Evaluating the correlations of cost and utility parameters from summary statistics for probabilistic analysis in economic evaluations

Objectives: The correlations between economic modeling input parameters directly impact the variance and may impact the expected values of model outputs. However, correlation coefficients are not often reported in the literature. We aim to understand the correlations between model inputs for probabilistic analysis from summary statistics.

Methods: We provide proof that for correlated random variables X and Y (e.g. inpatient visits and outpatient visits), the Pearson correlation coefficients of sample means and samples are equal to each other ($corr\left(X,Y\right)=corr\left(\stackrel{-}{X},\stackrel{-}{Y}\right)$). Therefore, when studies report summary statistics of correlated parameters, we can quantify the correlation coefficient between parameters.

Results: We use examples to illustrate how to estimate the correlation coefficient between the incidence rates of non-severe and severe hypoglycemia events, and the common coefficient of five cost components for patients with diabetic foot ulcers. We further introduce three types of correlations for utilities and provide two examples to estimate the correlations for utilities based on published data. We also evaluate how correlations between cost parameters and utility parameters impact the cost-effectiveness results using a Markov model for major depression.

Conclusion: Incorporation of the correlations can improve the precision of cost-effectiveness results and increase confidence in evidence-based decision-making. Further empirical evidence is warranted.