A Non-parametric Survival Estimate After Elimination of a Cause of Failure

In competing risks analysis, the primary interest of researchers is the estimation of the net survival probability (NSP) if a cause of failure could be eliminated from a population. The Kaplan-Meier product-limit estimator under the assumption that the eliminated risk is non-informative to the other remaining risks, has been widely used in the estimation of the NSP. The assumption implies that the hazard of the remaining risks before and after the elimination are equal and it could be biased. This paper addressed this possible bias by proposing a non-parametric multistate approach that accounts for an informative eliminated risk in the estimation procedure, whereby the hazard probabilities of the remaining risks before and after the elimination of a risk are not assumed to be equal. When a non-informative eliminated risk was assumed, it was shown that the proposed multistate estimator reduces to the Kaplan-Meier estimator. For illustration purposes, the proposed procedure was implemented on a published dataset and the change in hazard after elimination of a cause is investigated. Comparing the results to those obtained from using the Kaplan-Meier method, it was found that in the presence of (both constant and non-constant) informative eliminated risk, the proposed multistate approach was more sensitive and flexible.