Separable Effects of Semicompeting Risks: The Effects of Hepatitis B on Liver Cancer via Liver Cirrhosis

We are interested in how patients with hepatitis B progress to liver cirrhosis (an intermediate outcome) and liver cancer (a primary outcome). The separable effect has recently been proposed to study causal effects in the setting of competing risks. In this work, we extend the separable effect approach to semicompeting risks involving a primary and intermediate outcome. We decompose the exposure to hepatitis B virus into two disjoint components: the first component affects liver cancer directly, that is, direct effect, and the other affects liver cancer through liver cirrhosis, that is, indirect effect. Under such an effect separation, the identification formula of counterfactual risk for liver cancer that we derive for semicompeting risks is a function of cause-specific hazards and transition hazards of multistate models. It can be reduced to the formula for competing risks as a special case. We propose nonparametric and semiparametric methods to estimate the causal effects and study their asymptotic properties. The model-free nonparametric method is robust but less efficient for confounder adjustment; the model-based semiparametric method flexibly accommodates confounders by treating them as covariates. We conduct comprehensive simulations to study the performance of the proposed methods. Our data analyses of the hepatitis study show that there exist both direct and indirect effects of hepatitis B infection on the incidence of liver cancer through liver cirrhosis.