Mónica Hernández Alava

Tails from the Peak District: Adjusted Limited Dependent Variable Mixture Models of EQ-5D Questionnaire Health State Utility Values

OBJECTIVES Health utility data generated by using the EuroQol five-dimensional (EQ-5D) questionnaire are right bounded at 1 with a substantial gap to the next set of observations, left bounded, and multimodal. These features present challenges to the estimation of the effect of clinical and socioeconomic characteristics on health utilities. Our objective was to develop and demonstrate an appropriate method for dealing with these features. METHODS We developed a statistical model that incorporates an adjusted limited dependent variable approach to reflect the upper bound and the large gap in feasible EQ-5D questionnaire values. Further flexibility was then gained by adopting a mixture modeling framework to address the multimodality of the EQ-5D questionnaire distribution. We compared the performance of these approaches with that of those frequently adopted in the literature (linear and Tobit models) by using data from a clinical trial of patients with rheumatoid arthritis. RESULTS We found that three latent classes are appropriate in estimating EQ-5D questionnaire values from function, pain, and sociodemographic factors. Superior performance of the adjusted limited dependent variable mixture model was achieved in terms of Akaike and Bayesian information criteria, root mean square error, and mean absolute error. Unlike other approaches, the adjusted limited dependent variable mixture model fits the data well at high EQ-5D questionnaire levels and cannot predict unfeasible EQ-5D questionnaire values. CONCLUSIONS The distribution of the EQ-5D questionnaire is characterized by features that raise statistical challenges. It is well known that standard approaches do not perform well for this reason. This article developed an appropriate method to reflect these features by combining limited dependent variable and mixture modeling and demonstrated superior performance in a rheumatoid arthritis setting. Further refinement of the general framework and testing in other data sets are warranted. Analysis of utility data should apply methods that recognize the distributional features of the data.

The relationship between EQ-5D, HAQ and pain in patients with rheumatoid arthritis

Objective. This study aims to provide robust estimates of EQ-5D as a function of the HAQ and pain in patients with RA. Method. Repeated observations were made of patients diagnosed with RA in a US observational cohort (n = 100 398 observations) who provided data on HAQ, pain on a visual analogue scale and the EQ-5D questionnaire. We used a bespoke statistical method based on mixture modelling to appropriately reflect the characteristics of the EQ-5D instrument and to compare this with results from standard multiple regression. Results. EQ-5D can be predicted from summary HAQ and pain scores. We identify four different classes of respondents who differ in terms of disease severity. Unlike the multiple regression, the mixture model exhibits very good fit to the data and does not suffer from problems of bias or predict values outside the feasible range. Conclusion. It is appropriate to model the relationship between HAQ and EQ-5D but only if suitable statistical methods are applied. Linear models underestimate the quality-adjusted life year benefits, and therefore the cost-effectiveness, of therapies. The bespoke mixture model approach outlined here overcomes this problem. The addition of pain as an explanatory variable greatly improves the estimates. Reimbursement agencies rely on these types of analyses when formulating policy on the use of new drug therapies. Clinicians as well as economists should be concerned with these issues.

A comparison of direct and indirect methods for the estimation of health utilities from clinical outcomes.

Background: Analysts frequently estimate health state utility values from other outcomes. Utility values like EQ-5D have characteristics that make standard statistical methods inappropriate. We have developed a bespoke, mixture model approach to directly estimate EQ-5D. An indirect method, “response mapping,” first estimates the level on each of the 5 dimensions of the EQ-5D and then calculates the expected tariff score. These methods have never previously been compared. Methods: We use a large observational database from patients with rheumatoid arthritis (N = 100,398). Direct estimation of UK EQ-5D scores as a function of the Health Assessment Questionnaire (HAQ), pain, and age was performed with a limited dependent variable mixture model. Indirect modeling was undertaken with a set of generalized ordered probit models with expected tariff scores calculated mathematically. Linear regression was reported for comparison purposes. Impact on cost-effectiveness was demonstrated with an existing model. Results: The linear model fits poorly, particularly at the extremes of the distribution. The bespoke mixture model and the indirect approaches improve fit over the entire range of EQ-5D. Mean average error is 10% and 5% lower compared with the linear model, respectively. Root mean squared error is 3% and 2% lower. The mixture model demonstrates superior performance to the indirect method across almost the entire range of pain and HAQ. These lead to differences in cost-effectiveness of up to 20%. Conclusions: There are limited data from patients in the most severe HAQ health states. Modeling of EQ-5D from clinical measures is best performed directly using the bespoke mixture model. This substantially outperforms the indirect method in this example. Linear models are inappropriate, suffer from systematic bias, and generate values outside the feasible range.

