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A generalized Bayesian nonlinear mixed-effects regression model for zero-inflated longitudinal count data in

Divan Aristo Burger1, Robert Schall2,3, Rianne Jacobs4

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

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Summary

Bayesian nonlinear mixed-effects models accurately analyze zero-inflated tuberculosis CFU counts. Conventional models on log-transformed data may underestimate drug effectiveness, recommending zero-inflated models on the original scale.

Keywords:
Bayesianbactericidal activitylongitudinalmixed-effectszero inflated

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Area of Science:

  • Biostatistics
  • Infectious Disease Modeling
  • Pharmacometrics

Background:

  • Longitudinal count data, common in clinical trials, often exhibit excess zeros.
  • Colony forming unit (CFU) counts in tuberculosis (TB) drug trials present such data challenges.
  • Standard nonlinear mixed-effects models (NLME) may not adequately handle zero-inflation and longitudinal dependencies.

Purpose of the Study:

  • To develop and evaluate Bayesian generalized nonlinear mixed-effects (NLME) regression models for zero-inflated longitudinal count data.
  • To compare the performance of proposed models against conventional NLME models using simulated and real TB trial data.
  • To provide a robust method for calculating Bayes factors for model comparison.

Main Methods:

  • Investigation of Bayesian generalized nonlinear mixed-effects (NLME) regression models.
  • Application to colony forming unit (CFU) counts from extended bactericidal activity tuberculosis (TB) trials.
  • Development of a generalized method for calculating marginal likelihoods to determine Bayes factors.
  • Simulation studies to assess model accuracy, precision, and credibility interval coverage.

Main Results:

  • The proposed zero-inflated negative binomial regression model demonstrated good accuracy, precision, and credibility interval coverage in simulations.
  • Conventional normal NLME models applied to log-transformed CFU counts, treating zeros as censored data, showed potential undercoverage of true bactericidal activity.
  • Bayesian generalized NLME models offer a more reliable approach for analyzing zero-inflated longitudinal count data.

Conclusions:

  • Zero-inflated NLME regression models are recommended for analyzing CFU counts on their original scale.
  • Conventional NLME models on logarithmic scales may provide misleading results for TB drug efficacy.
  • The developed methodology enhances the analysis of zero-inflated longitudinal data in clinical trials, particularly for infectious diseases like TB.