Two measures often used in a cost-effectiveness analysis are the incremental cost-effectiveness ratio (ICER) and the net health benefit (NHB). Inferences on these two quantities are often hindered by highly skewed cost data. In this paper, we derived the Edgeworth expansions for the studentized t-statistics for the two measures and showed how they could be used to guide inferences. In particular, we used the expansions to study the theoretical performance of existing confidence intervals based on normal theory and to derive transformational confidence intervals for the ICER and the NHB. We conducted a simulation study to compare our new intervals with several existing methods. The methods evaluated included the normal theory interval, the Fieller's interval, the bootstrap percentile interval, and the bootstrap bias-corrected acceleration (BCa) interval. We found that our new intervals give good coverage accuracy and are narrower compared to the current recommendation.