Research Articles

Network meta-analysis (NMA) is gaining popularity in evidence synthesis and network meta-regression (NMR) allows us to incorporate potentially important covariates into network meta-analysis. In this paper, 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 (DIC) and the logarithm of the Pseudo-marginal likelihood (LPML) 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.

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.

A flexible class of multivariate meta-regression models are proposed for Individual Patient Data (IPD). The methodology is well motivated from 26 pivotal Merck clinical trials that compare statins (cholesterol lowering drugs) in combination with ezetimibe and statins alone on treatment-naïve patients and those continuing on statins at baseline. The research goal is to jointly analyze the multivariate outcomes, Low Density Lipoprotein Cholesterol (LDL-C), High Density Lipoprotein Cholesterol (HDL-C), and Triglycerides (TG). These three continuous outcome measures are correlated and shed much light on a subject’s lipid status. The proposed multivariate meta-regression models allow for different skewness parameters and different degrees of freedom for the multivariate outcomes from different trials under a general class of skew t-distributions. The theoretical properties of the proposed models are examined and an efficient Markov chain Monte Carlo (MCMC) sampling algorithm is developed for carrying out Bayesian inference under the proposed multivariate meta-regression model. In addition, the Conditional Predictive Ordinates (CPOs) are computed via an efficient Monte Carlo method. Consequently, the logarithm of the pseudo marginal likelihood and Bayesian residuals are obtained for model comparison and assessment, respectively. A detailed analysis of the IPD meta data from the 26 Merck clinical trials is carried out to demonstrate the usefulness of the proposed methodology.

Crohn's disease (CD) is a life‐long condition associated with recurrent relapses characterized by abdominal pain, weight loss, anemia, and persistent diarrhea. In the US, there are approximately 780 000 CD patients and 33 000 new cases added each year. In this article, we propose a new network meta‐regression approach for modeling ordinal outcomes in order to assess the efficacy of treatments for CD. Specifically, we develop regression models based on aggregate covariates for the underlying cut points of the ordinal outcomes as well as for the variances of the random effects to capture heterogeneity across trials. Our proposed models are particularly useful for indirect comparisons of multiple treatments that have not been compared head‐to‐head within the network meta‐analysis framework. Moreover, we introduce Pearson residuals and construct an invariant test statistic to evaluate goodness‐of‐fit in the setting of ordinal outcome data. A detailed case study demonstrating the usefulness of the proposed methodology is carried out using aggregate ordinal outcome data from 16 clinical trials for treating CD.

Motivated by the self-thinning meta-data, a randomeffects 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.

We examine a class of multivariate meta-regression models in the presence of individual patient data. The methodology is well motivated from several studies of cholesterol-lowering drugs where the goal is to jointly analyze the multivariate outcomes, low density lipoprotein cholesterol, high density lipoprotein cholesterol, and triglycerides. These three continuous outcome measures are correlated and shed much light on a subject's lipid status. One of the main goals in lipid research is the joint analysis of these three outcome measures in a meta-regression setting. Since these outcome measures are not typically multivariate normal, one must consider classes of distributions that allow for skewness in one or more of the outcomes. In this paper, we consider a new general class of multivariate skew distributions for multivariate meta-regression and examine their theoretical properties. Using these distributions, we construct a Bayesian model for the meta-data and develop an efficient Markov chain Monte Carlo computational scheme for carrying out the computations. In addition, we develop a multivariate L measure for model comparison, Bayesian residuals for model assessment, and a Bayesian procedure for detecting outlying trials. The proposed multivariate L measure, Bayesian residuals, and Bayesian outlying trial detection procedure are particularly suitable and computationally attractive in the multivariate meta-regression setting. A detailed case study demonstrating the usefulness of the proposed methodology is carried out in an individual patient data multivariate meta-regression setting using 26 pivotal Merck clinical trials that compare statins (cholesterol-lowering drugs) in combination with ezetimibe and statins alone on treatment-naïve patients and those continuing on statins at baseline.

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.

Multivariate meta-regression models are commonly used in settings where the response variable is naturally multidimensional. Such settings are common in cardiovascular and diabetes studies where the goal is to study cholesterol levels once a certain medication is given. In this setting, the natural multivariate endpoint is low density lipoprotein cholesterol (LDL-C), high density lipoprotein cholesterol (HDL-C), and triglycerides (TG) (LDL-C, HDL-C, TG). In this article, we examine study level (aggregate) multivariate meta-data from 26 Merck sponsored double-blind, randomized, active, or placebo-controlled clinical trials on adult patients with primary hypercholesterolemia. Our goal is to develop a methodology for carrying out Bayesian inference for multivariate meta-regression models with study level data when the within-study sample covariance matrix S for the multivariate response data is partially observed. Specifically, the proposed methodology is based on postulating a multivariate random effects regression model with an unknown within-study covariance matrix $\Sigma$ in which we treat the within-study sample correlations as missing data, the standard deviations of the within-study sample covariance matrix S are assumed observed, and given $\Sigma$, S follows a Wishart distribution. Thus, we treat the off-diagonal elements of S as missing data, and these missing elements are sampled from the appropriate full conditional distribution in a Markov chain Monte Carlo (MCMC) sampling scheme via a novel transformation based on partial correlations. We further propose several structures (models) for $\Sigma$, which allow for borrowing strength across different treatment arms and trials. The proposed methodology is assessed using simulated as well as real data, and the results are shown to be quite promising. Supplementary materials for this article are available online.

