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The joint modeling of repeated measurements and time-to-event provides a general framework to describe better the link between the progression of disease through longitudinal measurements and time-to-event outcome. In the survival data, a sample of individuals is frequently grouped into clusters. In some applications, these clusters could be arranged spatially, for example, based on geographical regions. There are two benefits of considering spatial variation in these data, enhancing the efficiency and accuracy of the parameters estimations, and investigating the survivorship spatial pattern. On the other hand, in survival data, there is a situation that subjects are supposed to experience more than one type of event potentially, but the occurrence of one type of event prevents the occurrence of the others. In this article, we considered a Bayesian joint model of longitudinal and competing risks outcomes for spatially clustered HIV/AIDS data. The data were from a registry-based study carried in Hamadan Province, Iran, from December 1997 to June 2020. In this joint model, a linear mixed effects model was used for the longitudinal submodel and a cause-specific hazard model with spatial and spatial-risk random effects was used for the survival submodel. Also, a latent structure was defined by random effects to link both event times and longitudinal processes. We used a univariate intrinsic conditional autoregressive (ICAR) distribution and a multivariate ICAR distribution for modeling the areal spatial and spatial-risk random effects, respectively. The performance of our proposed model using simulation studies and analysis of HIV/AIDS data were assessed.

Analyzing the progression of Alzheimer's disease (AD) is challenging due to lacking sensitivity in currently available measures. AD stages are typically defined based on cognitive cut-offs, but this results in heterogeneous patient groups. More accurate modeling of the continuous progression of the disease would enable more accurate patient prognosis. To address these issues, we propose a new multivariate continuous-time disease progression (MCDP) model. The model is formulated as a nonlinear mixed-effects model that aligns patients based on their predicted disease progression along a continuous latent disease timeline. The model is evaluated using long-term follow-up data from 2152 participants in the Alzheimer's Disease Neuroimaging Initiative. The MCDP model was used to simultaneously model three cognitive scales; the Alzheimer's Disease Assessment Scale-cognitive subscale, the Mini-Mental State Examination, and the Clinical Dementia Rating scale-sum of boxes. Compared with univariate modeling and previously proposed multivariate disease progression models, the MCDP model showed superior ability to predict future patient trajectories. Finally, based on the multivariate disease timeline estimated using the MCDP model, the sensitivity of the individual items of the cognitive scales along the different stages of disease was analyzed. The analysis showed that delayed memory recall items had the highest sensitivity in the early stages of disease, whereas language and attention items were sensitive later in disease.

Multiple correlated traits/phenotypes are often collected in genetic association studies and they may share a common genetic mechanism. Joint analysis of correlated phenotypes has well-known advantages over one-at-a-time analysis including gain in power and better understanding of genetic etiology. However, when the phenotypes are of discordant types such as binary and continuous, the joint modeling is more challenging. Another research area of current interest is discovery of rare genetic variants. Currently there is no method available for detecting association of rare (or common) haplotypes with multiple discordant phenotypes jointly. Our goal is to fill this gap specifically for two discordant phenotypes. We consider a rare haplotype association method for a binary phenotype, logistic Bayesian LASSO (univariate LBL) and its extension for two correlated binary phenotypes (bivariate LBL-2B). Under this framework, we propose a haplotype association test with binary and continuous phenotypes jointly (bivariate LBL-BC). Specifically, we use a latent variable to induce correlation between the two phenotypes. We carry out extensive simulations to investigate bivariate LBL-BC and compare it with univariate LBL and bivariate LBL-2B. In most settings, bivariate LBL-BC performs the best. In only two situations, bivariate LBL-BC has similar performance-when the two phenotypes are (1) weakly or not correlated and the target haplotype affects the binary phenotype only and (2) strongly positively correlated and the target haplotype affects both phenotypes in positive direction. Finally, we apply the method to a data set on lung cancer and nicotine dependence and detect several haplotypes including a rare one.

When conducting a meta-analysis involving prevalence data for an outcome with several subtypes, each of them is typically analyzed separately using a univariate meta-analysis model. Recently, multivariate meta-analysis models have been shown to correspond to a decrease in bias and variance for multiple correlated outcomes compared to univariate meta-analysis, when some studies only report a subset of the outcomes. In this article, we propose a novel Bayesian multivariate random effects model to account for the natural constraint that the prevalence of any given subtype cannot be larger than that of the overall prevalence. Extensive simulation studies show that this new model can reduce bias and variance when estimating subtype prevalences in the presence of missing data, compared to standard univariate and multivariate random effects models. The data from a rapid review on occupation and lower urinary tract symptoms by the Prevention of Lower Urinary Tract Symptoms (PLUS) Research Consortium are analyzed as a case study to estimate the prevalence of urinary incontinence and several incontinence subtypes among women in suspected high risk work environments.

