Background: One of the epidemiologist's most basic tasks is estimation of disease occurrence. To perform this task, the epidemiologist frequently models variability in disease occurrence using one of three distributions--the binomial, the Poisson or the exponential distribution. Although epidemiologists often use them and their properties appear in standard texts, we know of no text or review that compares and contrasts epidemiological application of these distributions.
Methods: In this commentary, we discuss these three basic distributions. We note key assumptions as well as limitations, and compare results from analyses based on each distribution.
Results and conclusions: We illustrate that the three distributions, although superficially different, often lead to similar results. We argue that epidemiologists should often obtain similar results regardless of which distribution they use. We also point out that application of all three distributions can be inappropriate if assumptions of independence or homogeneity of risks fail to hold. Finally, we briefly review how these basic distributions can be used to justify use of other distributions, such as the Gaussian distribution, for studying disease-exposure associations.