Improved prediction of extreme random effects in joint models: WRaPs

Abstract

Mixed models are popular for the prediction of subject-specific repeated outcomes or center performance among many centers. When the goal is to identify extreme or poor outcomes, standard random effects predictions may, however, suffer from regression to the mean and underestimate values in the tail of their distribution. Optimally weighted random effect estimators have recently been proposed to mitigate this. Motivated by clinical settings where repeated outcomes may end in death, we extend that method to predict poor outcome defined as 'death or substandard repeated measures'. We start from joint models with shared random effects for the longitudinal and survival outcome and estimate their random effects by minimizing squared weighted prediction errors given available data on survival and repeated measures. As for mixed models, weights are chosen to more heavily penalize errors in the tails. We call the results WRaPs: Weighted Random effect Predictors. For basic models and a select set of weights analytical closed form solutions are derived from the usual joint model parameters. For the more complex setting, computational solutions are developed in rjags using MCMC methods within the Bayesian paradigm. We illustrate finite sample properties of the proposed method in Type I simulations with random intercept and slope; and apply the new approach to predict individual future outcomes and survival in a randomized study with glioblastoma patients.