Power, sample size and smallest detectable effect determination for multivariate studies.

This paper discusses some general methods for determining approximate power, sample size, and smallest detectable effect for studies of multiple risk factors. These methods are based on standard large-sample formulae for determining the power of chi-square tests, and emphasis is given to determinations for Pearson chi 2 tests in multiway contingency tables. The methods are illustrated in application to the design of a clinical trial of the preventive effect of alpha-tocopherol, ascorbic acid and beta-carotene on colon polyp recurrence, and a case-control study of the joint effect of smoking and asbestos exposure on lung cancer incidence.