Reflection on modern methods: a note on variance estimation when using inverse probability weighting to handle attrition in cohort studies

TL;DR

This paper examines variance estimation methods in inverse probability weighting for cohort study attrition, highlighting that naive estimators underestimate variance while robust and linearized estimators perform better.

Contribution

It develops a linearization-based variance estimator that accounts for weight estimation, comparing it to naive and robust methods through simulations.

Findings

Naive variance estimator severely underestimates variance.

Robust and linearized estimators are approximately unbiased in various scenarios.

Researchers should avoid naive variance estimation and prefer robust or linearized methods.

Abstract

The inverse probability weighting (IPW) method is used to handle attrition in association analyses derived from cohort studies. It consists in weighting the respondents at a given follow-up by their inverse probability to participate. Weights are estimated first and then used in a weighted association model. When the IPW method is used, instead of using a so-called na{\"i}ve variance estimator, the literature recommends using a robust variance estimator. However, the latter may overestimate the variance because the weights are considered known rather than estimated. In this note, we develop, by a linearization technique, an estimator accounting for the weight estimation phase and explain how it differs from na{\"i}ve and robust variance estimators. We compare the three variance estimators through simulations under several MAR and MNAR scenarios. We found that both the robust and linearized variance estimators were approximately unbiased, even in MNAR scenarios. The naive variance estimator severely underestimated the variance. We encourage researchers to be careful with variance estimation when using the IPW method, avoiding na{\"i}ve estimator and opting for a robust or linearized estimator. R and SAS codes are provided to implement them in their own studies.