Bayesian Inference for Multivariate Meta-regression with a Partially Observed Within-Study Sample Covariance Matrix

Bayesian semiparametric mixed effects models for meta-analysis of the literature data : An application to cadmium toxicity studies

We propose Bayesian semiparametric mixed effects models with measurement error to analyze the literature data collected from multiple studies in a meta-analytic framework. We explore this methodology for risk assessment in cadmium toxicity studies, where the primary objective is to investigate dose-response relationships between urinary cadmium concentrations and β 2 -microglobulin. In the proposed model, a nonlinear association between exposure and response is described by a Gaussian process with shape restrictions, and study-specific random effects are modeled to have either normal or unknown distributions with Dirichlet process mixture priors. In addition, nonparametric Bayesian measurement error models are incorporated to flexibly account for the uncertainty resulting from the usage of a surrogate measurement of a true exposure. We apply the proposed model to analyze cadmium toxicity data imposing shape constraints along with measurement errors and study-specific random effects across varying characteristics, such as population gender, age, or ethnicity.

Bayesian network meta-regression hierarchical models using heavy-tailed multivariate random effects with covariate-dependent variances

Network meta-analysis (NMA) is gaining popularity in evidence synthesis and network meta-regression allows us to incorporate potentially important covariates into network meta-analysis. In this article, we propose a Bayesian network meta-regression hierarchical model and assume a general multivariate t distribution for the random treatment effects. The multivariate t distribution is desired for heavy-tailed random effects and converges to the multivariate normal distribution when the degrees of freedom go to infinity. Moreover, in NMA, some treatments are compared only in a single study. To overcome such sparsity, we propose a log-linear regression model for the variances of the random effects and incorporate aggregate covariates into modeling the variance components. We develop a Markov chain Monte Carlo sampling algorithm to sample from the posterior distribution via the collapsed Gibbs technique. We further use the deviance information criterion and the logarithm of the pseudo-marginal likelihood for model comparison. A simulation study is conducted and a detailed analysis from our motivating case study is carried out to further demonstrate the proposed methodology.

Do the combined blood pressure effects of exercise and antihypertensive medications add up to the sum of their parts? A systematic meta-review

Objective

To compare the blood pressure (BP) effects of exercise alone (EXalone), medication alone (MEDSalone) and combined (EX+MEDScombined) among adults with hypertension.

Data sources

PubMed, Scopus, Cumulative Index to Nursing and Allied Health Literature, SPORTDiscus and the Cochrane Library.

Eligibility criteria

Randomised controlled trails (RCTs) or meta-analyses (MAs) of controlled trials that: (1) involved healthy adults>18 year with hypertension; (2) investigated exercise and BP; (3) reported preintervention and postintervention BP and (4) were published in English. RCTs had an EX+MEDScombined arm; and an EXalone arm and/or an MEDSalone arm; and MAs performed moderator analyses.

Design

A systematic network MA and meta-review with the evidence graded using the Physical Activity Guidelines for Americans Advisory Committee system.

Outcome

The BP response for EXalone, MEDSalone and EX+MEDScombined and compared with each other.

Results

Twelve RCTs qualified with 342 subjects (60% women) who were mostly physically inactive, middle-aged to older adults. There were 13 qualifying MAs with 28 468 participants (~50% women) who were mostly Caucasian or Asian. Most RCTs were aerobic (83.3%), while the MAs involved traditional (46%) and alternative (54%) exercise types. Strong evidence demonstrates EXalone, MEDSalone and EX+MEDScombined reduce BP and EX+MEDScombined elicit BP reductions less than the sum of their parts. Strong evidence indicates EX+MEDScombined potentiate the BP effects of MEDSalone. Although the evidence is stronger for alternative than traditional types of exercise, EXaloneelicits greater BP reductions than MEDSalone.

Conclusions

The combined BP effects of exercise and medications are not additive or synergistic, but when combined they bolster the antihypertensive effects of MEDSalone.

PROSPERO registration number

The protocol is registered at PROSPERO CRD42020181754.

Bayesian Meta-Regression Model Using Heavy-Tailed Random-effects with Missing Sample Sizes for Self-thinning Meta-data

Motivated by the self-thinning meta-data, a random-effects meta-analysis model with unknown precision parameters is proposed with a truncated Poisson regression model for missing sample sizes. The random effects are assumed to follow a heavy-tailed distribution to accommodate outlying aggregate values in the response variable. The logarithm of the pseudo-marginal likelihood (LPML) is used for model comparison. In addition, in order to determine which self-thinning law is more supported by the meta-data, a measure called "Plausibility Index (PI)" is developed. A simulation study is conducted to examine empirical performance of the proposed methodology. Finally, the proposed model and the PI measure are applied to analyze a self-thinning meta-data set in details.

