A variety of statistical methods for interval-censored data have been actively researched and developed in various disease areas since 1970s, when research on the new infectious disease HIV/AIDS attracted attention. In oncology, the data are obtained as partially interval-censored, such as progression free survival time, where the application of the usual survival data analysis method is often performed after imputing right-point of the censoring interval. However, other single point imputation methods such as left-point or midpoint also could be candidates, and a lot of research has been done on the statistical properties of single/multiple imputations, but it was limited to only simulation studies. In our study, we examine the characteristics of deterministic (left-, mid, and right-point) imputations from a theoretical aspect, and show that midpoint imputation is the most preferable if the true distribution is the exponential distribution. In our simulation, we compared the performance of these three deterministic single-point imputation methods and Finkelstein’s proportional hazards model without imputation in the setting of the selection design, so called a pick-the-winner design, in which the most promising treatment is identified based on the point estimate. The correct selection probability and performance measures of a regression coefficient were used for evaluation criteria. Midpoint imputation or left-point imputation was shown to be the best depending on the simulation condition.
