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Skewness01:06

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The measures of central tendency calculated from a data set may not reveal much about its intrinsic distribution. If a plot is made of the data set’s values, the mean and the median may not only differ, but also the plot may have more values on one side of the central tendencies. Such a data set is said to be skewed towards that side.
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If the frequency distribution of a data set is more inclined towards smaller or larger values, the distribution is said to be skewed. If data values are skewed to the right, then the distribution is called positively skewed. Conversely, if the plot is skewed to the left, the distribution is called negatively skewed.
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The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
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Bayesian regression analysis of skewed tensor responses.

Inkoo Lee1, Debajyoti Sinha2, Qing Mai2

  • 1Department of Statistics, Rice University, Houston, Texas, USA.

Biometrics
|August 19, 2022
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Summary

This study introduces a novel Bayesian tensor regression method to analyze skewed and missing data in periodontal disease (PD) research. The new approach offers improved interpretation of covariate effects and is implemented in the R package BSTN.

Keywords:
Markov chain Monte Carloperiodontal diseaseskewnesstensor regression

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Area of Science:

  • Biostatistics
  • Clinical Data Analysis
  • Tensor Regression Modeling

Background:

  • Tensor regression analysis is increasingly used in clinical fields like neuroimaging, genomics, and dental medicine.
  • Periodontal disease (PD) studies often involve complex, skewed, and missing biomarker data across multiple tooth sites.

Purpose of the Study:

  • To develop a novel Bayesian tensor response regression method to address skewness and missingness in PD data.
  • To facilitate the interpretation of covariate effects on both marginal and joint distributions of tensor responses.
  • To enable evaluation of covariate effects on sparse subsets of tensor components.

Main Methods:

  • Proposed a new Bayesian tensor response regression model.
  • The model accommodates missing-at-random responses using a closure property.
  • Developed Markov chain Monte Carlo (MCMC) tools for implementation and evaluation.

Main Results:

  • The proposed method demonstrated substantial advantages over existing methods in simulation studies.
  • Application to a real PD clinical dataset showed the method's practical utility.
  • The R package BSTN is available on GitHub for implementing the model.

Conclusions:

  • The novel Bayesian tensor regression method effectively handles skewed and missing data in complex clinical settings.
  • The method provides robust interpretation of covariate effects and is readily implementable.
  • This approach offers significant improvements for analyzing multi-biomarker data in periodontal disease research.