Sample Size for a Binomial Proportion with Autocorrelation.

A flexible sample size computation is desired for a binomial outcome consisting of repeated binary measures with autocorrelation over time. This type of outcome is common in viral shedding studies, in which each individual's outcome is a proportion: the number of samples on which virus is detected out of number of samples assessed. Autocorrelation between proximal samples occurs in some conditions such as herpes infection, in which reactivation is episodic. We determine a sample size computation that accounts for: (1) participant-level differences in outcome frequency, (2) autocorrelation in time between samples, and (3) varying number of samples per participant. In addition, we develop a computation appropriate for crossover designs that accounts for the dependence of the investigational treatment effect on the pretreatment detection frequency. The computations are validated through comparison with real and simulated data, and sensitivity to misspecification of parameter values is examined graphically.