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REVIEW 2 major objections 5 minor 68 references

Bayesian variable selection in a Cox proportional hazards model with the "Sum of Single Effects" prior

T0 review · 2 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read CoxPH-SuSiE gives time-to-event fine-mapping calibrated posterior inclusion probabilities and credible sets.

desk verdict Useful new method for TTE fine-mapping, but the calibration evidence is undercut by an additive-hazards simulation that is mislabeled as proportional hazards. read the letter →

arxiv 2506.06233 v1 pith:HOJA43XP submitted 2025-06-06 stat.ME q-bio.QMstat.AP

Yunqi Yang , Karl Tayeb , Peter Carbonetto , Xiaoyuan Zhong , Carole Ober , Matthew Stephens This is my paper
classification stat.MEq-bio.QMstat.AP MSC 62F1562N0162P10
keywords Bayesianvariableselectiontime-to-eventdataCoxproportionalhazardsSuSiEpriorgeneticfine-mappingposteriorinclusionprobabilitycrediblesetsUKBiobank
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper introduces CoxPH-SuSiE, a Bayesian variable-selection method for time-to-event outcomes that pairs the Cox proportional hazards model with the 'Sum of Single Effects' (SuSiE) prior. The aim is genetic fine-mapping: given a genomic region, find which variants affect the age at which a disease occurs, with posterior inclusion probabilities (PIPs) and 95% credible sets that quantify uncertainty honestly. The paper argues that CoxPH-SuSiE does this where earlier survival-data variable-selection methods did not: in simulations built on real GTEx and UK Biobank genotypes, its PIPs were the best calibrated among the methods compared, and its credible sets reached or nearly reached their 95% target coverage. Applied to asthma age-of-diagnosis data in UK Biobank, the method found 14 risk SNPs in 8 loci, 6 with PIP above 50%, including two known pathogenic variants in the filaggrin gene.

What carries the argument

The load-bearing object is the Laplace-approximate Bayes factor (Eq. 12) for a single-variable CoxPH regression with an offset, computed from the maximum partial-likelihood estimate $\hat b$, its standard error $s$, and the likelihood ratio. This approximation turns each single-effect update into a Gaussian integral, allowing the SuSiE prior — $b = \sum_{l=1}^L b_l \gamma_l$, where each $\gamma_l$ is a one-hot vector — to be fitted by generalized Iterative Bayesian Stepwise Selection (gIBSS), which cycles through $L$ single effects, updates offsets to remove already-found effects, and recomputes posterior inclusion probabilities. Credible sets are then formed by sorting variants by PIP and adding them until the cumulative probability exceeds the target level, with optional pruning by 'purity', the smallest absolute correlation within the set.

What would settle it

Simulate time-to-event data under the true proportional-hazards model with event rate $\lambda_i(t) = \lambda_0(t)\exp(x_i^\top b)$ rather than the linear-hazard scheme used in Appendix D, plant a single causal variant, run CoxPH-SuSiE, and check whether its 95% credible sets contain the causal variant in at least 95% of replicates and whether SNPs with PIP near 0.95 are causal about 95% of the time.

Watch

Extended reading notes

Core claim

The central claim is that the SuSiE machinery — representing the regression coefficients as a sum of L single-effect vectors and iterating single-variable regressions — transfers to the Cox partial likelihood, and that the transfer only works if the single-variable Bayes factors are computed with the Laplace approximation (12) rather than the commonly used asymptotic Bayes factor. With that choice, CoxPH-SuSiE produces posterior inclusion probabilities that are better calibrated than those from R2BGLiMS, BVSNLP, survival.svb, and SuSiE-RSS in both GTEx and UK Biobank simulations, and 95% credible sets whose coverage reaches or comes very close to the nominal level. The paper also shows that the method scales to hundreds of thousands of samples and thousands of highly correlated SNPs, and that it can expose secondary association signals, as illustrated by the asthma fine-mapping analysis.

Load-bearing premise

The load-bearing premise is that the quadratic (Laplace) approximation to each single-variable Cox partial log-likelihood stays accurate when applied over and over inside the iterative gIBSS routine, which the authors themselves describe as a heuristic with no proven convergence guarantee.

