohort (SomaScan v4) and the Generation Scotland cohort (mass spectrometry).
Prediction Performance:
- Across 14 disease outcomes, vampW reduced RMSE by >30% compared to CoxPH variants and >26% compared to DeepSurv.
- The method demonstrated high transferability across diverse genetic ancestries, maintaining predictive utility in minority populations (African and South Asian).
- In data-scarce regimes (small sample sizes), vampW outperformed deep learning methods on standard survival benchmarking datasets (METABRIC, SUPPORT, SAC3, GBSG).

Significance and Claims
The paper claims that vampW offers a powerful, unified computational framework for dissecting the genomic architecture of complex diseases. Its significance lies in:

Accuracy and Interpretability: It provides accurate variable selection with interpretable hazard structures and uncertainty quantification, addressing the "black box" nature of some deep learning approaches.
Efficiency: It achieves state-of-the-art performance in both association testing and time-to-event prediction, outperforming both traditional statistical methods and deep learning approaches, particularly in scenarios with high correlation and limited data.
Clinical Utility: By predicting absolute age at onset rather than just relative risk, vampW facilitates more actionable patient screening and preventative medicine strategies.

The authors conclude that joint modeling via vampW is essential for reducing false discoveries and uncovering novel disease pathways that marginal testing misses, ultimately advancing the understanding of disease onset mechanisms.

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