Causal inference for multiple treatments using fractional factorial designs

We consider the design and analysis of multi-factor experiments using fractional factorial and incomplete designs within the potential outcome framework. These designs are particularly useful when limited resources make running a full factorial design infeasible. We connect our design-based methods to standard regression methods. We further motivate the usefulness of these designs in multi-factor observational studies, where certain treatment combinations may be so rare that there are no measured outcomes in the observed data corresponding to them. Therefore, conceptualizing a hypothetical fractional factorial experiment instead of a full factorial experiment allows for appropriate analysis in those settings. We illustrate our approach using biomedical data from the 2003-2004 cycle of the National Health and Nutrition Examination Survey to examine the effects of four common pesticides on body mass index.