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REVIEW 2 major objections 2 minor 26 references

Built-in Selection Bias in Proportional Hazards Models with Omitted Covariates: Simulation Evidence and Alternative Approaches

T0 review · 2 major / 2 minor · reviewed 2026-06-26 · grok-4.3

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Pith's one-line read Hazard ratios from Cox models are biased by omitted covariates even in randomized trials.

desk verdict The paper runs simulations to quantify how much omitted covariates bias Cox HRs even in RCTs and compares a few standard fixes, but the underlying non-collapsibility point is already established. read the letter →

arxiv 2606.19982 v1 pith:A2QSUACZ submitted 2026-06-18 stat.ME

Ayoub Bifenzi , Helene Jacqmin-Gadda This is my paper · ORCID
classification stat.ME
keywords hazardratioproportionalhazardsnon-collapsibilityomittedcovariatesselectionbiasfrailtymodelsacceleratedfailuretimerandomizedtrials
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

The paper shows that hazard ratios from proportional hazards models are non-collapsible, producing selection bias when important covariates are omitted from the analysis. This bias occurs even when the omitted covariates are independent of treatment assignment at baseline, as holds in randomized trials. Simulations quantify the bias magnitude in semi-parametric Cox models and parametric proportional hazards models under varying unmeasured heterogeneity. Alternative approaches such as frailty models, accelerated failure time models, and direct estimates of survival differences are compared for robustness. The methods are applied to data from a randomized radiation therapy trial to show practical differences.

What carries the argument

Non-collapsibility of the hazard ratio due to its conditioning on survival up to each time point.

What would settle it

A simulation or dataset in which all relevant covariates are measured and the estimated hazard ratio equals the known marginal effect without adjustment for frailty would falsify the built-in bias claim.

Watch

Extended reading notes

Core claim

Hazard ratios derived from the Cox proportional hazards model are subject to built-in selection bias in the presence of unmeasured heterogeneity arising from omitted important covariates, even when these covariates are independent of the main exposure at baseline.

Load-bearing premise

Omitted covariates affect the outcome hazard while remaining independent of treatment assignment at baseline.

Editorial extensions

If this is right

  • The estimated treatment hazard ratio will not equal the true marginal effect when covariates are omitted.
  • Frailty models recover an adjusted hazard ratio that accounts for unobserved heterogeneity.
  • Accelerated failure time model parameters remain collapsible and unaffected by the same selection mechanism.
  • Nonparametric survival differences or time-dependent effect models provide treatment effect measures free of the non-collapsibility bias.

Reading between the lines

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

  • Researchers may need to report survival probabilities rather than hazard ratios to obtain collapsible effect measures in trials with potential unmeasured factors.
  • Meta-analyses that pool hazard ratios from different studies could systematically distort summary effects if covariate sets differ across trials.
  • The mechanism implies that adding measured covariates after randomization can change the hazard ratio estimate in ways not explained by confounding alone.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 2 minor

Summary. The paper claims that hazard ratios from the Cox proportional hazards model exhibit built-in selection bias due to non-collapsibility when important covariates are omitted, even if those covariates are independent of treatment at baseline (as holds in RCTs). It reviews relevant literature on unobserved heterogeneity, conducts simulations to quantify bias in the semi-parametric Cox PH and parametric PH models across scenarios, compares these to alternatives including frailty-model HRs, AFT regression coefficients, and nonparametric survival differences (Kaplan-Meier or Cox with time-dependent effects), and demonstrates the alternatives on the RTOG 9202 randomized trial data.

Significance. If the simulations confirm substantial and systematic bias under the stated conditions, the work would usefully consolidate known theoretical results on non-collapsibility, supply concrete numerical evidence of its practical magnitude, and evaluate established remedies, thereby informing reporting practices for treatment effects in survival analyses of randomized trials.

major comments (2)
  1. [Abstract] Abstract: the simulation plan and alternatives are described but no quantitative results, model specifications, or data-generating details are supplied, preventing assessment of whether the evidence supports the central claim of built-in bias.
  2. [Simulation study] Simulation study: without explicit statements of the data-generating process (baseline hazard, distribution and effect sizes of omitted covariates, censoring mechanism, sample sizes, and number of replications), it is impossible to verify that the design isolates non-collapsibility from other sources of bias.
minor comments (2)
  1. [Abstract] The abstract would benefit from one or two key quantitative findings (e.g., range of bias observed) to convey the practical importance of the results.
  2. [Methods] Notation for the frailty distribution and the precise definition of the AFT acceleration factor should be stated explicitly when first introduced.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments, which highlight opportunities to improve the clarity and reproducibility of our manuscript. We address each major comment below and will incorporate revisions to strengthen the presentation of our simulation evidence on non-collapsibility in proportional hazards models.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the simulation plan and alternatives are described but no quantitative results, model specifications, or data-generating details are supplied, preventing assessment of whether the evidence supports the central claim of built-in bias.

    Authors: We agree that the abstract would be strengthened by including key quantitative results and a concise statement of the simulation design. In the revised manuscript, we will add specific findings (e.g., the percentage attenuation in the Cox HR under moderate omitted covariate effects) along with brief mentions of the baseline hazard form, omitted covariate distribution, and sample size. This will allow readers to immediately gauge the magnitude of the reported bias while remaining within abstract length constraints. revision: yes

  2. Referee: [Simulation study] Simulation study: without explicit statements of the data-generating process (baseline hazard, distribution and effect sizes of omitted covariates, censoring mechanism, sample sizes, and number of replications), it is impossible to verify that the design isolates non-collapsibility from other sources of bias.

