# New, Shorter Small‐Sample Intervals for Vaccine Efficacy

## TL;DR

This paper introduces a Bayesian method to improve vaccine efficacy estimation for small and medium sample sizes, outperforming existing methods in accuracy.

## Contribution

A novel Bayesian approach that improves vaccine efficacy estimation by incorporating informative statistics from surveillance times and recruitment processes.

## Key findings

- The proposed method improves parameter interval estimation for small to medium sample sizes.
- The model outperforms maximum likelihood in scenarios with limited events.
- MCMC simulations are efficient due to the method's parameterization.

## Abstract

In this work we illustrate a method to improve estimation of Vaccine Efficacy (VE), a vastly employed measure of effect in vaccine clinical research, with small and medium sample sizes. We introduce a comprehensive Bayesian approach that improves upon existing methodologies, explicitly considering patient recruitment processes to inform parameter estimation. In particular—in contrast to most methods currently used—in our proposed methodology the total number of cases as well as the censored surveillance times are seen as informative statistics, with underlying distributions which are used to derive the full likelihood. It turns out that our model depends on first and second moments of the surveillance times regardless of the recruitment process and, for finite sample sizes, it improves on the maximum likelihood method, which depends only on the first moment. The methodology is validated through extensive numerical simulations, demonstrating substantial improvements in parameter interval estimation across diverse scenarios and under multiple recruitment plans, when the number of events—and roughly the sample sizes—are small to medium. For large sample sizes, our method is equivalent to maximum likelihood. Markov Chain Monte Carlo (MCMC) simulations are needed and can be conducted very efficiently, due to an appropriate parameterization.