The effect of missing data on design efficiency in repeated cross-sectional multi-period two-arm parallel cluster randomized trials

The reduced efficiency of the cluster randomized trial design may be compensated by implementing a multi-period design. The trial then becomes longitudinal, with a risk of intermittently missing observations and dropout. This paper studies the effect of missing data on design efficiency in trials where the periods are the days of the week and clusters are followed for at least one week. The multilevel model with a decaying correlation structure is used to relate outcome to period and treatment condition. The variance of the treatment effect estimator is used to measure efficiency. When there is no data loss, efficiency increases with increasing number of subjects per day and number of weeks. Different weekly measurement schemes are used to evaluate the impact of planned missing data designs: the loss of efficiency due to measuring on fewer days is largest for few subjects per day and few weeks. Dropout is modeled by the Weibull survival function. The loss of efficiency due to dropout increases when more clusters drop out during the course of the trial, especially if the risk of dropout is largest at the beginning of the trial. The largest loss is observed for few subjects per day and a large number of weeks. An example of the effect of waiting room environments in reducing stress in dental care shows how different design options can be compared. An R Shiny app allows researchers to interactively explore various design options and to choose the best design for their trial.