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SUMMARY Random effects meta-analyses have been widely applied in evidence synthesis for various types of medical studies. However, standard inference methods (e.g. restricted maximum likelihood estimation) usually underestimate statistical errors and possibly provide highly overconfident results under realistic situations; for instance, coverage probabilities of confidence intervals can be substantially below the nominal level. The main reason is that these inference methods rely on large sample approximations even though the number of synthesized studies is usually small or moderate in practice. In this article, we solve this problem using a unified inference method based on Monte Carlo conditioning for broad application to random effects meta-analysis. The developed method provides improved confidence intervals with coverage probabilities that are closer to the nominal level than standard methods. As specific applications, we provide new inference procedures for three types of meta-analysis: conventional univariate meta-analysis for pairwise treatment comparisons, meta-analysis of diagnostic test accuracy, and multiple treatment comparisons via network meta-analysis. We also illustrate the practical effectiveness of these methods via real data applications and simulation studies.

SUMMARY In randomized controlled trials (RCTs) with time-to-event outcomes, the difference in restricted mean survival times (RMSTD) offers an absolute measure of the treatment effect on the time scale. Computation of the RMSTD relies on the choice of a time horizon, $\tau$. In a meta-analysis, varying follow-up durations may lead to the exclusion of RCTs with follow-up shorter than $\tau$. We introduce an individual patient data multivariate meta-analysis model for RMSTD estimated at multiple time horizons. We derived the within-trial covariance for the RMSTD enabling the synthesis of all data by borrowing strength from multiple time points. In a simulation study covering 60 scenarios, we compared the statistical performance of the proposed method to that of two univariate meta-analysis models, based on available data at each time point and based on predictions from flexible parametric models. Our multivariate model yields smaller mean squared error over univariate methods at all time points. We illustrate the method with a meta-analysis of five RCTs comparing transcatheter aortic valve replacement (TAVR) with surgical replacement in patients with aortic stenosis. Over 12, 24, and 36 months of follow-up, those treated by TAVR live 0.28 [95% confidence interval (CI) 0.01 to 0.56], 0.46 (95% CI $-$0.08 to 1.01), and 0.79 (95% CI $-$0.43 to 2.02) months longer on average compared to those treated by surgery, respectively.

Univariate semiparametric methods are often used in modeling nonlinear age trajectories for imaging data, which may result in efficiency loss and lower power for identifying important age-related effects that exist in the data. As observed in multiple neuroimaging studies, age trajectories show similar nonlinear patterns for the left and right corresponding regions and for the different parts of a big organ such as the corpus callosum. To incorporate the spatial similarity information without assuming spatial smoothness, we propose a multivariate semiparametric regression model with a spatial similarity penalty, which constrains the variation of the age trajectories among similar regions. The proposed method is applicable to both cross-sectional and longitudinal region-level imaging data. We show the asymptotic rates for the bias and covariance functions of the proposed estimator and its asymptotic normality. Our simulation studies demonstrate that by borrowing information from similar regions, the proposed spatial similarity method improves the efficiency remarkably. We apply the proposed method to two neuroimaging data examples. The results reveal that accounting for the spatial similarity leads to more accurate estimators and better functional clustering results for visualizing brain atrophy pattern.Functional clustering; Longitudinal magnetic resonance imaging (MRI); Penalized B-splines; Region of interest (ROI); Spatial penalty.

To conduct comparative effectiveness research using electronic health records (EHR), many covariates are typically needed to adjust for selection and confounding biases. Unfortunately, it is typical to have missingness in these covariates. Just using cases with complete covariates will result in considerable efficiency losses and likely bias. Here, we consider the covariates missing at random with missing data mechanism either depending on the response or not. Standard methods for multiple imputation can either fail to capture nonlinear relationships or suffer from the incompatibility and uncongeniality issues. We explore a flexible Bayesian nonparametric approach to impute the missing covariates, which involves factoring the joint distribution of the covariates with missingness into a set of sequential conditionals and applying Bayesian additive regression trees to model each of these univariate conditionals. Using data augmentation, the posterior for each conditional can be sampled simultaneously. We provide details on the computational algorithm and make comparisons to other methods, including parametric sequential imputation and two versions of multiple imputation by chained equations. We illustrate the proposed approach on EHR data from an affiliated tertiary care institution to examine factors related to hyperglycemia.

