Cost-effectiveness analyses (CEAs) alongside randomised controlled trials (RCTs) are increasingly designed to collect resource use and preference-based health status data for the purpose of healthcare technology assessment. However, because of the way these measures are collected, they are prone to missing data, which can ultimately affect the decision of whether an intervention is good value for money. We examine how missing cost and effect outcome data are handled in RCT-based CEAs, complementing a previous review (covering 2003–2009, 88 articles) with a new systematic review (2009–2015, 81 articles) focussing on two different perspectives. First, we provide guidelines on how the information about missingness and related methods should be presented to improve the reporting and handling of missing data. We propose to address this issue by means of a quality evaluation scheme, providing a structured approach that can be used to guide the collection of information, elicitation of the assumptions, choice of methods and considerations of possible limitations of the given missingness problem. Second, we review the description of the missing data, the statistical methods used to deal with them and the quality of the judgement underpinning the choice of these methods. Our review shows that missing data in within-RCT CEAs are still often inadequately handled and the overall level of information provided to support the chosen methods is rarely satisfactory.
Funding informationThe Foundation BLANCEFLOR Boncompagni Ludovisi, née Bildt ; Mapi Group Economic evaluations from individual-level data are an important component of the process of technology appraisal, with a view to informing resource allocation decisions. A critical problem in these analyses is that both effectiveness and cost data typically present some complexity (eg, nonnormality, spikes, and missingness) that should be addressed using appropriate methods. However, in routine analyses, standardised approaches are typically used, possibly leading to biassed inferences. We present a general Bayesian framework that can handle the complexity. We show the benefits of using our approach with a motivating example, the MenSS trial, for which there are spikes at one in the effectiveness and missingness in both outcomes. We contrast a set of increasingly complex models and perform sensitivity analysis to assess the robustness of the conclusions to a range of plausible missingness assumptions. We demonstrate the flexibility of our approach with a second example, the PBS trial, and extend the framework to accommodate the characteristics of the data in this study. This paper highlights the importance of adopting a comprehensive modelling approach to economic evaluations and the strategic advantages of building these complex models within a Bayesian framework.
Trial-based cost-effectiveness analyses (CEAs) are an important source of evidence in the assessment of health interventions. In these studies, cost and effectiveness outcomes are commonly measured at multiple time points, but some observations may be missing. Restricting the analysis to the participants with complete data can lead to biased and inefficient estimates. Methods, such as multiple imputation, have been recommended as they make better use of the data available and are valid under less restrictive Missing At Random (MAR) assumption. Linear mixed effects models (LMMs) offer a simple alternative to handle missing data under MAR without requiring imputations, and have not been very well explored in the CEA context. In this manuscript, we aim to familiarise readers with LMMs and demonstrate their implementation in CEA. We illustrate the approach on a randomised trial of antidepressant, and provide the implementation code in R and Stata. We hope that the more familiar statistical framework associated with LMMs, compared to other missing data approaches, will encourage their implementation and move practitioners away from inadequate methods.
Summary
Trial‐based economic evaluations are typically performed on cross‐sectional variables, derived from the responses for only the completers in the study, using methods that ignore the complexities of utility and cost data (e.g. skewness and spikes). We present an alternative and more efficient Bayesian parametric approach to handle missing longitudinal outcomes in economic evaluations, while accounting for the complexities of the data. We specify a flexible parametric model for the observed data and partially identify the distribution of the missing data with partial identifying restrictions and sensitivity parameters. We explore alternative non‐ignorable missingness scenarios through different priors for the sensitivity parameters, calibrated on the observed data. Our approach is motivated by, and applied to, data from a trial assessing the cost‐effectiveness of a new treatment for intellectual disability and challenging behaviour.
Statistical modelling of sports data has become more and more popular in the recent years and different types of models have been proposed to achieve a variety of objectives: from identifying the key characteristics which lead a team to win or lose to predicting the outcome of a game or the team rankings in national leagues. Although not as popular as football or basketball, volleyball is a team sport with both national and international level competitions in almost every country. However, there is almost no study investigating the prediction of volleyball game outcomes and team rankings in national leagues. We propose a Bayesian hierarchical model for the prediction of the rankings of volleyball national teams, which also allows to estimate the results of each match in the league. We consider two alternative model specifications of different complexity which are validated using data from the women's volleyball Italian Serie A1 2017-2018 season.
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