Eliciting Dirichlet and Gaussian copula prior distributions for multinomial models

In this paper, we propose novel methods of quantifying expert opinion about prior distributions for multinomial models. Two different multivariate priors are elicited using median and quartile assessments of the multinomial probabilities. First, we start by eliciting a univariate beta distribution for the probability of each category. Then we elicit the hyperparameters of the Dirichlet distribution, as a tractable conjugate prior, from those of the univariate betas through various forms of reconciliation using least-squares techniques. However, a multivariate copula function will give a more flexible correlation structure between multinomial parameters if it is used as their multivariate prior distribution. So, second, we use beta marginal distributions to construct a Gaussian copula as a multivariate normal distribution function that binds these marginals and expresses the dependence structure between them. The proposed method elicits a positive-definite correlation matrix of this Gaussian copula. The two proposed methods are designed to be used through interactive graphical software written in Java

Chronic airflow obstruction attributable to poverty in the multinational Burden of Obstructive Lung Disease (BOLD) study.

Poverty is strongly associated with all-cause and chronic obstructive pulmonary disease (COPD) mortality. Less is known about the contribution of poverty to spirometrically defined chronic airflow obstruction (CAO)-a key characteristic of COPD. Using cross-sectional data from an asset-based questionnaire to define poverty in 21 sites of the Burden of Obstructive Lung Disease study, we estimated the risk of CAO attributable to poverty. Up to 6% of the population over 40 years had CAO attributable to poverty. Understanding the relationship between poverty and CAO might suggest ways to improve lung health, especially in low-income and middle-income countries

Informing reimbursement decisions using cost-effectiveness modelling: a guide to the process of generating elicited priors to capture model uncertainties

In informing decisions, utilising health technology assessment (HTA), expert elicitation can provide valuable information, particularly where there is a less-developed evidence-base at the point of market access. In these circumstances, formal methods to elicit expert judgements are preferred to improve the accountability and transparency of the decision-making process, help reduce bias and the use of heuristics, and also provide a structure that allows uncertainty to be expressed. Expert elicitation is the process of transforming the subjective and implicit knowledge of experts into their quantifiable expressions. The use of expert elicitation in HTA is gaining momentum, and there is particular interest in its application to diagnostics, medical devices and complex interventions such as in public health or social care. Compared with the gathering of experimental evidence, elicitation constitutes a reasonably low-cost source of evidence. Given its inherent subject nature, the potential biases in elicited evidence cannot be ignored and, due to its infancy in HTA, there is little guidance to the analyst wishing to conduct a formal elicitation exercise. This article attempts to summarise the stages of designing and conducting an expert elicitation, drawing on key literature and examples, most of which are not in HTA. In addition, we critique their applicability to HTA, given its distinguishing features. There are a number of issues that the analyst should be mindful of, in particular the need to appropriately characterise the uncertainty associated with model inputs and the fact that there are often numerous parameters required, not all of which can be defined using the same quantities. This increases the need for the elicitation task to be as straightforward as possible for the expert to complete