The identification of predefined groups of genes ("gene-sets") which are differentially expressed between two conditions ("gene-set analysis", or GSA) is a very popular analysis in bioinformatics. GSA incorporates biological knowledge by aggregating over genes that are believed to be functionally related. This can enhance statistical power over analyses that consider only one gene at a time. However, currently available GSA approaches are based on univariate two-sample comparison of single genes. This means that they cannot test for multivariate hypotheses such as differences in covariance structure between the two conditions. Yet interplay between genes is a central aspect of biological investigation and it is likely that such interplay may differ between conditions. This paper proposes a novel approach for gene-set analysis that allows for truly multivariate hypotheses, in particular differences in gene-gene networks between conditions. Testing hypotheses concerning networks is challenging due the nature of the underlying estimation problem. Our starting point is a recent, general approach for high-dimensional two-sample testing. We refine the approach and show how it can be used to perform multivariate, network-based gene-set testing. We validate the approach in simulated examples and show results using high-throughput data from several studies in cancer biology.

Inference in mixed models is often based on the marginal distribution obtained from integrating out random effects over a pre-specified, often parametric, distribution. In this paper, we present the so-called gradient function as a simple graphical exploratory diagnostic tool to assess whether the assumed random-effects distribution produces an adequate fit to the data, in terms of marginal likelihood. The method does not require any calculations in addition to the computations needed to fit the model, and can be applied to a wide range of mixed models (linear, generalized linear, non-linear), with univariate as well as multivariate random effects, as long as the distribution for the outcomes conditional on the random effects is correctly specified. In case of model misspecification, the gradient function gives an important, albeit informal, indication on how the model can be improved in terms of random-effects distribution. The diagnostic value of the gradient function is extensively illustrated using some simulated examples, as well as in the analysis of a real longitudinal study with binary outcome values.

We discuss sample size determination for clinical trials evaluating the joint effects of an intervention on two potentially correlated co-primary time-to-event endpoints. For illustration, we consider the most common case, a comparison of two randomized groups, and use typical copula families to model the bivariate endpoints. A correlation structure of the bivariate logrank statistic is specified to account for the correlation among the endpoints, although the between-group comparison is performed using the univariate logrank statistic. We propose methods to calculate the required sample size to compare the two groups and evaluate the performance of the methods and the behavior of required sample sizes via simulation.

SUMMARY The receiver operating characteristic (ROC) curve is the most widely used measure for evaluating the discriminatory performance of a continuous marker. Often, covariate information is also available and several regression methods have been proposed to incorporate covariate information in the ROC framework. Until now, these methods are only developed for the case where the covariate is univariate or multivariate. We extend ROC regression methodology for the case where the covariate is functional rather than univariate or multivariate. To this end, semiparametric- and nonparametric-induced ROC regression estimators are proposed. A simulation study is performed to assess the performance of the proposed estimators. The methods are applied to and motivated by a metabolic syndrome study in Galicia (NW Spain).

Skew-normal and skew-t distributions have proved to be useful for capturing skewness and kurtosis in data directly without transformation. Recently, finite mixtures of such distributions have been considered as a more general tool for handling heterogeneous data involving asymmetric behaviors across subpopulations. We consider such mixture models for both univariate as well as multivariate data. This allows robust modeling of high-dimensional multimodal and asymmetric data generated by popular biotechnological platforms such as flow cytometry.We develop Bayesian inference based on data augmentation and Markov chain Monte Carlo (MCMC) sampling. In addition to the latent allocations, data augmentation is based on a stochastic representation of the skew-normal distribution in terms of a random-effects model with truncated normal random effects. For finite mixtures of skew normals, this leads to a Gibbs sampling scheme that draws from standard densities only. This MCMC scheme is extended to mixtures of skew-t distributions based on representing the skew-t distribution as a scale mixture of skew normals.As an important application of our new method, we demonstrate how it provides a new computational framework for automated analysis of high-dimensional flow cytometric data. Using multivariate skew-normal and skew-t mixture models, we could model non-Gaussian cell populations rigorously and directly without transformation or projection to lower dimensions.

