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

Miguel Angel Luque-Fernandez,Camille Maringe,Aurélien Belot,Bernard Rachet,Manuela Quaresma,Michel P Coleman

doi:10.1186/s12874-016-0234-z

Miguel Angel Luque-Fernandez, Camille Maringe + Show 4 more

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https://doi.org/10.1186/s12874-016-0234-z

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Abstract

BackgroundIn 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 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.MethodsWe 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.ResultsAll 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.ConclusionWe 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.Electronic supplementary materialThe online version of this article (doi:10.1186/s12874-016-0234-z) contains supplementary material, which is available to authorized users.

Highlights

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
To estimate relative loss in efficiency (RLE) for each Piecewise exponential regression excess mortality (PEREM) model corrected for overdispersion, the model not corrected for overdispersion was the reference [27]
The Pearson χ 2 deviance residuals were non-normally distributed for the uncorrected PEREM model (ShapiroWilk test for normality p-value = 0.01) [29], and the overdispersion parameter (φ) was 21.3 % times higher than expected suggesting the presence of overdispersion

Summary

Introduction

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. The main advantage of the relative survival setting is that it provides a measure of patients survival and mortality associated with cancer without the need for information on the specific cause of death [1]. These measures of survival and mortality are known as the net survival and the excess mortality respectively [2,3,4]. Piecewise exponential regression excess mortality (PEREM) models derive adjusted excess mortality rates accounting for the expected mortality of the background population [5, 6]

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