A Noise-Tolerant Inference Procedure for Quasi-Monte Carlo Likelihood Estimation of a Joint Model for Multiple Longitudinal Markers and Competing Risks.

Despite increasingly widespread use, complex joint models for longitudinal and survival data can be difficult to estimate. Notably, this could be due to the computation of the intractable integral over random effects involved in the likelihood and whose dimensionality increases with the number of shared random effects. In this article, we propose approximating the integral over random effects through a Quasi-Monte Carlo (QMC) approach combined with a noise-tolerant Quasi-Newton algorithm to consider the likelihood randomness induced by the QMC framework. From a simulation study, we demonstrate the suitability of the noise-tolerant Quasi-Newton algorithm to estimate the parameters of a shared random-effect joint model for two longitudinal markers in the presence of two competing events. The noise-tolerant Quasi-Newton algorithm is also compared with a Quasi-Newton algorithm with common draws in the QMC approach that showed good performance. Finally, we illustrate the interest of the noise-tolerant Quasi-Newton algorithm on kidney transplantation data. We jointly modeled the evolution of serum creatinine and donor-specific antibody immunization, as well as their associations with the cause-specific risks of graft failure and death with a functioning graft, using data from the French prospective and observational DIVAT cohort of kidney transplant recipients. The proposed noise-tolerant inference procedure for QMC likelihood estimation is shown to be relevant for estimating a joint model with multiple longitudinal markers and competing risks.