Bayesian discrimination with longitudinal data.

The motivation for the methodological development is a double-blind clinical trial designed to estimate the effect of regular injection of growth hormone, with the purpose of identifying growth hormone abusers in sport. The data formed part of a multicentre investigation jointly sponsored by the European Union and the International Olympic Committee. The data are such that for each individual there is a matrix of marker variables by time point (nominally 8 markers at each of 7 time points). Data arise out of a double-blind trial in which individuals are given growth hormone at one of two dose levels or placebo daily for 28 days. Monitoring by means of blood samples is at 0, 21, 28, 30, 33, 42 and 84 days. We give a new method of Bayesian discrimination for multivariate longitudinal data. This involves a Kronecker product covariance structure for the time by measurements (markers) data on each individual. This structure is estimated by an empirical Bayes approach, using an ECM algorithm, within a Bayesian Gaussian discrimination model. In future one may have markers for an individual at one or more time points. The method gives probabilities that an individual is on placebo or on one of the two dose regimes.