SAS macro, BSMED, is for meta-experimental design for survival data. BSMED uses an exponential regression model and a log-linear fixed-effects model for the meta-regression survival model.

Quantitative Evaluation of Safety in Drug Development compared to a frequentist design. In this chapter, we provide an in-depth discussion of meta-regression models, the general methodology for Bayesian meta-analysis design, prior elicitation based on historical data, and computational algorithms. The design of a phase 2/3 development program including a noninferiority clinical trial for CV risk assessment in T2DM studies is presented to illustrate the methodology.

Recently, the Center for Drug Evaluation and Research at the Food and Drug Administration released a guidance that makes recommendations about how to demonstrate that a new antidiabetic therapy to treat type 2 diabetes is not associated with an unacceptable increase in cardiovascular risk. One of the recommendations from the guidance is that phases II and III trials should be appropriately designed and conducted so that a meta-analysis can be performed. In addition, the guidance implies that a sequential meta-analysis strategy could be adopted. That is, the initial meta-analysis could aim at demonstrating the upper bound of a 95% confidence interval (CI) for the estimated hazard ratio to be < 1.8 for the purpose of enabling a new drug application or a biologics license application. Subsequently after the marketing authorization, a final meta-analysis would need to show the upper bound to be < 1.3. In this context, we develop a new Bayesian sequential meta-analysis approach using survival regression models to assess whether the size of a clinical development program is adequate to evaluate a particular safety endpoint. We propose a Bayesian sample size determination methodology for sequential meta-analysis clinical trial design with a focus on controlling the familywise type I error rate and power. We use the partial borrowing power prior to incorporate the historical survival meta-data into the Bayesian design. We examine various properties of the proposed methodology, and simulation-based computational algorithms are developed to generate predictive data at various interim analyses, sample from the posterior distributions, and compute various quantities such as the power and the type I error in the Bayesian sequential meta-analysis trial design. We apply the proposed methodology to the design of a hypothetical antidiabetic drug development program for evaluating cardiovascular risk.

In this paper, we propose a class of Box–Cox transformation regression models with multidimensional random effects for analyzing multivariate responses for individual patient data in meta‐analysis. Our modeling formulation uses a multivariate normal response meta‐analysis model with multivariate random effects, in which each response is allowed to have its own Box–Cox transformation. Prior distributions are specified for the Box–Cox transformation parameters as well as the regression coefficients in this complex model, and the deviance information criterion is used to select the best transformation model. Because the model is quite complex, we develop a novel Monte Carlo Markov chain sampling scheme to sample from the joint posterior of the parameters. This model is motivated by a very rich dataset comprising 26 clinical trials involving cholesterol‐lowering drugs where the goal is to jointly model the three‐dimensional response consisting of low density lipoprotein cholesterol (LDL‐C), high density lipoprotein cholesterol (HDL‐C), and triglycerides (TG) (LDL‐C, HDL‐C, TG). Because the joint distribution of (LDL‐C, HDL‐C, TG) is not multivariate normal and in fact quite skewed, a Box–Cox transformation is needed to achieve normality. In the clinical literature, these three variables are usually analyzed univariately; however, a multivariate approach would be more appropriate because these variables are correlated with each other. We carry out a detailed analysis of these data by using the proposed methodology.

In this paper, we propose a class of multivariate random effects models allowing for the inclusion of study-level covariates to carry out meta-analyses. As existing algorithms for computing maximum likelihood estimates often converge poorly or may not converge at all when the random effects are multi-dimensional, we develop an efficient expectation-maximization algorithm for fitting multi-dimensional random effects regression models. In addition, we also develop a new methodology for carrying out variable selection with study-level covariates. We examine the performance of the proposed methodology via a simulation study. We apply the proposed methodology to analyze metadata from 26 studies involving statins as a monotherapy and in combination with ezetimibe. In particular, we compare the low-density lipoprotein cholesterol-lowering efficacy of monotherapy and combination therapy on two patient populations (naïve and non-naïve patients to statin monotherapy at baseline), controlling for aggregate covariates. The proposed methodology is quite general and can be applied in any meta-analysis setting for a wide range of scientific applications and therefore offers new analytic methods of clinical importance.

Recent guidance from the Food and Drug Administration for the evaluation of new therapies in the treatment of type 2 diabetes (T2DM) calls for a program-wide meta-analysis of cardiovascular (CV) outcomes. In this context, we develop a new Bayesian meta-analysis approach using survival regression models to assess whether the size of a clinical development program is adequate to evaluate a particular safety endpoint. We propose a Bayesian sample size determination methodology for meta-analysis clinical trial design with a focus on controlling the type I error and power. We also propose the partial borrowing power prior to incorporate the historical survival meta data into the statistical design. Various properties of the proposed methodology are examined and an efficient Markov chain Monte Carlo sampling algorithm is developed to sample from the posterior distributions. In addition, we develop a simulation-based algorithm for computing various quantities, such as the power and the type I error in the Bayesian meta-analysis trial design. The proposed methodology is applied to the design of a phase 2/3 development program including a noninferiority clinical trial for CV risk assessment in T2DM studies.

Allergic rhinitis is an allergic inflammation of the nasal membranes. The symptoms include disorders in nose and eyes. Studies have been carried out on safety and efficacy evaluation of triamcinolone acetonide aqueous nasal spray. To combine the results from different studies, we propose random-coefficient regression models. The properties of the proposed models are examined. The models are compared via the deviance information criterion (DIC), and Bayesian computations are carried out via MCMC sampling. A set of meta-data from nine clinical trials is analyzed in detail via the proposed methodology.