Cause-specific failure probability with covariate effects

Abstract

When infectious diseases were the main killers, elimination of their effects on mortality rates was possible. However, in modern society in which chronic diseases are major causes of death, elimination of disease effect is no longer relevant in estimating mortality rates. The cause-specific failure probability (CSFP) under the unrealistic assumption of elimination of other causes (net probability) is always larger than that under the practical situation where all other causes act simultaneously (crude probability), given competing risks. The proportional hazards model is fit to estimate the CSFP when covariate effects are considered. Fitting the model is performed simply by treating the patients who fail due to other causes as censored observations. When the coefficient of a covariate is positively related to the hazards of other causes, the estimate of net probability is increased over that of crude probability according to the increasing value of the covariate. The more the association of a covariate is related to other causes, the larger the difference is. However, the interpretation is complicated because the probability is related to one or more of the cause-specific hazards, and these hazards are also influenced by covariates. If the proportionality assumption of Cox's model is violated for an explanatory variable, stratification for the variable is desirable and CSFP is estimated in each stratum. If the proportional hazards model fits selected causes, strata, or time zones, a combination of non-parametric and semiparametric hazard and survival functions can be used to estimate the CSFP. An illustrative example is given for prostate cancer patients in Hawaii.