title: Adjusting for overdispersion in piecewise exponential regression models to estimate excess mortality rate in population-based research.
abstract: 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 xiare equal is strong and may fail to account for overdispersion 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.
  
  
  
  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.
  
  
  
  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.
  
  
  
  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.
authors.affiliation: Department of Non-Communicable Disease Epidemiology, Faculty of Epidemiology and Population Health, London School of Hygiene and Tropical Medicine, Cancer Survival Group, Keppel Street, London, WC1E 7HT, UK. miguel-angel.luque@lshtm.ac.uk.
authors.forename: Miguel Angel
authors.initials: MA
authors.lastname: Luque-Fernandez
authors.affiliation: Department of Non-Communicable Disease Epidemiology, Faculty of Epidemiology and Population Health, London School of Hygiene and Tropical Medicine, Cancer Survival Group, Keppel Street, London, WC1E 7HT, UK.
authors.forename: Aurélien
authors.initials: A
authors.lastname: Belot
authors.affiliation: Department of Non-Communicable Disease Epidemiology, Faculty of Epidemiology and Population Health, London School of Hygiene and Tropical Medicine, Cancer Survival Group, Keppel Street, London, WC1E 7HT, UK.
authors.forename: Manuela
authors.initials: M
authors.lastname: Quaresma
authors.affiliation: Department of Non-Communicable Disease Epidemiology, Faculty of Epidemiology and Population Health, London School of Hygiene and Tropical Medicine, Cancer Survival Group, Keppel Street, London, WC1E 7HT, UK.
authors.forename: Camille
authors.initials: C
authors.lastname: Maringe
authors.affiliation: Department of Non-Communicable Disease Epidemiology, Faculty of Epidemiology and Population Health, London School of Hygiene and Tropical Medicine, Cancer Survival Group, Keppel Street, London, WC1E 7HT, UK.
authors.forename: Michel P
authors.initials: MP
authors.lastname: Coleman
authors.affiliation: Department of Non-Communicable Disease Epidemiology, Faculty of Epidemiology and Population Health, London School of Hygiene and Tropical Medicine, Cancer Survival Group, Keppel Street, London, WC1E 7HT, UK.
authors.forename: Bernard
authors.initials: B
authors.lastname: Rachet
mesh_terms: D001943:Breast Neoplasms / Q000401:mortality*; D005260:Female; D006801:Humans; D015233:Models, Statistical; D009026:Mortality; D012044:Regression Analysis; D016019:Survival Analysis
keywords: Cancer; Epidemiologic methods; Proportional hazard models; Regression analysis; Survival analysis