📊 statistics

Performance of prior event rate ratio method in the presence of differential mortality or dropout

This study extends previous research on the Prior Event Rate Ratio (PERR) method by demonstrating that while the traditional estimator remains biased under various differential mortality and dropout scenarios, an alternative estimator using only completers (PERR_Comp) significantly reduces bias and provides unbiased estimates unless mortality or dropout is directly influenced by prior events.

Original authors: Yin Bun Cheung, Xiangmei Ma

Published 2026-02-03

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Yin Bun Cheung, Xiangmei Ma

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

Imagine you are a detective trying to figure out if a new medicine actually works. You look at real-world records of patients, but there's a catch: some patients are sicker than others before they even start the treatment. This "sickness" is a hidden clue (a confounder) that makes it hard to tell if the medicine helped or if the patients were just naturally different to begin with.

To solve this, researchers use a clever trick called the Prior Event Rate Ratio (PERR). Think of it like a "before-and-after" photo comparison, but for time.

The Detective's Trick (How PERR Works)

Instead of just looking at what happened after the medicine started, the PERR method looks at two time periods for every patient:

The "Before" Period: Time before they took the medicine.
The "After" Period: Time after they started the medicine.

The method compares the treated group to a control group (people who didn't take the medicine). It calculates how often an event (like getting sick) happened in the "After" period versus the "Before" period for both groups. By taking the ratio of these two comparisons, the method tries to cancel out the "hidden clues" (confounders) that were present in both time periods. It's like saying, "If this group was twice as sick before the medicine, and they are still twice as sick after the medicine, then the medicine didn't change anything."

The Problem: The "Dropout" Mystery

A previous study warned that this trick breaks down if people start dropping out of the study (dying or leaving) at different rates. They claimed that if the reason people left was a mix of their treatment, their hidden sickness, and their past health, the PERR method would give a wrong answer.

This paper says: "Wait a minute, it's not that simple."

The authors argue that the PERR method isn't just one single tool; it's a toolbox. Depending on how you use the tools inside, you might get different results. They tested two specific ways to use the PERR method:

The "Old Way" (PERRPrev): This method uses data from everyone in the "Before" period, but only uses data from people who stayed until the end in the "After" period.
- The Analogy: Imagine you are judging a race. You count the runners who started the race, but in the second half, you only count the runners who didn't quit. If the people who quit were mostly the slow runners, your final score will be wrong.
- The Result: The authors confirmed that this "Old Way" does indeed get biased (wrong) when people drop out for complex reasons.
The "New Way" (PERRComp): This method is stricter. It only looks at people who finished the whole study (completers) for both the "Before" and "After" periods.
- The Analogy: This is like saying, "We will only judge the race based on the runners who finished the entire marathon." We ignore anyone who quit, for both the first half and the second half.
- The Result: This method is much more robust.
  - If people drop out because of their past health or the treatment, this method is still mostly accurate.
  - If people drop out specifically because of what happened to them in the "Before" period (e.g., if getting sick before the medicine made them quit), this method gets a little bit biased, but the error is only about one-third as bad as the "Old Way."
  - If people drop out for reasons unrelated to their past health (just random or due to the treatment itself), this method gives a perfectly accurate answer.

The Big Takeaway

The paper concludes that the PERR method isn't "broken"; it just depends on which version you use.

If you use the version that mixes data from dropouts and completers, you risk getting a wrong answer when people leave the study for complex reasons.
If you use the version that only looks at people who stayed the whole time, you get a much more reliable answer. It only fails if the very act of getting sick in the past is what caused them to leave the study.

In short, the authors are telling researchers: "Don't throw the whole PERR method away because of one bad scenario. Just choose the right version of the tool for your specific situation, and you can still get the truth."

