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REVIEW 3 major objections 5 minor 27 references

Bias reduction method for prior event rate ratio, with application to emergency department visit rates in patients with advanced cancer

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The paper proposes that embedding the conditional frailty model into the prior event rate ratio framework reduces bias from event dependence, and supports this with simulations and an emergency department visit example.

desk verdict Sensible incremental extension of PERR to handle event dependence, but the 'about 5% bias' summary only holds in the main scenario; the supplementary simulations show the method can worsen bias in some transient positive-event-dependence settings. read the letter →

arxiv 2507.11861 v1 pith:KVMNLJZR submitted 2025-07-16 stat.ME stat.AP

Xiangmei Ma , Chetna Malhotra , Eric Andrew Finkelstein , Yin Bun Cheung This is my paper
classification stat.MEstat.AP MSC 62N0162P10
keywords prioreventrateratioconditionalfrailtydependencerecurrenteventsconfoundingcontrolpalliativecareemergencydepartmentvisitsreal-worldevidence
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 proposes a fix for a known weakness of the prior event rate ratio (PERR), a method that controls confounding by using each treated person's pre-treatment event rate as their own control. PERR assumes that having an earlier outcome event does not change the rate of later events; when this "event dependence" assumption fails, PERR estimates can be badly biased. The authors incorporate the conditional frailty model -- a Cox-type model with separate baseline hazards for each event count and a patient-level random effect -- into PERR estimation. Simulations show the resulting PERRCF estimator cuts median absolute relative bias to about 5%, whereas the crude PERR can be off by up to about 96%, and coverage of 95% confidence intervals improves from as low as 41% toward the nominal level. In an advanced-cancer sample, the method changes the estimated emergency department visit rate ratio for palliative care from 1.45 (crude PERR) to 1.22 (PERRCF), versus 3.61 from conventional adjusted Cox regression.

What carries the argument

The operating mechanism is the conditional frailty model for recurrent events. It stratifies the baseline hazard $\lambda_{0j}(t)$ by event count $j$, so a person is only compared with others who have had the same number of events, and it adds a subject-level random effect $\omega_i$, modeled as gamma-distributed, to offset the selection bias this stratification creates. In the paper's equation (2), the treatment, period, and treatment-by-period interaction terms from the Andersen-Gill formulation of PERR are kept, and $\exp(\beta_3)$ is the bias-reduced PERR estimate. Estimation is carried out with standard frailty-model software, and the simulation pools high event strata at the 95th percentile of event counts to avoid sparse strata.

What would settle it

Generate recurrent-event data under a different dependence mechanism, for example where the effect of a past event depends on time since that event rather than on the running event count, or where frailty is log-normal instead of gamma, and check whether PERRCF's relative bias stays near 5%. If bias grows substantially in such scenarios, the method's protection is limited to the assumed mechanism.

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Extended reading notes

Core claim

The paper's central claim is that the conditional frailty method can be embedded in the prior event rate ratio estimator to remove bias from event dependence. In equation (2), the outcome hazard for event stratum $j$ is $\lambda_{ij}(t) = \omega_i \lambda_{0j}(t) \exp(\beta_1 \, \mathrm{trt}_i + \beta_2 \, \mathrm{post}_i + \beta_3 \, \mathrm{trt}_i \times \mathrm{post}_i)$, where stratification by event count controls the dependence created by past events and the person-level gamma frailty $\omega_i$ offsets the selection that stratification induces. The quantity $\exp(\beta_3)$ is the PERRCF hazard ratio. Simulation under constant and transient, positive and negative event dependence shows that this estimator consistently reduces relative bias and RMSE relative to the unadjusted PERRAG estimator, with median absolute relative bias near 5%; the authors also find that using the conditional frailty adjustment when there is no event dependence introduces only mild bias, so the assumption should still be checked first.

Load-bearing premise

The load-bearing premise is that the conditional frailty model correctly describes how event dependence actually works: dependence must act only through the event count stratum, and the leftover person-level heterogeneity must follow the gamma distribution assumed for the frailty.

Editorial extensions

If this is right

  • PERRCF provides a concrete way to use PERR when the absence-of-event-dependence assumption fails, so the method can be applied to recurrent outcomes such as emergency department visits.
  • Because negative event dependence biases PERR toward the null and positive event dependence biases it away, the conditional frailty adjustment corrects estimates in both directions, as the simulation shows.
  • Coverage of nominal 95% confidence intervals improves from values as low as 41% to roughly the nominal level in most simulated scenarios, making inference more reliable.
  • The example suggests that the large palliative care hazard ratio from conventional regression (3.61) is largely an artifact of confounding and event dependence; the corrected PERR estimate is 1.22 with a wide confidence interval.