In this article, we study the estimation of high-dimensional single index models when the response variable is censored. We hybrid the estimation methods for high-dimensional single-index models (but without censorship) and univariate nonparametric models with randomly censored responses to estimate the index parameters and the link function and apply the proposed methods to analyze a genomic dataset from a study of diffuse large B-cell lymphoma. We evaluate the finite sample performance of the proposed procedures via simulation studies and establish large sample theories for the proposed estimators of the index parameter and the nonparametric link function under certain regularity conditions.

Existing missing data methods for functional data mainly focus on reconstructing missing measurements along a single function-a univariate functional data setting. Motivated by a renal study, we focus on a bivariate functional data setting, where each sampling unit is a collection of two distinct component functions, one of which may be missing. Specifically, we propose a Bayesian multiple imputation approach based on a bivariate functional latent factor model that exploits the joint changing patterns of the component functions to allow accurate and stable imputation of one component given the other. We further extend the framework to address multilevel bivariate functional data with missing components by modeling and exploiting inter-component and intra-subject correlations. We develop a Gibbs sampling algorithm that simultaneously generates multiple imputations of missing component functions and posterior samples of model parameters. For multilevel bivariate functional data, a partially collapsed Gibbs sampler is implemented to improve computational efficiency. Our simulation study demonstrates that our methods outperform other competing methods for imputing missing components of bivariate functional data under various designs and missingness rates. The motivating renal study aims to investigate the distribution and pharmacokinetic properties of baseline and post-furosemide renogram curves that provide further insights into the underlying mechanism of renal obstruction, with post-furosemide renogram curves missing for some subjects. We apply the proposed methods to impute missing post-furosemide renogram curves and obtain more refined insights.

Meta-analysis is a practical and powerful analytic tool that enables a unified statistical inference across the results from multiple studies. Notably, researchers often report the results on multiple related markers in each study (eg, various α-diversity indices in microbiome studies). However, univariate meta-analyses are limited to combining the results on a single common marker at a time, whereas existing multivariate meta-analyses are limited to the situations where marker-by-marker correlations are given in each study. Thus, here we introduce two meta-analysis methods, multi-marker meta-analysis (mMeta) and adaptive multi-marker meta-analysis (aMeta), to combine multiple studies throughout multiple related markers with no priori results on marker-by-marker correlations. mMeta is a statistical estimator for a pooled estimate and its SE across all the studies and markers, whereas aMeta is a statistical test based on the test statistic of the minimum P-value among marker-specific meta-analyses. mMeta conducts both effect estimation and hypothesis testing based on a weighted average of marker-specific pooled estimates while estimating marker-by-marker correlations non-parametrically via permutations, yet its power is only moderate. In contrast, aMeta closely approaches the highest power among marker-specific meta-analyses, yet it is limited to hypothesis testing. While their applications can be broader, we illustrate the use of mMeta and aMeta to combine microbiome studies throughout multiple α-diversity indices. We evaluate mMeta and aMeta in silico and apply them to real microbiome studies on the disparity in α-diversity by the status of human immunodeficiency virus (HIV) infection. The R package for mMeta and aMeta is freely available at https://github.com/hk1785/mMeta.

Patient electronic health records, viewed as continuous-time right-censored survival data, can be used to estimate adverse drug reaction risk. Temporal outcome misclassification may occur as a result of errors in follow-up. These errors can be due to a failure to observe the incidence time of the adverse event of interest (due to misdiagnosis or nonreporting, etc) or an actual misdiagnosis of a competing adverse event. As the misclassifying event is often unobservable in the original data, we apply an internal validation sampling approach to produce consistent estimation in the presence of such errors. We introduce a univariate survival model and a cause-specific hazards model in which misclassification may also manifest as a diagnosis of an alternate adverse health outcome other than that of interest. We develop a method of maximum likelihood estimation of the model parameters and establish consistency and asymptotic normality of the estimators using standard results. We also conduct simulation studies to numerically investigate the finite sample properties of these estimators and the impact of ignoring the misclassification error.

