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. 2012 Jan-Feb;32(1):56-69.
doi: 10.1177/0272989X11416988. Epub 2011 Oct 18.

Regression estimators for generic health-related quality of life and quality-adjusted life years

Anirban Basu  1   2 , Andrea Manca  3
Affiliations

Regression estimators for generic health-related quality of life and quality-adjusted life years

Anirban Basu et al. Med Decis Making. 2012 Jan-Feb.

Abstract

Purpose: To develop regression models for outcomes with truncated supports, such as health-related quality of life (HRQoL) data, and account for features typical of such data such as a skewed distribution, spikes at 1 or 0, and heteroskedasticity.

Methods: Regression estimators based on features of the Beta distribution. First, both a single equation and a 2-part model are presented, along with estimation algorithms based on maximum-likelihood, quasi-likelihood, and Bayesian Markov-chain Monte Carlo methods. A novel Bayesian quasi-likelihood estimator is proposed. Second, a simulation exercise is presented to assess the performance of the proposed estimators against ordinary least squares (OLS) regression for a variety of HRQoL distributions that are encountered in practice. Finally, the performance of the proposed estimators is assessed by using them to quantify the treatment effect on QALYs in the EVALUATE hysterectomy trial. Overall model fit is studied using several goodness-of-fit tests such as Pearson's correlation test, link and reset tests, and a modified Hosmer-Lemeshow test.

Results: The simulation results indicate that the proposed methods are more robust in estimating covariate effects than OLS, especially when the effects are large or the HRQoL distribution has a large spike at 1. Quasi-likelihood techniques are more robust than maximum likelihood estimators. When applied to the EVALUATE trial, all but the maximum likelihood estimators produce unbiased estimates of the treatment effect.

Conclusion: One and 2-part Beta regression models provide flexible approaches to regress the outcomes with truncated supports, such as HRQoL, on covariates, after accounting for many idiosyncratic features of the outcomes distribution. This work will provide applied researchers with a practical set of tools to model outcomes in cost-effectiveness analysis.

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Figures

Figure 1
Figure 1
Distribution of QALYs by treatment arms of Abdominal hysterectomy (AH) and Laparoscopic assisted hysterectomy (ALH) in the EVALUATE trial
Figure 2
Figure 2
Gallery of distributions for generic and disease-specific quality of life from selected clinical trials and observational studies.
Figure 3
Figure 3
Typical distributions for the data generating processes used in simulations.
Figure 4
Figure 4. Mean residuals across deciles of linear predictors (or predictor) across alternative estimators
*Deciles of linear predictor for OLS, MLE & QMLE; Deciles of predictions for two-part QMLE
See this image and copyright information in PMC

References

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