September 2005
In many applications, interest focuses on assessing the relationship between a predictor and a multivariate outcome variable, and there may be prior knowledge about the shape of the regression curves. For example, regression functions relating dose of a possible risk factor to different adverse outcomes can often be assumed to tbe nondecreasing. In such cases, interest focuses on (1) assessing evidence of an overall adverse effect; (2) determining which outcomes are most affected; and (3) estimating outcome-specific regression curves. This article proposes a Bayesian approach for addressing this problem, motivated by multi-site tumor data from carcinogenicity experiments. A multivariate smoothing spline model is specified, which accommodates dependency in the multiple curves through a hierarchical Markov random field prior for the basis coefficients, while also allowing for residual correlation. A Gibbs sampler is proposed for posterior computation, and the approach is applied to data on body weight and tumor occurrence.
Keywords: Factor model; Functional data analysis; Monotone curves; Multiple outcomes; Multiplicity problem; Seemingly unrelated regression; Smoothing; Tumor data.
The manuscript is available in PDF formats.