Causal Inference for Multiple Non-Randomized Treatments using Fractional Factorial Designs
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When interest lies in assessing the effect of multiple treatments on an outcome and an experiment is not feasible, a precise and rigorous analysis of observational data can help address causal questions of interest. This setting involves attempting to approximate an experiment from observational data. With multiple treatments, this experiment would be a factorial design. However, certain treatment combinations may be so rare that, for some combinations, we have no measured outcomes in the observed data. We propose to conceptualize a hypothetical fractional factorial experiment instead of a full factorial experiment and layout a framework for analysis in this setting. We connect our design-based methods to standard regression methods. We finish by illustrating our approach using biomedical data from the 2003-2004 cycle of the National Health and Nutrition Examination Survey to estimate the effects of four common pesticides on body mass index.
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