A nonparametric dependent competing risk method for net survival analysis

Quantifying disease-specific survival in patients with competing risks is generally done when reliable cause of death (CoD) information is available. With known CoD, cause-specific and cumulative incidence functions for competing risk data are applicable in estimating disease-specific survival. When CoD is unreliable, unknown, or subject to misspecifications, relative survival methods are used for estimating disease-specific survival. This estimator, under the independent competing risks assumption, is the ratio of all-cause survival in the disease-specific cohort group to the known expected survival from a general reference population. The disease-specific death competes with other causes of mortality, potentially creating interdependence among the CoD. The standard ratio estimate is only valid when death from disease and death from competing causes are independent. We relaxed this assumption by formulating the dependence between the times to disease-specific death and competing causes of mortality using a copula. We fit a nonparametric copula-based approach to the distribution of disease-specific death which reduces to the ratio estimator under independence. This nonparametric method is robust compared to the previously proposed copula-based parametric method. We demonstrate the utility of our method through simulation studies and an application to French breast cancer registry data.