Sample size determination for fold-increase endpoints defined by paired interval-censored data

Medical studies often define binary end-points by comparing the ratio of a pair of measurements at baseline and end-of-study to a clinically meaningful cut-off. For example, vaccine trials may define a response as at least a four-fold increase in antibody titers from baseline to end-of-study. Accordingly, sample size is determined based on comparisons of proportions. Since the pair of measurements is quantitative, modeling the bivariate cumulative distribution function to estimate the proportion gives more precise results than using dichotomization of data. This is known as the distributional approach to the analysis of proportions. However, this can be complicated by interval-censoring. For example, due to the nature of some laboratory measurement methods, antibody titers are interval-censored. We derive a sample size formula based on the distributional approach for paired interval-censored data. We compare the sample size requirement in detecting an intervention effect using the distributional approach to a conventional approach of dichotomization. Some practical guidance on applying the sample size formula is given.