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The trend odds model for ordinal data.

Ana W Capuano1, Jeffrey D Dawson

  • 1Department of Biostatistics, University of Iowa College of Public Health, Iowa City, IA 52240, USA. ana_capuano@rush.edu

Statistics in Medicine
|December 11, 2012
PubMed
Summary
This summary is machine-generated.

This study introduces a trend odds model for analyzing ordinal data when proportional odds assumptions are violated. This flexible model improves statistical power in detecting trends in scientific data.

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Area of Science:

  • Statistics
  • Biostatistics
  • Data Analysis

Background:

  • Ordinal data are prevalent across scientific disciplines.
  • Ordinal logistic regression models commonly assume proportional odds, which may not always hold.
  • Violations of the proportional odds assumption can lead to inaccurate analyses.

Purpose of the Study:

  • To introduce and explore a trend odds model as an alternative to traditional ordinal logistic regression.
  • To investigate the relationship between the trend odds model and latent distributions (logistic, normal, exponential).
  • To assess the performance of the trend odds model in simulations and a real-world example.

Main Methods:

  • Algebraic and graphical demonstrations of the trend odds model's relationship with latent distributions.
  • Fitting the trend odds model using SAS Proc NLMIXED.
  • Simulation studies comparing the proportional odds and trend odds models under various conditions.
  • Application to a swine influenza dataset.

Main Results:

  • The trend odds model demonstrates consistency with scale changes in latent logistic, normal, and exponential distributions.
  • The model shows improved statistical power compared to the proportional odds model when proportionality is moderately to severely violated.
  • Scale changes in logistic and exponential latent distributions align with linear or near-linear odds increases.

Conclusions:

  • The trend odds model offers a valuable extension for analyzing ordinal data when proportional odds assumptions are not met.
  • This model enhances analytical flexibility and statistical power in scenarios with non-proportional odds.
  • The trend odds model provides a robust framework for understanding monotonic relationships in ordinal data across scientific fields.