Connected Hopf algebras and iterated Ore extensions

We investigate when a skew polynomial extension T = R[x; {\sigma}, {\delta}] of a Hopf algebra R admits a Hopf algebra structure, substantially generalising a theorem of Panov. When this construction is applied iteratively in characteristic 0 one obtains a large family of connected noetherian Hopf algebras of finite Gelfand-Kirillov dimension, including for example all enveloping algebras of finite dimensional solvable Lie algebras and all coordinate rings of unipotent groups. The properties of these Hopf algebras are investigated

Modelling the cost effectiveness of interferon beta and glatiramer acetate in the management of multiple sclerosis

OBJECTIVE: To evaluate the cost effectiveness of four disease modifying treatments (interferon betas and glatiramer acetate) for relapsing remitting and secondary progressive multiple sclerosis in the United Kingdom. DESIGN: Modelling cost effectiveness. SETTING: UK NHS. PARTICIPANTS: Patients with relapsing remitting multiple sclerosis and secondary progressive multiple sclerosis. MAIN OUTCOME MEASURES: Cost per quality adjusted life year gained. RESULTS: The base case cost per quality adjusted life year gained by using any of the four treatments ranged from £42 000 ($66 469; 61 630) to £98 000 based on efficacy information in the public domain. Uncertainty analysis suggests that the probability of any of these treatments having a cost effectiveness better than £20 000 at 20 years is below 20%. The key determinants of cost effectiveness were the time horizon, the progression of patients after stopping treatment, differential discount rates, and the price of the treatments. CONCLUSIONS: Cost effectiveness varied markedly between the interventions. Uncertainty around point estimates was substantial. This uncertainty could be reduced by conducting research on the true magnitude of the effect of these drugs, the progression of patients after stopping treatment, the costs of care, and the quality of life of the patients. Price was the key modifiable determinant of the cost effectiveness of these treatments

Estimating population cardinal health state valuation models from individual ordinal (rank) health state preference data

Ranking exercises have routinely been used as warm-up exercises within health state valuation surveys. Very little use has been made of the information obtained in this process. Instead, research has focussed upon the analysis of health state valuation data obtained using the visual analogue scale, standard gamble and time trade off methods. Thurstone’s law of comparative judgement postulates a stable relationship between ordinal and cardinal preferences, based upon the information provided by pairwise choices. McFadden proposed that this relationship could be modelled by estimating conditional logistic regression models where alternatives had been ranked. In this paper we report the estimation of such models for the Health Utilities Index Mark 2 and the SF-6D. The results are compared to the conventional regression models estimated from standard gamble data, and to the observed mean standard gamble health state valuations. For both the HUI2 and the SF-6D, the models estimated using rank data are broadly comparable to the models estimated on standard gamble data and the predictive performance of these models is close to that of the standard gamble models. Our research indicates that rank data has the potential to provide useful insights into community health state preferences. However, important questions remain

Estimating population cardinal health state valuation models from individual ordinal (rank) health state preference data

Ranking exercises have routinely been used as warm-up exercises within health state valuation surveys. Very little use has been made of the information obtained in this process. Instead, research has focussed upon the analysis of health state valuation data obtained using the visual analogue scale, standard gamble and time trade off methods. Thurstone’s law of comparative judgement postulates a stable relationship between ordinal and cardinal preferences, based upon the information provided by pairwise choices. McFadden proposed that this relationship could be modelled by estimating conditional logistic regression models where alternatives had been ranked. In this paper we report the estimation of such models for the Health Utilities Index Mark 2 and the SF-6D. The results are compared to the conventional regression models estimated from standard gamble data, and to the observed mean standard gamble health state valuations. For both the HUI2 and the SF-6D, the models estimated using rank data are broadly comparable to the models estimated on standard gamble data and the predictive performance of these models is close to that of the standard gamble models. Our research indicates that rank data has the potential to provide useful insights into community health state preferences. However, important questions remain.health state valuation; HUI-2; SF-6D

Estimating population cardinal health state valuation models from individual ordinal (rank) health state preference data

