Bias correction for censored data with exponential lifetimes

The analysis of censored data presents several problems including infinite maximum likelihood estimates and biased estimates. In this paper we consider modifying the score equation for the maximum likelihood estimate so that the bias is reduced, following Firth (1993). This method is considered for the case of right censored failure time data having an exponential distribution and the means of the observations are given by a log-linear model. For some situations the modified score equations can be integrated and the method is equivalent to a penalised maximum likelihood approach. We additionally show that the estimates are finite under weak conditions. A small sample study indicates that the modified estimates have good properties and have mean square error behaving like 1/n.