Sensitivity analysis of longitudinal count responses: a local influence approach and application to medical data

Alejandra Tapia, Viviana Giampaoli, Maria del Pilar Diaz, VICTOR ELISEO LEIVA SANCHEZ

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6 Scopus citations

Abstract

Longitudinal count responses are often analyzed with a Poisson mixed model. However, under overdispersion, these responses are better described by a negative binomial mixed model. Estimators of the corresponding parameters are usually obtained by the maximum likelihood method. To investigate the stability of these maximum likelihood estimators, we propose a methodology of sensitivity analysis using local influence. As count responses are discrete, we are unable to perturb them with the standard scheme used in local influence. Then, we consider an appropriate perturbation for the means of these responses. The proposed methodology is useful in different applications, but particularly when medical data are analyzed, because the removal of influential cases can change the statistical results and then the medical decision. We study the performance of the methodology by using Monte Carlo simulation and applied it to real medical data related to epilepsy and headache. All of these numerical studies show the good performance and potential of the proposed methodology.

Original languageEnglish
Pages (from-to)1021-1042
Number of pages22
JournalJournal of Applied Statistics
Volume46
Issue number6
DOIs
StatePublished - 26 Apr 2019

Keywords

  • Approximation of integrals
  • local influence
  • longitudinal data
  • Monte Carlo and Metropolis-Hastings methods
  • Poisson and negative binomial distributions

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