Statistical issues in survival analysis (Part XVVVVVIII)
November 20, 2024 Most of the literature on mixture cure models has focused on using Cox proportional hazards regression for the basis of the model, but the proportional hazards assumption over time can make this difficult, therefore, the authors have focused on using the accelerated failure time model (AFT). They also preferred the AFT since it focuses on estimating survival rather than hazard and they estimated a smoothed estimate of the baseline survival function via estimating the baseline hazard function. For the cure probability, they used a logistic model where gamma parameters were the main coefficients describing the incidence. In estimating the baseline hazard, they found that methods like M-or B-splines were not useful since they require specification of the boundary knots so they instead focused on Gaussian basis function also known as a Gaussian kernel. In order to fit their mixture cure AFT model, they maximized the log-likelihood function using a roughness penalty function. However, they used an iterative alternating algorithm which employed quasi-Newton schemes to update beta and gamma parameters first followed by a multiplicative-iterative (MI) scheme. A marginal likelihood