Propensity score-based diagnostics for categorical response regression models.

Area of Science:

• Statistics
• Biostatistics
• Epidemiology

Background:

• Goodness-of-fit statistics for categorical response models typically partition subjects based on predicted probabilities.
• Existing methods rely on predicted response probabilities (propensity scores) for model assessment.
• A need exists for robust diagnostics applicable to various sampling designs and capable of detecting general misspecification.

Purpose of the Study:

• To introduce a novel retrospective approach for assessing goodness-of-fit in statistical models.
• To adapt causal inference balancing scores for model adequacy diagnostics.
• To develop and generalize model diagnostics for binary logistic and proportional odds models.

Main Methods:

• Utilized a retrospective approach by borrowing the concept of balancing scores from causal inference.
• Inspected the conditional distribution of predictors given propensity scores within each response category.
• Developed graphical and numerical summaries for binary logistic models and generalized them for proportional odds models.

Main Results:

• The proposed balancing score diagnostics can be applied to both prospective and retrospective sampling designs.
• The methods demonstrated the ability to ascertain general forms of model misspecification.
• Simulations and real-world data examples (Parkinson's disease, diabetes biomarkers) illustrated the utility of the proposed diagnostics.

Conclusions:

• The balancing score approach offers a valuable new tool for assessing the adequacy of statistical models, particularly logistic and proportional odds models.
• This method provides a flexible and powerful way to detect model misspecification across different study designs.
• The diagnostics are illustrated with practical applications, showing their relevance in epidemiological research.