Causal Inference for Multiple Non-Randomized Treatments using Fractional Factorial Designs

We explore a framework for addressing causal questions in an observational setting with multiple treatments. 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 there are no measured outcomes in the observed data corresponding to them. We propose to conceptualize a hypothetical fractional factorial experiment instead of a full factorial experiment and lay out 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.