In longitudinal studies, subjects may be lost to follow up and, thus, present incomplete response sequences. When the mechanism underlying the dropout is nonignorable, we need to account for dependence between the longitudinal and the dropout process. We propose to model such a dependence through discrete latent effects, which are outcome-specific and account for heterogeneity in the univariate profiles. Dependence between profiles is introduced by using a probability matrix to describe the corresponding joint distribution. In this way, we separately model dependence within each outcome and dependence between outcomes. The major feature of this proposal, when compared with standard finite mixture models, is that it allows the nonignorable dropout model to properly nest its ignorable counterpart. We also discuss the use of an index of (local) sensitivity to nonignorability to investigate the effects that assumptions about the dropout process may have on model parameter estimates. The proposal is illustrated via the analysis of data from a longitudinal study on the dynamics of cognitive functioning in the elderly.

Time series analysis of fMRI data is an important area of medical statistics for neuroimaging data. Spatial models and Bayesian approaches for inference in such models have advantages over more traditional mass univariate approaches; however, a major challenge for such analyses is the required computation. As a result, the neuroimaging community has embraced approximate Bayesian inference based on mean-field variational Bayes (VB) approximations. These approximations are implemented in standard software packages such as the popular statistical parametric mapping software. While computationally efficient, the quality of VB approximations remains unclear even though they are commonly used in the analysis of neuroimaging data. For reliable statistical inference, it is important that these approximations be accurate and that users understand the scenarios under which they may not be accurate. We consider this issue for a particular model that includes spatially varying coefficients. To examine the accuracy of the VB approximation, we derive Hamiltonian Monte Carlo (HMC) for this model and conduct simulation studies to compare its performance with VB in terms of estimation accuracy, posterior variability, the spatial smoothness of estimated images, and computation time. As expected, we find that the computation time required for VB is considerably less than that for HMC. In settings involving a high or moderate signal-to-noise ratio (SNR), we find that the 2 approaches produce very similar results suggesting that the VB approximation is useful in this setting. On the other hand, when one considers a low SNR, substantial differences are found, suggesting that the approximation may not be accurate in such cases and we demonstrate that VB produces Bayes estimators with larger mean squared error. A comparison of the 2 computational approaches in an application examining the hemodynamic response to face perception in addition to a comparison with the traditional mass univariate approach in this application is also considered. Overall, our work clarifies the usefulness of VB for the spatiotemporal analysis of fMRI data, while also pointing out the limitation of VB when the SNR is low and the utility of HMC in this case.

In clinical research and development, interim monitoring is critical for better decision-making and minimizing the risk of exposing patients to possible ineffective therapies. For interim futility or efficacy monitoring, predictive probability methods are widely adopted in practice. Those methods have been well studied for univariate variables. However, for longitudinal studies, predictive probability methods using univariate information from only completers may not be most efficient, and data from on-going subjects can be utilized to improve efficiency. On the other hand, leveraging information from on-going subjects could allow an interim analysis to be potentially conducted once a sufficient number of subjects reach an earlier time point. For longitudinal outcomes, we derive closed-form formulas for predictive probabilities, including Bayesian predictive probability, predictive power, and conditional power and also give closed-form solutions for predictive probability of success in a future trial and the predictive probability of success of the best dose. When predictive probabilities are used for interim monitoring, we study their distributions and discuss their analytical cutoff values or stopping boundaries that have desired operating characteristics. We show that predictive probabilities utilizing all longitudinal information are more efficient for interim monitoring than that using information from completers only. To illustrate their practical application for longitudinal data, we analyze 2 real data examples from clinical trials.

The use of outcome-dependent sampling with longitudinal data analysis has previously been shown to improve efficiency in the estimation of regression parameters. The motivating scenario is when outcome data exist for all cohort members but key exposure variables will be gathered only on a subset. Inference with outcome-dependent sampling designs that also incorporates incomplete information from those individuals who did not have their exposure ascertained has been investigated for univariate but not longitudinal outcomes. Therefore, with a continuous longitudinal outcome, we explore the relative contributions of various sources of information toward the estimation of key regression parameters using a likelihood framework. We evaluate the efficiency gains that alternative estimators might offer over random sampling, and we offer insight into their relative merits in select practical scenarios. Finally, we illustrate the potential impact of design and analysis choices using data from the Cystic Fibrosis Foundation Patient Registry.

Multilevel item response theory (MLIRT) models have been widely used to analyze the multivariate longitudinal data of mixed types (e.g., categorical and continuous) in clinical studies. The MLIRT models often have unidimensional assumption, that is, the multiple outcomes are clinical manifestations of a univariate latent variable. However, the unidimensional assumption may be unrealistic because some diseases may be heterogeneous and characterized by multiple impaired domains with variable clinical symptoms and disease progressions. We relax this assumption and propose a multidimensional latent trait linear mixed model (MLTLMM) to allow multiple latent variables and within-item multidimensionality (one outcome can be a manifestation of more than one latent variable). We conduct extensive simulation studies to assess the unidimensional MLIRT model and the proposed MLTLMM model. The simulation studies suggest that the MLTLMM model outperforms unidimensional model when the multivariate longitudinal outcomes are manifested by multiple latent variables. The proposed model is applied to two motivating studies of amyotrophic lateral sclerosis: a clinical trial of ceftriaxone and the Pooled Resource Open-Access ALS Clinical Trials database. Copyright © 2017 John Wiley & Sons, Ltd.

