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

How much does teenage parenthood affect long term outcomes? A systematic review.

Background: The rates of teenage pregnancy in the UK are relatively high. Although early entry to parenthood can be a positive experience, most studies find large adverse effects on long term outcomes for the mother, child and father, in addition to being costly for the NHS. This is why the government launched its Teenage Pregnancy Strategy in 1999. However, there is growing evidence that teenage pregnancy might be mainly an indicator of disadvantage which is the underlying cause of the negative outcomes. Methods: A systematic literature review was undertaken of studies which used a UK dataset to quantify any long term outcomes of a teenage birth upon the mother, father or child. Studies were included if they used appropriate methods to isolate the causal effect of early parenthood. The databases searched included Medline, Cochrane, EconLit and Web of Science. Results: Six studies were identified by the review; five studies considered the mother’s socioeconomic outcomes, one study reported the child’s outcomes, and no studies met the inclusion criteria for the father’s outcomes. The studies suggested that early motherhood accounts for relatively few of the negative long term socioeconomic outcomes and it is predominantly an indicator of a disadvantaged family background. Conclusion: Limited evidence is available to understand the long term outcomes associated with teenage birth within the UK for the mother, father and child. Current econometric studies suggest that effective interventions to prevent teenage pregnancies will not eradicate the poorer long term socioeconomic outcomes often associated with early motherhood. Thus policy should focus on reducing initial disadvantage in addition to preventing teenage pregnancy. Additional econometric analyses around the mothers’, fathers’ and children’s long term socioeconomic and health-related outcomes would be valuable

Enabling QALY estimation in mental health trials and care settings: mapping from the PHQ-9 and GAD-7 to the ReQoL-UI or EQ-5D-5L using mixture models

Purpose Patient-reported outcome measures (PROMs) are commonly collected in trials and some care settings, but preference-based PROMs required for economic evaluation are often missing. For these situations, mapping models are needed to predict preference-based (aka utility) scores. Our objective is to develop a series of mapping models to predict preference-based scores from two mental health PROMs: Patient Health Questionnaire-9 (PHQ-9; depression) and Generalised Anxiety Questionnaire-7 (GAD-7; anxiety). We focus on preference-based scores for the more physical-health-focussed EQ-5D (five-level England and US value set, and three-level UK cross-walk) and more mental-health-focussed Recovering Quality-of-Life Utility Index (ReQoL-UI). Methods We used trial data from the Improving Access to Psychological Therapies (IAPT) mental health services (now called NHS Talking Therapies), England, with a focus on people with depression and/or anxiety caseness. We estimated adjusted limited dependent variable or beta mixture models (ALDVMMs or Betamix, respectively) using GAD-7, PHQ-9, age, and sex as covariates. We followed ISPOR mapping guidance, including assessing model fit using statistical and graphical techniques. Results Over six data collection time-points between baseline and 12-months, 1340 observed values (N ≤ 353) were available for analysis. The best fitting ALDVMMs had 4-components with covariates of PHQ-9, GAD-7, sex, and age; age was not a probability variable for the final ReQoL-UI mapping model. Betamix had practical benefits over ALDVMMs only when mapping to the US value set. Conclusion Our mapping functions can predict EQ-5D-5L or ReQoL-UI related utility scores for QALY estimation as a function of variables routinely collected within mental health services or trials, such as the PHQ-9 and/or GAD-7

Estimating informal care inputs associated with EQ-5D for use in economic evaluation.

OBJECTIVES: This paper estimates informal care need using the health of the patient. The results can be used to predict changes in informal care associated with changes in the health of the patient measured using EQ-5D. METHODS: Data was used from a prospective survey of inpatients containing 59,512 complete responses across 44,494 individuals. The number of days a friend or relative has needed to provide care or help with normal activities in the last 6 weeks was estimated using the health of the patient measured by EQ-5D, ICD chapter and other health and sociodemographic data. A variety of different regression models were estimated that are appropriate for the distribution of the informal care dependent variable, which has large spikes at 0 (zero informal care) and 42 days (informal care every day). RESULTS: The preferred model that most accurately predicts the distribution of the data is the zero-inflated negative binomial with variable inflation. The results indicate that improving the health of the patient reduces informal care need. The relationship between ICD chapter and informal care need is not as clear. CONCLUSIONS: The preferred zero-inflated negative binomial with variable inflation model can be used to predict changes in informal care associated with changes in the health of the patient measured using EQ-5D and these results can be applied to existing datasets to inform economic evaluation. Limitations include recall bias and response bias of the informal care data, and restrictions of the dataset to exclude some patient groups

Catalogues of EQ-5D-3L health-related quality of life scores for 199 chronic conditions and health risks for use in the UK and the USA

Background Health-related quality of life (HRQoL) measures are essential in economic evaluation, but sometimes primary sources are unavailable, and information from secondary sources is required. Existing HRQoL UK/US catalogues are based on earlier diagnosis classification systems, amongst other issues. A recently published Danish catalogue merged EQ-5D-3L data from national health surveys with national registers containing patient information on ICD-10 diagnoses, healthcare activities and socio-demographics. Aims To provide (1) UK/US EQ-5D-3L-based HRQoL utility population catalogues for 199 chronic conditions on the basis of ICD-10 codes and health risks and (2) regression models controlling for age, sex, comorbidities and health risks to enable predictions in other populations. Methods UK and US EQ-5D-3L value sets were applied to the EQ-5D-3L responses of the Danish dataset and modelled using adjusted limited dependent variable mixture models (ALDVMMs). Results Unadjusted mean utilities, percentiles and adjusted disutilities based on two ALDVMMs with different control variables were provided for both countries. Diseases from groups M, G, and F consistently had the smallest utilities and the largest negative disutilities: fibromyalgia (M797), sclerosis (G35), rheumatism (M790), dorsalgia (M54), cerebral palsy (G80-G83), post-traumatic stress disorder (F431), dementia (F00-2), and depression (F32, etc.). Risk factors, including stress, loneliness, and BMI30+, were also associated with lower HRQoL. Conclusions This study provides comprehensive catalogues of UK/US EQ-5D-3L HRQoL utilities. Results are relevant in cost-effectiveness analysis, for NICE submissions, and for comparing and identifying facets of disease burden

Estimating the relationship between EQ-5D-5L and EQ-5D-3L: results from a UK population study

Objectives The aim of this study was to estimate the relationship between EQ-5D-3L and EQ-5D-5L, in both directions, using a single model. Methods An online survey containing both variants of EQ-5D, with randomised ordering, was administered to a large UK sample in 2020. A joint statistical model of the ten EQ-5D responses (five at 5L, five at 3L), using a multi-equation ordinal regression framework was estimated. The joint model ensures mappings in either direction are fully consistent with the information in the sample and satisfy Bayes’ rule. Three extensions enhance model flexibility: a copula specification allows differing degrees of correlation between the 3L and 5L responses at the upper and lower extremes of health; a normal mixture residual distribution gives flexibility in the distributional form of responses; and a common factor captures correlations in responses across the five dimensions. Results Almost 50,000 responses were received. Thirty-five percent of respondents reported an existing medical condition. Ninety percent of possible 3L and 43% of possible 5L health states were observed. The preferred model specification includes age, sex and the responses to the EQ-5D instrument. Close alignment to the observed data was observed both in within-sample and out-of-sample comparisons. Conclusion The results from this study provide a means of translating evidence to or from EQ-5D-3L to or from 5L based on a large-scale UK population survey with randomised ordering. Mapping can be performed either using descriptive system responses, individual utility scores or summary statistics