Bayesian heterogeneity in a meta-analysis with two studies and binary data.

The meta-analysis of two trials is valuable in many practical situations, such as studies of rare and/or orphan diseases focussed on a single intervention. In this context, additional concerns, like small sample size and/or heterogeneity in the results obtained, might make standard frequentist and Bayesian techniques inappropriate. In a meta-analysis, moreover, the presence of between-sample heterogeneity adds model uncertainty, which must be taken into consideration when drawing inferences. We suggest that the most appropriate way to measure this heterogeneity is by clustering the samples and then determining the posterior probability of the cluster models. The meta-inference is obtained as a mixture of all the meta-inferences for the cluster models, where the mixing distribution is the posterior model probability. We present a simple two-component form of Bayesian model averaging that is unaffected by characteristics such as small study size or zero-cell counts, and which is capable of incorporating uncertainties into the estimation process. Illustrative examples are given and analysed, using real sparse binomial data.

Horizontal equity in access to public GP services by socioeconomic group: potential bias due to a compartmentalised approach.

BACKGROUND: Horizontal equity in access to public general practitioner (GP) services by socioeconomic group has been addressed econometrically by testing the statement "equal probability of using public GP services for equal health care needs, regardless of socioeconomic status". Based on survey data, the conventional approach has been to estimate binomial econometric models in which when the respondent reports having visited a public GP, it counts as 1, otherwise it counts as 0. This is what we call a compartmentalised approach. Those respondents who did not visit a public GP but visited instead another doctor (specialist or private GP) would count as 0 (despite having used instead other modes of health care), thus conclusions of the compartmentalised approach might be biased. In such cases, a multinomial econometric model -that we called comprehensive approach- would be more appropriate to analyse horizontal equity in access to public GP services. The objective of this paper is to test for this potential bias by comparing a compartmentalised and a comprehensive approach, when analysing horizontal equity in access to public GP. METHODS: Using data from the 2016/17 Spanish National Health Survey, we estimate the probability of visiting a public GP as determined by socioeconomic status, health care need and demographic characteristics. We use binomial and multinomial logit and probit models in order to highlight the potential differences in the conclusions regarding socioeconomic inequities in access to public GP services. Socioeconomic status is proxied by education level, social class and employment situation. RESULTS: Our results show that conclusions are sensitive to the approach selected. Particularly, the horizontal inequity favouring individuals with lower education that resulted from the compartmentalised approach disappears under a comprehensive approach and only a social class effect remains. CONCLUSION: An analysis of horizontal equity in access to a particular health care service (like public GP services) undertaken following a compartmentalised approach should be compared with a comprehensive approach in order to test that there is no bias as a consequence of considering as zeros the utilisation of other types of health care.

Bayesian robustness in meta-analysis for studies with zero responses.

Statistical meta-analysis is mostly carried out with the help of the random effect normal model, including the case of discrete random variables. We argue that the normal approximation is not always able to adequately capture the underlying uncertainty of the original discrete data. Furthermore, when we examine the influence of the prior distributions considered, in the presence of rare events, the results from this approximation can be very poor. In order to assess the robustness of the quantities of interest in meta-analysis with respect to the choice of priors, this paper proposes an alternative Bayesian model for binomial random variables with several zero responses. Particular attention is paid to the coherence between the prior distributions of the study model parameters and the meta-parameter. Thus, our method introduces a simple way to examine the sensitivity of these quantities to the structure dependence selected for study. For illustrative purposes, an example with real data is analysed, using the proposed Bayesian meta-analysis model for binomial sparse data. Copyright © 2016 John Wiley & Sons, Ltd.

Objective Bayesian meta-analysis for sparse discrete data.

This paper presents a Bayesian model for meta-analysis of sparse discrete binomial data, which are out of the scope of the usual hierarchical normal random-effect models. Treatment effectiveness data are often of this type. The crucial linking distribution between the effectiveness conditional on the healthcare center and the unconditional effectiveness is constructed from specific bivariate classes of distributions with given marginals. This assures coherency between the marginal and conditional prior distributions utilized in the analysis. Further, we impose a bivariate class of priors that is able to accommodate a wide range of heterogeneity degrees between the multicenter clinical trials involved. Applications to real multicenter data are given and compared with previous meta-analysis.