Model selection in high-dimensional settings has received substantial attention in recent years, however similar advancements in the low-dimensional setting have been lacking. In this article, we introduce a new variable selection procedure for low to moderate scale regressions (n > p). This method repeatedly splits the data into two sets, one for estimation and one for validation, to obtain an empirically optimized threshold which is then used to screen for variables to include in the final model. In an extensive simulation study we show that the proposed variable selection technique enjoys superior performance compared to candidate methods (backward elimination via repeated data splitting(1), univariate screening at 0.05 level, adaptive LASSO, SCAD), being amongst those with the lowest inclusion of noisy predictors while having the highest power to detect the correct model and being unaffected by correlations among the predictors. We illustrate the methods by applying them to a cohort of patients undergoing hepatectomy at our institution.

Outcome-dependent sampling (ODS) scheme is a cost-effective sampling scheme where one observes the exposure with a probability that depends on the outcome. The well-known such design is the case-control design for binary response, the case-cohort design for the failure time data, and the general ODS design for a continuous response. While substantial work has been carried out for the univariate response case, statistical inference and design for the ODS with multivariate cases remain under-developed. Motivated by the need in biological studies for taking the advantage of the available responses for subjects in a cluster, we propose a multivariate outcome-dependent sampling (multivariate-ODS) design that is based on a general selection of the continuous responses within a cluster. The proposed inference procedure for the multivariate-ODS design is semiparametric where all the underlying distributions of covariates are modeled nonparametrically using the empirical likelihood methods. We show that the proposed estimator is consistent and developed the asymptotically normality properties. Simulation studies show that the proposed estimator is more efficient than the estimator obtained using only the simple-random-sample portion of the multivariate-ODS or the estimator from a simple random sample with the same sample size. The multivariate-ODS design together with the proposed estimator provides an approach to further improve study efficiency for a given fixed study budget. We illustrate the proposed design and estimator with an analysis of association of polychlorinated biphenyl exposure to hearing loss in children born to the Collaborative Perinatal Study. Copyright © 2016 John Wiley & Sons, Ltd.

We present a general coregionalization framework for developing coregionalized multivariate Gaussian conditional autoregressive (cMCAR) models for Bayesian analysis of multivariate lattice data in general and multivariate disease mapping data in particular. This framework is inclusive of cMCARs that facilitate flexible modelling of spatially structured symmetric or asymmetric cross-variable local interactions, allowing a wide range of separable or non-separable covariance structures, and symmetric or asymmetric cross-covariances, to be modelled. We present a brief overview of established univariate Gaussian conditional autoregressive (CAR) models for univariate lattice data and develop coregionalized multivariate extensions. Classes of cMCARs are presented by formulating precision structures. The resulting conditional properties of the multivariate spatial models are established, which cast new light on cMCARs with richly structured covariances and cross-covariances of different spatial ranges. The related methods are illustrated via an in-depth Bayesian analysis of a Minnesota county-level cancer data set. We also bring a new dimension to the traditional enterprize of Bayesian disease mapping: estimating and mapping covariances and cross-covariances of the underlying disease risks. Maps of covariances and cross-covariances bring to light spatial characterizations of the cMCARs and inform on spatial risk associations between areas and diseases. Copyright © 2016 John Wiley & Sons, Ltd.

We present a cancer phase I clinical trial design of a combination of two drugs with the goal of estimating the maximum tolerated dose curve in the two-dimensional Cartesian plane. A parametric model is used to describe the relationship between the doses of the two agents and the probability of dose limiting toxicity. The model is re-parameterized in terms of the probabilities of toxicities at dose combinations corresponding to the minimum and maximum doses available in the trial and the interaction parameter. Trial design proceeds using cohorts of two patients receiving doses according to univariate escalation with overdose control (EWOC), where at each stage of the trial, we seek a dose of one agent using the current posterior distribution of the MTD of this agent given the current dose of the other agent. The maximum tolerated dose curve is estimated as a function of Bayes estimates of the model parameters. Performance of the trial is studied by evaluating its design operating characteristics in terms of safety of the trial and percent of dose recommendation at dose combination neighborhoods around the true MTD curve and under model misspecifications for the true dose-toxicity relationship. The method is further extended to accommodate discrete dose combinations and compared with previous approaches under several scenarios. Copyright © 2016 John Wiley & Sons, Ltd.

