Sequential monitoring for comparison of changes in a response variable in clinical studies

The spending function approach proposed by Lan and DeMets (1983, Biometrika 70, 659-663) for sequential monitoring of clinical trials is applied to situations where comparison of changes in a continuous response variable between two groups is the primary concern. Death, loss to follow-up, and missed visits could cause follow-up measurements to be right-censored or missing for some participants. Furthermore, the probability of being censored may be dependent on the parameter value of the response variable (informative censoring). We propose to compare treatment effects by comparing areas under the expected response change curves between the two groups. When the response curves are linear as a function of time in both groups, this comparison is equivalent to comparing the rates of change in the response variable. Covariances of the sequential test statistics are derived. Conditions for having independent increments are presented. For studies designed to evaluate long-term treatment effects, spending functions obtained by shifting the usual spending functions (Kim and DeMets, 1987, Biometrika 74, 149-154) to the right and then rescaling to the remaining interval are also proposed. Such a shifted spending function is applied to the monitoring plan for the Lung Health Study (Anthonisen, 1989, American Review of Respiratory Diseases 140, 871-872).