Strategy to control biases in prior event rate ratio method, with application to palliative care in patients with advanced cancer

Objectives: Prior event rate ratio (PERR) is a method shown to perform well in mitigating confounding in real-world evidence research but it depends on several model assumptions. We propose an analytic strategy to correct biases arising from violation of two model assumptions, namely, population homogeneity and event-independent treatment. Study Design and Setting: We reformulate PERR estimation by embedding a treatment-by-period interaction term in an analytic model for recurrent event data, which is robust to bias arising from unobserved heterogeneity. Based on this model, we propose a set of methods to examine the presence of event-dependent treatment and to correct the resultant bias. We evaluate the proposed methods by simulation and apply it to a de-identified dataset on palliative care and emergency department visits in patients with advanced cancer. Results: Simulation results showed that the proposed method could mitigate the two sources of bias in PERR. In the palliative care study, analysis by the Cox model showed that patients who had started receiving palliative care had higher incidence of emergency department visits than their match controls (hazard ratio 3.31; 95% confidence interval 2.78 to 3.94). Using PERR without the proposed bias control strategy indicated a 19% reduction of the incidence (0.81; 0.64 to 1.02). However, there was evidence of event-dependent treatment. The proposed correction method showed no effect of palliative care on ED visits (1.00; 0.79 to 1.26). Conclusions: The proposed analytic strategy can control two sources of biases in the PERR approach. It enriches the armamentarium for real-world evidence research.

💡 Research Summary

The paper addresses two fundamental assumptions underlying the Prior Event Rate Ratio (PERR) method, a popular tool for confounding control in real‑world evidence (RWE) studies. The first assumption is population homogeneity: the standard Cox model used in PERR implicitly assumes that all individuals share the same baseline hazard, ignoring unobserved heterogeneity (“frailty”). The second assumption is event‑independent treatment (EDT), meaning that the occurrence of the outcome does not influence the timing of treatment initiation. Violations of either assumption can bias the PERR estimate, yet existing literature only offers limited solutions for heterogeneity and none for EDT.

To overcome these limitations, the authors reformulate PERR using a single Cox‑type model that includes a treatment‑by‑period interaction term: λi(t)=λ0(t)·exp(β1·trt_i+β2·post_i+β3·trt_i·post_i). Here β1 captures the hazard ratio (HR) in the pre‑treatment period, β1+β3 captures the HR in the post‑treatment period, and exp(β3) is exactly the traditional PERR estimate (HR_post/HR_pre). By fitting this model within the Andersen‑Gill (AG) framework for recurrent events, they obtain a version called PERR‑AG that is robust to unobserved heterogeneity because the AG risk set retains individuals after they experience an event, unlike the standard Cox time‑to‑first‑event approach.

For EDT, the authors posit that the instantaneous hazard of starting treatment, h_trt(t), is multiplied by a factor θ for a duration δ after an outcome event. If θ>1, events accelerate treatment; if 0<θ<1, they delay it. The average shift in treatment time (Δt_i) can be expressed analytically in terms of θ and δ. Since δ is unknown in practice, the authors partition the pre‑treatment period into M equal‑length sub‑intervals (gaps) of length Δ*. They then fit an AG model that includes interaction terms between treatment and each gap (β3m·trt·gap_m). The coefficient for the last gap (β3M) is used as a diagnostic: a statistically significant β3M (p<0.05) indicates the presence of EDT. The set of consecutive gaps with significant β3m defines the estimated duration Δ̂, while the corresponding β3M provides an estimate of θ̂.

When EDT is detected, the control group’s index times are shifted forward by Δ̂·(θ̂−1) to mimic the same event‑dependent treatment dynamics observed in the treated group. The modified control dataset (data(control*)) is then compared with the original treated dataset (data(treat)) using the PERR‑AG model, yielding an EDT‑adjusted treatment effect that is no longer biased by event‑dependence.

Simulation studies replicate a realistic palliative‑care (PC) scenario with 1,600 matched subjects, 150‑day pre‑ and post‑periods, and varying baseline event rates, heterogeneity levels, and EDT parameters. Key findings from 1,000 replicates per scenario include: (1) The original PERR and a “PERR‑Cox” implementation are both biased when heterogeneity is present, whereas PERR‑AG remains unbiased and has the smallest root‑mean‑square error (RMSE). (2) The EDT detection algorithm correctly identifies the presence of EDT in >90 % of simulations with strong θ (0.25 or 4) and in 55‑82 % when θ is moderate (0.5 or 2). Even when the true θ varies within the duration, the method performs well. (3) After applying the EDT correction, the adjusted PERR‑AG estimates recover the true treatment effect (e.g., HR = 0.5) with coverage probabilities close to the nominal 95 % and markedly reduced RMSE, whereas uncorrected estimates can have coverage as low as 38 %.

The methodology is applied to a de‑identified electronic health record dataset from Singapore’s National Cancer Centre, comprising 2,571 stage‑IV cancer patients observed from December 2017 to August 2022. After excluding pre‑study PC users and 1:1 matching on age, sex, and cancer type, a PERR cohort of 1,658 patients (829 treated, 829 controls) is formed, with up to 150 days before and after the PC initiation date. Cox analysis of the post‑period shows a hazard ratio of 3.31 (95 % CI 2.78‑3.94) for emergency department (ED) visits among PC patients, but the pre‑period HR is even larger (4.12), indicating baseline imbalance. The traditional PERR‑Cox yields a ratio of 0.81 (95 % CI 0.64‑1.02), suggesting a modest reduction. PERR‑AG, which accounts for heterogeneity, gives HR_pre = 4.63, HR_post = 3.18, and a PERR of 0.69 (95 % CI 0.55‑0.86).

Applying the EDT detection model with five 10‑day gaps shows no significant interaction for the last gap (p = 0.48), leading to an estimated θ̂≈1.0 and Δ̂≈10 days—essentially no event‑dependent treatment. Consequently, the EDT‑adjusted PERR‑AG estimate is HR = 1.00 (95 % CI 0.79‑1.26), indicating that after correcting for both heterogeneity and potential EDT, palliative care does not have a statistically discernible effect on ED visit rates.

In summary, the authors present a comprehensive strategy to make PERR robust to two major sources of bias: unobserved heterogeneity and event‑dependent treatment. By embedding a treatment‑by‑period interaction within an Andersen‑Gill recurrent‑event framework and by systematically testing for and correcting EDT, they provide a practical, statistically sound workflow for RWE investigators. Simulation results confirm the method’s ability to recover unbiased treatment effects across a range of realistic scenarios, and the real‑world application demonstrates its relevance to clinical questions where conventional PERR may give misleading conclusions. The approach broadens the methodological toolkit for observational pharmaco‑epidemiology and health‑services research, offering a path toward more reliable causal inference from routinely collected health data.