In randomized screening trials, the survival time of a screened participant involves three components: (1) the lead time, or time by which diagnosis is advanced simply by virtue of the screen, (2) the survival time in the absence of screening, and (3) the benefit time, or time by which survival is truly extended due to screening, if any. When the effect of benefit time on survival is additive and survival is measured from time of start of study, the difference in the location parameters of the two survival curves (control and screened arms) is equal to the average benefit time. Similarly, when the effect of lead time on survival is additive, but when survival is measured from time of diagnosis, the difference in location parameters is equal to the sum of the average lead time and average benefit time. Using influence functions, it can be shown that the previously proposed estimators of average lead time and average benefit time are asymptotically equivalent to classical sample means. This result suggests a method for obtaining standard errors via asymptotic variances as well as generalizations which may be more robust to assumptions of duration of preclinical disease. However, this method depends upon the assumption that the case groups used for the analysis are comparable in terms of natural history of disease in the absence of screening. Approaches have been proposed for identifying comparable case groups; any such approach adds variability to the estimators. We investigate the effect of this source of variation and propose one way of reducing it so as to obtain approximately valid confidence intervals for average lead time and average benefit time.