Optimal sampling strategies for two-stage studies

The optimal allocation of available resources is the concern of every investigator in choosing a study design. The recent development of statistical methods for the analysis of two-stage data makes these study designs attractive for their economy and efficiency. However, little work has been done on deriving two-stage designs that are optimal under the kinds of constraints encountered in practice. The methods presented in this paper provide a means of deriving designs that will maximize precision for a fixed total budget or minimize the study cost necessary to achieve a desired precision. These optimal designs depend on the relative information content and the relative cost of gathering the first- and second-stage data. In place of the usual sample size calculations, the investigator can use pilot data to estimate the study size and second-stage sampling fractions. The gains in efficiency that can result from such carefully designed studies are illustrated here by deriving and implementing optimal designs using data from the Coronary Artery Surgery Study (Circulation 1980;62:254-61).