This article describes the evolution of applied exponential family models,
starting at 1972, the year of publication of the seminal papers on generali
zed linear models and on Cox regression, and leading to multivariate (i) ma
rginal models and inference based on estimating equations and (ii) random e
ffects models and Bayesian simulation-based posterior inference. By referri
ng to recent work in generic epidemiology, on semiparametric methods for li
nkage analysis and on transmission/disequilibrium tests for haplotype trans
mission this paper illustrates the potential for the recent advances in app
lied probability and statistics to contribute to new and unified tools for
statistical genetics. Finally, it is emphasized that there is a need for we
ll-defined postgraduate education paths in medical statistics in the year 2
000 and thereafter.