Model-based hypothesis tests for the causal mediation of semi-competing risks

Yun-Lin Ho, Ju-Sheng Hong and Yen-Tsung Huang ()
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Yun-Lin Ho: National Taiwan University
Ju-Sheng Hong: Academia Sinica
Yen-Tsung Huang: Academia Sinica

Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, 2024, vol. 30, issue 1, No 5, 119-142

Abstract: Abstract Analyzing the causal mediation of semi-competing risks has become important in medical research. Semi-competing risks refers to a scenario wherein an intermediate event may be censored by a primary event but not vice versa. Causal mediation analyses decompose the effect of an exposure on the primary outcome into an indirect (mediation) effect: an effect mediated through a mediator, and a direct effect: an effect not through the mediator. Here we proposed a model-based testing procedure to examine the indirect effect of the exposure on the primary event through the intermediate event. Under the counterfactual outcome framework, we defined a causal mediation effect using counting process. To assess statistical evidence for the mediation effect, we proposed two tests: an intersection–union test (IUT) and a weighted log-rank test (WLR). The test statistic was developed from a semi-parametric estimator of the mediation effect using a Cox proportional hazards model for the primary event and a series of logistic regression models for the intermediate event. We built a connection between the IUT and WLR. Asymptotic properties of the two tests were derived, and the IUT was determined to be a size $$\alpha $$ α test and statistically more powerful than the WLR. In numerical simulations, both the model-based IUT and WLR can properly adjust for confounding covariates, and the Type I error rates of the proposed methods are well protected, with the IUT being more powerful than the WLR. Our methods demonstrate the strongly significant effects of hepatitis B or C on the risk of liver cancer mediated through liver cirrhosis incidence in a prospective cohort study. The proposed method is also applicable to surrogate endpoint analyses in clinical trials.

Keywords: Causal mediation model; Cox proportional hazards model; Nonparametric maximum likelihood estimator; Semi-competing risks; Intersection–union test; Weighted log-rank test (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10985-023-09595-7

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