Adjusting for overdispersion in piecewise exponential regression models to estimate excess mortality rate in population-based research

Background: In population-based cancer research, piecewise exponential regression models are used to derive adjusted estimates of excess mortality due to cancer using the Poisson generalized linear modelling framework. However, the assumption that the conditional mean and variance of the rate parameter given the set of covariates x(i) are equal is strong and may fail to account for over dispersion given the variability of the rate parameter (the variance exceeds the mean). Using an empirical example, we aimed to describe simple methods to test and correct for overdispersion. Methods: We used a regression-based score test for overdispersion under the relative survival framework and proposed different approaches to correct for overdispersion including a quasi-likelihood, robust standard errors estimation, negative binomial regression and flexible piecewise modelling. Results: All piecewise exponential regression models showed the presence of significant inherent overdispersion (p-value < 0.001). However, the flexible piecewise exponential model showed the smallest overdispersion parameter (3.2 versus 21.3) for non-flexible piecewise exponential models. Conclusion: We showed that there were no major differences between methods. However, using a flexible piecewise regression modelling, with either a quasi-likelihood or robust standard errors, was the best approach as it deals with both, overdispersion due to model misspecification and true or inherent overdispersion.