Assessing the sensitivity of net monetary benefits using non-linear models
Justin E. Bekelman, University of Pennsylvania 
*Elizabeth A. Handorf, University of Pennsylvania 
Daniel F. Heitjan, University of Pennsylvania 
Nandita Mitra, University of Pennsylvania 

Keywords: Cost-effectiveness, Sensitivity analysis, Net Monetary Benefit, Unmeasured confounding

Observational data are often used to estimate the Net Monetary Benefit (NMB) of treatment alternatives used in current practice. Because observational data are subject to unmeasured confounding, it is important to assess the sensitivity of the estimate. Here, we derive general expressions to quantify the bias in the expected value of costs and effects due to unmeasured confounders, and show how the estimated NMB can be adjusted to account for this bias. Many existing methods for cost-effectiveness outcomes use linear models, but due to the skewed nature of cost and survival outcomes, non-linear methods may be more appropriate. Here, we present a method to estimate the NMB where costs are modeled using the Gamma distribution and survival times are modeled using the Weibull distribution. Based on these models, we derive bias adjustment formulas that are suitable for any unmeasured confounder which has a distribution that can be characterized using a moment-generating function. Our adjustments allow costs and survival times to be influenced by either the same or different unmeasured confounders. Given parameter values of specific hypothesized unmeasured confounders, an investigator can easily apply the corrections to the predicted means from cost and survival models. Because costs and effects are often correlated and the covariance structure of the difference in means from non-linear models is quite complex, we use a non-parametric bootstrap approach to generate confidence intervals. We evaluate the performance of our method using simulations, incorporating both censoring and correlated outcomes. We use the regression framework to define the parameters of the cost and effect distributions, and then induce a correlation in the simulated cost and effect outcomes using Clayton’s copula. To correctly estimate mean costs in the presence of censoring, we use the inverse probability weighting method. Finally, we apply our method to an economic evaluation of two treatment alternatives for stage II/III muscle-invasive bladder cancer using SEER-Medicare data.