Doubly robust estimation and causal inference in longitudinal studies with dropout and truncation by death

Abstract

Motivated by aging research, we propose an estimator of the effect of a time-varying exposure on an outcome in longitudinal studies with dropout and truncation by death. We use an inverse-probability weighted (IPW) estimator to derive a doubly robust augmented inverse-probability weighted (AIPW) estimator. IPW estimation involves weights for the exposure mechanism, dropout, and mortality; AIPW estimation additionally involves estimating data-generating models via regression. We demonstrate that the estimators identify a causal contrast that is a function of principal strata effects under a set of assumptions. Simulations show that AIPW estimation is unbiased when weights or outcome regressions are correct, and that AIPW estimation is more efficient than IPW estimation when all models are correct. We apply the method to a study of vitamin D and gait speed among older adults.

Keywords: Causal inference; Longitudinal data analysis; Missing data; Observational studies.

Figure 1.

Directed acyclic graph of the hypothesized pathway linking to . comprises confounders, is vital status, and is observation status, where the absence of an arrow from to encodes missing at random. The bold line is the causal pathway through which can affect . Dashed lines represent relations between and subsequent variables that are not of scientific interest. Under this DAG, a completers-only analysis would need to condition on to remove selection bias.

Figure 2.

Directed acyclic graph expanded to two follow-up visits. The most general causal diagram is shown under the assumption of missing at random, where a variable may affect any future variable with the exception that are assumed not to affect as indicated by the absence of arrows from to , . Bold lines show that can affect through both a direct pathway and an indirect pathway mediated by . Under this DAG, no conditioning set is sufficient to remove selection bias in a conventional completers-only analysis.