EQ-5D-5L versus EQ-5D-3L: The Impact on Cost Effectiveness in the United Kingdom

OBJECTIVES To model the relationship between the three-level (3L) and the five-level (5L) EuroQol five-dimensional questionnaire and examine how differences have an impact on cost effectiveness in case studies. METHODS We used two data sets that included the 3L and 5L versions from the same respondents. The EuroQol Group data set (n = 3551) included patients with different diseases and a healthy cohort. The National Data Bank data set included patients with rheumatoid disease (n = 5205). We estimated a system of ordinal regressions in each data set using copula models to link responses of the 3L instrument to those of the 5L instrument and its UK tariff, and vice versa. Results were applied to nine cost-effectiveness studies. RESULTS Best-fitting models differed between the EuroQol Group and the National Data Bank data sets in terms of the explanatory variables, copulas, and coefficients. In both cases, the coefficients of the covariates and latent factors between the 3L and the 5L instruments were significantly different, indicating that moving between instruments is not simply a uniform re-alignment of the response levels for most dimensions. In the case studies, moving from the 3L to the 5L caused a decrease of up to 87% in incremental quality-adjusted life-years gained from effective technologies in almost all cases. Incremental cost-effectiveness ratios increased, often substantially. Conversely, one technology with a significant mortality gain saw increased incremental quality-adjusted life-years. CONCLUSIONS The 5L shifts mean utility scores up the utility scale toward full health and compresses them into a smaller range, compared with the 3L. Improvements in quality of life are valued less using the 5L than using the 3L. The 3L and the 5L can produce substantially different estimates of cost effectiveness. There is no simple proportional adjustment that can be made to reconcile these differences.

Modelling the relationship between the WOMAC osteoarthritis index and EQ-5D

ObjectiveEconomic evaluation typically is conducted using health state utilities to estimate treatment benefits. However, such outcomes are often missing from studies of clinical effectiveness. This study aims to bridge that gap by providing appropriate methods to link values from the Western Ontario and McMaster Universities Osteoarthritis Index (WOMAC) to the EQ-5D utility instrument.MethodPatients from a large registry of Spanish patients (n = 7072 observations) with knee or hip osteoarthritis who completed both WOMAC and EQ-5D was used. A mixture model approach was used based on distributions bespoke to the EQ-5D UK value set to estimate EQ-5D as a function of WOMAC pain, stiffness and function subscores.ResultsA five class mixture model provides very close fit to the observed data at all levels of disease severity. The overall mean (0.542 vs 0.542), median (0.620 vs 0.636) and the percentage of observations at full health (15 vs 14.8) were very similar between the observed data and the estimated model respectively. Stiffness has limited relationship to EQ-5D, whereas functional disability and pain are strong predictors.ConclusionEQ-5D can be reliably estimated from WOMAC subscale scores without any systematic bias using these results.

Cost-effectiveness of treatment strategies using combination disease-modifying anti-rheumatic drugs and glucocorticoids in early rheumatoid arthritis

OBJECTIVE The aim of this study was to estimate the cost-effectiveness of combination DMARDs with short-term glucocorticoids in early active RA using data from the 2-year Combination of Anti-Rheumatic Drugs in Early RA (CARDERA) trial. METHODS CARDERA enrolled 467 patients with active RA of <24-months duration. All patients received MTX; half received step-down prednisolone and half ciclosporin in a placebo-controlled factorial design. Differences in mean costs and quality-adjusted life-years (QALYs) over 24-months follow-up were estimated using patient-level data from a UK health service perspective and 2011-12 costs. RESULTS Two-year costs for each treatment strategy showed primary care costs were negligible across all groups. Drug costs were lowest with MTX/ciclosporin and triple therapy. Hospital costs were lowest with MTX/prednisolone and triple therapy. Triple therapy was least costly and most effective; it dominated all other strategies. At positive values for a QALY in the typical UK range (£20 000-30 000) the probability that triple therapy was the most cost-effective strategy was 0.9. Results were robust to methods used to impute missing data. CONCLUSION Intensive treatment of early RA with triple therapy (two DMARDs and short-term glucocorticoids) is both clinically effective and cost effective.