To describe the spatial distribution of diseases, a number of methods have been proposed to model relative risks within areas. Most models use Bayesian hierarchical methods, in which one models both spatially structured and unstructured extra-Poisson variance present in the data. For modelling a single disease, the conditional autoregressive (CAR) convolution model has been very popular. More recently, a combined model was proposed that 'combines' ideas from the CAR convolution model and the well-known Poisson-gamma model. The combined model was shown to be a good alternative to the CAR convolution model when there was a large amount of uncorrelated extra-variance in the data. Less solutions exist for modelling two diseases simultaneously or modelling a disease in two sub-populations simultaneously. Furthermore, existing models are typically based on the CAR convolution model. In this paper, a bivariate version of the combined model is proposed in which the unstructured heterogeneity term is split up into terms that are shared and terms that are specific to the disease or subpopulation, while spatial dependency is introduced via a univariate or multivariate Markov random field. The proposed method is illustrated by analysis of disease data in Georgia (USA) and Limburg (Belgium) and in a simulation study. We conclude that the bivariate combined model constitutes an interesting model when two diseases are possibly correlated. As the choice of the preferred model differs between data sets, we suggest to use the new and existing modelling approaches together and to choose the best model via goodness-of-fit statistics. Copyright © 2016 John Wiley & Sons, Ltd.

This paper outlines a latent process model for forecasting multiple health outcomes arising from a common environmental exposure. Traditionally, surveillance models in environmental health do not link health outcome measures, such as morbidity or mortality counts, to measures of exposure, such as air pollution. Moreover, different measures of health outcomes are treated as independent, while it is known that they are correlated with one another over time as they arise in part from a common underlying exposure. We propose modelling an environmental exposure as a latent process, and we describe the implementation of such a model within a hierarchical Bayesian framework and its efficient computation using integrated nested Laplace approximations. Through a simulation study, we compare distinct univariate models for each health outcome with a bivariate approach. The bivariate model outperforms the univariate models in bias and coverage of parameter estimation, in forecast accuracy and in computational efficiency. The methods are illustrated with a case study using healthcare utilization and air pollution data from British Columbia, Canada, 2003-2011, where seasonal wildfires produce high levels of air pollution, significantly impacting population health. Copyright © 2016 John Wiley & Sons, Ltd.

Generic drugs have been commercialized in numerous countries. Most of these countries approve the commercialization of a generic drug when there is evidence of bioequivalence between the generic drug and the reference drug. Generally, the pharmaceutical industry is responsible for the bioequivalence test under the supervision of a regulatory agency. This procedure is concluded after a statistical data analysis. Several agencies adopt a standard statistical analysis based on procedures that were previously established. In practice, we face situations in which this standard model does not fit to some sets of bioequivalence data. In this study, we propose an evaluation of bioequivalence using univariate and bivariate models based on an extended generalized gamma distribution and a skew-t distribution, under a Bayesian perspective. We introduce a study of the empirical power of hypothesis tests for univariate models, showing advantages in the use of an extended generalized gamma distribution. Three sets of bioequivalence data were analyzed under these new procedures and compared with the standard model proposed by the majority of regulatory agencies. In order to verify that the asymmetrical distributions are usually better fitted for the data, when compared with the standard model, model discrimination methods were used, such as the Deviance Information Criterion (DIC) and quantile-quantile plots. The research concluded that, in general, the use of the extended generalized gamma distribution may be more appropriate to model bioequivalence data in the original scale. Copyright © 2016 John Wiley & Sons, Ltd.

This paper introduces a test of superiority of new anti-infective drug B over comparator drug A based on a randomized clinical trial. This test can be used to demonstrate assay (trial) sensitivity for noninferiority trials and rigorously tailor drug choice for individual patients. Our approach uses specialized baseline covariates XA ,XB , which should predict the benefits of drug A and drug B, respectively. Using a response surface model for the treatment effect, we test for superiority at the (XA ,XB ) point that is most likely to show superiority. We identify this point based on estimates from a novel half-blind pseudo likelihood, where we augment a blinded likelihood (mixed over the treatment indicator) with likelihoods for the overall success rates for drug A and drug B (mixed over XA ,XB ). The augmentation results in much better estimates than those based on the mixed blinded likelihood alone but, interestingly, the estimates almost behave as if they were based on fully blinded data. We also develop an analogous univariate method using XA for settings where XB has little variation. Permutation methods are used for testing. If the "half-blind" test rejects, pointwise confidence interval can be used to identify patients who would benefit from drug B. We compare the new tests to other methods with an example and via simulations.