Reading between the lines

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

  • Inference: The same conditional frailty adjustment could be attached to other PERR implementations, including pairwise Cox versions, not only the Andersen-Gill formulation used here.
  • Inference: Because the paper notes that joint modelling with mortality is not yet combined with this adjustment, a natural next step is a joint frailty model that handles event dependence and non-differential mortality in one estimator; such a model would generalize PERR to settings with substantial death-related dropout.
  • Inference: The method's practical success may depend on having enough subjects in each event-count stratum, so applications with very few recurrent events per person may need pooling rules similar to the paper's 95th-percentile pooling to avoid small-stratum instability.
  • Inference: A direct validation test would be to apply PERRCF to a recurrent event outcome with a known null treatment effect; if the estimate remains near 1.0 while PERRAG shows bias, the simulation result transfers to real data.
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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

3 major / 5 minor

Summary. The paper proposes incorporating the conditional frailty (CF) method into prior event rate ratio (PERR) estimation, yielding a PERRCF estimator that aims to reduce bias when the PERR assumption of no event dependence is violated. The proposal is evaluated by simulation under four event-dependence patterns (positive/negative, constant/transient) across three baseline hazard shapes, and is illustrated in a study of emergency department visit rates and palliative care in advanced cancer patients in Singapore. The simulation results in the main text generally favor PERRCF over the Andersen-Gill–based PERRAG, with median absolute relative bias around 5% in the main scenarios, but the paper also reports that applying CF when no event dependence exists introduces bias. The empirical application shows positive event dependence by DRIM and yields PERRCF HR 1.22 (95% CI 0.61 to 2.43) compared with PERRAG HR 1.45 (95% CI 0.80 to 2.62).

Significance. If the central claim is supported, the paper provides a practical extension of PERR for recurrent-event outcomes, addressing a recognized limitation of the PERR approach. The method is built on established conditional frailty models, so the novelty is incremental, but the application is clinically relevant and the simulation covers a range of event-dependence scenarios. The paper ships simulation code on GitHub, which is a reproducible-research strength. However, the evidence as presented is less uniform than the conclusions suggest: the supplementary tables contain scenarios where PERRCF increases absolute bias, and the summary statistic of 'about 5%' is computed only from the main table. The paper also does not test misspecification of the assumed event-dependence mechanism, which limits the generality of the recommendation.

major comments (3)
  1. [Section 3.1 and Tables 1, S1, S2] The claim that the proposed method 'reduced relative bias as well as RMSE in the presence of event dependence' is contradicted by the supplementary results. In Table S1 (baseline shape k=1.2), the positive transient event-dependence scenario with HR=0.5 and ψ=1.0 gives PERRCF relative bias +13.9% versus PERRAG relative bias -7.1%; in Table S2 (k=1.0) the same scenario gives +9.4% versus -7.3%. In these two scenarios the CF adjustment increases absolute bias instead of reducing it. The 'median of the absolute values of R. Bias was 5%' reported in Section 3.1 is computed only from Table 1; across the 24 event-dependence scenarios in Tables 1, S1, and S2 the median absolute PERRCF relative bias is approximately 8–9%. The conclusions should be qualified by event-dependence pattern and baseline hazard shape, and the exceptional scenarios should be explicitly discussed rather than summarized as 'roughly similar'.
  2. [Equation (2) and Section 2.2 / Online Supplementary S1] The simulation data-generating process is structurally aligned with the fitted model: event dependence is generated through the event count (equations (3) and (4) in S1) and a gamma-distributed person-level frailty, which is exactly the mechanism assumed in equation (2). Consequently, the simulation evaluates PERRCF only under correct model specification. The paper does not examine misspecification of the event-dependence mechanism (e.g., non-gamma frailty, dependence on event timing beyond the specified exponential decay, or effect modification by covariates). Because the central recommendation is to use PERRCF whenever DRIM indicates event dependence, this limitation should be stated explicitly, and caution is warranted when the true mechanism is likely to differ from the assumed form.
  3. [Section 3.1, 'None' rows] The paper acknowledges that applying CF when no event dependence exists introduces approximately ±10% bias, but it does not emphasize the corresponding coverage probabilities. In Table 1 (None, HR=2.0) the PERRCF coverage is 78.6%, and in Table S1 (None, HR=2.0) it is 76.2%. This is more than a mild cost, and it strengthens the paper's own recommendation to evaluate the no-event-dependence assumption before applying CF. The discussion should present this coverage loss as a meaningful limitation of the proposed strategy, not merely a 'mild' bias.
minor comments (5)
  1. [Abstract and Section 3.1] The phrase 'median of absolute level of relative bias at about 5%' should be qualified to refer to the main simulation scenarios (k=0.8), since the full set of scenarios including the supplementary tables has a higher median and contains reversal cases.
  2. [Section 3.1] The sentence 'In the scenarios with no event dependence but the CF method was applied, there was about +/- 10% bias' should also report the coverage probabilities (78.6% and 76.2% in the HR=2.0 rows of Tables 1 and S1) so that readers see the full cost of unnecessary CF adjustment.
  3. [Section 2.1] The reference to Stata's 'strmcure' program (reference [18]) should be accompanied by a brief description of the command and confirmation that it fits the stratified shared-frailty model in equation (2) rather than a mixture-cure model.
  4. [References] Reference [8] is cited as a preprint; if the PERR-AG work has since been published in a peer-reviewed venue, the citation should be updated.
  5. [Table 2 and application] In the empirical analysis, giving the distribution of ED visits per patient (e.g., range and dispersion) would help readers interpret the DRIM odds ratio of 1.35 and the high event rates in the prior period.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the method applies an existing frailty estimator to PERR and evaluates it by simulation; self-citations are not load-bearing.

