Designing Longitudinal Studies with Repeated Measures: The Case of Salivary Cortisol in the Multi-Ethnic Study of Atherosclerosis

Defining the times at which samples are collected is an important aspect of longitudinal study design. Unfortunately, sampling times are often determined based on convenience and their optimality is seldom established statistically. Such convenient sampling strategy is likely to undermine the statistical efficiency of the study, especially in those cases where the response profile over time is nonlinear. Using the example of salivary cortisol, which exhibits a the nonlinear shape across the days, we discuss an approach for identifying efficient sampling protocols for studies where longitudinal measurements are collected. We model the response curves using conditionally linear mixed models, which allow some parameters to be nonlinear and accommodate flexible shapes of the longitudinal process. Our approach incorporates multi level random effects to account for between- subject and between-day variability commonly seen in epidemiological studies of the stress response. Furthermore, we propose a framework to include overall study costs when choosing the best sampling protocol.