Hypothesis Tests of Direct and Indirect Effects Under Various Semicompeting Risks Models

The semicompeting risks problem involves two time-to-event outcomes where the intermediate outcome may be censored by the primary outcome but not vice versa. It has been shown that semicompeting risks can be formulated as a mediation model, where both the direct effect (DE) and the indirect effect (IE) are studied. This article proposes unified testing procedures based on current causal approaches to evaluate DE and IE under three classic semicompeting risks models: the Clayton copula, gamma frailty, and multistate models. We study the correspondence of the DE and IE with the model parameters and establish testing rules for the two effects under the three models. For statistical inference, we use the U-statistic approach for the Clayton copula model and nonparametric maximum likelihood estimation for the multistate and gamma frailty models. The simulation study shows that among the three models, the Clayton copula model attains the best statistical power if the model assumption holds but has the potential bias caused by model misspecification; the gamma frailty model is the most robust model by sacrificing the efficiency; the multistate model balances the efficiency and robustness. We apply the proposed method to a hepatitis study, and the aforementioned models unanimously suggest that both hepatitis B and C lead to a higher incidence of liver cancer by increasing liver cirrhosis incidence.