Modification of the Greenwood Formula for Correlated Response Times

Life-table methodology for interval-censored survival times is used to estimate marginal survival probabilities from data consisting of independent cohorts of correlated responses. We restrict our attention to situations where response times within cohorts are exchangeable and the marginal survival distributions are the same for all individuals within any cohort. A modification of the Greenwood formula is derived for estimating variances and covariances of the estimates of the marginal survival probabilities. Simulation results show that this formula provides accurate adjustments for within-cohort correlations in finite samples. Comparisons with a nonparametric maximum likelihood estimator indicate negligible loss in efficiency from using simple life-table estimators of marginal survival probabilities that ignore the within-cohort correlations. Data from an angioplasty study where more than one procedure is performed on some patients are used to illustrate this methodology.