Technical Summary: Performance of Prior Event Rate Ratio Method in the Presence of Differential Mortality or Dropout

Problem Statement
The Prior Event Rate Ratio (PERR) method is a statistical framework designed to control for both measured and unmeasured confounding in real-world evaluations of medical treatments using electronic medical records. While PERR has been applied to various treatments, its validity is challenged by the presence of differential mortality or dropout. A widely cited simulation study previously demonstrated that PERR estimates of treatment effect on binary outcomes become biased when mortality/dropout rates are jointly influenced by treatment, confounders, and prior events. However, that study was limited in scope, examining only a single specific PERR estimator and a single scenario of differential mortality. This paper addresses the gap in understanding by investigating whether the observed bias is an inherent flaw of the PERR framework or a consequence of specific operational choices within that framework.

Methodology
The authors conducted a series of simulation studies to replicate and extend previous findings. The study evaluated three distinct estimators:

$PERR_{Prev}$ : The estimator used in the previous literature, which includes only completers (those without mortality/dropout) in the numerator (post-treatment period) but includes all subjects (completers and non-completers) in the denominator (prior period).
$PERR_{Comp}$ : An alternative estimator proposed in this study, which restricts the analysis to completers only, utilizing data from completers in both the numerator and the denominator.
Relative Risk (RR): A standard estimator that does not utilize the prior event period to adjust for confounding.

The simulations were performed under four distinct scenarios regarding the determinants of mortality/dropout ( $M_2$ ):

Scenario 1: $M_2$ is influenced by treatment ( $X$ ), confounder ( $C$ ), and prior event ( $Y_1$ ). This replicates the specific scenario from the previous study.
Scenario 2: $M_2$ is influenced by confounder ( $C$ ) and prior event ( $Y_1$ ), but not treatment.
Scenario 3: $M_2$ is influenced by confounder ( $C$ ) and treatment ( $X$ ), but not prior event.
Scenario 4: $M_2$ is influenced by confounder ( $C$ ) only.

Across all scenarios, mortality/dropout rates were varied from 0% to 20%. Each scenario involved 10,000 replicates with a sample size of 100,000 persons per replicate. The true treatment effect was set at a Relative Risk (RR) of 2.

Key Results

Replication of Previous Bias: In Scenario 1, the study successfully replicated the under-estimation bias of $PERR_{Prev}$ as mortality/dropout rates increased. At a 20% rate, the mean estimate for $PERR_{Prev}$ was 1.83 (true RR=2).
Performance of $PERR_{Comp}$ : In Scenario 1, $PERR_{Comp}$ demonstrated significantly reduced bias compared to $PERR_{Prev}$ . At a 20% mortality rate, the mean estimate for $PERR_{Comp}$ was 2.05. The magnitude of bias for $PERR_{Comp}$ was approximately one-third that of $PERR_{Prev}$ .
Scenarios 3 and 4 (No Prior Event Influence): A critical finding emerged in scenarios where mortality/dropout was not directly influenced by the prior event ( $Y_1$ ). In these cases (Scenarios 3 and 4), $PERR_{Comp}$ provided accurate, unbiased estimates of the treatment effect regardless of the mortality/dropout rate. Conversely, $PERR_{Prev}$ continued to produce biased estimates in these scenarios.
Confounding vs. Censoring: The standard RR estimator showed substantial confounding bias when no mortality occurred. As mortality rates increased, the bias from differential mortality partially cancelled out the confounding bias in the RR estimates, a phenomenon not observed with the PERR estimators in the same manner.

Significance and Claims
The paper argues that the PERR method should be viewed as a methodological framework rather than a single fixed estimator. Its performance is contingent upon the specific operationalization chosen. The authors claim that the previously reported sensitivity of PERR to differential mortality is not a universal property of the method but is specific to the $PERR_{Prev}$ estimator.

The study concludes that $PERR_{Comp}$ , which utilizes data exclusively from completers, provides unbiased estimates of treatment effect unless the mortality or dropout is directly influenced by the prior event. When prior event does influence mortality, $PERR_{Comp}$ still offers a substantial reduction in bias compared to the traditional estimator. The authors maintain a modest scope, noting that while these findings clarify the performance of PERR for binary outcomes, further investigation is required to determine how these specifications apply to event rate outcomes.

The Detective's Trick (How PERR Works)

The Problem: The "Dropout" Mystery

The Big Takeaway

More like this