full rationale

The paper's derivation chain is an application rather than a derivation whose conclusion is already contained in its inputs. Equation (1) specifies the Andersen-Gill implementation of PERR, and equation (2) embeds the conditional frailty estimator; both are presented as model specifications from the recurrent-events literature, with PERR HR read directly as exp(beta3). The central claim that PERRCF reduces bias under event dependence is evaluated by a simulation that generates recurrent-event data under explicit hazard functions (Supplementary S1) and then compares PERRAG with PERRCF. This is an empirical evaluation of finite-sample performance, not a quantity forced by construction: the estimator and the data generator are not defined in terms of one another, and the bias/RMSE reductions are simulation outputs. Self-citations (refs 8, 9, 11) point to the authors' earlier, independently published methodology for the AG form of PERR, the DRIM assumption check, and the conditional frailty approach in vaccine studies. None is used as a uniqueness theorem or as the sole justification of a premise: equation (1) is stated in full in the paper, DRIM is used as a standard diagnostic, and the CF model is also attributed to non-author literature (ref 10). Thus there is no self-definitional, fitted-input-called-prediction, or self-citation load-bearing circularity. A separate concern that the supplementary tables show scenarios where PERRCF increases bias relative to PERRAG is a matter of evidence consistency and generalizability, not circularity.

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

The central methodological claim rests on the PERR assumptions (constant confounding, non-differential mortality) and on the conditional frailty specification. The simulation evidence uses fixed design parameters, and the empirical illustration does not test misspecification. No new entities are introduced beyond the standard frailty random effect.

free parameters (3)
  • Simulation event-dependence magnitude (zeta or psi) = ±1.0
    The simulation sets the event-dependence effect to ±1.0 to create scenarios; the measured bias reduction depends on this magnitude.
  • Simulation frailty variance (sigma_omega^2) = 0.5
    Used in simulation data generation and correctly specified in the fitted CF model; performance may differ under misspecification.
  • Baseline hazard shape parameter k = 0.8, 1.0, 1.2
    Varied in sensitivity analyses; results are roughly similar across values, but the main tables use k=1.0 or k=1.2.
assumptions (4)
  • domain assumption The magnitude of confounding is constant over time (prior vs post periods)
    PERR identification relies on constant confounding; the paper restricts the analysis window to 70 days to mitigate but cannot verify it (Section 2.3).
  • domain assumption Non-differential mortality with respect to treatment after conditioning
    Authors note in Discussion that non-differential mortality is required and not addressed in the CF extension.
  • domain assumption The conditional frailty model with event-count stratification and gamma frailty correctly captures event dependence
    Equation (2) assumes this structure; simulation generates data under it, so real-world misspecification is untested.
  • standard math Standard Cox/AG model regularity and independent censoring assumptions
    Underlying model assumptions from the time-to-event literature, invoked without proof in Sections 2.1 and 2.2.

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Cite this review

Pith. "Pith review of Bias reduction method for prior event rate ratio, with application to emergency department visit rates in patients with advanced cancer." pith.science (2026). https://pith.science/paper/KVMNLJZR

@misc{pith2026250711861,
  author       = {Pith},
  title        = {Pith review of: Bias reduction method for prior event rate ratio, with application to emergency department visit rates in patients with advanced cancer},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KVMNLJZR}},
  note         = {Machine review of arXiv:2507.11861}
}
read the original abstract

Objectives: Prior event rate ratio (PERR) is a promising approach to control confounding in observational and real-world evidence research. One of its assumptions is that occurrence of outcome events does not influence later event rate, or in other words, absence of 'event dependence'. This study proposes, evaluates and illustrates a bias reduction method when this assumption is violated. Study Design and Setting: We propose the conditional frailty method for implementation of PERR in the presence of event dependence and evaluate its performance by simulation. We demonstrate the use of the method with a study of emergency department visit rate and palliative care in patients with advanced cancer in Singapore. Results: Simulations showed that, in the presence of negative (positive) event dependence, the crude PERR estimate of treatment effect was biased towards (away from) the null value. The proposed method successfully reduced the bias, with median of absolute level of relative bias at about 5%. Dynamic random-intercept modelling revealed positive event dependence in emergency department visits among patients with advanced cancer. While conventional time-to-event regression analysis with covariate adjustment estimated higher rate of emergency department visits among palliative care recipients (HR=3.61, P<0.001), crude PERR estimate and the proposed PERR estimate were 1.45 (P=0.22) and 1.22 (P=0.57), respectively. Conclusions: The proposed bias reduction method mitigates the impact of violation of the PERR assumption of absence of event dependence. It allows broader application of the PERR approach.

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Reviewed August 6, 2026 · model on record in the stance chip above.