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Component over Composite: Mitigating Type I Error Inflation when Imputing "Days Alive and at Home"

This paper demonstrates through simulation that imputing the individual components of the "Days Alive and at Home" composite outcome, rather than the composite itself, effectively mitigates type I error inflation and preserves statistical power in clinical trials.

Original authors: Mia S. Tackney, Sarah Dawson, Letao Yuan, Dominique-Laurent Couturier, Sofia S. Villar

Published 2026-05-20

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CC BY 4.0

Original authors: Mia S. Tackney, Sarah Dawson, Letao Yuan, Dominique-Laurent Couturier, Sofia S. Villar

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 trying to measure how many days a patient spends "alive and at home" after a major surgery. Let's call this score DAH (Days Alive and at Home). It's a bit like a video game score that counts up the days you are safe and comfortable, but it gets reset to zero if you die or if you have to go back to the hospital.

To calculate this score, you need three pieces of information:

How long the patient stayed in the hospital immediately after surgery.
How long they stayed in the hospital if they had to go back later (readmissions).
Whether they are still alive.

The Problem: Missing Pieces of the Puzzle

In real life, getting all this data is tricky. The hospital usually has perfect records for the first stay and for whether someone died. But tracking where a patient is after they leave the hospital (like checking a diary they fill out themselves) is harder. Sometimes patients forget to write in the diary, or they stop responding.

This creates a "missing piece" problem. If a patient is missing even one day of their diary, the old way of doing things was to throw away their entire score. It's like saying, "Because you forgot to write down what you ate for lunch on Tuesday, we can't count your entire week's diet." This wastes a lot of useful information.

Another way to fix this is to use a computer program to "guess" (impute) the missing days. However, the paper warns that if you try to guess the total score directly, the computer might get confused.

The Experiment: Testing Different Guessing Strategies

The authors ran a massive computer simulation (like a virtual trial) based on a real heart surgery study called NOTACS. They created 10,000 fake scenarios with different amounts of missing data to see which method worked best.

They tested two main approaches:

The "All-or-Nothing" Guess (Composite Level): The computer looks at the final score. If a piece is missing, it guesses the whole score based on the patient's age, sex, etc.
The "Piece-by-Piece" Guess (Component Level): The computer guesses the missing parts separately. It uses the known hospital stay length to help guess the missing diary days, then adds them up to get the final score.

The Big Discovery: A Warning About "Predictive Mean Matching"

The paper found a specific danger with the first method (guessing the whole score). When the computer used a popular technique called Predictive Mean Matching (PMM) to guess the missing scores, it started making wild errors.

The Analogy: Imagine a teacher grading a test. If a student misses one question, the teacher tries to guess the entire test score based on the student's age. If the teacher guesses that a student who missed a question actually got a perfect score (or a zero), just because of how the math works, the class average becomes fake.

In the simulation, this "All-or-Nothing" guessing method caused the Type I Error to skyrocket.

What is Type I Error? It's a "false alarm." It's when the study concludes that a new treatment works, when in reality, it does nothing.
The Result: When 25% of the data was missing, this bad method made false alarms happen 32% of the time (instead of the safe 5% limit). It was like a smoke detector going off every time you toasted bread, making you think there was a fire when there wasn't.

The Solution: Build the Score Brick by Brick

The paper recommends the second method: Guessing the pieces separately.

The Analogy: Instead of guessing the final height of a building, you measure the foundation (which you know perfectly), then guess the height of the missing floors one by one, and finally add them up. Because you are using the solid foundation (the known hospital stay) to help guess the missing floors, the final result is much more accurate.

This "Piece-by-Piece" method kept the false alarm rate low (around 5%) and gave the study the best chance to find real differences between treatments.

Summary of Findings

Don't throw away data: If a patient misses a few diary entries, don't delete their whole record. Use the data you do have.
Don't guess the total score directly: Trying to guess the final "Days Alive and at Home" number all at once using certain computer methods leads to false conclusions.
Do guess the parts: It is safer and more accurate to guess the missing hospital days separately, using the known hospital stay as a guide, and then calculate the final score.

The authors conclude that for this specific type of medical outcome, the "Piece-by-Piece" approach is the only safe way to handle missing data without tricking the study into thinking a treatment works when it doesn't.

Technical Summary: Component vs. Composite Imputation for "Days Alive and at Home"

Problem Statement
"Days Alive and at Home" (DAH) is a composite outcome increasingly used in post-operative randomized controlled trials (RCTs), such as the NOTACS trial. DAH combines three distinct components: (i) initial length of hospital stay, (ii) total length of readmissions or post-discharge care, and (iii) mortality. A critical challenge in analyzing DAH is handling missing data. Unlike simple outcomes, DAH components often have different missingness rates and mechanisms; for instance, initial hospital stay and mortality data are typically complete (collected at trial sites), while post-discharge location data (often from participant diaries) are prone to missingness.

