# Analyzing Left-Truncated Samples with the Cox Model in the Presence of Missing Covariates

## TL;DR

This paper examines how to handle missing data in time-to-event studies with delayed enrollment, using methods like multiple imputation and AIPW.

## Contribution

The study evaluates the performance of MI and AIPW in left-truncated samples with missing covariates through simulations.

## Key findings

- MI and AIPW may be approximately unbiased when truncation is very low.
- Biased estimation of the covariate distribution can cause MI to perform poorly.
- AIPW may rely heavily on correct estimation of the probability of non-missing covariates.

## Abstract

Delayed enrollment of subjects into a time-to-event study may result in a sample with biased outcome and covariate distributions. Additionally, missing covariate data may arise in these studies when information is difficult to collect due to patient burden or high testing costs. Some common missing data strategies, such as multiple imputation (MI) and augmented inverse probability weighting (AIPW), involve modeling the distribution of the missing covariate, which may be inaccurate with a left-truncated sample. Through simulation studies, we explore the performance of these methods in estimating Cox regression parameters under a variety of truncation and missing data scenarios. We find that MI and AIPW may be approximately unbiased when truncation is very low. Otherwise, biased estimation of the covariate distribution can cause MI to perform poorly. Similarly, AIPW may rely more heavily on correct estimation of the probability of having non-missing covariates in some settings. We apply these approaches to a Parkinson’s disease dementia biomarker study. In analyzing left-truncated data with missing covariates, careful consideration of the data characteristics and method assumptions is needed to obtain valid results.

The online version contains supplementary material available at 10.1007/s12561-024-09442-9.