Non-ignorable loss to follow-up: correcting mortality estimates based on additional outcome ascertainment

Abstract

Loss to follow-up (LTFU) is a common problem in many epidemiological studies. In antiretroviral treatment (ART) programs for patients with human immunodeficiency virus (HIV), mortality estimates can be biased if the LTFU mechanism is non-ignorable, that is, mortality differs between lost and retained patients. In this setting, routine procedures for handling missing data may lead to biased estimates. To appropriately deal with non-ignorable LTFU, explicit modeling of the missing data mechanism is needed. This can be based on additional outcome ascertainment for a sample of patients LTFU, for example, through linkage to national registries or through survey-based methods. In this paper, we demonstrate how this additional information can be used to construct estimators based on inverse probability weights (IPW) or multiple imputation. We use simulations to contrast the performance of the proposed estimators with methods widely used in HIV cohort research for dealing with missing data. The practical implications of our approach are illustrated using South African ART data, which are partially linkable to South African national vital registration data. Our results demonstrate that while IPWs and proper imputation procedures can be easily constructed from additional outcome ascertainment to obtain valid overall estimates, neglecting non-ignorable LTFU can result in substantial bias. We believe the proposed estimators are readily applicable to a growing number of studies where LTFU is appreciable, but additional outcome data are available through linkage or surveys of patients LTFU.

Keywords: HIV; antiretroviral treatment; inverse probability weighting; linkage; loss to follow-up; missing not at random.

Figure 1

Directed Acyclic Graphs (DAGs): Pearls do-calculus and its application for our framework.

Figure 2

Simulation results for 7 different strategies: Non-informative censoring (NIC), complete case analysis (CC), multiple imputation before ascertainment (MI), multiple imputation after ascertainment (MI (asc.)), IPW estimates after ascertainment with constant weights (IPW (asc,cw)), logistic regression based weights (IPW (asc,lw), and Bayesian model averaging weights (IPW (asc,maw)). Levels of ascertainment relate to the percentage of missing outcome information that was ascertained.

Figure 3

Kaplan-Meier curves for different strategies: Non-informative censoring (NIC), complete case analysis (CC), multiple imputation before ascertainment (MI), multiple imputation after ascertainment (MI (asc.)), IPW estimates after ascertainment with constant weights (IPW (asc.,cw)), logistic regression based weights (IPW (asc.,lw))