Abstract
This paper considers the estimation of lifetime distribution based on missing-censoring data. Using the simple empirical approach rather than the maximum likelihood argument, we obtain the parametric estimations of lifetime distribution under the assumption that the failure time follows exponential or gamma distribution. We also derive the nonparametric estimation for both continuous and discrete failure distributions under the assumption that the censoring distribution is known. The loss of efficiency due to missing-censoring is shown to be generally small if the data model is specified correctly. Identifiability issue of the lifetime distribution with missing-censoring data is also addressed.
Highlights
Let T be a random variable representing the failure time of the subject under study
We provide a systematic treatment for missing-censoring data by using a simple empirical approach
It is interesting to notice that the estimated variance for estimator λ2 is less than that of the estimator λ1, this implies that observed censoring times do not provide much information in the estimation of lifetime distribution, and the mismeasurement for censoring will not significantly affect the estimation of lifetime distribution
Summary
Let T be a random variable representing the failure time of the subject under study. In many applications, such as in biological sciences and in clinical trials for cancer research, the failure time T may not be always observable due to the presence of censoring time C, which is assumed to be independent of T. We identify the estimable variables based on observed data, and express the target parameters or functions in terms of those estimable variables, and the target parameters or functions can be estimated consistently from those expressions in a natural way. Based on this simple method, we derive the parametric estimators and their biases and variances when the lifetime distribution is exponential and gamma. We consider the nonparametric estimation of the lifetime distribution when failure time and censoring time are either discrete or continuous. A short discussion is presented in Section 5 while some theoretical derivations are deferred to Appendix
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