Bivariate random-effects meta-analysis (BVMA) is a method of data synthesis that accounts for treatment effects measured on two outcomes. BVMA gives more precise estimates of the population mean and predicted values than two univariate random-effects meta-analyses (UVMAs). BVMA also addresses bias from incomplete reporting of outcomes. A few tutorials have covered technical details of BVMA of categorical or continuous outcomes. Limited guidance is available on how to analyze datasets that include trials with mixed continuous-binary outcomes where treatment effects on one outcome or the other are not reported. Given the advantages of Bayesian BVMA for handling missing outcomes, we present a tutorial for Bayesian BVMA of incompletely reported treatment effects on mixed bivariate outcomes. This step-by-step approach can serve as a model for our intended audience, the methodologist familiar with Bayesian meta-analysis, looking for practical advice on fitting bivariate models. To facilitate application of the proposed methods, we include our WinBUGS code. As an example, we use aggregate-level data from published trials to demonstrate the estimation of the effects of vitamin K and bisphosphonates on two correlated bone outcomes, fracture, and bone mineral density. We present datasets where reporting of the pairs of treatment effects on both outcomes was 'partially' complete (i.e., pairs completely reported in some trials), and we outline steps for modeling the incompletely reported data. To assess what is gained from the additional work required by BVMA, we compare the resulting estimates to those from separate UVMAs. We discuss methodological findings and make four recommendations. Copyright © 2015 John Wiley & Sons, Ltd.

We analyse paediatric ophthalmic data from a large sample of children aged between 3 and 8 years. We use a Bayesian additive conditional bivariate copula regression model with sinh-arcsinh marginal densities with location, scale, and shape parameters that depend smoothly on a covariate. We perform Bayesian inference about the unknown quantities of our model using a specially tailored Markov chain Monte Carlo algorithm. We gain new insights about the processes, which determine transformations in visual acuity with respect to age, including the nature of joint changes in both eyes as modelled with the age-related copula dependence parameter. We analyse posterior predictive distributions to identify children with unusual sight characteristics, distinguishing those who are bivariate, but not univariate outliers. In this way, we provide an innovative tool that enables clinicians to identify children with unusual sight who may otherwise be missed. We compare our simultaneous Bayesian method with a two-step frequentist generalised additive modelling approach.

The classic concordance correlation coefficient measures the agreement between two variables. In recent studies, concordance correlation coefficients have been generalized to deal with responses from a distribution from the exponential family using the univariate generalized linear mixed model. Multivariate data arise when responses on the same unit are measured repeatedly by several methods. The relationship among these responses is often of interest. In clustered mixed data, the correlation could be present between repeated measurements either within the same observer or between different methods on the same subjects. Indices for measuring such association are needed. This study proposes a series of indices, namely, intra-correlation, inter-correlation, and total correlation coefficients to measure the correlation under various circumstances in a multivariate generalized linear model, especially for joint modeling of clustered count and continuous outcomes. The proposed indices are natural extensions of the concordance correlation coefficient. We demonstrate the methodology with simulation studies. A case example of osteoarthritis study is provided to illustrate the use of these proposed indices. Copyright © 2014 John Wiley & Sons, Ltd.

Developing sophisticated statistical methods for go/no-go decisions is crucial for clinical trials, as planning phase III or phase IV trials is costly and time consuming. In this paper, we develop a novel Bayesian methodology for determining the probability of success of a treatment regimen on the basis of the current data of a given trial. We introduce a new criterion for calculating the probability of success that allows for inclusion of covariates as well as allowing for historical data based on the treatment regimen, and patient characteristics. A new class of prior distributions and covariate distributions is developed to achieve this goal. The methodology is quite general and can be used with univariate or multivariate continuous or discrete data, and it generalizes Chuang-Stein's work. This methodology will be invaluable for informing the scientist on the likelihood of success of the compound, while including the information of covariates for patient characteristics in the trial population for planning future pre-market or post-market trials.

The proportional subdistribution hazards model (i.e. Fine-Gray model) has been widely used for analyzing univariate competing risks data. Recently, this model has been extended to clustered competing risks data via frailty. To the best of our knowledge, however, there has been no literature on variable selection method for such competing risks frailty models. In this paper, we propose a simple but unified procedure via a penalized h-likelihood (HL) for variable selection of fixed effects in a general class of subdistribution hazard frailty models, in which random effects may be shared or correlated. We consider three penalty functions, least absolute shrinkage and selection operator (LASSO), smoothly clipped absolute deviation (SCAD) and HL, in our variable selection procedure. We show that the proposed method can be easily implemented using a slight modification to existing h-likelihood estimation approaches. Numerical studies demonstrate that the proposed procedure using the HL penalty performs well, providing a higher probability of choosing the true model than LASSO and SCAD methods without losing prediction accuracy. The usefulness of the new method is illustrated using two actual datasets from multi-center clinical trials.

