A Multistate Approach to Estimating the Net Survival Function in the Presence of Competing Risks

In competing risks analysis, formulation and estimation of the net survival function is usually done by the traditional Latent Failure Time approach with Kaplan Meier Estimator. However, this approach involves identifiability problems and based on unverified assumptions of independent risks and equal hazard of the crude and the net. It has been argued that even under independent risks, the equal hazard assumption may not be true in many practical problems. An extended multistate approach by Islam (1994) is proposed in estimating the net survival function without the equal hazard assumption and allows for the presence of informative eliminated risks. A comparison of the results of the proposed procedure to that of the Kaplan Meier Estimator is illustrated on an adapted dataset. The proposed method shows that when noninformative eliminated risks are assumed, the net hazard and the crude hazard are equal, as in the Kaplan Meier Estimator. The proposed procedure is shown to be useful when informative eliminated risks are present and may result in unequal hazard even under independent risks.