The Design of Observational Longitudinal Studies

TL;DR

This paper provides formulas and methods for designing observational longitudinal studies with binary exposures and continuous responses, focusing on optimizing power and cost efficiency.

Contribution

It introduces a comprehensive framework for calculating power, sample size, and measurement frequency, including optimal design strategies under cost constraints.

Findings

Formulas for power, N, and r under various covariance structures.

Optimal design strategies balancing power and cost.

Implementation in freely available software.

Abstract

This paper considers the design of observational longitudinal studies with a continuous response and a binary time-invariant exposure, where, typically, the exposure is unbalanced, the mean response in the two groups differs at baseline and the measurement times might not be the same for all participants. We consider group differences that are constant and those that increase linearly with time. We study power, number of study participants (N) and number of repeated measures (r), and provide formulas for each quantity when the other two are fixed, for compound symmetry, damped exponential and random intercepts and slopes covariances. When both N and r can be chosen by the investigator, we study the optimal combination for maximizing power subject to a cost constraint and minimizing cost for fixed power. Intuitive parameterizations are used for all quantities. All calculations are implemented in freely available software.