REGRESSION ESTIMATORS FOR QUALITY OF LIFE AND QUALITY-ADJUSTED LIFE YEARS

   Purpose: A large literature exists on developing appropriate regression models for cost data, primarily due to the idiosyncracies in the distribution of costs that makes application of additive models and ordinary least square (OLS) regressions inapplicable to such data. However, less attention has been paid to the appropriate use of regression estimators on the effectiveness side, especially quality of life data, despite sharing many of the idiosyncracies of the costs data. Developing regression models that address these characteristics of the quality of life (QOL) data is the main goal of this paper.

   Methods: We use beta distributions and develop regression models based on them. We present both a single equation estimator and a two-part estimator (to model the spikes at one or zero), and develop estimation algorithms based on maximum-likelihood, quasi-likelihood and Bayesian Markov-Chain Monte Carlo methods.   We define incremental and marginal effects of covariates on the mean QOL, and show how to estimate these effects and derive standard errors for them.   We present a variety of real-life applications to show the variations in QOL distribution that we encounter in practice.  One of those application comes from the UK multicentre EVALUATE hysterectomy trial.  We compare and contrast the results from our proposed (one-part) regression approach with those obtained from the widely used OLS regression in terms of estimating the treatment effect on the mean outcome after controlling for other covariates. Overall model fit is studied using the battery of goodness of fit tests.

   Results:  We find that the proposed method fit the QOL data much better than simple OLS regressions. The treatment effect is estimated to be 0.008 (SE = 0.011; 90% CI: -0.022, 0.038 ) QOL units under standard OLS regression whereas it is estimated to be 0.014 (SE = 0.0085; 90% CI: 0.00002, 0.028) used our proposed method.

   Conclusions: One and two-part Beta regression models provide flexible approaches to regress the mean of an outcome with truncated support such as quality of life on covariates. We find substantial benefits, both in terms of bias and efficiency, of these regressions over traditional OLS approaches in modeling QOL outcomes in real applications. We hope that this work will provide applied researchers with a practical set of tools to appropriately model outcomes in cost-effectiveness analysis.