Methods for the estimation of direct and indirect vaccination effects by combining data from individual- and cluster-randomized trials

Abstract

Both individually and cluster randomized study designs have been used for vaccine trials to assess the effects of vaccine on reducing the risk of disease or infection. The choice between individually and cluster randomized designs is often driven by the target estimand of interest (eg, direct versus total), statistical power, and, importantly, logistic feasibility. To combat emerging infectious disease threats, especially when the number of events from one single trial may not be adequate to obtain vaccine effect estimates with a desired level of precision, it may be necessary to combine information across multiple trials. In this article, we propose a model formulation to estimate the direct, indirect, total, and overall vaccine effects combining data from trials with two types of study designs: individual-randomization and cluster-randomization, based on a Cox proportional hazards model, where the hazard of infection depends on both vaccine status of the individual as well as the vaccine status of the other individuals in the same cluster. We illustrate the use of the proposed model and assess the potential efficiency gain from combining data from multiple trials, compared to using data from each individual trial alone, through two simulation studies, one of which is designed based on a cholera vaccine trial previously carried out in Matlab, Bangladesh.

Keywords: multiple trials; randomized studies; vaccine effects.

Figure 1

An illustration of direct, indirect, total and overall vaccine effect corresponding to coverage $p$. The total effect (Total₁) corresponding to 100% coverage is also shown. Each oval represents a cluster. The dashed rectangle on the left represents data from individual-randomized trials (IRTs) where study participants are randomized to vaccine with probability $p$. The dashed rectangle on the right represents data from cluster-randomized trials (CRTs) where the randomization unit is cluster.

Figure 2

Boxplots of the proportion of observed events among study participants within each cluster with varying vaccine coverage rates. A: 50% vaccination coverage from IRT (Trial 1); 0% (control) and 100% (treated) coverage from CRT (Trial 2) in Setting A. B: 25% and 50% vaccination coverage from IRTs (Trial 1 and 2); 0% (control) and 100% (treated) coverage from CRT (Trial 3) in Setting B.