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

This paper proposes and validates an analytic strategy that corrects biases in the Prior Event Rate Ratio (PERR) method caused by population heterogeneity and event-dependent treatment, demonstrating its application in palliative care research where the corrected analysis revealed no significant effect of palliative care on emergency department visits compared to uncorrected models.

Original authors: Xiangmei Ma, Grace Meijuan Yang, Qingyuan Zhuang, Yin Bun Cheung

Published 2026-03-03

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Xiangmei Ma, Grace Meijuan Yang, Qingyuan Zhuang, Yin Bun Cheung

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The "Time-Traveling Detective" Method: Fixing Flawed Medical Studies

Imagine you are a detective trying to solve a mystery: Does a new type of care (Palliative Care) actually stop patients from rushing to the Emergency Room (ER), or does it make them go there more often?

In the real world, you can't just run a perfect experiment where you flip a coin to decide who gets care and who doesn't (like in a lab). Instead, you have to look at old medical records. But here's the problem: Medical records are messy.

People who get Palliative Care are usually sicker to begin with. If you just compare them to healthy people, it looks like Palliative Care is "bad" because the sick people still go to the ER. If you compare them to other sick people, you might still get it wrong because the "sick" people are sick in different ways.

This paper introduces a clever new way to clean up this messy data so we can find the true answer.

The Old Tool: The "Prior Event Rate Ratio" (PERR)

Think of the old method (PERR) as a Time-Traveling Scale.

The Setup: You take a patient who got Palliative Care. You look at their life before they got the care (the "Prior" period) and their life after (the "Post" period).
The Match: You find a "twin" patient who never got the care. You pretend this twin got the care on the exact same day the real patient did.
The Weighing:
- You weigh how often the real patient went to the ER before vs. after.
- You weigh how often the twin went to the ER before vs. after.
- You compare the two.

The Problem: This scale assumes the world is perfectly static. It assumes that if a patient had an ER visit, it didn't change their future behavior. But in reality, events change behavior.

If a patient has a scary ER visit, they might panic and call their doctor immediately, getting Palliative Care sooner than they otherwise would have. Or, if they have a bad ER visit, they might avoid the hospital for a while.

The old method gets confused by this. It sees the ER visit and the sudden start of care and thinks, "Aha! The care caused the ER visit!" (or vice versa), when really, the ER visit just triggered the decision to start care. This is called Event-Dependent Treatment Bias. It's like a detective blaming the suspect for the crime, when the crime actually just made the suspect show up at the police station.

The New Strategy: The "Smart Detective"

The authors (Ma, Yang, Zhuang, and Cheung) built a Smarter Detective Kit with two main upgrades:

Upgrade 1: The "Recurring Event" Lens (Fixing Hidden Differences)

The old method only looked at the first time someone went to the ER. It ignored everyone else.

The Analogy: Imagine judging a runner's speed by only looking at their first step. If they trip on step 1, you think they are slow. But maybe they are a sprinter who just stumbled!
The Fix: The new method uses a model (called the Andersen-Gill model) that looks at every trip to the ER, not just the first one. It accounts for the fact that some people are just naturally "fragile" or "high-risk" (like a runner with a bad knee). This prevents the study from being fooled by hidden differences between patients.

Upgrade 2: The "Time-Shift" Correction (Fixing the Panic Reaction)

This is the big innovation. The authors realized that if a patient has an ER visit, it might push their start date for Palliative Care forward or backward.

The Analogy: Imagine you are waiting for a bus. Suddenly, it starts raining (the ER visit). You run to the bus stop earlier than you planned. If you analyze your schedule without knowing it rained, you'll think you were always an early bird.
The Fix: The new method detects this "rain." It calculates how much the ER visit changed the timing of the care. Then, it rewinds or fast-forwards the clock for the control group (the "twins") to match the reality.
- If the real patient started care sooner because of an ER visit, the method shifts the twin's "start date" earlier too.
- Now, both groups are being compared on a level playing field, as if the ER visit didn't mess up the timing.

