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A contaminated regression model for count health data.

Arnoldus F Otto1, Johannes T Ferreira1, Salvatore Daniele Tomarchio2

  • 1Department of Statistics, University of Pretoria, Pretoria, South Africa.

Statistical Methods in Medical Research
|January 20, 2025
PubMed
Summary
This summary is machine-generated.

We introduce a new statistical model, the contaminated negative binomial (cNB) distribution, to better analyze health count data, especially when mild outliers are present. This flexible model improves upon existing methods for medical research involving count outcomes.

Keywords:
Kurtosismild outliersnegative binomialoverdispersionskewness

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Area of Science:

  • Biostatistics
  • Health Services Research
  • Statistical Modeling

Background:

  • Count data, common in health research (e.g., hospital stays, doctor visits), is often modeled using Poisson or negative binomial (NB) regression.
  • Standard NB models struggle with overdispersion and the influence of mild outliers, potentially leading to inaccurate inferences in real-world health data.

Purpose of the Study:

  • To propose a novel contaminated negative binomial (cNB) distribution and regression model to effectively handle count data with mild outliers.
  • To enhance the analysis of health-related count data by incorporating covariates into the flexible cNB framework.

Main Methods:

  • Developed the contaminated negative binomial (cNB) distribution, incorporating parameters for outlier proportion and contamination degree.
  • Proposed the cNB regression model to leverage covariates for improved estimation of the mean of count variables.
  • Utilized an expectation-maximization algorithm for parameter estimation and evaluated its performance through simulation studies.

Main Results:

  • The cNB distribution offers flexibility in accommodating mild outliers, providing a more robust alternative to standard NB models.
  • Parameter recovery studies demonstrated the effectiveness of the expectation-maximization algorithm for cNB model estimation.
  • Sensitivity analyses and application to two health datasets showed that the cNB model outperforms established count data models.

Conclusions:

  • The proposed cNB regression model provides a robust and interpretable approach for analyzing count data in health research, particularly when mild outliers are present.
  • The developed methodology, implemented in an R package, offers a valuable tool for biostatisticians and health researchers dealing with complex count data.
  • The cNB model enhances inference by effectively managing overdispersion and outliers, leading to more reliable conclusions in health studies.