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Register a new userMeasurement Error in Meta-Analysis (MEMA) -- a Bayesian framework for continuous outcome data
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Added by
Harlan Campbell
Publication date
2020
fields
Mathematical Statistics
and research's language is
English
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Ideally, a meta-analysis will summarize data from several unbiased studies. Here we consider the less than ideal situation in which contributing studies may be compromised by measurement error. Measurement error affects every study design, from randomized controlled trials to retrospective observational studies. We outline a flexible Bayesian framework for continuous outcome data which allows one to obtain appropriate point and interval estimates with varying degrees of prior knowledge about the magnitude of the measurement error. We also demonstrate how, if individual-participant data (IPD) are available, the Bayesian meta-analysis model can adjust for multiple participant-level covariates, measured with or without measurement error.
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A composite likelihood is a non-genuine likelihood function that allows to make inference on limited aspects of a model, such as marginal or conditional distributions. Composite likelihoods are not proper likelihoods and need therefore calibration for their use in inference, from both a frequentist and a Bayesian perspective. The maximizer to the composite likelihood can serve as an estimator and its variance is assessed by means of a suitably defined sandwich matrix. In the Bayesian setting, the composite likelihood can be adjusted by means of magnitude and curvature methods. Magnitude methods imply raising the likelihood to a constant, while curvature methods imply evaluating the likelihood at a different point by translating, rescaling and rotating the parameter vector. Some authors argue that curvature methods are more reliable in general, but others proved that magnitude methods are sufficient to recover, for instance, the null distribution of a test statistic. We propose a simple calibration for the marginal posterior distribution of a scalar parameter of interest which is invariant to monotonic and smooth transformations. This can be enough for instance in medical statistics, where a single scalar effect measure is often the target.
In a network meta-analysis, some of the collected studies may deviate markedly from the others, for example having very unusual effect sizes. These deviating studies can be regarded as outlying with respect to the rest of the network and can be influential on the pooled results. Thus, it could be inappropriate to synthesize those studies without further investigation. In this paper, we propose two Bayesian methods to detect outliers in a network meta-analysis via: (a) a mean-shifted outlier model and (b), posterior predictive p-values constructed from ad-hoc discrepancy measures. The former method uses Bayes factors to formally test each study against outliers while the latter provides a score of outlyingness for each study in the network, which allows to numerically quantify the uncertainty associated with being outlier. Furthermore, we present a simple method based on informative priors as part of the network meta-analysis model to down-weight the detected outliers. We conduct extensive simulations to evaluate the effectiveness of the proposed methodology while comparing it to some alternative, available outlier diagnostic tools. Two real networks of interventions are then used to demonstrate our methods in practice.
Objective Bayesian inference procedures are derived for the parameters of the multivariate random effects model generalized to elliptically contoured distributions. The posterior for the overall mean vector and the between-study covariance matrix is deduced by assigning two noninformative priors to the model parameter, namely the Berger and Bernardo reference prior and the Jeffreys prior, whose analytical expressions are obtained under weak distributional assumptions. It is shown that the only condition needed for the posterior to be proper is that the sample size is larger than the dimension of the data-generating model, independently of the class of elliptically contoured distributions used in the definition of the generalized multivariate random effects model. The theoretical findings of the paper are applied to real data consisting of ten studies about the effectiveness of hypertension treatment for reducing blood pressure where the treatment effects on both the systolic blood pressure and diastolic blood pressure are investigated.
A novel aggregation scheme increases power in randomized controlled trials and quasi-experiments when the intervention possesses a robust and well-articulated theory of change. Longitudinal data analyzing interventions often include multiple observations on individuals, some of which may be more likely to manifest a treatment effect than others. An interventions theory of change provides guidance as to which of those observations are best situated to exhibit that treatment effect. Our power-maximizing weighting for repeated-measurements with delayed-effects scheme, PWRD aggregation, converts the theory of change into a test statistic with improved Pitman efficiency, delivering tests with greater statistical power. We illustrate this method on an IES-funded cluster randomized trial testing the efficacy of a reading intervention designed to assist early elementary students at risk of falling behind their peers. The salient theory of change holds program benefits to be delayed and non-uniform, experienced after a students performance stalls. This intervention is not found to have an effect, but the PWRD techniques effect on power is found to be comparable to that of a doubling of (cluster-level) sample size.
This article presents an approach to Bayesian semiparametric inference for Gaussian multivariate response regression. We are motivated by various small and medium dimensional problems from the physical and social sciences. The statistical challenges revolve around dealing with the unknown mean and variance functions and in particular, the correlation matrix. To tackle these problems, we have developed priors over the smooth functions and a Markov chain Monte Carlo algorithm for inference and model selection. Specifically, Dirichlet process mixtures of Gaussian distributions are used as the basis for a cluster-inducing prior over the elements of the correlation matrix. The smooth, multidimensional means and variances are represented using radial basis function expansions. The complexity of the model, in terms of variable selection and smoothness, is then controlled by spike-slab priors. A simulation study is presented, demonstrating performance as the response dimension increases. Finally, the model is fit to a number of real world datasets. An R package, scripts for replicating synthetic and real data examples, and a detailed description of the MCMC sampler are available in the supplementary materials online.
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