The Real-World Test: Palliative Care in Singapore

The team tested this new detective kit on real data from cancer patients in Singapore.

The Old Way (The Flawed Scale):

Result: It looked like Palliative Care reduced ER visits by about 19%.
The Trap: It seemed like a success story.

The New Way (The Smart Detective):

Step 1: They checked for "panic reactions." They found that patients who had an ER visit were much more likely to start Palliative Care immediately after. The ER visit was driving the decision to start care.
Step 2: They applied the "Time-Shift" correction.
Result: The effect disappeared. The new analysis showed that Palliative Care had zero effect on the number of ER visits (1.00).

What does this mean?
It doesn't mean Palliative Care is useless! It means that in the real world, the people who get Palliative Care are the ones who are already having a crisis (ER visits). The care didn't cause the ER visits, nor did it magically stop them in this specific dataset. The old method was just confused by the timing.

The Takeaway

This paper is like giving researchers a calibration tool for their scales.

In the past, we might have celebrated a medical treatment because a flawed method made it look like a hero. Now, with this new strategy, we can:

See through the noise of hidden patient differences.
Untangle the timing of cause and effect.

It ensures that when we say a treatment works (or doesn't), we aren't just being fooled by the chaos of real life. It helps us make better decisions for patients, doctors, and healthcare systems.

1. Problem Statement

The Prior Event Rate Ratio (PERR) method is a widely used statistical approach in real-world evidence (RWE) research designed to control for both measured and unmeasured confounders by comparing event rates before and after treatment initiation. However, the standard PERR method relies on strict model assumptions that, when violated, lead to significant bias:

Population Homogeneity: The standard PERR often utilizes the Cox proportional hazards model, which assumes homogeneity (no unobserved heterogeneity or "frailty"). In reality, unobserved heterogeneity causes selection bias, leading to biased treatment effect estimates.
Event-Independent Treatment: The method assumes that the occurrence of outcome events does not influence the timing of treatment initiation. In practice, Event-Dependent Treatment (EDT) occurs (e.g., a patient experiencing an emergency department visit may trigger an earlier palliative care referral). If outcome events increase treatment rates, the pre-treatment event rate appears artificially high, causing the PERR estimate to be biased downward (underestimating the treatment effect).

Currently, there is no established method to correct for EDT bias within the PERR framework.

2. Methodology

The authors propose a three-part analytic strategy to address these limitations:

A. Reformulation of PERR using the Andersen-Gill (AG) Model

Instead of fitting two separate Cox models for pre- and post-periods, the authors reformulate PERR into a single Cox model with a treatment-by-period interaction term:
$\lambda_i(t) = \lambda_0(t) \exp(\beta_1 \times trt_i + \beta_2 \times post_i + \beta_3 \times trt_i \times post_i)$

Key Innovation: They replace the standard Cox model with the Andersen-Gill (AG) model for recurrent event data. Unlike the Cox model, which only considers the first event and excludes subjects from risk sets after an event, the AG model allows subjects to remain in the risk set after experiencing events.
Benefit: The AG model is robust to unobserved heterogeneity (frailty), thereby eliminating the selection bias inherent in the traditional Cox-based PERR. The interaction term ( $\beta_3$ ) yields the PERR estimate.

B. Detection of Event-Dependent Treatment (EDT)

To detect EDT, the authors propose partitioning the pre-treatment period into sub-periods immediately preceding the treatment index date.

They fit an AG model to the pre-treatment data only, introducing gap indicators ( $gap_{mi}$ ) for consecutive time windows before treatment.
The coefficient for the interaction between treatment and the final gap ( $b_{3M}$ ) estimates the magnitude of EDT ( $\theta$ ).
Algorithm: They use an exploratory approach with $M$ sub-periods of equal length ( $\delta$ ). If the coefficient for the sub-period immediately preceding treatment is significant, EDT is confirmed. The duration of the effect ( $\hat{\delta}$ ) is determined by summing consecutive significant sub-periods.

