PNS300 HOW TO INTERPRET AND ACCOUNT FOR OVER/UNDER-DISPERSION WHEN MODELLING INCIDENCE RATES WITH POISSON MODELS

Abstract

Our aim was to investigate the impact of over/under-dispersion when modelling incidence rates (e.g. mortality rate) with Poisson models. Events were simulated using parametric time-to-event models with varying rates, hazard functions (decreasing, constant or increasing hazards), levels of censoring, and observation truncation periods (to emulate a fixed duration study). The simulated data were analysed using Poisson, quasi-Poisson and negative binomial regression models to estimate both bias (estimated rate - true rate) and deviations from equidispersion (mean = variance, a critical Poisson assumption). When constant hazards were assumed, mild over-dispersion was observed. Higher over-dispersion was observed with decreasing hazards, while increasing hazards resulted in under-dispersion. Individual censoring and observation time truncation interacted with the hazard function shape and rate in determining over/under-dispersion. Analysis with Poisson and quasi-Poisson models provided unbiased estimates in cases of no censoring or time-truncation. When high over-dispersion was observed, negative binomial model provided heavily biased estimates of the rates. When Poisson regression is employed to model incidence rates, traditional approaches to account for deviations from equidispersion may not be helpful to understand its extent and the reasons for it. Exploratory analysis of the complementary time-to-event outcome data can provide more insight. If the objectives of the study are estimation, Poisson and quasi-Poisson models are robust to mild deviations from equidispersion. For prediction and extrapolation purposes, the use of parametric time-to-event models is recommended. Alternatively, piecewise exponential models can be used to mimic increasing/decreasing hazards over time. Use of negative binomial models in modelling incidence rates is not recommended.