Treatment effects on count outcomes with non-normal covariates

Area of Science:

• Statistics
• Biostatistics
• Applied Research

Background:

• Negative binomial regression is standard for count outcomes with covariates.
• Traditional methods average treatment effects over empirical distributions.
• A moment-based approach offers improved inference with normally distributed covariates.

Purpose of the Study:

• To extend the moment-based approach for non-normally distributed continuous covariates.
• To accommodate multiple treatment conditions and categorical covariates.
• To provide a more robust framework for estimating treatment effects in applied research.

Main Methods:

• Proposing three methods for non-normal continuous covariates: alternative distributions, joint distribution factorization, and Gaussian mixture approximations.
• Utilizing a saturated model for categorical covariates to avoid distributional assumptions.
• Extending the moment-based approach for multiple treatments and conditional effects with categorical covariates.

Main Results:

• Demonstrated methods for incorporating non-normal covariates into moment-based aggregate effect calculations.
• Successfully extended the moment-based approach to handle multiple treatment conditions.
• Enabled computation of conditional effects for categorical covariates within the extended framework.

Conclusions:

• The proposed extensions enhance the moment-based approach for broader applicability in count data analysis.
• These methods offer more reliable and flexible estimation of treatment effects, especially with complex covariate structures.
• The study provides a valuable extension for applied researchers dealing with non-normal data and multiple treatment scenarios.