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

Valuation of preference-based measures: Can existing preference data be used to select a smaller sample of health states?

Background Different countries have different preferences regarding health, and there are different value sets for popular preference-based measures across different countries. However, the cost of collecting data to generate country-specific value sets can be prohibitive for countries with smaller population size or low- and middle-income countries (LMIC). This paper explores whether existing preference weights could be modelled alongside a small own country valuation study to generate representative estimates. This is explored using a case study modelling UK data alongside smaller US samples to generate US estimates. Methods We analyse EQ-5D valuation data derived from representative samples of the US and UK populations using time trade-off to value 42 health states. A nonparametric Bayesian model was applied to estimate a US value set using the full UK dataset and subsets of the US dataset for 10, 15, 20 and 25 health states. Estimates are compared to a US value set estimated using US values alone using mean predictions and root mean square error. Results The results suggest that using US data elicited for 20 health states alongside the existing UK data produces similar predicted mean valuations and RMSE as the US value set, while 25 health states produce the exact features. Conclusions The promising results suggest that existing preference data could be combined with a small valuation study in a new country to generate preference weights, making own country value sets more achievable for LMIC. Further research is encouraged

Use of Bayesian methods to model the SF-6D health state preference based data

Abstract Background Conventionally, models used for health state valuation data have been frequentists. Recently a number of researchers have investigated the use of Bayesian methods in this area. The aim of this paper is to put on the map of modelling a new approach to estimating SF-6D health state utility values using Bayesian methods. This will help health care professionals in deriving better health state utilities of the original UK SF-6D for their specialized applications. Methods The valuation study is composed of 249 SF-6D health states valued by a representative sample of the UK population using the standard gamble technique. Throughout this paper, we present four different models, including one simple linear regression model and three random effect models. The predictive ability of these models is assessed by comparing predicted and observed mean SF-6D scores, R2/adjusted R2 and RMSE. All analyses were carried out using Bayesian Markov chain Monte Carlo (MCMC) simulation methods freely available in the specialist software WinBUGS. Results The random effects model with interaction model performs best under all criterions, with mean predicted error of 0.166, R2/adjusted R2 of 0.683 and RMSE of 0.218. Conclusions The Bayesian models provide flexible approaches to estimate mean SF-6D utility estimates, including characterizing the full range of uncertainty inherent in these estimates. We hope that this work will provide applied researchers with a practical set of tools to appropriately model outcomes in cost-effectiveness analysis

Analysis of SF-6D Health State Utility Scores: Is Beta Regression Appropriate?

Background: Typically, modeling of health-related quality of life data is often troublesome since its distribution is positively or negatively skewed, spikes at zero or one, bounded and heteroscedasticity. Objectives: In the present paper, we aim to investigate whether Bayesian beta regression is appropriate for analyzing the SF-6D health state utility scores and respondent characteristics. Methods: A sample of 126 Lebanese members from the American University of Beirut valued 49 health states defined by the SF-6D using the standard gamble technique. Three different models were fitted for SF-6D via Bayesian Markov chain Monte Carlo (MCMC) simulation methods. These comprised a beta regression, random effects and random effects with covariates. Results from applying the three Bayesian beta regression models were reported and compared based on their predictive ability to previously used linear regression models, using mean prediction error (MPE), root mean squared error (RMSE) and deviance information criterion (DIC). Results: For the three different approaches, the beta regression model was found to perform better than the normal regression model under all criteria used. The beta regression with random effects model performs best, with MPE (0.084), RMSE (0.058) and DIC (−1621). Compared to the traditionally linear regression model, the beta regression provided better predictions of observed values in the entire learning sample and in an out-of-sample validation. Conclusions: Beta regression provides a flexible approach to modeling health state values. It also accounted for the boundedness and heteroscedasticity of the SF-6D index scores. Further research is encouraged

Use of Bayesian Markov Chain Monte Carlo Methods to Model Kuwait Medical Genetic Center Data: An Application to Down Syndrome and Mental Retardation

Logit, probit and complementary log-log models are the most widely used models when binary dependent variables are available. Conventionally, these models have been frequentists. This paper aims to demonstrate how such models can be implemented relatively quickly and easily from a Bayesian framework using Gibbs sampling Markov chain Monte Carlo simulation methods in WinBUGS. We focus on the modeling and prediction of Down syndrome (DS) and Mental retardation (MR) data from an observational study at Kuwait Medical Genetic Center over a 30-year time period between 1979 and 2009. Modeling algorithms were used in two distinct ways; firstly, using three different methods at the disease level, including logistic, probit and cloglog models, and, secondly, using bivariate logistic regression to study the association between the two diseases in question. The models are compared in terms of their predictive ability via R2, adjusted R2, root mean square error (RMSE) and Bayesian Deviance Information Criterion (DIC). In the univariate analysis, the logistic model performed best, with R2 (0.1145), adjusted R2 (0.114), RMSE (0.3074) and DIC (7435.98) for DS, and R2 (0.0626), adjusted R2 (0.0621), RMSE (0.4676) and DIC (23120) for MR. In the bivariate case, results revealed that 7 and 8 out of the 10 selected covariates were significantly associated with DS and MR respectively, whilst none were associated with the interaction between the two outcomes. Bayesian methods are more flexible in handling complex non-standard models as well as they allow model fit and complexity to be assessed straightforwardly for non-nested hierarchical models

Expected value of sample information for Weibull survival data

Expected value of sample information (EVSI) involves simulating data collection, Bayesian updating, and re-examining decisions. Bayesian updating in Weibull models typically requires Markov chain Monte Carlo (MCMC). We examine five methods for calculating posterior expected net benefits: two heuristic methods (data lumping and pseudo-normal); two Bayesian approximation methods (Tierney & Kadane, Brennan & Kharroubi); and the gold standard MCMC. A case study computes EVSI for 25 study options. We compare accuracy, computation time and trade-offs of EVSI versus study costs. Brennan & Kharroubi (B&K) approximates expected net benefits to within ±1% of MCMC. Other methods, data lumping (+54%), pseudo-normal (−5%) and Tierney & Kadane (+11%) are less accurate. B&K also produces the most accurate EVSI approximation. Pseudo-normal is also reasonably accurate, whilst Tierney & Kadane consistently underestimates and data lumping exhibits large variance. B&K computation is 12 times faster than the MCMC method in our case study. Though not always faster, B&K provides most computational efficiency when net benefits require appreciable computation time and when many MCMC samples are needed. The methods enable EVSI computation for economic models with Weibull survival parameters. The approach can generalize to complex multi-state models and to survival analyses using other smooth parametric distributions. Copyright © 2007 John Wiley & Sons, Ltd.

Title: A comparison of United States and United Kingdom EQ-5D health states valuations using a nonparametric Bayesian method

Few studies have compared preference values of health states obtained in different countries. This paper applies a nonparametric model to estimate and compare EQ-5D health state valuation data obtained from two countries using Bayesian methods. The data set is the US and UK EQ-5D valuation studies where a sample of 42 states defined by the EQ-5D was valued by representative samples of the general population from each country using the time trade-off technique. We estimate a function applicable across both countries which explicitly accounts for the differences between them, and is estimated using the data from both countries. The paper discusses the implications of these results for future applications of the EQ-5D and further work in this field