The literature on causal effect estimation tends to focus on the population mean estimand, which is less informative as medical treatments are becoming more personalized and there is increasing awareness that subpopulations of individuals may experience a group-specific effect that differs from the population average. In fact, it is possible that there is underlying systematic effect heterogeneity that is obscured by focusing on the population mean estimand. In this context, understanding which covariates contribute to this treatment effect heterogeneity (TEH) and how these covariates determine the differential treatment effect (TE) is an important consideration. Towards such an understanding, this paper briefly reviews three approaches used in making causal inferences and conducts a simulation study to compare these approaches according to their performance in an exploratory evaluation of TEH when the heterogeneous subgroups are not known a priori. Performance metrics include the detection of any heterogeneity, the identification and characterization of heterogeneous subgroups, and unconfounded estimation of the TE within subgroups. The methods are then deployed in a comparative effectiveness evaluation of drug-eluting versus bare-metal stents among 54 099 Medicare beneficiaries in the continental United States admitted to a hospital with acute myocardial infarction in 2008.