Methods for statistical inference for cost-effectiveness (C/E) ratios for individual treatment and for incremental cost-effectiveness (delta C/ delta E) ratios when two treatments are compared are presented. In a lemma, we relate the relative magnitude of two C/E ratios to the delta C/ delta E ratio. We describe a statistical procedure to test for dominance, or admissibility, that can be used to eliminate an inferior treatment. The one-sided Bonferroni's confidence interval procedure is generalized to the two-sided case. The method requires only that two confidence intervals be available, one for cost and one for effectiveness. We describe Fieller-based confidence intervals and show them to be shorter than Bonferroni intervals. When distribution assumptions hold and variance and covariance estimates are available, Fieller intervals are preferable. However, Bonferroni intervals can be applied in more diverse situations and are easier to calculate. A simple Bonferroni based technique, and a likelihood ratio statistic given by Siegel, Laska and Meisner, for testing the null hypothesis that the C/E ratios of two treatments are equal is presented. The approaches are applied to the data from a phase II clinical trial of a new treatment for sepsis considered previously by others.