Statistical issues in survival analysis (Part XVI)
October 15, 2023 The authors discussed how to handle model joint survival and longitudinal modeling in the presence of informative censoring caused by informative dropouts by participants in a study. The authors framed this in terms of palliative care studies where the quality of life (QOL) is the longitudinal portion of the study which had dropout. To fill this void, they developed a new semiparametric model for analyzing data in palliative care studies or other studies with relatively short life expectancy. Their joint model shown has two models: a semiparametric mixed effect submodel to handle the longitudinal QOL data and a competing risks survival submodel with piecewise hazards for time to death and dropout time. They modeled death and dropout as competing risks rather than censor dropouts. Their mixed effects models used splines for the longitudinal trajectories, linear or non-linear. In the setup for their model, they calculated the administrative censoring time as the duration between the study completion time and and the enrollment time so that time is either chosen per subject as the death time, dropout time, or administrative censoring time and death and dropout are treated as competing risks. The model was written in mixed effect modeling format, where they used a piecewise-exponential competing risk model for time to event data with a frailty term at the individual level, which is the same random effect term used in the longitudinal model. The model also had separate baseline hazard functions for each competing risk. They used regression splines on the non-parametric functions that appear in the mixed effects model format, using the same knots for the three function at equally spaced quantiles. The splines they used had linear spline basis functions, but no justification for this choice of basis function was provided as to why they chose linear. The optimal number of knots were determined by use of Akaike’s Information Criterion, which they decided to use instead of the Bayesian Information Criterion since it uses a smaller penalty on the number of parameters. The authors then showed one way of analyzing the log-likelihood and then an alternative way using an EM algorithm but treating the random effect as missing data, where in the M-step, a closed form solution for coefficient and variance parameters should occur for the longitudinal submodel and the cumulative baseline hazard of survival submodel. Thereafter, a one-step Newton-Raphson method could be used to