Control percentile test procedures for censored data

In life testing and survival analyses which involve the use of expensive equipment the cost of continuing an experiment until all the items on test have failed can be quite high. In these situations it is reasonable to make a statistical test when a pre-specified percentile, e.g. median of the control group has been observed. This article adapts some existing procedures for complete samples to randomly censored data. The results of Lo and Singh (1985) who extended the Bahadur representation of quantiles to the censored case enable us to use the methods of Gastwirth (1968) and Hettmansperger (1973) which were based on Bahadur's result to extend the procedures of Mathisen (1943), Gart (1963) and Slivka (1970).The large sample efficiency of the control median test is the same as that of Brookmeyer and Crowley's (1982) extension of the usual median test. For the two-sample shift problem with observations following the double-exponential law, the median remains the optimum percentile to use until the censoring becomes quite heavy. On the other hand, in the two-sample scale parameter problem for data from an exponential distribution the percentile (80th in the uncensored case) yielding the asymptotically most powerful test in the family of control percentile tests no longer is optimum. The effect becomes noticeable when 25% or more of the data is censored.