COST-EFFECTIVENESS ANALYSES THAT USE RANDOMIZED TRIALS: INSTRUMENTAL VARIABLE APPROACHES FOR HANDLING NON-COMPLIANCE

Purpose:

In cost-effectiveness analyses (CEA) alongside randomized controlled trials (RCTs) that have non-compliance with the treatment assigned, studies typically report Intention-to-treat (ITT) and Per Protocol (PP) analyses. However, a PP analysis is likely to provide a biased estimate of the complier average causal effect (CACE). We propose an instrumental variable (IV) approach for providing unbiased CACEs in CEA.

Method:

Instrumental variable (IV) estimation can provide unbiased CACEs if the standard identification assumptions are satisfied, but cost-effectiveness data raises important additional challenges. In particular, IV methods need recognise the correlation between cost and health outcomes. We consider IV approaches estimated by two-stage least squares (2SLS) regression; the first stage regression estimates the effect of the treatment assigned on that received, and the second stage regression includes the predicted treatment received  as an independent variable in the outcome models.  Initially we estimate incremental costs and outcomes by separate univariate 2SLS regressions assuming the endpoints are uncorrelated. By contrast, our proposed method is a bivariate 2SLS regression, which recognises the correlation between costs and outcomes. We fit this model by maximum likelihood with standard errors estimated by a non-parametric bootstrap procedure that resamples pairs of costs and effects to acknowledge the correlation, and also recognises the uncertainty in both stages of the estimation procedure.

We illustrate these approaches in a reanalysis of the REFLUX study, where about one third of patients randomized to surgery received medical management. We also considered the relative performance of the methods in a simulation study, where costs and outcomes are assumed Normally distributed, correlated (-0.40), and there is 30% non-compliance. We report the bias and confidence interval coverage in estimating Incremental Net Benefits (INBs).

Result:

In the REFLUX study, the INBs [SE] estimated according to ITT and PP were £4267 (4379)and £3063 [4718]. The IV approaches reported estimated INBs of £5817 [5924] (univariate) and £5723 [5853] (joint estimation method). The simulation found that both IV methods provided unbiased INB estimates, and coverage levels that were close to the nominal level for the univariate approach (94.6%), but too conservative for the joint approach (97.8%).

Conclusion:

This bivariate approach can provide unbiased estimates of the cost-effectiveness of the treatment received. The current bootstrap implementation overestimates the variance, and may require a shrinkage correction.