Bayesian inference for network meta-regression using multivariate random effects with applications to cholesterol lowering drugs

Low-density lipoprotein cholesterol (LDL-C) has been identified as a causative factor for atherosclerosis and related coronary heart disease, and as the main target for cholesterol- and lipid-lowering therapy. Statin drugs inhibit cholesterol synthesis in the liver and are typically the first line of therapy to lower elevated levels of LDL-C. On the other hand, a different drug, Ezetimibe, inhibits the absorption of cholesterol by the small intestine and provides a different mechanism of action. Many clinical trials have been carried out on safety and efficacy evaluation of cholesterol lowering drugs. To synthesize the results from different clinical trials, we examine treatment level (aggregate) network meta-data from 29 double-blind, randomized, active, or placebo-controlled statins +/$-$ Ezetimibe clinical trials on adult treatment-naïve patients with primary hypercholesterolemia. In this article, we propose a new approach to carry out Bayesian inference for arm-based network meta-regression. Specifically, we develop a new strategy of grouping the variances of random effects, in which we first formulate possible sets of the groups of the treatments based on their clinical mechanisms of action and then use Bayesian model comparison criteria to select the best set of groups. The proposed approach is especially useful when some treatment arms are involved in only a single trial. In addition, a Markov chain Monte Carlo sampling algorithm is developed to carry out the posterior computations. In particular, the correlation matrix is generated from its full conditional distribution via partial correlations. The proposed methodology is further applied to analyze the network meta-data from 29 trials with 11 treatment arms.

Bayesian Modeling and Inference for Nonignorably Missing Longitudinal Binary Response Data with Applications to HIV Prevention Trials

Missing data are frequently encountered in longitudinal clinical trials. To better monitor and understand the progress over time, one must handle the missing data appropriately and examine whether the missing data mechanism is ignorable or nonignorable. In this article, we develop a new probit model for longitudinal binary response data. It resolves a challenging issue for estimating the variance of the random effects, and substantially improves the convergence and mixing of the Gibbs sampling algorithm. We show that when improper uniform priors are specified for the regression coefficients of the joint multinomial model via a sequence of one-dimensional conditional distributions for the missing data indicators under nonignorable missingness, the joint posterior distribution is improper. A variation of Jeffreys prior is thus established as a remedy for the improper posterior distribution. In addition, an efficient Gibbs sampling algorithm is developed using a collapsing technique. Two model assessment criteria, the deviance information criterion (DIC) and the logarithm of the pseudomarginal likelihood (LPML), are used to guide the choices of prior specifications and to compare the models under different missing data mechanisms. We report on extensive simulations conducted to investigate the empirical performance of the proposed methods. The proposed methodology is further illustrated using data from an HIV prevention clinical trial.

An improved method for bivariate meta-analysis when within-study correlations are unknown

Multivariate meta-analysis, which jointly analyzes multiple and possibly correlated outcomes in a single analysis, is becoming increasingly popular in recent years. An attractive feature of the multivariate meta-analysis is its ability to account for the dependence between multiple estimates from the same study. However, standard inference procedures for multivariate meta-analysis require the knowledge of within-study correlations, which are usually unavailable. This limits standard inference approaches in practice. Riley et al proposed a working model and an overall synthesis correlation parameter to account for the marginal correlation between outcomes, where the only data needed are those required for a separate univariate random-effects meta-analysis. As within-study correlations are not required, the Riley method is applicable to a wide variety of evidence synthesis situations. However, the standard variance estimator of the Riley method is not entirely correct under many important settings. As a consequence, the coverage of a function of pooled estimates may not reach the nominal level even when the number of studies in the multivariate meta-analysis is large. In this paper, we improve the Riley method by proposing a robust variance estimator, which is asymptotically correct even when the model is misspecified (ie, when the likelihood function is incorrect). Simulation studies of a bivariate meta-analysis, in a variety of settings, show a function of pooled estimates has improved performance when using the proposed robust variance estimator. In terms of individual pooled estimates themselves, the standard variance estimator and robust variance estimator give similar results to the original method, with appropriate coverage. The proposed robust variance estimator performs well when the number of studies is relatively large. Therefore, we recommend the use of the robust method for meta-analyses with a relatively large number of studies (eg, m≥50). When the sample size is relatively small, we recommend the use of the robust method under the working independence assumption. We illustrate the proposed method through 2 meta-analyses.