Statistical issues in survival analysis (Part VII)
May 24, 2023 The authors developed a semiparametric maximum likelihood estimation procedure via a kernel smoothed-aided expectation-maximization algorithm. The variances for this were estimated through weighted bootstrap. The authors focused on this for the illness-death model with accelerated failure time models (AFT) for each transition to different states of state0: healthy, state1: disease, and state2: death. There is not a lot in the literature about AFT frailty models on top of this. The authors laid out the AFT frailty models for each transition, which are multiplicative. In a table prior to this, the authors laid out the literature of Cox frailty and AFT frailty, but they only go back to 2010, when Cox frailty model definitely existed way before then. Finally they setup their likelihood with all transitions and treated the frailtiies as a missing data problem using the EM algorithm referring to the Dempster, Laird, and Rubin paper from 1977. In the M-step estimation, they decided to fit a smoothed kernel-smoothing approach to accommodate their semicompeting risks setting The authors used the function, aftgee, in the R package, to start with naïve estimates of the coefficients which are rank based and also used adaptive quadrature through the function, integrate. Finally the “code”, they stated, although unclear if they meant integrate, applies the EM algorithm. For bandwidth paramters, they used modified versions of the optimal bandwidths of Jones et al (1990 and 1991). For variance estimation, they employed a weighted bootstrap, where weights are derived from a standard exponential distribution assigned to each observation. Finally, the authors also employed a goodness of fit (GOF) method based on randomized survival probabilities (RSP), which replaces the the survival probability of a censored failure time with a uniform random number between 0 and the survival probability at