Regression modelling is one of the most widely utilized approaches in epidemiological analyses. It provides a method of identifying statistical associations, from which potential causal associations relevant to disease control may then be investigated. Multivariable regression – a single dependent variable (outcome, usually disease) with multiple independent variables (predictors) – has long been the standard model. Generalizing multivariable regression to multivariate regression – all variables potentially statistically dependent – offers a far richer modelling framework. Through a series of simple illustrative examples we compare and contrast these approaches. The technical methodology used to implement multivariate regression is well established – Bayesian network structure discovery – and while a relative newcomer to the epidemiological literature has a long history in computing science. Applications of multivariate analysis in epidemiological studies can provide a greater understanding of disease processes at the population level, leading to the design of better disease control and prevention programs.