Ranking exercises have routinely been used as warm-up exercises within health state valuation surveys. Very little use has been made of the information obtained in this process. Instead, research has focussed upon the analysis of health state valuation data obtained using the visual analogue scale, standard gamble and time trade off methods. Thurstone’s law of comparative judgement postulates a stable relationship between ordinal and cardinal preferences, based upon the information provided by pairwise choices. McFadden proposed that this relationship could be modelled by estimating conditional logistic regression models where alternatives had been ranked. In this paper we report the estimation of such models for the Health Utilities Index Mark 2 and the SF-6D. The results are compared to the conventional regression models estimated from standard gamble data, and to the observed mean standard gamble health state valuations. For both the HUI2 and the SF-6D, the models estimated using rank data are broadly comparable to the models estimated on standard gamble data and the predictive performance of these models is close to that of the standard gamble models. Our research indicates that rank data has the potential to provide useful insights into community health state preferences. However, important questions remain

Calculating partial expected value of perfect information via Monte Carlo sampling algorithms

Partial expected value of perfect information (EVPI) calculations can quantify the value of learning about particular subsets of uncertain parameters in decision models. Published case studies have used different computational approaches. This article examines the computation of partial EVPI estimates via Monte Carlo sampling algorithms. The mathematical definition shows 2 nested expectations, which must be evaluated separately because of the need to compute a maximum between them. A generalized Monte Carlo sampling algorithm uses nested simulation with an outer loop to sample parameters of interest and, conditional upon these, an inner loop to sample remaining uncertain parameters. Alternative computation methods and shortcut algorithms are discussed and mathematical conditions for their use considered. Maxima of Monte Carlo estimates of expectations are biased upward, and the authors show that the use of small samples results in biased EVPI estimates. Three case studies illustrate 1) the bias due to maximization and also the inaccuracy of shortcut algorithms 2) when correlated variables are present and 3) when there is nonlinearity in net benefit functions. If relatively small correlation or nonlinearity is present, then the shortcut algorithm can be substantially inaccurate. Empirical investigation of the numbers of Monte Carlo samples suggests that fewer samples on the outer level and more on the inner level could be efficient and that relatively small numbers of samples can sometimes be used. Several remaining areas for methodological development are set out. A wider application of partial EVPI is recommended both for greater understanding of decision uncertainty and for analyzing research priorities

National or population level interventions addressing the social determinants of mental health - an umbrella review

Background: Social circumstances in which people live and work impact the population’s mental health. We aimed to synthesise evidence identifying effective interventions and policies that influence the social determinants of mental health at national or scaled population level. We searched five databases (Cochrane Library, Global Health, MEDLINE, EMBASE and PsycINFO) between Jan 1st 2000 and July 23rd 2019 to identify systematic reviews of population-level interventions or policies addressing a recognised social determinant of mental health and collected mental health outcomes. There were no restrictions on country, sub-population or age. A narrative overview of results is provided. Quality assessment was conducted using Assessment of Multiple Systematic Reviews (AMSTAR 2). This study was registered on PROSPERO (CRD42019140198). Results: We identified 20 reviews for inclusion. Most reviews were of low or critically low quality. Primary studies were mostly observational and from higher income settings. Higher quality evidence indicates more generous welfare benefits may reduce socioeconomic inequalities in mental health outcomes. Lower quality evidence suggests unemployment insurance, warm housing interventions, neighbourhood renewal, paid parental leave, gender equality policies, community-based parenting programmes, and less restrictive migration policies are associated with improved mental health outcomes. Low quality evidence suggests restriction of access to lethal means and multi-component suicide prevention programmes are associated with reduced suicide risk. Conclusion: This umbrella review has identified a small and overall low-quality evidence base for population level interventions addressing the social determinants of mental health. There are significant gaps in the evidence base for key policy areas, which limit ability of national policymakers to understand how to effectively improve population mental health

Estimating population cardinal health state valuation models from individual ordinal (rank) health state preference data

Ranking exercises have routinely been used as warm-up exercises within health state valuation surveys. Very little use has been made of the information obtained in this process. Instead, research has focussed upon the analysis of health state valuation data obtained using the visual analogue scale, standard gamble and time trade off methods. Thurstone’s law of comparative judgement postulates a stable relationship between ordinal and cardinal preferences, based upon the information provided by pairwise choices. McFadden proposed that this relationship could be modelled by estimating conditional logistic regression models where alternatives had been ranked. In this paper we report the estimation of such models for the Health Utilities Index Mark 2 and the SF-6D. The results are compared to the conventional regression models estimated from standard gamble data, and to the observed mean standard gamble health state valuations. For both the HUI2 and the SF-6D, the models estimated using rank data are broadly comparable to the models estimated on standard gamble data and the predictive performance of these models is close to that of the standard gamble models. Our research indicates that rank data has the potential to provide useful insights into community health state preferences. However, important questions remain