EXAMINING THE EFFECT OF CORRELATED PARAMETERS ON REGRESSION METAMODELING

�� Purpose: Regression metamodeling (RM) is a useful technique for efficiently revealing parameter sensitivities in a model in terms of marginal effects of each parameter on policy-relevant outcomes using the output from probabilistic sensitivity analysis (PSA). The present study examined the performance of RM when model parameters are correlated.�   �� Methods: �A metamodel is a statistical model that can summarize model parameter sensitivities from PSA by regressing model outcomes on the model input parameters.� Coefficients from RM can be interpreted as changes in the model outcome due to a change in the corresponding input.� Decision models with two or more parameters that are highly correlated may present an important limitation of RM, as collinear variables do in multivariate regression. �Increased correlation in RM parameters may widen the confidence intervals of the coefficient estimates. We used a previously published model of treating herpes simplex encephalopathy, where the outcome is the expected utility of undergoing a brain biopsy.� We incorporated a correlation between two of the model parameters: the probability of dying because of biopsy (pDieBiopsy) and the probability of developing severe complications following biopsy (pSevereBiopsy).� We ran 10,000 PSA simulations for each hypothetical correlation level between these two parameters, varying the correlation value (rho) from 0 to 1.� We then examined the precision of the estimated RM coefficients at each value of rho.�   �� Results: �The figure shows the RM coefficients of pDieBiopsy and pSevereBiopsy (solid line), and their confidence intervals (gray region) for various correlation coefficient values.� The negative coefficients indicate that an increase in the value of either parameter results in a reduction in the expected utility of biopsy.� The confidence intervals maintains the same width at various correlation levels except for near exact correlation (i.e., when rho = 1).� We found similar results with other correlated parameters.�   �� Conclusion: We found RM to accurately predict parameter sensitivities except when these parameters are in near perfect correlation.� In these situations, including correlated parameters in the model may be unnecessary because one of the correlated parameters can be expressed as a function of the other one. Using standard regression diagnostics (e.g., the condition index) to identify situations of high multicollinearity may be appropriate when performing RM. ��