Monte Carlo Investigation of a Model for Competing Risks

Summary

A random sample of N animals from an infinite population was observed until all animals in the sample had died. At death, the cause of death was recorded. The observation period was divided into n intervals, not necessarily of equal length, and the number of animals dying from each cause of death was calculated for each time interval. It was desired to estimate the mortality probabilities in a population in which one cause of death had been eliminated. The estimation was to be performed with a sample from a population in which all causes of death were operating. It was based on an estimation procedure developed by Kimball (Bull Int Stat Inst 36: 193–204, 1958). To provide some information on the small sample properties of the estimates, a large-scale random-sampling experiment was designed and carried out. This empirical study based on a population exposed to four distinct risks reflected favorably on the estimation procedure. The sampling distributions of two estimates were approximately normal, while the third was positively skewed. The biases in the estimates of the mortality probabilities were negligible. The distributions of the variance estimates approximated a chi-square distribution, as would be expected.