Current standard practice often defines the composite DAH outcome as missing if any component is missing, followed by Complete Case Analysis (CCA) or Multiple Imputation (MI) of the composite value. However, DAH possesses complex distributional characteristics—specifically zero-inflation, left-skewness, and bimodality—which may render standard parametric imputation models misspecified. Furthermore, the interaction between different missing data mechanisms across components and the use of non-parametric tests (like the Mann-Whitney-Wilcoxon test) for analysis creates a gap in understanding how to properly handle missingness without inflating Type I error rates.

Methodology
The authors conducted a simulation study motivated by the design and interim data of the NOTACS trial (N=1280). The study evaluated several strategies for handling missing data in DAH90 (Days Alive and at Home over 90 days) when the primary analysis is a Mann-Whitney-Wilcoxon test.

Data Generation: DAH90 outcomes were generated using a model developed by Yuan et al. (2026), which decomposes the outcome into:
- Initial hospital stay ( $v_i$ ): Modeled via a right-censored zero-inflated Poisson inverse Gaussian (ZICPIG) distribution.
- Readmission days ( $y_{Ri}$ ): Modeled via a zero-adjusted beta binomial (ZABB) distribution.
- Mortality ( $d_i$ ): Modeled via a Bernoulli distribution.
  The composite outcome is calculated as $y_i = [90 - (v_i + y_{Ri})]I(d_i = 0)$ .
Missing Data Mechanisms: Five scenarios were simulated:
- Missing Completely at Random (MCAR).
- Missing at Random (MAR) dependent on Age, Sex, or both.
- Missing Not at Random (MNAR) dependent on Age.
  Missingness was applied to the post-discharge period, creating "Partial" (intermittent) and "Missing" (complete loss of post-discharge data) states.
Comparison Methods:
- Complete Case Analysis (CCA): Restricting analysis to participants with full data. A variant ("derived") calculated DAH as zero for deceased participants with missing location data.
- MI-Composite: Imputing the final DAH90 value directly if any component is missing. This included parametric regression ("norm") and Predictive Mean Matching (PMM).
- MI-Component: Imputing the missing readmission component ( $y_{Ri}$ ) conditional on covariates and the fully observed initial stay ( $v_i$ ), then reconstructing the DAH90 value ("passive imputation"). This included parametric ("norm"), PMM, and a binomial approach that utilized partially observed data.
Analysis: For each of 10,000 simulation runs, the Mann-Whitney-Wilcoxon test was performed on $M=35$ imputed datasets. Since Rubin's Rules are not valid for rank-based statistics, the median of the $M$ p-values was reported. Performance was measured by Type I error rate (under the Null), Power (under the Alternative), and bias in the probabilistic index ( $\theta$ ) and median difference.

Key Results

Type I Error Inflation: The study found that imputing the composite outcome directly using Predictive Mean Matching (MI-Composite PMM) leads to significant Type I error inflation. Under the Null scenario with 25% missing data, the Type I error rate for MI-Composite (PMM) rose to 32.2%, far exceeding the nominal 5%. This inflation is attributed to the misspecification of the imputation model for the complex, zero-inflated distribution of the composite outcome, which can result in implausible imputations (e.g., high values imputed for the "clump-at-zero").
Component-Level Imputation: Imputing at the component level (MI-Component) generally maintained Type I error rates close to the nominal 5% and preserved statistical power. This approach effectively utilizes the fully observed initial hospital stay as a predictor for the missing readmission data.
Parametric vs. PMM: While MI-Component (PMM) performed well regarding Type I error control, MI-Component (parametric "norm") showed better performance in terms of bias reduction for the estimated effect sizes ( $\theta$ and median differences), despite the paper noting that "norm" can sometimes lead to greater biases in testing scenarios compared to PMM in specific contexts.
Partial Data: The "MI-Component (binomial)" approach, which attempts to retain partially observed post-discharge data, failed to handle the skewed distribution of readmissions effectively, leading to Type I error inflation similar to the composite PMM approach.
Complete Case Analysis: CCA maintained Type I error control under MCAR but resulted in reduced power. Under MAR, CCA led to bias and power loss.

Significance and Claims
The paper argues that naive approaches to missing data in DAH trials—specifically defining the composite as missing if any part is missing and applying standard MI (particularly PMM) to the composite—are statistically unsound due to the complex distribution of DAH. The authors claim that:

Component-level imputation is superior: It mitigates Type I error inflation by respecting the distinct distributions of the components and utilizing fully observed data (initial stay) as predictors.
PMM on composites is risky: The use of Predictive Mean Matching on the composite level is cautioned against, as it can lead to severe Type I error inflation, potentially invalidating trial conclusions.
Current reporting is insufficient: The paper highlights a gap in the literature where trials rarely report missingness by component or justify their handling methods, despite the known heterogeneity in missing data mechanisms for composite outcomes.

The authors conclude that for trials using DAH outcomes analyzed via non-parametric tests, imputing at the component level is the recommended strategy. They note that future work is needed to develop imputation approaches compatible with more granular definitions of DAH (e.g., accounting for levels of care) and to establish sensitivity analyses for the Missing at Random assumption.