A Minimum-Cost Strategy for Cluster Recruitment Wenyaw Chan Program in Biometry School of Public Health University of Texas  Houston U.S.A. Nan Fu Peng Institute of Statistics National Chiao Tung University Hsinchu Taiwan Summary It is becoming increasingly common for the design of a clinical study to involve cluster samples. Very few researches investigated the appropriate number of clusters. None of them treat cluster size and the number of clusters as random variables. In reality, the recruitment of clusters can not be reached at one time and the cluster sizes are usually random. The longer the recruitment takes the more expensive the total study costs will be. This paper provides a strategy for sequential recruitment of clusters, which can minimize the total study cost. By treating the number of additional observational subjects required at each time point as a Markov Chain, we derive an iterative procedure for optimal strategy and study the property of this strategy, especially the duration of the cluster recruitment. This strategy is also extended to search for an optimal number of centers in a multi-center clinical trial. Key words: Cluster sample; Markov chain; Principle of optimality; Sequential method. 1. Introduction The number of clusters has been an important planning issue in a clinical study involving cluster samples, especially when study budget is limited. Some re- searches have proposed the calculation of the sample size for the observational subjects in cluster randomization trials [see, for example, Donner 1992) and Donner and Klar 1994)]. Others have discussed the appropriate number of clus- ters based on power analysis [see, for example Hsieh 1988)]. Very few investi- Biometrical Journal 42 2000) 7, 877±886