Considering the sample sizes as truncated Poisson random variables in mixed effects models

Célia Nunes; Elsa Moreira; Sandra S Ferreira; Dário Ferreira; João T Mexia

doi:10.1080/02664763.2019.1641188

Considering the sample sizes as truncated Poisson random variables in mixed effects models

J Appl Stat. 2019 Jul 14;47(13-15):2641-2657. doi: 10.1080/02664763.2019.1641188. eCollection 2020.

Authors

Célia Nunes¹, Elsa Moreira², Sandra S Ferreira¹, Dário Ferreira¹, João T Mexia²

Affiliations

¹ Department of Mathematics and Center of Mathematics and Applications, University of Beira Interior, Covilhã, Portugal.
² CMA - Center of Mathematics and its Applications, Faculty of Science and Technology, New University of Lisbon, Lisbon, Portugal.

Abstract

When applying analysis of variance, the sample sizes may not be previously known, so it is more appropriate to consider them as realizations of random variables. A motivating example is the collection of observations during a fixed time span in a study comparing, for example, several pathologies of patients arriving at a hospital. This paper extends the theory of analysis of variance to those situations considering mixed effects models. We will assume that the occurrences of observations correspond to a counting process and the sample dimensions have Poisson distribution. The proposed approach is applied to a study of cancer patients.

Keywords: 62J10; 62J12; 62J99; F-tests; L extensions models; Random sample sizes; cancer registries; counting processes; mixed effects.

Grants and funding

This work was partially supported by the FCT- Fundação para a Ciência e Tecnologia, under the projects UID/MAT/00212/2019 and UID/MAT/00297/2019.