Inverse probability weighted estimators of vaccine effects accommodating partial interference and censoring

Abstract

Estimating population-level effects of a vaccine is challenging because there may be interference, that is, the outcome of one individual may depend on the vaccination status of another individual. Partial interference occurs when individuals can be partitioned into groups such that interference occurs only within groups. In the absence of interference, inverse probability weighted (IPW) estimators are commonly used to draw inference about causal effects of an exposure or treatment. Tchetgen Tchetgen and VanderWeele proposed a modified IPW estimator for causal effects in the presence of partial interference. Motivated by a cholera vaccine study in Bangladesh, this paper considers an extension of the Tchetgen Tchetgen and VanderWeele IPW estimator to the setting where the outcome is subject to right censoring using inverse probability of censoring weights (IPCW). Censoring weights are estimated using proportional hazards frailty models. The large sample properties of the IPCW estimators are derived, and simulation studies are presented demonstrating the estimators' performance in finite samples. The methods are then used to analyze data from the cholera vaccine study.

Keywords: causal inference; interference; right censoring; survival.

Figure 1.

Absolute bias of the IPCW estimator (left) and corresponding Wald 95% confidence interval coverage (right) for different numbers of groups for α = 0.5. The dotted line in the right plot corresponds to 95% coverage. This figure appears in color in the electronic version of this article.

Figure 2.

Estimated cumulative probability of cholera over time when vaccinated or unvaccinated for α = 0.3 (left), α = 0.45 (center) and α = 0.6 (right). This figure appears in color in the electronic version of this article.

Figure 3.

Direct, indirect, total and overall effect estimates (×1000) for different allocation strategies at time t = 1 year. Indirect, total, and overall effects are with respect to α₂ = 0.4. The shaded regions denote pointwise 95% confidence intervals of the estimates.