The Incidence of Disease and the Poisson Assumption

• Activity Number: 481
• Type: Contributed
• Date/Time: Wednesday, August 4, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Lawrence Lessner*+
• Companies: New York State Department of Health
• Keywords: incidence ; Poisson approximation ; point process

Abstract

It is typical and/or customary to model the incidence of human disease during an interval of calendar time as a Poisson process, or at least consider the number of cases in the interval to be a Poisson distributed. In this work we show that the incidence of disease occurring during an interval is in fact an empiric point process on the interval, and explore the consequences of this result. In particular, theorems from the approximation theory of point processes (Barbour, Karr, and Serfling) are used to assess the use of Poisson point processes to approximate the incidence of disease. There are a number of applications of these results to applied statistics and epidemiology. Yes, there are instances of incidence which are not well approximated by the Poisson distribution.