C. Correction for EDT Bias

If EDT is detected, the authors propose a heuristic correction method:

Concept: Adjust the index times (treatment start dates) for the control group to mimic the event-dependence observed in the treated group.
Mechanism: Using the estimated magnitude ( $\hat{\theta}$ ) and duration ( $\hat{\delta}$ ), the control group's index times are shifted backward or forward based on their own pre-index events, according to a derived shift equation:
$\Delta t_i = t_{trt,i}^* - t_{trt,i}$
(Where $t^*$ is the realized time and $t$ is the underlying time).
Result: The PERR analysis is then re-run comparing the treated group against this modified control group ( $data(control^*)$ ), ensuring both groups are subject to the same event-dependent timing bias, thus canceling it out.

3. Key Contributions

Model Reformulation: Demonstrated that PERR can be efficiently implemented as a single AG model with an interaction term, simplifying computation and enabling robustness against unobserved heterogeneity.
Novel EDT Correction: Developed the first systematic strategy to detect and correct for bias arising from event-dependent treatment in PERR studies.
Empirical Validation: Provided extensive simulation evidence showing that the proposed method significantly reduces bias and improves confidence interval coverage compared to uncorrected methods.
Real-World Application: Applied the strategy to a palliative care dataset, fundamentally changing the study's conclusion from a "protective effect" to a "null effect," highlighting the critical importance of bias correction in RWE.

4. Results

Simulation Studies

Unobserved Heterogeneity: The traditional PERR and PERRCox (Cox-based) showed significant bias and poor coverage probabilities (as low as 51.7%) when heterogeneity existed. The proposed PERRAG (AG-based) remained unbiased with coverage probabilities near 95%.
EDT Detection: The method successfully detected EDT duration ( $\hat{\delta}$ ) with high accuracy (92–96% for strong effects) and provided accurate estimates of the magnitude ( $\hat{\theta}$ ).
EDT Correction: In scenarios with EDT, uncorrected PERRAG estimates were heavily biased (e.g., true HR=0.5 estimated as 0.433 with 66.1% coverage). The corrected estimates closely matched the true treatment effect (Mean HR $\approx$ 0.50) with coverage probabilities restored to ~94%.

Palliative Care (PC) Study Application

Context: Analysis of emergency department (ED) visits in advanced cancer patients ( $N=1658$ matched pairs).
Cox Model Result: Patients starting PC had a higher ED visit rate than controls (HR 3.31).
Uncorrected PERR: Suggested PC reduced ED visits by 19% (HR 0.81, 95% CI 0.64–1.02).
EDT Detection: Analysis revealed a significant elevation in ED visits in the 5 weeks prior to PC initiation ( $\hat{\theta} = 4.76$ ), indicating that acute events triggered PC referrals.
Corrected Result: After applying the EDT correction, the adjusted PERR showed no effect of palliative care on ED visits (HR 1.00, 95% CI 0.79–1.26). The initial finding of a protective effect was an artifact of uncorrected EDT bias.

5. Significance

This paper significantly advances the methodology of real-world evidence research. By addressing two major sources of bias (unobserved heterogeneity and event-dependent treatment), the proposed strategy:

Enhances Validity: Provides a more rigorous framework for causal inference in observational studies where randomization is not feasible.
Prevents Misinterpretation: The palliative care case study serves as a cautionary tale, demonstrating that without correcting for EDT, researchers may falsely conclude that an intervention is effective when it is not (or vice versa).
Broadens Applicability: The strategy enriches the "armamentarium" for researchers evaluating treatments in fields like oncology, cardiology, and infectious diseases where recurrent events and treatment triggers are common.

Limitations Noted: The correction method is heuristic and lacks a formal mathematical proof of bias removal. Additionally, the method assumes the event rate in the prior period does not affect the post-period rate, an assumption not addressed in this study.