Nonparametric estimation for partially-complete time and type of failure data

Many statistical models focus on a random variable that represents time until failure and an indicator variable that denotes type of failure. When censoring mechanisms are introduced, an incomplete observation on the failure time often precludes observation of the indicator. In addition to conventional outcomes, for which observations on the time until failure and the type of failure are both complete or both incomplete, this paper considers partially-complete outcomes, for which only one of the random variables if fully observed. An iterative algorithm yields distribution-free estimates of the joint law governing this random pair; these estimates converge to the maximum likelihood solution. Recent developments permit approximations to the information and covariance matrices. Several special cases lead to closed-form estimates of the underlying distribution. Data from two recent clinical trials are used to illustrate the proposed techniques.