In multicenter studies, because patients from the same hospitals are likely of similar characteristics and tested by the same laboratory, the times of response to a treatment within hospitals tend to be positively correlated. A life table analysis without taking this intraclass correlation into account can be misleading. To account for the intraclass correlation between the times of response within hospitals, we employ the Dirichlet-multinomial distribution. By use of the multivariate delta method, we have derived an asymptotic generalized variance of the estimated survival distribution, which includes Greenwood's variance formula as a special case when the intraclass correlation equals 0. Furthermore, we have applied the Multivariate Central Limit Theorem together with the variance derived here to develop two closed-form interval estimators of the survival distribution. One interval estimator is obtained by simply using an asymptotically unbiased point estimator of the underlying survival distribution plus and minus an appropriate percentile of the standard normal distribution times the square root of the generalized variance, and the other is derived from a quadratic equation proposed here. On the basis of Monte Carlo simulation, we have evaluated the finite-sample performance of the interval estimator using Greenwood's formula and the two interval estimators developed here. We note that the coverage probability of the interval estimator using Greenwood's formula can be seriously less than the desired confidence level when both the intraclass correlation and the number of patients per hospital are large. We further note that the estimator with direct use of the square root of the generalized variance derived here, which improves the performance of the interval estimator using Greenwood's formula, may still produce an interval estimate with the coverage probability less than the desired confidence level. On the other hand, except for estimation of a small right tail of the survival distribution, we have demonstrated that the estimator derived from the proposed quadratic equation can perform reasonably well in a variety of situations considered in this paper.