MODELING PATIENT-LEVEL DEPENDENCE IN COST-EFFECTIVENESS ANALYSIS USING COPULAS

Purpose. A number of ways have been suggested to model dependence between cost and effectiveness. The availability of patient-level data enables us to model dependence at the patient level. Using Bayesian methods, we propose a way to model the dependence between cost and effectiveness with a copula, which is a function to construct a joint distribution from marginals allowing non-linear dependence.

 Methods. We developed a model based on the joint distribution of cost and outcome (survival), assuming the Weibull and log-normal marginals together with a Clayton copula. The model was applied to adults aged 25-74 from the NHANES I Epidemiologic Followup Study who experienced at least one hospital stay during the period 1971-1992 (N=7866). Cost was measured by hospital days per year and outcome is censored. Both cost and survival were conditioned on age, systolic blood pressure, and the number of major chronic conditions. Using the estimated parameters, incremental cost and effectiveness (DC and DE) were obtained for a hypothetical intervention for high blood pressure where patients aged 60 having no chronic conditions reduced blood pressure below 140. Two types of analysis were conducted: one took into account predictive uncertainty for an individual and is shown by the Bayesian predictive distribution.  The other focused on the expected outcomes for a group of patients shown by the expected values conditioned on the patient’s characteristics and parameters. Flat prior was assumed for the parameters.

 Results. Age, high blood pressure, and the number of the chronic conditions were negatively correlated with survival and positively correlated with hospital days per year. Based on the posterior mean of the dependence parameter in the Clayton copula (1.12,  S.D. 0.04), the correlation between DC and DE was -0.22 for the analysis at patient level, while it was 0 between the conditional expectation of DC and DE for a group of the same type of patients. Enormous variability was observed for an individual compared to the group (S.D. 6.48 vs. 0.08 for DC; 14.10 vs. 0.48 for DE.)

 Conclusions. It is possible to model dependence at patient level using copulas. The dependence influences results for an individual, which would be useful information for patient-level decision making. Further research is needed on heterogeneity among patients in the model and the prior assumption.