A statistical framework is presented for examining cost and effect data on competing interventions obtained from an RCT or from an observational study. Parameters of the join distribution of costs and effects or a regression function linking costs and effects are used to define cost-effectiveness (c-e) measures. Several new c-e measures are proposed that utilize the linkage between costs and effects on the patient level. These measures reflect perspectives that are different from those of the commonly used measures, such as the ratio of expected cost to expected effect, and they can lead to different relative rankings of the interventions. The cost-effectiveness of interventions are assessed statistically in a two stage procedure that first eliminates clearly inferior interventions. Members of the remaining admissible set are then rank ordered according to a c-e preference measure. Statistical techniques, particularly in the multivariate normal case, are given for several commonly used c-e measures. These techniques provide methods for obtaining confidence intervals, for testing the hypothesis of admissibility and for the equality of interventions, and for ranking interventions. The ideas are illustrated for a hypothetical clinical trial of antipsychotic agents for community-based persons with mental illness.