Modeling the joint effect of intensity and duration of alcohol drinking with bivariate spline models

Spline functions, defined as piecewise polynomials with a fixed degree, whose joint points are called knots, are highly flexible tools to modeling non-linearity between a response and some continuous covariates. In epidemiological studies, the number and position of knots usually have an important meaning. Therefore, special attention should be posed to techniques that allow to choose the number and position of knots. Here, we will follow one of the most recent approaches to variable selection in a Bayesian context. Estimating the positions of the knots is not easy and, for a fixed degree, regression coefficients and locations of knots have to be estimated simultaneously, turning the estimation into a non-linear optimisation problem. The aim of the present work is to: 1. introduce a two-step Bayesian procedure within the semiparametric generalised linear model framework, to be applied in epidemiological studies where the effect of a continuous exposure on risk is under investigation; 2. show how this framework is applied in a bivariate context, where the aim is to modeling the joint effect of intensity and duration of alcohol drinking in cancer of the oral cavity.