Variance Estimation of an Efficient Estimator of the Mean with Current Status Data

In biostatistical applications, interest often focuses on the estimation of the distribution of time T between two consecutive events. In some cases, the initial event time is observed and the subsequent event is only known to happen before or after an observed monitoring time Y. This data conforms to the well understood singly-censored current status data, also known as interval censored data, case 1. Currently, there are some statistical software packages such as survival, interval, and Icens that are designed to analyze this singly censored current status data. However, they either fail to directly provide an estimated variance for the estimator of the mean or reach an extremely underestimated value. In this paper, we review Huang and Wellner and propose a method based on their variance expression of the estimator of the mean. The efficiency of our method is compared with those of bootstrap variance estimate, an open source statistical software R's survfit's variance estimate, and sampling variability. Our simulation study shows that our proposed variance estimator is better than the other methods in terms of accuracy and efficiency.