An Efficient Estimation Method for Longitudinal Data Using Bayesian Conditional Transformation Models

Bayesian conditional transformation models (BCTMs) address the direct estimation of the conditional distribution function of a random variable conditional on a set of explanatory . The BCTMs infer the conditional distribution by applying a transformation function of given towards a baseline distribution free of parameters to be estimated. The benefit of these models is that the explanatory variables impact the whole conditional distribution of given instead of only the mean, variance, kurtosis, or skewness. The transformation functions are an essential part of the model, and they range from loss‐complex and low‐parameterized functions to complex relationships between explanatory variables and response variables represented by nonlinear functions. The general construction of the BCTM class explores monotonic B‐splines for parameterizing the transformation function. Smoothness and regularization are accomplished through an adequate prior distribution for the parameters. We proposed a new estimation procedure for the BCTM based on the integrated nested Laplace approximation, which is tested through a simulation study. Also, two longitudinal studies using real data are considered. The first application is a cardiovascular study and compares our proposed algorithm, named integrated Laplace with Bayesian conditional transformation models (ILBCTM), with the original Markov chain Monte Carlo–based algorithm for BCTM. We obtained similar results with a shorter computational time. The second application considers the ILBCTM in a study of the mortality rate of bronchial and lung cancer in Brazil.