Covariance adjustment on propensity parameters for continuous treatment in linear models

Area of Science:

• Epidemiology
• Biostatistics
• Econometrics

Background:

• Propensity scores are standard for binary treatments in observational studies.
• Recent literature extends propensity scores to ordinal and continuous treatments.
• Controlling confounding is vital for valid causal inference.

Purpose of the Study:

• To establish sufficient conditions for selecting propensity parameters to control confounding in continuous treatment settings.
• To investigate confounding control within regression-based adjustment in linear models.
• To clarify adjustment strategies based on structural model complexity.

Main Methods:

• Utilized the definition of propensity function and parameterizations from Imai and van Dyk.
• Explored conditions for selecting propensity parameters for continuous treatments.
• Applied regression-based adjustment in linear models.
• Examined scenarios with treatment as the sole predictor versus inclusion of baseline covariates.

Main Results:

• Identified sufficient conditions for selecting propensity parameters to control confounding for continuous treatments.
• Demonstrated that adjusting for propensity parameters characterizing treatment expectation is sufficient when treatment is the only predictor.
• Showed that baseline covariates must also be adjusted when included in the structural model.

Conclusions:

• The selection of propensity parameters for confounding control in continuous treatments depends on the structural model.
• Accurate estimation of continuous treatment effects requires careful consideration of both propensity parameters and relevant covariates.
• The findings provide guidance for applying propensity score methods in complex observational studies.