Comparing survival functions with interval-censored data in the presence of an intermediate clinical event

Abstract

The primary endpoint is considered a time metric such as the time taken to reach a well-defined endpoint in the presence of an intermediate clinical event (IE). A subject may experience an IE including an intervention during the period of follow-up. When an IE occurs, it may change the survival distribution. When deriving the statistics of Nam and Zelen (2001), the data was divided into two parts according to an IE; one part was right-censored data that does not reach the time of experiencing an IE and the other part was left-truncated and right-censored data, which is having an IE and truncation at that time. Considering the primary endpoint was interval-censored, we extended the approach of Finkelstein (1986) as accommodating left-truncated data. After that, for convenience, we applied multiple imputation techniques to left truncated and interval-censored data. Firstly, we proposed a uniform method to impute data of uniform weight in a characterized set.

The second method applies the non-parametric maximum likelihood estimator (NPMLE) from the original data as weight. We applied two forms of variance, which are formed by adding and subtracting within- and between variance for all proposed models. Both variances worked efficiently, but the first one was slightly over- while the second one was marginally underestimated. Through simulation, the stratified log-rank test is unsatisfactory when the proportion of an IE is different between two groups. When the survival distribution is changed after experiencing an IE in addition to the difference proportion of an IE for two groups, the log-rank test is not appropriate. The proposed methods satisfied a nominal level of 0.05 and had superior power to compare the proposed methods with the log-rank and stratified log-rank tests for all scenarios.