Time Parameterizations in Cluster Randomized Trial Planning

Models for cluster randomized trials conducted over multiple time periods should account for underlying temporal trends. However, in practice there is often limited knowledge or data available to inform the choice of time parameterization of these trends, or to anticipate the implications of this choice on trial planning. In this article, we establish a sufficient condition for when the choice of time parameterization does not affect the form of the variance of the treatment effect estimator, thereby simplifying the planning of these trials.