    Authors: We acknowledge the need for greater explicitness. Although the simulation methods are described in the main text, we will add a new summary table (or expanded subsection) that lists every parameter: baseline hazard (Weibull shape/scale), omitted covariate distribution and coefficients, treatment effect size, independent censoring mechanism and rate, sample sizes per arm, and number of Monte Carlo replications. This will make transparent that the design holds treatment independent of the omitted covariate at baseline, thereby isolating the non-collapsibility mechanism from confounding or other biases. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity

full rationale

The paper presents an overview of known non-collapsibility properties of the Cox PH hazard ratio drawn from the existing literature, followed by independent simulation experiments that quantify bias under omitted covariates (independent of treatment at baseline) and comparisons against frailty models, AFT regression, and nonparametric survival differences. No load-bearing step equates a fitted quantity to a prediction by construction, invokes a self-citation as an unverified uniqueness theorem, or renames an input as an output; the simulation design and alternative estimators are externally specified and falsifiable against the generated data.

Assumptions & free parameters 0 free parameters · 2 assumptions · 0 invented entities

Abstract-only review yields limited visibility into simulation details; no explicit free parameters or invented entities are described.

assumptions (2)
  • domain assumption Proportional hazards assumption holds in the fitted models
    Paper evaluates bias within standard Cox and parametric PH frameworks that assume proportional hazards.
  • domain assumption Omitted covariates are independent of treatment at baseline in RCTs
    Abstract explicitly invokes this independence to isolate the built-in selection bias mechanism.

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Cite this review

Pith. "Pith review of Built-in Selection Bias in Proportional Hazards Models with Omitted Covariates: Simulation Evidence and Alternative Approaches." pith.science (2026). https://pith.science/paper/A2QSUACZ

@misc{pith2026260619982,
  author       = {Pith},
  title        = {Pith review of: Built-in Selection Bias in Proportional Hazards Models with Omitted Covariates: Simulation Evidence and Alternative Approaches},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/A2QSUACZ}},
  note         = {Machine review of arXiv:2606.19982}
}
read the original abstract

In time-to-event analysis, the hazard ratio (HR) derived from the Cox proportional hazards (PH) model is the most commonly used and widely reported measure for assessing treatment effects. However, hazard ratios are non-collapsible due to their inherent conditioning on survival up to each time point. As a result, they are subject to built-in selection bias in the presence of unmeasured heterogeneity arising from omitted important covariates, even when these covariates are independent of the main exposure at baseline, as is the case in randomized controlled trials. This article aims to provide an overview of key findings from the literature on how unobserved heterogeneity, due to omitted covariates that affect the outcome, can bias the estimation of the treatment hazard ratio in standard proportional hazards models, even in randomized trials where treatment is assigned independently of such covariates. Through simulations, we evaluate the extent of bias in the semi-parametric Cox PH model and parametric PH model under various scenarios of unmeasured heterogeneity. We then compare these standard models to alternative approaches that either account for this issue or are considered robust to it. These alternatives include the hazard ratio estimated from frailty models, regression parameters from an Accelerated Failure Time (AFT) model, and survival differences between treatment groups estimated nonparametrically using Kaplan-Meier curves or based on a Cox model with time-dependent effect of the exposure. We illustrate the practical relevance of the explored alternatives through a real data application to a randomized controlled trial from the Radiation Therapy Oncology Group (RTOG 9202).

Figures

Figures reproduced from arXiv: 2606.19982 by the authors.

Figure 1
Figure 1. Directed acyclic graph showing the relationships between variables [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Estimated density of U among individuals at risk at different time points, accross the two groups of treatment: treated group (X = 1, solid lines) and non treated group (X = 0, dashed lines). To illustrate this mechanism more concretely, we simulated a dataset of size n = 40000, where event times were generated from a PHM with Weibull baseline hazard, and two ex￾planatory variables X ∼ Ber(0.5) and U ∼ N (0, 1), hav… view at source ↗
Figure 3
Figure 3. Comparison of the true marginal log-hazard ratio (solid blue line) with estimates from [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Results of the simulation study with U ∼ N (0, 1). For each βU ∈ {0.2, 0.4, 0.8, 1}, boxplots display the 2.5%, 25%, 75%, and 97.5% quantiles, as well as the mean, of the difference between the true and estimated values of the regression coefficient from the following …
Figure 5
Figure 5. Figure 5: Results of the simulation study with U following a log-gamma(1, 1) distribution. For each βU ∈ {0.2, 0.4, 0.8, 1}, boxplots display the 2.5%, 25%, 75%, and 97.5% quantiles, as well as the mean, of the difference between the true and estimated values of the regression c…
Figure 6
Figure 6. Figure 6: Results of the simulation study with U ∼ Ber(0.5). For each βU ∈ {0.2, 0.4, 0.8, 1}, boxplots display the 2.5%, 25%, 75%, and 97.5% quantiles, as well as the mean, of the difference between the true and estimated values of the regression coefficient from the following …
Figure 7
Figure 7. Figure 7: Results of the simulation study with U ∼ N (0, 1). For each βU ∈ {0.2, 0.4, 0.8, 1}, boxplots display the 2.5%, 25%, 75%, and 97.5% quantiles, together with the mean, of the dif￾ference between the estimated and true survival difference between exposure groups, obtaine…

Discussion (0). Continue with ORCID to comment.

Reference graph

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