Editorial extensions

If this is right

  • Time-to-event fine-mapping can now report both PIPs and credible sets, quantities that none of the earlier survival-based variable-selection methods provided.
  • A SNP with PIP above 0.95 should be a true causal variant roughly 84% of the time in UK Biobank-scale data, compared with at most 35% for the other methods tested.
  • The Laplace Bayes factor should replace the asymptotic Bayes factor in single-variable survival regressions, since it is more accurate at nearly the same computational cost.
  • The method's cost is $O(npL)$ per iteration and parallelizes over covariates, making biobank-scale fine-mapping of age-at-onset traits practical.
  • The asthma application shows that credible-set fine-mapping can reveal multiple independent signals at one locus, as at 2q12.1 and 10p14, which marginal association tests alone would miss.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper: if the observed calibration holds more generally, CoxPH-SuSiE PIPs could be aggregated across biobank traits to prioritize variants whose effects are shared across multiple time-to-event phenotypes.
  • The same template — a SuSiE prior plus a Laplace-approximated single-variable Bayes factor — could be carried to logistic or Poisson regression, giving case-control and count fine-mapping the same calibrated credible sets; the paper notes the generality but does not test it.
  • A stress test worth running: replace the quadratic approximation inside gIBSS with numerical quadrature on small data sets; if credible sets and PIPs barely change, the Laplace step is not the main source of error, and if they change a lot, the calibration observed here may depend on the approximation.
  • Because the simulation scheme in Appendix D generates event times with rates linear in the genotype, the proportional-hazards assumption is only approximately satisfied; rerunning with strictly exponential hazards would reveal whether the good calibration is robust to the true data-generating mechanism.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The paper extends the "Sum of Single Effects" (SuSiE) approach to Bayesian variable selection to time-to-event outcomes under the Cox proportional hazards model, calling the resulting method CoxPH-SuSiE. The method approximates single-variable Cox partial likelihood Bayes factors using a Laplace approximation, embeds these in a SuSiE-style iterative algorithm (gIBSS), and outputs posterior inclusion probabilities and credible sets. The authors validate the Laplace Bayes factor against numerical quadrature, compare PIP calibration and credible set coverage in simulations against three existing TTE variable-selection methods, and apply the method to fine-mapping eight asthma loci in UK Biobank, reporting 14 asthma risk SNPs in credible sets. The central claim is that CoxPH-SuSiE provides well-calibrated PIPs and 95% credible sets in high-LD, large-sample settings, and outperforms existing TTE fine-mapping methods.

Significance. If the central claim holds, CoxPH-SuSiE would be the first TTE fine-mapping method to deliver both calibrated posterior inclusion probabilities and credible sets in settings with very strong linkage disequilibrium and large sample sizes. The paper is commendable for making its code and data-analysis pipelines publicly available, for validating the Laplace Bayes factor against numerical quadrature, and for explicitly acknowledging the heuristic nature of gIBSS. The real-data application is a useful demonstration of the method, with plausible biological follow-up (e.g., the 10p14/GATA3 regulatory sequence and the FLG stop-gain variants). The main risk to significance is that the simulation evidence, which underpins the central claim, may be generated under an additive hazards model rather than the Cox proportional hazards model the method is designed for.

major comments (2)
  1. [Appendix D, steps 3-4; Table 1] The simulation procedure used to generate all TTE fine-mapping data (and used implicitly in Section 4's Bayes factor comparisons) does not generate data under the Cox proportional hazards model. Step 3 sets λ_i^s = b0 + x_i^T b, and Step 4 simulates T_i ~ Expon(λ_i^s). The hazard is therefore λ(t; x_i) = b0 + x_i^T b, an additive hazards model, not the Cox PH form λ(t; x_i) = λ0(t) exp(x_i^T b). The statement in Appendix D that data simulated this way "satisfies the proportional hazard assumption" is incorrect. Moreover, with the GTEx simulation setting in Table 1 (effect variance 1) and coefficients sampled from N(0,1), the linear predictor b0 + x_i^T b can easily be negative for genotype values 1 or 2 when a coefficient is negative, making the exponential rate invalid. Because Figures 3-5 and the PIP calibration and credible set coverage claims rest entirely on this procedure, the evidence for the central claim is currently compromised. I ask the authors to rerun the simulations under a true PH data-generating process (for example, T_i ~ Expon(exp(b0 + x_i^T b)) with the same genotype matrices, effect sizes, and censoring behavior) and compare the resulting calibration and coverage plots; if calibration and coverage are preserved, the concern is resolved, otherwise the central claim needs to be qualified.
  2. [Section 3.3 (gIBSS), Section 4, Section 5] The paper honestly acknowledges that gIBSS is not known to optimize any objective function and has no convergence guarantee. However, the numerical validation that is used to support the method's approximate posterior inferences is the same simulation procedure criticized above. Thus the two key approximations—the Laplace BF and the gIBSS iterates—are jointly validated only under an additive hazards model, not under the Cox PH model. The repeated application of the Laplace approximation to conditional models with offsets updated from previous effects could accumulate error, and the lack of an objective function means the algorithm's output may depend on initialization, iteration count, or stopping rule. I request additional evidence that the method converges in practice (e.g., sensitivity analyses with different initializations and larger maximum iteration counts) and that the calibration conclusions hold under a true Cox PH DGP. This is compatible with the paper's stated reliance on numerical experiments, but the experiments must target the actual model.
minor comments (5)
  1. [Appendix D, eq. (28)] The displayed expression for the censoring rate contains notational imprecision: the expectation should be over the sum of Bernoulli indicators Pr(C_i < T_i), not over the indicator itself as written; please rewrite for clarity.
  2. [Figure 5] The text refers to "median MAS" but MAS is defined as the mean absolute correlation within a credible set; please clarify which summary is plotted, or use a consistent term.
  3. [Section 6, paragraph after eq. (22)] There is a typo: "associations onlyl" should be "associations only."
  4. [Algorithm 1] The stopping criterion is referred to in the loop but never specified; please state the convergence criterion used in the implementation (e.g., change in elbo-like quantity or maximum absolute change in PIPs).
  5. [Section 4, first paragraph] The text says the simulations in Section 4 use a "single-SNP CoxPH model," but if the same Appendix D procedure is used, that model is additive hazards; please either align the terminology with the corrected simulation design or specify the exact hazard form used for the BF comparison.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the CoxPH-SuSiE derivation follows from the Cox partial likelihood and SuSiE prior, with self-citations used only as background and comparators.