With the fast growing field of epigenetics comes the need to better understand the intricacies of DNA methylation data analysis. High-throughput profiling using techniques, such as Illumina's BeadArray assay, enable the quantitative assessment of methylation. Challenges arise from the fact that resulting methylation levels (so-called beta values) are proportions between 0 and 1, often from an asymmetric, bimodal distribution with peaks close to 0 and 1. Therefore, the majority of standard statistical approaches do not apply. The logit transformation into so-called M-values is a common approach to circumvent this problem and aims to allow the use of common statistical methods. However, it can be observed that the transformation from beta to M-values does not necessarily result in an approximately homoscedastic distribution. Often, bimodality, asymmetry and heteroscedasticity are conserved even after transformation. We give an overview and discussion of methods suggested in the recent years that attempt to address the characteristics of methylation data in univariate screening settings. In order to identify 'differential' methylation with respect to covariates of interest while adjusting for confounders, we compare parametric methods, such as linear and beta regression, and nonparametric methods, such as rank-based regression. Our goal is to sensitise researchers to the challenges and issues that arise from this type of data as well as to present possible solutions.

The present study investigates the performance of several statistical tests to detect publication bias in diagnostic meta-analysis by means of simulation. While bivariate models should be used to pool data from primary studies in diagnostic meta-analysis, univariate measures of diagnostic accuracy are preferable for the purpose of detecting publication bias. In contrast to earlier research, which focused solely on the diagnostic odds ratio or its logarithm ($\ln\omega$), the tests are combined with four different univariate measures of diagnostic accuracy. For each combination of test and univariate measure, both type I error rate and statistical power are examined under diverse conditions. The results indicate that tests based on linear regression or rank correlation cannot be recommended in diagnostic meta-analysis, because type I error rates are either inflated or power is too low, irrespective of the applied univariate measure. In contrast, the combination of trim and fill and $\ln\omega$ has non-inflated or only slightly inflated type I error rates and medium to high power, even under extreme circumstances (at least when the number of studies per meta-analysis is large enough). Therefore, we recommend the application of trim and fill combined with $\ln\omega$ to detect funnel plot asymmetry in diagnostic meta-analysis. Please cite this paper as published in Statistics in Medicine (https://doi.org/10.1002/sim.6177)., Comment: arXiv admin note: text overlap with arXiv:2002.04775 by other authors

A multivariate meta-analysis of two or more correlated outcomes is expected to improve precision compared with a series of independent, univariate meta-analyses especially when there are studies reporting some but not all outcomes. Multivariate meta-analysis requires estimates of the within-study correlations, which are seldom available. Existing methods for analysing multiple outcomes simultaneously are limited to pairwise treatment comparisons. We propose a model for a joint, simultaneous synthesis of multiple dichotomous outcomes in a network of interventions and introduce a simple way to elicit expert opinion for the within-study correlations by utilizing a set of conditional probability parameters. We implement our multiple-outcomes network meta-analysis model within a Bayesian framework, which allows incorporation of expert information. As an example, we analyse two correlated dichotomous outcomes, response to the treatment and dropout rate, in a network of pharmacological interventions for acute mania. The produced estimates have narrower confidence intervals compared with the simple network meta-analysis. We conclude that the proposed model and the suggested prior elicitation method for correlations constitute a useful framework for performing network meta-analysis for multiple outcomes.

The statistical methodology for the design and analysis of clinical Phase II dose-response studies, with related software implementation, is well developed for the case of a normally distributed, homoscedastic response considered for a single timepoint in parallel group study designs. In practice, however, binary, count, or time-to-event endpoints are encountered, typically measured repeatedly over time and sometimes in more complex settings like crossover study designs. In this paper, we develop an overarching methodology to perform efficient multiple comparisons and modeling for dose finding, under uncertainty about the dose-response shape, using general parametric models. The framework described here is quite broad and can be utilized in situations involving for example generalized nonlinear models, linear and nonlinear mixed effects models, Cox proportional hazards models, with the main restriction being that a univariate dose-response relationship is modeled, that is, both dose and response correspond to univariate measurements. In addition to the core framework, we also develop a general purpose methodology to fit dose-response data in a computationally and statistically efficient way. Several examples illustrate the breadth of applicability of the results. For the analyses, we developed the R add-on package DoseFinding, which provides a convenient interface to the general approach adopted here. Copyright © 2013 John Wiley & Sons, Ltd.

