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One of the most common questions statisticians encounter during interaction with clinical investigators is “How many subjects do I need for this study?” Clinicians are often surprised to find out that the required sample size depends on a number of factors. Obtaining such information for sample size calculation is not trivial, and often involves preliminary studies, literature review, and, more than occasionally, educated guess. The validity of clinical research is judged not by the results but by how it is designed and conducted. Accurate sample size calculation ensures that a study has adequate power to detect clinically meaningful effects and avoids the waste in resources and the risk of exposing excessive patients to experimental treatments caused by an overpowered study.

In this book we focus on sample size determination for studies with correlated outcomes, which are widely implemented in medical, epidemiological, and behavioral studies. Correlated outcomes are usually categorized into two types: clustered and longitudinal. The former arises from trials where randomization is performed at the level of some aggregates (e.g., clinics) of research subjects (e.g., patients). The latter arises when the outcome is measured at multiple time points during follow-up from each subject. A key difference between these two types is that for a clustered design, subjects within a cluster are considered exchangeable, while for a longitudinal design, the multiple measurements from the each subject are distinguished by their unique time stamps.

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