On the Maximum-Likelihood Estimation of Failure Probabilities in the Presence of Competing Risks

摘要

The paper is concerned with the statistical problem of estimating failure rates of a population exposed to several simultaneous hazards or risks. Two distinct models are discussed: (a) a model that is appropriate when the risk-specific hazard rates can be assumed constant over the study period, and (b) a model that assumes the risk-specific hazard rates are linear functions of time. For both models the method of finding the maximum-likelihood estimators is developed. The linear model situation includes a discussion of how a nonlinear programming procedure can be used to obtain estimates of the parameters. The paper investigates the statistical properties of these estimators using a suitable simulation technique. (Author)