Bayesian models for cost-effectiveness analysis in the presence of structural zero costs

Bayesian modelling for cost-effectiveness data has received much attention in both the health economics and the statistical literature in recent years. Cost-effectiveness data are characterised by a relatively complex structure of relationships linking the suitable measure of clinical benefit (\eg QALYs) and the associated costs. Simplifying assumptions, such as (bivariate) normality of the underlying distributions are usually not granted, particularly for the cost variable, which is characterised by markedly skewed distributions. In addition, individual-level datasets are often characterised by the presence of structural zeros in the cost variable. Hurdle models can be used to account for the presence of excess zeros in a distribution and have been applied in the context of cost data. We extend their application to cost-effectiveness data, defining a full Bayesian model which consists of a selection model for the subjects with null costs, a marginal model for the costs and a conditional model for the measure of effectiveness (conditionally on the observed costs). The model is presented using a working example to describe its main features.Comment: 15 pages, 2 figure

Evidence of bias in the Eurovision song contest: modelling the votes using Bayesian hierarchical models

The Eurovision Song Contest is an annual musical competition held among active members of the European Broadcasting Union since 1956. The event is televised live across Europe. Each participating country presents a song and receive a vote based on a combination of tele-voting and jury. Over the years, this has led to speculations of tactical voting, discriminating against some participants and thus inducing bias in the final results. In this paper we investigate the presence of positive or negative bias (which may roughly indicate favouritisms or discrimination) in the votes based on geographical proximity, migration and cultural characteristics of the participating countries through a Bayesian hierarchical model. Our analysis found no evidence of negative bias, although mild positive bias does seem to emerge systematically, linking voters to performers.Comment: 16 pages, 3 figure

Calculating the Expected Value of Sample Information using Efficient Nested Monte Carlo: A Tutorial

Objective: The Expected Value of Sample Information (EVSI) quantifies the economic benefit of reducing uncertainty in a health economic model by collecting additional information. This has the potential to improve the allocation of research budgets. Despite this, practical EVSI evaluations are limited, partly due to the computational cost of estimating this value using the "gold-standard" nested simulation methods. Recently, however, Heath et al developed an estimation procedure that reduces the number of simulations required for this "gold-standard" calculation. Up to this point, this new method has been presented in purely technical terms. Study Design: This study presents the practical application of this new method to aid its implementation. We use a worked example to illustrate the key steps of the EVSI estimation procedure before discussing its optimal implementation using a practical health economic model. Methods: The worked example is based on a three parameter linear health economic model. The more realistic model evaluates the cost-effectiveness of a new chemotherapy treatment which aims to reduce the number of side effects experienced by patients. We use a Markov Model structure to evaluate the health economic profile of experiencing side effects. Results: This EVSI estimation method offers accurate estimation within a feasible computation time, seconds compared to days, even for more complex model structures. The EVSI estimation is more accurate if a greater number of nested samples are used, even for a fixed computational cost. Conclusions: This new method reduces the computational cost of estimating the EVSI by nested simulation

A Review of Methods for the Analysis of the Expected Value of Information

Over recent years Value of Information analysis has become more widespread in health-economic evaluations, specifically as a tool to perform Probabilistic Sensitivity Analysis. This is largely due to methodological advancements allowing for the fast computation of a typical summary known as the Expected Value of Partial Perfect Information (EVPPI). A recent review discussed some estimations method for calculating the EVPPI but as the research has been active over the intervening years this review does not discuss some key estimation methods. Therefore, this paper presents a comprehensive review of these new methods. We begin by providing the technical details of these computation methods. We then present a case study in order to compare the estimation performance of these new methods. We conclude that the most recent development based on non-parametric regression offers the best method for calculating the EVPPI efficiently. This means that the EVPPI can now be used practically in health economic evaluations, especially as all the methods are developed in parallel with

Methods for Population Adjustment with Limited Access to Individual Patient Data: A Review and Simulation Study

Population-adjusted indirect comparisons estimate treatment effects when access to individual patient data is limited and there are cross-trial differences in effect modifiers. Popular methods include matching-adjusted indirect comparison (MAIC) and simulated treatment comparison (STC). There is limited formal evaluation of these methods and whether they can be used to accurately compare treatments. Thus, we undertake a comprehensive simulation study to compare standard unadjusted indirect comparisons, MAIC and STC across 162 scenarios. This simulation study assumes that the trials are investigating survival outcomes and measure continuous covariates, with the log hazard ratio as the measure of effect. MAIC yields unbiased treatment effect estimates under no failures of assumptions. The typical usage of STC produces bias because it targets a conditional treatment effect where the target estimand should be a marginal treatment effect. The incompatibility of estimates in the indirect comparison leads to bias as the measure of effect is non-collapsible. Standard indirect comparisons are systematically biased, particularly under stronger covariate imbalance and interaction effects. Standard errors and coverage rates are often valid in MAIC but the robust sandwich variance estimator underestimates variability where effective sample sizes are small. Interval estimates for the standard indirect comparison are too narrow and STC suffers from bias-induced undercoverage. MAIC provides the most accurate estimates and, with lower degrees of covariate overlap, its bias reduction outweighs the loss in effective sample size and precision under no failures of assumptions. An important future objective is the development of an alternative formulation to STC that targets a marginal treatment effect.Comment: 73 pages (34 are supplementary appendices and references), 8 figures, 2 tables. Full article (following Round 4 of minor revisions). arXiv admin note: text overlap with arXiv:2008.0595

survHE: Survival Analysis for Health Economic Evaluation and Cost-Effectiveness Modeling

Survival analysis features heavily as an important part of health economic evaluation, an increasingly important component of medical research. In this setting, it is important to estimate the mean time to the survival endpoint using limited information (typically from randomized trials) and thus it is useful to consider parametric survival models. In this paper, we review the features of the R package survHE, specifically designed to wrap several tools to perform survival analysis for economic evaluation. In particular, survHE embeds both a standard, frequentist analysis (through the R package flexsurv) and a Bayesian approach, based on Hamiltonian Monte Carlo (via the R package rstan) or integrated nested Laplace approximation (with the R package INLA). Using this composite approach, we obtain maximum flexibility and are able to pre-compile a wide range of parametric models, with a view of simplifying the modelers' work and allowing them to move away from non-optimal work flows, including spreadsheets (e.g., Microsoft Excel)