The use of covariate information in the sequential analysis of dichotomous response experiments

A method is presented for the sequential analysis of experiments involving two treatments to which response is dichotomous. Composite hypotheses about the difference in success probabilities are tested, and covariate information is utilized in the analysis. The method is based upon a generalization of Bartlett’s (1946) procedure for using the maximum likelihood estimate of a nuisance parameter in a Sequential Probability Ratio Test (SPRT). Treatment assignment rules studied include pure randomization, randomized blocks, and an adaptive rule which tends to assign the superior treatment to the majority of subjects. It is shown that the use of covariate information can result in important reductions in the expected sample size for specified error probabilities, and that the use of covariate information is essential for the elimination of bias when adaptive assignment rules are employed. Designs of the type presented are easily generated, as the termination criterion is the same as for a Wald SPRT of simple hypotheses.