Patients who have undergone renal transplantation are monitored longitudinally at irregular time intervals over 10 years or more. This yields a set of biochemical and physiological markers containing valuable information to anticipate a failure of the graft. A general linear, generalized linear, or nonlinear mixed model is used to describe the longitudinal profile of each marker. To account for the correlation between markers, the univariate mixed models are combined into a multivariate mixed model (MMM) by specifying a joint distribution for the random effects. Due to the high number of markers, a pairwise modeling strategy, where all possible pairs of bivariate mixed models are fitted, is used to obtain parameter estimates for the MMM. These estimates are used in a Bayes rule to obtain, at each point in time, the prognosis for long-term success of the transplant. It is shown that allowing the markers to be correlated can improve this prognosis.

The analyses of observational longitudinal studies involving concurrent changes in treatment and medical conditions present difficulties because of the multitude of directions of potential relationships: past medication influences current symptoms; past symptoms influence current medication; and current medication is associated with current symptoms. In the context of a long-term study of non-randomized pharmacological treatment of schizophrenic relapse, we present an analysis of bivariate discrete-time transitional data with binary responses in an attempt to understand the transitional and concurrent relationships between schizophrenia relapse and medication use. A naive analysis does not show any association between previous medication and current relapse. However, we provide evidence suggesting that current treatment may impact current relapse for those who have previously taken medication, but not for those who haven't taken medication in the past. When univariate models are specified to assess these associations, the bivariate nature of the problem requires a choice of which response, relapse or medication, should be the dependent variable. In this case, the choice of relapse or medication as a dependent variable does matter. Hence, our results derive from models where both relapse and medication are treated as dependent variables. Specifically, we specify a bivariate log odds ratio for current relapse and current medication use and a separate univariate logit component for each of these outcomes. Each of these components contains transitional associations with previous relapse and medication. Such models represent extensions of univariate transitional association models (e.g. Diggle et al. (1994)) and correspond to bivariate transitional models (e.g. Zeger and Liang (1991)). We incorporate changes in transitional associations into the full-data parametric model for final inference, and investigate if these temporal changes are due to learning effects or the impact of drop-out. We also perform residual analyses and sensitivity analyses in the context of missing data patterns.

Multiple outcomes multivariate meta-analysis (MOMA) is gaining in popularity as a tool for jointly synthesizing evidence coming from studies that report effect estimates for multiple correlated outcomes. Models for MOMA are available for the case of the pairwise meta-analysis of two treatments for multiple outcomes. Network meta-analysis (NMA) can be used for handling studies that compare more than two treatments; however, there is currently little guidance on how to perform an MOMA for the case of a network of interventions with multiple outcomes. The aim of this paper is to address this issue by proposing two models for synthesizing evidence from multi-arm studies reporting on multiple correlated outcomes for networks of competing treatments. Our models can handle continuous, binary, time-to-event or mixed outcomes, with or without availability of within-study correlations. They are set in a Bayesian framework to allow flexibility in fitting and assigning prior distributions to the parameters of interest while fully accounting for parameter uncertainty. As an illustrative example, we use a network of interventions for acute mania, which contains multi-arm studies reporting on two correlated binary outcomes: response rate and dropout rate. Both multiple-outcomes NMA models produce narrower confidence intervals compared with independent, univariate network meta-analyses for each outcome and have an impact on the relative ranking of the treatments.