Regression and decomposition with ordinal health outcomes

Area of Science:

• Biostatistics
• Health Economics
• Epidemiology

Background:

• Ordinal health outcome data (e.g., depression severity) are often numerically coded (1, 2, 3,...) for analysis.
• The interpretation of regression results, particularly Ordinary Least Squares (OLS), can be ambiguous when applied to such ordinal data if cardinal values are assumed.

Purpose of the Study:

• To clarify the interpretation of OLS regression estimands for ordinal health outcomes, distinguishing between descriptive and predictive uses.
• To demonstrate the validity of OLS-based decomposition methods, such as Blinder-Oaxaca, for analyzing health disparities.
• To empirically assess the rural-urban depression gap in U.S. working-age adults and identify contributing factors.

Main Methods:

• Theoretical analysis of OLS regression interpretation for ordinal data, emphasizing its role as a 'best linear approximation'.
• Application of Blinder-Oaxaca-type decomposition using OLS estimators, showing numerical equivalence to counterfactual survival function decomposition.
• Empirical analysis using 2022 U.S. data for working-age adults, incorporating a novel nonparametric estimator alongside OLS.

Main Results:

• OLS regression interpretation for descriptive purposes does not require cardinal values; it provides a best linear approximation of conditional survival function summaries.
• OLS-based Blinder-Oaxaca decomposition is numerically equivalent to counterfactual decomposition, regardless of the cardinal nature of the assigned values.
• Empirical findings indicate a higher incidence of depression in the rural U.S. working-age population.
• 33%-39% of the rural-urban depression disparity is explained by income, education, age, sex, and geographic region.
• Detailed decomposition highlights income as the primary driver of the explained rural-urban depression gap.

Conclusions:

• OLS regression is a valid and interpretable tool for analyzing ordinal health outcomes in descriptive contexts and for disparity decomposition.
• Socioeconomic factors, particularly income, play a crucial role in explaining the higher depression rates observed in the rural population.
• The study validates the use of OLS-based decomposition methods for understanding health disparities.