While transformations (logX, etc.) may 'squeeze' the original distribution of costs to 'look' better (more normally distributed), there is a lot that's left unattended when doing so (references below).
As an example, costs seen in the eConsult intervention are quite skewed:
A simple way to process actual costs is to add 1 (or 2) extra parameters to the classic mean and variance (or SD): the 'fatness of tail' (df for t-distribution) and the skew parameter; an intro into the 'how to' is here, presented at MMM-Storrs, CT).
Here I point to the Mplus way of testing such a model, an annotated syntax/output is posted at Researchgate, it shows how and why one models the costs differently.
References
1. Anderson, D., Villagra, V., Coman, E. N., Zlateva, I., Hutchinson, A., Villagra, J., & Olayiwola, J. N. (2018). A Cost-Effectiveness Analysis of Cardiology eConsults for Medicaid Patients. The American journal of managed care, 24(1), e9-e16.
2. Loisel, P., et al., Cost‐benefit and cost‐effectiveness analysis of a disability prevention model for back pain management: a six year follow up study. Occupational and Environmental Medicine, 2002. 59(12): p. 807‐815.
3. Lee, S. and G. McLachlan, On mixtures of skew normal and skew t distributions. Advances in Data Analysis and Classification, 2013. 7(3): p. 241‐266.
4. Lee, S. and G. McLachlan, Finite mixtures of multivariate skew t distributions: some recent and new results. Statistics and Computing, 2014. 24(2): p. 181‐202.
5. Asparouhov, T. and B. Muthén, Structural Equation Models and Mixture Models With Continuous Nonnormal Skewed Distributions. Structural Equation Modeling: A Multidisciplinary Journal, 2015 : p. 1‐19.
