Estimates of the effects of treatment on cost from observational studies are subject to bias if there are unmeasured confounders. It is therefore advisable in practice to assess the potential magnitude of such biases. We derive a general adjustment formula for loglinear models of mean cost and explore special cases under plausible assumptions about the distribution of the unmeasured confounder. We assess the performance of the adjustment by simulation, in particular, examining robustness to a key assumption of conditional independence between the unmeasured and measured covariates given the treatment indicator. We apply our method to SEER-Medicare cost data for a stage II/III muscle-invasive bladder cancer cohort. We evaluate the costs for radical cystectomy vs. combined radiation/chemotherapy, and find that the significance of the treatment effect is sensitive to plausible unmeasured Bernoulli, Poisson and Gamma confounders.
"Evaluating costs with unmeasured confounding: A sensitivity analysis for the treatment effect." Ann. Appl. Stat. 7 (4) 2062 - 2080, December 2013. https://doi.org/10.1214/13-AOAS665