Good Practice Guidelines for the use of Statistical Regression Models in Economic Evaluations

Decision-analytic models (DAMs) used to evaluate the cost effectiveness of interventions are pivotal sources of evidence used in economic evaluations. Parameter estimates used in the DAMs are often based on the results of a regression analysis, but there is little guidance relating to these. This study had two objectives. The first was to identify the frequency of use of regression models in economic evaluations, the parameters they inform, and the amount of information reported to describe and support the analyses. The second objective was to provide guidance to improve practice in this area, based on the review. The review concentrated on a random sample of economic evaluations submitted to the UK National Institute for Health and Clinical Excellence (NICE) as part of its technology appraisal process. Based on these findings, recommendations for good practice were drafted, together with a checklist for critiquing reporting standards in this area. Based on the results of this review, statistical regression models are in widespread use in DAMs used to support economic evaluations, yet reporting of basic information, such as the sample size used and measures of uncertainty, is limited. Recommendations were formed about how reporting standards could be improved to better meet the needs of decision makers. These recommendations are summarised in a checklist, which may be used by both those conducting regression analyses and those critiquing them, to identify what should be reported when using the results of a regression analysis within a DAM.

Common Scale Valuations across Different Preference-Based Measures: Estimation Using Rank Data

Background. Different preference-based measures (PBMs) used to estimate quality-adjusted life years (QALYs) provide different utility values for the same patient. Differences are expected since values have been obtained using different samples, valuation techniques, and descriptive systems. Previous studies have estimated the relationship between pairs of PBMs using patient self-reported data. However, there is a need for an approach capable of generating values directly on a common scale for a range of PBMs using the same sample of general population respondents and valuation technique but keeping the advantages of the different descriptive systems. Methods. General public survey data (n = 501) in which respondents ranked health states described using subsets of 6 PBMs were analyzed. We develop a new model based on the mixed logit to overcome 2 key limitations of the standard rank-ordered logit model—namely, the unrealistic choice pattern (independence of irrelevant alternatives) and the independence of repeated observations. Results. There are substantial differences in the estimated parameters between the 2 models (mean difference 0.07), leading to different orderings across the measures. Estimated values for the best states described by different PBMs are substantially and significantly different using the standard model, unlike our approach, which yields more consistent results. Limitations. Data come from an exploratory study that is relatively small both in sample size and coverage of health states. Conclusions. This study develops a new, flexible econometric model specifically designed to reflect appropriately the features of rank data. Results support the view that the standard model is not appropriate in this setting and will yield very different and apparently inconsistent results. PBMs can be compared using a common scale by implementation of this new approach.

The effects of breastfeeding on childhood BMI: a propensity score matching approach

Background Many studies have found a statistical association between breastfeeding and childhood adiposity. This paper investigates whether breastfeeding has an effect on subsequent childhood body mass index (BMI) using propensity scores to account for confounding. Methods We use data from the Millennium Cohort Study, a nationally representative UK cohort survey, which contains detailed information on infant feeding and childhood BMI. Propensity score matching is used to investigate the mean BMI in children breastfed exclusively and partially for different durations of time. Results We find statistically significant influences of breastfeeding on childhood BMI, particularly in older children, when breastfeeding is prolonged and exclusive. At 7 years, children who were exclusively breastfed for 16 weeks had a BMI 0.28 kg/m2 (95% confidence interval 0.07 to 0.49) lower than those who were never breastfed, a 2% reduction from the mean BMI of 16.6 kg/m2. Conclusions For this young cohort, even small effects of breastfeeding on BMI could be important. In order to reduce BMI, breastfeeding should be encouraged as part of wider lifestyle intervention. This evidence could help to inform public health bodies when creating public health guidelines and recommendations.

Development of Methods for the Mapping of Utilities Using Mixture Models: Mapping the AQLQ-S to the EQ-5D-5L and the HUI3 in Patients with Asthma

Background Studies have shown that methods based on mixture models work well when mapping clinical to preference-based methods. Objectives To develop these methods in different ways and to compare performance in a case study. Methods Data from 856 patients with asthma allowed mapping between the Asthma Quality of Life Questionnaire and both the five-level EuroQol five-dimensional questionnaire (EQ-5D-5L) and the health utilities index mark 3 (HUI3). Adjusted limited dependent variable mixture models and beta-based mixture models were estimated. Optional inclusion of the gap between full health and the next value as well as a mass point at the next feasible value were explored. Results In all cases, model specifications formally modeling the gap between full health and the next feasible value were an improvement on those that did not. Mapping to the HUI3 required more components in the mixture models than did mapping to the EQ-5D-5L because of its uneven distribution. The optimal beta-based mixture models mapping to the HUI3 included a probability mass at the utility value adjacent to full health. This is not the case when estimating the EQ-5D-5L, because of the low proportion of observations at this point. Conclusions Beta-based mixture models marginally outperformed adjusted limited dependent variable mixture models with the same number of components in this data set. Nevertheless, they require a larger number of parameters and longer estimation time. Both mixture model types closely fit both EQ-5D-5L and HUI data. Standard mapping approaches typically lead to biased estimates of health gain. The mixture model approaches exhibit no such bias. Both can be used with confidence in applied cost-effectiveness studies. Future mapping studies in other disease areas should consider similar methods.