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Cluster randomized designs are frequently employed in pragmatic clinical trials which test interventions in the full spectrum of everyday clinical settings in order to maximize applicability and generalizability. In this study, we propose to directly incorporate pragmatic features into power analysis for cluster randomized trials with count outcomes. The pragmatic features considered include arbitrary randomization ratio, overdispersion, random variability in cluster size, and unequal lengths of follow-up over which the count outcome is measured. The proposed method is developed based on generalized estimating equation (GEE) and it is advantageous in that the sample size formula retains a closed form, facilitating its implementation in pragmatic trials. We theoretically explore the impact of various pragmatic features on sample size requirements. An efficient Jackknife algorithm is presented to address the problem of underestimated variance by the GEE sandwich estimator when the number of clusters is small. We assess the performance of the proposed sample size method through extensive simulation and an application example to a real clinical trial is presented.

Prospective randomized clinical trials addressing biomarkers are time consuming and costly, but are necessary for regulatory agencies to approve new therapies with predictive biomarkers. For this reason, recently, there have been many discussions and proposals of various trial designs and comparisons of their efficiency in the literature. We compare statistical efficiencies between the marker-stratified design and the marker-based precision medicine design regarding testing/estimating 4 hypotheses/parameters of clinical interest, namely, treatment effects in each marker-positive and marker-negative cohorts, marker-by-treatment interaction, and the marker's clinical utility. As may be expected, the stratified design is more efficient than the precision medicine design. However, it is perhaps surprising to find out how low the relative efficiency can be for the precision medicine design. We quantify the relative efficiency as a function of design factors including the marker-positive prevalence rate, marker assay and classification sensitivity and specificity, and the treatment randomization ratio. It is interesting to examine the trends of the relative efficiency with these design parameters in testing different hypotheses. We advocate to use the stratified design over the precision medicine design in clinical trials with predictive biomarkers.