full rationale

I find no circular step in the paper's derivation chain. CoxPH-SuSiE is obtained by combining the Cox partial likelihood (Eq. 2) with the SuSiE prior (Eq. 3); the posterior computations for the single-variable SER (Eqs. 5-19) follow from Bayes' theorem after a quadratic (Laplace) approximation to the partial log-likelihood (Eq. 7), and the resulting approximate Bayes factor (Eq. 12) is checked against numerical quadrature in Section 4. The only fitted hyperparameter, the prior variance sigma_0^2, is estimated by an EM update (Eq. 21) derived from the same approximate likelihood; PIPs and credible sets are then posterior functionals, not refitted quantities, so there is no 'fitted input called prediction'. Citations to Wang et al. (2020) and Zou et al. (2022) supply the SuSiE prior, the definition of credible sets, and a comparator method; they are background/definitions and are not invoked as an external uniqueness theorem or as the sole justification of the paper's claims. The gIBSS algorithm is explicitly labeled heuristic with no convergence guarantee, so no variational equivalence is claimed. The Appendix D simulation procedure is a separate concern: it generates T_i ~ Expon(b0 + x_i^T b), an additive-hazards process rather than a Cox PH process, and the paper's assertion that such data 'satisfies the proportional hazard assumption' appears incorrect; this threatens the validity of the calibration evidence but is a correctness/simulation-fidelity issue, not a case of the derivation reducing to its own inputs.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

No new physical or biological entities are postulated. The model, priors, and approximations are statistical constructs; the key free choices are the prior variance, L, and purity threshold.

free parameters (3)
  • prior variance sigma_0l^2 = EM estimate per single effect, initialized to 1
    Controls the assumed effect-size scale for each single effect; estimated from the data by maximizing the approximate partial likelihood (Eq. 21), so the PIPs and credible sets depend on the fitted value.
  • number of single effects L = 5 in simulations, 10 in the asthma fine-mapping
    Model complexity chosen by the user; credible sets and PIPs depend on L, which the authors do not infer.
  • credible set purity threshold = 0.5
    CSs with minimum pairwise absolute correlation below 0.5 are discarded, changing the reported set of findings.
assumptions (4)
  • domain assumption Cox partial likelihood can be used as a likelihood in Bayes' theorem, justified by Kalbfleisch's limiting gamma process prior on the baseline hazard.
    Invoked in Section 3, first paragraph; this justifies replacing the full likelihood with the partial likelihood in all posterior computations.
  • ad hoc to paper The quadratic approximation of the log partial likelihood (Eq. 7) is accurate enough that approximate Bayes factors can replace exact ones.
    Used to derive Eqs. 9-12; validated only in numerical experiments, not with a theoretical error bound.
  • ad hoc to paper gIBSS iterations converge to a useful stationary point even though no objective function or convergence guarantee is known.
    Section 3.3 explicitly says the authors cannot prove convergence and rely on numerical experiments.
  • ad hoc to paper The linear-hazard simulation scheme generates data under the Cox proportional hazards model.
    Appendix D, steps 3-5: event rates are b0 + x_i'b, not lambda0 exp(x_i'b), so PH holds only approximately; the text asserts it holds.

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Cite this review

Pith. "Pith review of Bayesian variable selection in a Cox proportional hazards model with the "Sum of Single Effects" prior." pith.science (2026). https://pith.science/paper/HOJA43XP

@misc{pith2026250606233,
  author       = {Pith},
  title        = {Pith review of: Bayesian variable selection in a Cox proportional hazards model with the "Sum of Single Effects" prior},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HOJA43XP}},
  note         = {Machine review of arXiv:2506.06233}
}
read the original abstract

Motivated by genetic fine-mapping applications, we introduce a new approach to Bayesian variable selection regression (BVSR) for time-to-event (TTE) outcomes. This new approach is designed to deal with the specific challenges that arise in genetic fine-mapping, including: the presence of very strong correlations among the covariates, often exceeding 0.99; very large data sets containing potentially thousands of covariates and hundreds of thousands of samples. We accomplish this by extending the "Sum of Single Effects" (SuSiE) method to the Cox proportional hazards (CoxPH) model. We demonstrate the benefits of the new method, "CoxPH-SuSiE", over existing BVSR methods for TTE outcomes in simulated fine-mapping data sets. We also illustrate CoxPH-SuSiE on real data by fine-mapping asthma loci using data from UK Biobank. This fine-mapping identified 14 asthma risk SNPs in 8 asthma risk loci, among which 6 had strong evidence for being causal (posterior inclusion probability greater than 50%). Two of the 6 putatively causal variants are known to be pathogenic, and others lie within a genomic sequence that is known to regulate the expression of GATA3.

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.