Multilevel modelling of cost data: an application to thrombolysis and primary angioplasty in the UK NHS

Cost data are frequently collected from several locations and tend to be non negative and skewed. Generalised linear multilevel models provide a means of dealing with each of these issues. This paper compares several statistical models within this class using data drawn from an observational study of 3,000 patients treated for heart attack in 15 UK NHS hospitals. A number of alternative link functions and covariates were considered. We demonstrate that whilst it is important to take account of clustering in the data, the precise manner in which this is done is equally important. Models which allow for correlation between the random effects components and heteroskedasticity across all hospitals performed best in terms of model fit and made substantial di¤erences to cost estimates

Tails from the Peak District: adjusted censored mixture models of EQ-5D health state utility values

Health state utility data generated using the EQ-5D instrument are typically right bounded at one with a substantial gap to the next set of observations, left bounded by some negative value, and are multi modal. These features present challenges to the estimation of the e¤ect of clinical and socioeconomic characteristics on health utilities. We present an adjusted censored model and then use this in a flexible, mixture modelling framework to address these issues. We demonstrate superior performance of this model compared to linear regression and Tobit censored regression using a dataset from repeated observations of patients with rheumatoid arthritis. We �nd that three latent classes are appropriate in estimating EQ-5D from function, pain and sociodemographic factors. Analysis of utility data should apply methods that recognise the distributional features of the data

Tails from the Peak District: adjusted censored mixture models of EQ-5D health state utility values

Health state utility data generated using the EQ-5D instrument are typically right bounded at one with a substantial gap to the next set of observations, left bounded by some negative value, and are multi modal. These features present challenges to the estimation of the e¤ect of clinical and socioeconomic characteristics on health utilities. We present an adjusted censored model and then use this in a flexible, mixture modelling framework to address these issues. We demonstrate superior performance of this model compared to linear regression and Tobit censored regression using a dataset from repeated observations of patients with rheumatoid arthritis. We �nd that three latent classes are appropriate in estimating EQ-5D from function, pain and sociodemographic factors. Analysis of utility data should apply methods that recognise the distributional features of the data

Tails from the Peak District: adjusted censored mixture models of EQ-5D health state utility values

Health state utility data generated using the EQ-5D instrument are typically right bounded at one with a substantial gap to the next set of observations, left bounded by some negative value, and are multi modal. These features present challenges to the estimation of the e¤ect of clinical and socioeconomic characteristics on health utilities. We present an adjusted censored model and then use this in a flexible, mixture modelling framework to address these issues. We demonstrate superior performance of this model compared to linear regression and Tobit censored regression using a dataset from repeated observations of patients with rheumatoid arthritis. We �nd that three latent classes are appropriate in estimating EQ-5D from function, pain and sociodemographic factors. Analysis of utility data should apply methods that recognise the distributional features of the data

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

Background: Analysts often need to estimate health state utility values as a function of other outcome measures. Utility values like EQ-5D have several unusual characteristics that make standard statistical methods inappropriate. We have developed a bespoke approach based on mixture models to directly estimate EQ-5D. An indirect method, “response mapping”, first estimates the level on each of the five dimensions of the EQ-5D descriptive system and then calculates the expected tariff score. These methods have never previously been compared. Methods: We use a large observational database of patients diagnosed with Rheumatoid Arthritis (n=100,398 observations). Direct estimation of UK EQ-5D scores as a function of Health Assessment Questionnaire (HAQ), pain and age was performed using a limited dependent variable mixture model. Indirect modelling was undertaken using a set of generalized ordered probit models with expected tariff scores calculated mathematically. Linear regression was reported for comparison purposes. Results: The linear model fits poorly, particularly at the extremes of the distribution. Both the bespoke mixture model and the generalized ordered probit approach offer improvements in fit over the entire range of EQ-5D. Mean average error is 10% and 5% lower compared to 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. Limitations: There is limited data from patients in the most extreme HAQ health states. Conclusions: Modelling 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

Development of methods for the mapping of utilities using mixture models: An application to asthma

Objectives: To develop methods for mapping to preference-based measures using mixture model approaches. These methods are compared to map from the Asthma Quality of Life Questionnaire (AQLQ) to both EQ5D-5L and HUI-3 as the target health utility measures in an international dataset. Methods: Data from 856 patients with asthma collected as part of the Multi-Instrument Comparison (MIC) international project were used. Adjusted limited dependent variable mixture models (ALDVMMs) and beta-regression based mixture models were estimated. Optional inclusion of the gap between full health and the next value, and a mass point at the next feasible value were explored. Response-mapping could not be implemented due to missing data. Results: In all cases, model specifications which formally modelled the gap between full health and the next value were an improvement on those which did not. Mapping to HUI3 required more components in the mixture models than mapping to EQ5D-5L due to its uneven distribution. The optimal beta-based mixture models mapping to HUI3 included a probability mass at the utility value adjacent to full health. This is not the case when estimating EQ5D-5L, due to the low proportion of observations at this point. Conclusion: The beta-based mixture models marginally outperformed ALDVMM in this dataset when comparing models with the same number of components. This is at the expense of requiring a larger number of parameters and estimation time. Both model types are able to closely fit the data without biased characteristic of many mapping approaches. Skilled judgment is critical in determining the optimal model. Caution is required in ensuring a truly global maximum likelihood has been identified

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

Objective Economic 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. Method Patients 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. Results A 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. Conclusion EQ-5D can be reliably estimated from WOMAC subscale scores without any systematic bias using these results

Fitting adjusted limited dependent variable mixture models to EQ-5D

In this article, we describe the aldvmm command for fitting adjusted limited dependent variable mixture models to either UK or U.S. tariff EQ-5D data. We present and explain the command and postestimation command through examples. The aldvmm command requires use of Stas Kolenikov’s simulated annealing package (simann()), which can be easily installed by typing net install simann.pkg, from(http://web.missouri.edu/~kolenikovs/stata)

Misdiagnosis, Mistreatment, and Harm - When Medical Care Ignores Social Forces.

The Case Studies in Social Medicine demonstrate that when physicians use only biologic or individual behavioral interventions to treat diseases that stem from or are exacerbated by social factors, we risk harming the patients we seek to serve