Analysis of recurrent events: Nonparametric methods for random-interval count data

Many clinical trials require comparison among treatment groups of the rates over time of a particular recurrent event. The event typically reflects disease morbidity rather than mortality. Some examples are episodes of hypoglycemia in diabetics, angina pectoris in patients with heart disease, and seizures in epileptics. Trial protocol often requires that each patient report only the number of events occurring between clinic visits, so the exact times of the successive events are not available. In practice, patients are early, late, or miss scheduled visits, and follow-up may be censored. Thus each patient’s data consist of a sequence of consecutive random intervals and corresponding event counts, some of which may be missing. In this fashion the National Cooperative Gallstone Study (NCGS) recorded the incidence of nausea of patients with gallstone disease treated with chenodiol or placebo. We describe an estimator of the continuous time-dependent rate function for such data. Wei and Lachin (1984) presented a nonparametric method for the analysis of repeated measures with missing observations. We describe estimators of group differences and additional tests of location-shift-type hypotheses based on the Wei-Lachin vector of Wilcoxon-like rank statistics. These methods are applied to compare the recurrence rates of two treatment groups over time, using random-interval count data, by representing each patient’s empirical rate function as a vector corresponding to K fixed time intervals. Since this approach allows partially missing values, it uses the available data for patients lost to follow-up. We analyze the incidence of nausea over the first year of treatment of NCGS patients with gallstone disease. This analysis indicates that the recurrence rate of nausea for the placebo group was higher than the chenodiol-treated group for the first six months, but equal thereafter.