# Handling missing data when estimating causal effects with targeted maximum likelihood estimation

## TL;DR

This paper evaluates methods for handling missing data when using targeted maximum likelihood estimation for causal inference, finding that parametric multiple imputation with interactions performs best in most scenarios.

## Contribution

The study provides empirical guidance on handling missing data in TMLE-based causal inference, comparing eight methods across various missingness mechanisms.

## Key findings

- Parametric multiple imputation with interactions showed the best performance in bias and variance reduction across most settings.
- Complete-case analysis and extended TMLE had small biases when outcome did not influence missingness in other variables.
- Parametric MI without interactions had large bias when exposure/outcome models included interactions.

## Abstract

Targeted maximum likelihood estimation (TMLE) is increasingly used for doubly robust causal inference, but how missing data should be handled when using TMLE with data-adaptive approaches is unclear. Based on data (1992-1998) from the Victorian Adolescent Health Cohort Study, we conducted a simulation study to evaluate 8 missing-data methods in this context: complete-case analysis, extended TMLE incorporating an outcome-missingness model, the missing covariate missing indicator method, and 5 multiple imputation (MI) approaches using parametric or machine-learning models. We considered 6 scenarios that varied in terms of exposure/outcome generation models (presence of confounder-confounder interactions) and missingness mechanisms (whether outcome influenced missingness in other variables and presence of interaction/nonlinear terms in missingness models). Complete-case analysis and extended TMLE had small biases when outcome did not influence missingness in other variables. Parametric MI without interactions had large bias when exposure/outcome generation models included interactions. Parametric MI including interactions performed best in bias and variance reduction across all settings, except when missingness models included a nonlinear term. When choosing a method for handling missing data in the context of TMLE, researchers must consider the missingness mechanism and, for MI, compatibility with the analysis method. In many settings, a parametric MI approach that incorporates interactions and nonlinearities is expected to perform well.