Sample sizes for estimating the sensitivity of a monitoring system that generates repeated binary outcomes with autocorrelation

Sample size formulas are provided to determine how many events and how many patient care units are needed to estimate the sensitivity of a monitoring system. The monitoring systems we consider generate time series binary data that are autocorrelated and clustered by patient care units. Our application of interest is an automated hand hygiene monitoring system that assesses whether healthcare workers perform hand hygiene when they should. We apply an autoregressive order 1 mixed effects logistic regression model to determine sample sizes that allow the sensitivity of the monitoring system to be estimated at a specified confidence level and margin of error. This model overcomes a major limitation of simpler approaches that fail to provide confidence intervals with the specified levels of confidence when the sensitivity of the monitoring system is above 90%.