Causal Effect of Count Treatment on Ordinal Outcome Using Generalized Propensity Score: Application to Number of Antenatal Care and Age Specific Childhood Vaccination.

Background: Many of the studies in causal inference using propensity scores relied on binary treatments where it is estimated by logistic regression or machine learning algorithms. Since 2000s, attention has been given for multiple values (categorical) and continuous treatments and the propensity score associated with such treatments is called generalized propensity score (GPS). However, there is scant literature on the use of count treatments in causal inference. Besides, effective sample size, after weighting, along with other methods has not been practiced for GPS model performance measure. The study was done with the aim of using count treatments in causal inference; select appropriate GPS and outcome models for such treatment and ordinal outcome.

Method: A family of count models and a generalized boosted model (GBM) were used for GPS estimation. Their performance was measured in terms of covariate balancing power, effective sample size and the average treatment effect after GPS-based weighting. Marginal structural modeling (MSM) and covariate adjustment using GPS were used to estimate treatment effect on ordinal outcome. Stabilized inverse probability treatment weighting was used for covariate balancing assessment. Monte Carlo simulation study at various sample sizes with 1000 replication and household survey data were used in the study.

Result: GPS was trimmed at 1% and 99% which gave better results as compared to untrimmed results. The generalized boosted model performed well both in simulation and actual data producing a larger effective sample size and smaller metrics when estimating average treatment effect on the outcome. The MSM was found better than GPS as a covariate in the outcome model.

Conclusion: It is important to trim GPS when it approaches zero or one without loss of more information due to trimming. Effective sample size after weighting should be used along with other methods such as correlation and absolute standardized mean differences for GPS model selection. GBM should be used for GPS estimation for count treatments. MSM is important for the outcome model when weighting GPS method is used. Finally, the number of antenatal care services had an increasing effect on the probability of age-specific childhood vaccination.