Over 1300 federally-qualified health centers (FQHCs) in the US provide care to vulnerable populations in different contexts, addressing diverse patient health and socioeconomic characteristics. In this study, we use data envelopment analysis (DEA) to measure FQHC performance, applying several techniques to account for both quality of outputs and heterogeneity among FQHC operating environments. To address quality, we examine two formulations, the Two-Model DEA approach of Shimshak and Lenard (denoted S/L), and a variant of the Quality-Adjusted DEA approach of Sherman and Zhou (denoted S/Z). To mitigate the aforementioned heterogeneities, a data science approach utilizing latent class analysis (LCA) is conducted on a set of metrics not included in the DEA, to identify latent typologies of FQHCs. Each DEA quality approach is applied in both an aggregated (including all FQHCs in a single DEA model) and a partitioned case (solving a DEA model for each latent class, such that an FQHC is compared only to its peer group). We find that the efficient frontier for the aggregated S/L approach disproportionately included smaller FQHCs, whereas the aggregated S/Z approach's reference set included many larger FQHCs. The partitioned cases found that both the S/L and S/Z aggregated models disproportionately disfavored (different) members of certain classes with respect to efficiency scores. Based on these results, we provide general insights into the trade-offs of using these two models in conjunction with a clustering approach such as LCA.
Keywords: Data envelopment analysis; Data science; Latent class analysis; OR in health services; Public sector OR.