Although machine learning techniques that estimate propensity scores for observational studies with multivalued treatments have advanced rapidly in recent years, the development of propensity score adjustment techniques has not kept pace. While machine learning propensity models provide numerous benefits, they do not produce a single variable balancing score that can be used for propensity score stratification and matching. This issue motivates the development of a flexible ordinal propensity scoring methodology that does not require parametric assumptions for the propensity model. The proposed method fits a one-parameter power function to the cumulative distribution function (CDF) of the generalized propensity score (GPS) vector resulting from any machine learning propensity model, and is henceforth called the GPS-CDF method. The estimated parameter from the GPS-CDF method, , is a scalar balancing score that can be used to group similar subjects in outcome analyses. Specifically, subjects who received different levels of the treatment are stratified or matched based on their value to produce unbiased estimates of the average treatment effect (ATE). Simulation studies presented show remediation of covariate balance, minimal bias in ATEs, and maintain coverage probability. The proposed method is applied to the Mexican-American Tobacco use in Children (MATCh) study to determine whether an ordinal treatment of exposure to smoking imagery in movies causes cigarette experimentation in Mexican-American adolescents.
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