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Related Concept Videos

Skewness01:06

Skewness

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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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Types of Skewness01:09

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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.
For instance, in the middle of a pandemic, the geographical distribution of vaccine coverage may be positively skewed towards populations in the global north countries. However,...
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Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

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Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least...
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Microsoft Excel: Finding Central Tendency, Skew, and Kurtosis01:24

Microsoft Excel: Finding Central Tendency, Skew, and Kurtosis

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Central tendency refers to the central point or typical value of a dataset. It summarizes the data set with a single value that represents the center of its distribution. The three main measures of central tendency are:
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Parametric Survival Analysis: Weibull and Exponential Methods01:14

Parametric Survival Analysis: Weibull and Exponential Methods

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Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
Weibull Distribution
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Model Approaches for Pharmacokinetic Data: Distributed Parameter Models01:06

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models

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Pharmacokinetic models are mathematical constructs that represent and predict the time course of drug concentrations in the body, providing meaningful pharmacokinetic parameters. These models are categorized into compartment, physiological, and distributed parameter models.
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Bayesian censored piecewise regression mixture models with skewness.

Getachew A Dagne1

  • 1College of Public Health, MDC 56, University of South Florida, Tampa, Florida, USA.

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|February 15, 2022
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Summary

This study introduces advanced censored mixture regression models to analyze complex longitudinal data with multiple features. These models help identify predictor effects in diverse populations, offering new insights into multiphasic growth patterns.

Keywords:
Bayesian inferencechange-pointdevelopmental pathmixed-effects modelsskew distributions

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Area of Science:

  • Biostatistics and Statistical Modeling
  • Longitudinal Data Analysis
  • Regression Analysis

Background:

  • Longitudinal data often exhibit complex features like censoring, skewness, and measurement errors.
  • Identifying differential predictor effects in heterogeneous populations (subpopulations) is crucial.
  • Standard regression mixture models may not fully capture multiphasic trajectories and unobserved subgroups.

Purpose of the Study:

  • To extend regression mixture models to handle skew-normal distributions, left-censoring, and measurement errors.
  • To develop piecewise growth mixture modeling for multiphasic longitudinal data from unobserved subgroups.
  • To assess differential predictor effects in complex, heterogeneous longitudinal datasets.

Main Methods:

  • Development of censored mixture regression models incorporating skew-normal distributions.
  • Integration of piecewise growth mixture modeling to describe multiphasic trajectories.
  • Application of a Bayesian approach for model estimation and inference.

Main Results:

  • The proposed models effectively accommodate left-censoring, skewness, and measurement errors in covariates.
  • Piecewise growth mixture modeling successfully captures multiphasic trajectories over time.
  • Demonstrated utility in analyzing real-world data from an AIDS clinical study.

Conclusions:

  • The extended censored mixture regression models provide a robust framework for analyzing complex longitudinal data.
  • These methods enhance the ability to identify subgroup-specific predictor effects in heterogeneous populations.
  • The approach offers valuable tools for understanding multiphasic growth patterns in various scientific fields.