Two major physiological problems women experience at the time of menopause are hot flush and vaginal dryness. Exploratory investigations reveal that these two binary outcomes are very much dependent as both of them have predominant oestrogenic effects. A primary interest is to investigate how the bivariate association and the marginal univariate risks are affected by repeated measurements on each woman over several months. To achieve this we propose a very general class of bivariate binary models. Parametric inference is drawn on the basis of full non-parametric Bayesian approach under Dirichlet process mixture. Study addresses some more interesting phenomena on the effectiveness of tibolone treatment in reducing menopausal problems. A simulation study further strengthens the proposed methodology. Copyright © 2006 John Wiley & Sons, Ltd.