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Dirichlet Distribution Parameter Estimation With Applications in Microbiome Analyses.

Daniel T Fuller1, Sumona Mondal1, Shantanu Sur2

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Summary
This summary is machine-generated.

This study proposes the Dirichlet distribution to model microbial relative abundances directly, offering a more efficient and comparable alternative to existing methods for microbiome analysis.

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Area of Science:

  • Microbiome Research
  • Statistical Modeling
  • Bioinformatics

Background:

  • Accurate quantification of microbial composition is crucial for understanding human and environmental health.
  • Current microbiome analysis often relies on statistical modeling of taxonomic abundances, with relative abundances preferred over absolute abundances due to sequencing method dependency.
  • Limited literature exists on modeling relative abundances using appropriate probability distributions for robust statistical inference.

Purpose of the Study:

  • To propose and evaluate the Dirichlet distribution for directly modeling microbial relative abundances.
  • To compare the performance of different estimators (MMEs and MLE) for the Dirichlet distribution.
  • To assess the applicability and efficiency of Dirichlet modeling in real-world microbiome datasets.

Main Methods:

  • The Dirichlet distribution was employed to model relative abundances without data transformation.
  • A comprehensive simulation study compared biases and standard errors of Methods of Moments Estimators (MMEs) and Maximum Likelihood Estimator (MLE) under various sample size and dimension conditions.
  • The Maximum Likelihood Estimator (MLE) of the Dirichlet distribution was explored for its asymptotic properties using Fisher information.

Main Results:

  • The Maximum Likelihood Estimator (MLE) demonstrated superior performance in the simulation study, exhibiting minimal bias and standard errors.
  • Application to four real-world microbiome datasets showed that Dirichlet MLE (DMLE) results were comparable to the Bayesian Dirichlet-multinomial estimator (BDME).
  • The DMLE method required significantly less computational time compared to BDME, especially for large datasets and simulations.

Conclusions:

  • The Dirichlet distribution provides a robust and efficient framework for modeling microbial relative abundances.
  • The Dirichlet MLE (DMLE) is a reliable and computationally advantageous alternative to methods relying on absolute abundances.
  • This approach enhances statistical inference in microbiome analysis, offering comparable results with reduced computational burden.