Optimal Matching for Observational Studies That Integrate Quantitative and Qualitative Research

Abstract A quantitative study of treatment effects may form many matched pairs of a treated subject and an untreated control who look similar in terms of covariates measured prior to treatment. When treatments are not randomly assigned, one inevitable concern is that individuals who look similar in measured covariates may be dissimilar in unmeasured covariates. Another concern is that quantitative measures may be misinterpreted by investigators in the absence of context that is not recorded in quantitative data. When text information is automatically coded to form quantitative measures, examination of the narrative context can reveal the limitations of initial coding efforts. An existing proposal entails a narrative description of a subset of matched pairs, hoping in a subset of pairs to observe quite a bit more of what was not quantitatively measured or automatically encoded. A subset of pairs cannot rule out subtle biases that materially affect analyses of many pairs, but perhaps a subset of pairs can inform discussion of such biases, perhaps leading to a reinterpretation of quantitative data, or perhaps raising new considerations and perspectives. The large literature on qualitative research contends that open-ended, narrative descriptions of a subset of people can be informative. Here, we discuss and apply a form of optimal matching that supports such an integrated, quantitative-plus-qualitative study. The optimal match provides many closely matched pairs plus a subset of exceptionally close pairs suitable for narrative interpretation. We illustrate the matching technique using data from a recent study of police responses to domestic violence in Philadelphia, where the police report includes both quantitative and narrative information.