A Swapping Method and Exploratory Analysis for Average Treatment Effect Estimation Based on Partial Balancing and Simultaneous Inference of Regression Models
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Date
2017-01-01
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Mathematics and Statistics
Program
Statistics
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Distribution Rights granted to UMBC by the author.
Distribution Rights granted to UMBC by the author.
Abstract
To provide significant outcomes, it is imperative that health care professionals, medical practitioners and policy-makers acquire evidence of the effectiveness of different treatments or interventions. This is most commonly done by looking into treatment and control groups and determining if the treatment has a causal effect on the outcome. Ideally, treatment assignment is performed through randomization so that the groups formed are comparable with respect to their features; thus, randomized controlled trials are the gold standard. However, some factors, such as cost, time, and ethical issues behind the treatment, may make it difficult to assign treatments at random. This leads to the use of observational studies instead in assessing the treatment or intervention effect. The lack of randomization can be an issue for both observational studies and clinical trial studies so that systematic differences in the covariates of the treatment and control groups may exist, which poses an inherent problem in estimating average treatment effect. Current trends in data analysis utilize propensity score matching as a remedy to the imbalance among covariates between the treatment and control groups under comparison. However, assumed matched pairs or groups formed through propensity scores continue to reflect imbalance in the covariates between the two groups. Hence, an improved method is proposed, based on the direct classification of categorical covariates and balance between groups on continuous covariates, which consequently provides a more stable estimate of the average treatment effect. The proposed method begins with forming homogeneous subgroups in terms of qualitative features and then generates the estimates of average treatment effect using a method that infuses ``swapping" of models based on classical regression and eventual combination of such estimates over all subgroups based on meta-analyses procedures. The "swapping" procedure allows for the imputation of the missing potential outcome for units in one of the control and treatment groups while meta-analysis provides some means of combining the effect sizes calculated from each matched group while addressing the issue of homogeneity. Simulation studies show that the proposed method is able to capture the true treatment effect and provide more stable estimates in comparison to standard propensity score measures. Exploratory analysis via simultaneous regression inference is likewise presented to provide information on the magnitude of difference between the treatment and control regression models. The confidence bands generated through this analysis provide graphical representations of the average treatment effect.