Semiparametric normal transformation joint model of multivariate longitudinal and bivariate time‐to‐event data

Joint models for longitudinal and survival data (JMLSs) are widely used to investigate the relationship between longitudinal and survival data in clinical trials in recent years. But, the existing studies mainly focus on independent survival data. In many clinical trials, survival data may be bivariately correlated. To this end, this paper proposes a novel JMLS accommodating multivariate longitudinal and bivariate correlated time‐to‐event data. Nonparametric marginal survival hazard functions are transformed to bivariate normal random variables. Bayesian penalized splines are employed to approximate unknown baseline hazard functions. Incorporating the Metropolis‐Hastings algorithm into the Gibbs sampler, we develop a Bayesian adaptive Lasso method to simultaneously estimate parameters and baseline hazard functions, and select important predictors in the considered JMLS. Simulation studies and an example taken from the International Breast Cancer Study Group are used to illustrate the proposed methodologies.