LINEAR REGRESSION METAMODELING AS A TOOL TO SUMMARIZE AND PRESENT SIMULATION MODEL OUTPUTS

Purpose: To examine linear regression metamodeling as a tool to communicate the results of decision-analytical models.

Method: We illustrate our approach using two published cost-effectiveness analyses (CEA) of biologics in rheumatoid arthritis (RA).  For each study we created a dataset consisting of the inputs and outputs from the base-case and sensitivity analyses scenarios.  Each input was scaled in two ways: (1) the percentage deviation from the baseline value; and (2) the deviation from the baseline value divided by the variable's confidence interval. We regressed the log-transformed model outputs on the scaled inputs in a set of linear metamodels.  The resulting regression coefficients represented the percent change in an output due to one percent change in an input when using the first scaling approach; and the percent change in an output in relation to an input's confidence range when using the second scaling approach.  We refer to these coefficients as input effect sizes (IES) and input effect uncertainties (IEU) using the first and second scaling approaches, respectively.  

Result:   The linear regression metamodels accurately reproduced the outputs of both models.  The metamodel results were simpler and more informative than the original published results.  The intercept and the coefficients from the regressions represented the base-case and sensitivity analyses results, respectively.  For example, the intercept from one metamodel predicted an incremental cost-effectiveness ratio (ICER) of 26,370 pound/QALY compared to the published estimate of 27,014 pound/QALY.  The regression coefficients summarized the relationship of the inputs and the outputs.  For example, the IES of one input was -64%, indicating that when this input is doubled, the ICER will decrease by 64%.  The IES and IEU communicated each input's relative weight and uncertainty in relation to the model outputs, respectively. 

Conclusion: Linear regression metamodeling is a simple, yet powerful tool that can significantly simplify and enhance the communication of simulation analysis results.