Statistical issues in survival analysis (Part VI)
May 10, 2023 The authors Sun et al present a semi-competing risks framework using a flexible two-parameter copula-based semiparametric transformation model with interval censoring and left truncation. The semi-parametric transformation model allow both proportional hazards and proportional odds in both margins. Their data application, Chinese Longitudinal Healthy Longevity Study (CLHLS), pertains to disability, which is the main event, and then death and other causes became semi-competing risks. The authors first laid out their copula model for semi-competing risks data, utilizing Archimedean copulas to model the marginal survival function for each terminal time event, in which the dependence can be expressed by Kendall’s tau parameter. They assumed interval censoring due to the convention in longitudinal studies for this. Also, they presented four possible scenarios for censoring due to different possibilities for when the event, disability, or the event, death, could occur and also possibility for left truncation. They next laid out an observed data and joint likelihood with left truncation in Equation 4 and covered all their possible censoring scenarios. The authors also employed a semi-parametric transformation model for the marginal survival function of time. Finally, the authors discussed estimation and inference. They used a sieve likelihood with Bernstein polynomials, which is a method that can estimate infinite dimensional parameters and was applied to their interval censored data which had the absence of exact event times. The process used two steps and a pseudo likelihood function is estimated in the 2nd step which has to be done sinc the non-termnal event is dependently censored by the terminal event. They were then able to use standard optimization algorithms for the log-likelihood and obtain variances from the observed Fisher’s information. They then used a cumulative incidence function to