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

Author

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  • Alejandra Tapia
  • Viviana Giampaoli
  • Maria del Pilar Diaz
  • Victor Leiva

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.

Suggested Citation

  • Alejandra Tapia & Viviana Giampaoli & Maria del Pilar Diaz & Victor Leiva, 2019. "Sensitivity analysis of longitudinal count responses: a local influence approach and application to medical data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 46(6), pages 1021-1042, April.
    • Handle: RePEc:taf:japsta:v:46:y:2019:i:6:p:1021-1042
    DOI: 10.1080/02664763.2018.1531978
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    Cited by:

    1. Alejandra Tapia & Viviana Giampaoli & Víctor Leiva & Yuhlong Lio, 2020. "Data-Influence Analytics in Predictive Models Applied to Asthma Disease," Mathematics, MDPI, vol. 8(9), pages 1-19, September.
    2. Yonghui Liu & Guohua Mao & Víctor Leiva & Shuangzhe Liu & Alejandra Tapia, 2020. "Diagnostic Analytics for an Autoregressive Model under the Skew-Normal Distribution," Mathematics, MDPI, vol. 8(5), pages 1-19, May.

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