Regression Estimators for Generic Health-Related Quality of Life and Quality-Adjusted Life Years

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 one or zero, and heteroskedasticity. Methods Regression estimators based on features of the Beta distribution. Firstly, we present both a single equation and a two-part model, 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. Secondly, we present a simulation exercise 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, we assess the performance of the proposed estimators 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 Our 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 one. 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 two-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.

Mapping to Estimate Health-State Utility from Non–Preference-Based Outcome Measures: An ISPOR Good Practices for Outcomes Research Task Force Report

“…There is considerable evidence that these distributional features result in systematic bias when linear regression methods are used to analyze the EQ-5D-3L instrument, the most commonly studied patient reported outcome in the mapping literature 19,20,21 . Similar findings have been shown to apply to models like the Tobit 21 (designed to deal with limited dependent variables), two-part models 22 (which attempt to address the mass of observations seen at full health) and censored least absolute deviations models 23,24 .…”

“…One set of methods estimate the summary utility score directly. Amongst these direct methods, there is some empirical evidence to support the performance of two approaches: the limited dependent variable mixture model approach 21,14 and the beta-based regression approaches 19,25 . Both reflect the inherent limited nature of any utility score with the former also reflecting the other key characteristics of the utility distribution described above.…”

Variations in outcome and costs among NHS providers for common surgical procedures: econometric analyses of routinely collected data

“…The use of statistical methods that do not acknowledge the ordinal nature of the responses may result in logical inconsistencies, where outcomes are predicted that cannot possibly be derived from the questionnaire. 18,19 The first of our empirical analyses addresses these matters.…”

“…Both distributions exhibit typical characteristics of empirical EQ-5D distributions observed for a wide range of medical conditions, including multimodality, discontinuity and clustering at 1 ('full health'). 18,19 A total of 87.3% of patients report improvements in health as measured by the EQ-5D utility index, whereas 6.4% report deteriorations. Figure 5 shows hospital-level proportions of patients reporting each of the three potential responses (m = 1, 2, 3, i.e.…”

Economic and Health-Related Quality of Life Outcomes of Whiplash Associated Disorders

“…Thus two-part models, which explicitly accommodate the switch from "full health" to other states, are equally useful in dealing with health utilities as costs. Other, more complex regression methods such as beta regression have also been proposed, but there is little evidence that they lead to improvements in model fit 39 .…”