Estimation of the mitigated fraction from ordinal data in the evaluation of vaccine efficacy

Abstract

Vaccine efficacy can be established through the estimation of several numerical measures. A common measure of efficacy for vaccines, especially those designed to prevent a given disease, is the prevented fraction. Unfortunately, the prevented fraction can be used only when the outcome is dichotomous. It is worth noting that some useful vaccines reduce the severity of the targeted disease rather than entirely prevent its occurrence. The concept of the mitigated fraction was introduced in veterinary medicine to quantify the reduction in the severity of disease occurring in vaccinated animals as compared to non-vaccinated animals. The USDA’s Center for Veterinary Biologics (CVB) recommends a form of the mitigated fraction proposed by Siev (2005) which can be easily calculated when the disease severity can be graded by some continuous measure or by some discrete assessment resulting in unambiguous ranks. Current CVB guidance suggests that the mitigated fraction be estimated non-parametrically via the use of the Wilcoxon rank sum statistics. A survey of recent literature indicates a growing interest in measures of efficacy when the outcome variable is ordinal, especially when observations are clustered or measured longitudinally. Here, a parametric approach assuming a generalized linear mixed model (GLMM) with latent variable is developed for data collected in a completely randomized design (CRD) or a randomized complete block design (RCBD) and is then evaluated through simulation. Results show this parametric approach works well for both the CRD and RCBD. The GLMM approach can be extended to studies where more than two treatments are compared whereas the method of Siev (2005) can handle only two treatment groups (vaccinated and non-vaccinated). Furthermore, a Bayesian statistical approach has been briefly explored to estimate the mitigated fraction from an ordinal response observed in a completely randomized design. Extension of this Bayesian statistical approach for vaccine trials will also be discussed as future work.