Negative binomial (NB) regression is commonly used in intervention studies aiming at reducing the number of falls in patients with degenerative disease. Difficulties arise with classical estimation methods (maximum likelihood (ML) & moment-based estimators) when unexpected large counts are observed like the so-called ‘multiple fallers’ in Parkinson’s disease sufferers. In this work, we extend two approaches for building robust M-estimators developed for generalised linear models to NB regression. Robustness in the response is achieved by either 1) applying a bounded function to the Pearson residuals arising in the ML score equations; or 2) bounding the unscaled deviance components. An auxiliary weighted maximum likelihood estimator is introduced for the overdispersion parameter. We explore the impact of using different bounding score functions for both approaches and derived the asymptotic distribution of the new proposals. Simulations show that redescending estimators display smaller biases under contamination while remaining reasonably efficient at the assumed model. A unified notation shows that both approaches are actually very close provided that the bounding functions are chosen and tuned appropriately. An application to the PD-Fit study data, a recent intervention trial in Parkinson’s disease patients, will be presented as illustration.
This is joint work with William Aeberhard (School of Public Health, University of Sydney; Research Centre for Statistics, University of Geneva), Eva Cantoni (Research Centre for Statistics, University of Geneva)
Reference:
Aeberhard W, Cantoni E, Heritier S (2014). “Robust inference in the negative binomial regression with an application to falls data”, Biometrics, 70(4):920-931
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