Coupled error spending functions for parallel bivariate sequential tests

Sequential procedures are developed to facilitate marginal monitoring of bivariate response vectors in clinical trials. The general approach is based on an extension of the error spending function methodology of Lan and DeMets (1983, Biometrika 70, 659-663) and is sufficiently flexible that one may elect to fix the experimental type I error rate (Cook, 1994, Controlled Clinical Trials 15(3), 187-200) or the marginal type I error rates. Sample size calculations are described to ensure power requirements are satisfied for marginal tests of significance. Reformulating the procedures in terms of repeated confidence intervals (Jennison and Turnbull, 1989, Journal of the Royal Statistical Society, Series B 51, 305-361) lends added flexibility to the monitoring process. The developments are discussed in the context of responses with a bivariate normal distribution. Data from an asthma intervention trial are used for illustrative purposes.