Treatment effects for multiple outcomes can be meta-analyzed separately or jointly, but no systematic empirical comparison of the two approaches exists. From the Cochrane Library of Systematic Reviews, we identified 45 reviews, including 1473 trials and 258,675 patients, that contained two or three univariate meta-analyses of categorical outcomes for the same interventions that could also be analyzed jointly. Eligible were meta-analyses with at least seven trials reporting all outcomes for which the cross-classification tables were exactly recoverable (e.g., outcomes were mutually exclusive, or one was a subset of the other). This ensured known correlation structures. Outcomes in 40 reviews had an is-subset-of relationship, and those in 5 were mutually exclusive. We analyzed these data with univariate and multivariate models based on discrete and approximate likelihoods. Discrete models were fit in the Bayesian framework using slightly informative priors. The summary effects for each outcome were similar with univariate and multivariate meta-analyses (both using the approximate and discrete likelihoods); however, the multivariate model with the discrete likelihood gave smaller between-study variance estimates, and narrower predictive intervals for new studies. When differences in the summary treatment effects were examined, the multivariate models gave similar summary estimates but considerably longer (shorter) uncertainty intervals because of positive (negative) correlation between outcome treatment effects. It is unclear whether any of the examined reviews would change their overall conclusions based on multivariate versus univariate meta-analyses, because extra-analytical and context-specific considerations contribute to conclusions and, secondarily, because numerical differences were often modest.

Many authors have proposed different approaches to combine multiple endpoints in a univariate outcome measure in the literature. In case of binary or time-to-event variables, composite endpoints, which combine several event types within a single event or time-to-first-event analysis are often used to assess the overall treatment effect. A main drawback of this approach is that the interpretation of the composite effect can be difficult as a negative effect in one component can be masked by a positive effect in another. Recently, some authors proposed more general approaches based on a priority ranking of outcomes, which moreover allow to combine outcome variables of different scale levels. These new combined effect measures assign a higher impact to more important endpoints, which is meant to simplify the interpretation of results. Whereas statistical tests and models for binary and time-to-event variables are well understood, the latter methods have not been investigated in detail so far. In this paper, we will investigate the statistical properties of prioritized combined outcome measures. We will perform a systematical comparison to standard composite measures, such as the all-cause hazard ratio in case of time-to-event variables or the absolute rate difference in case of binary variables, to derive recommendations for different clinical trial scenarios. We will discuss extensions and modifications of the new effect measures, which simplify the clinical interpretation. Moreover, we propose a new method on how to combine the classical composite approach with a priority ranking of outcomes using a multiple testing strategy based on the closed test procedure.

The complexity of system biology means that any metabolic, genetic, or proteomic pathway typically includes so many components (e.g., molecules) that statistical methods specialized for overall testing of high-dimensional and commensurate outcomes are required. While many overall tests have been proposed, very few have power and sample size methods. We develop accurate power and sample size methods and software to facilitate study planning for high-dimensional pathway analysis. With an account of any complex correlation structure between high-dimensional outcomes, the new methods allow power calculation even when the sample size is less than the number of variables. We derive the exact (finite-sample) and approximate non-null distributions of the ‘univariate’ approach to repeated measures test statistic, as well as power-equivalent scenarios useful to generalize our numerical evaluations. Extensive simulations of group comparisons support the accuracy of the approximations even when the ratio of number of variables to sample size is large. We derive a minimum set of constants and parameters sufficient and practical for power calculation. Using the new methods and specifying the minimum set to determine power for a study of metabolic consequences of vitamin B6 deficiency helps illustrate the practical value of the new results. Free software implementing the power and sample size methods applies to a wide range of designs, including one group pre-intervention and post-intervention comparisons, multiple parallel group comparisons with one-way or factorial designs, and the adjustment and evaluation of covariate effects.

Making inferences about the average treatment effect using the random effects model for meta-analysis is problematic in the common situation where there is a small number of studies. This is because estimates of the between-study variance are not precise enough to accurately apply the conventional methods for testing and deriving a confidence interval for the average effect. We have found that a refined method for univariate meta-analysis, which applies a scaling factor to the estimated effects’ standard error, provides more accurate inference. We explain how to extend this method to the multivariate scenario and show that our proposal for refined multivariate meta-analysis and meta-regression can provide more accurate inferences than the more conventional approach. We explain how our proposed approach can be implemented using standard output from multivariate meta-analysis software packages and apply our methodology to two real examples. © 2013 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd.

Multivariate random effects meta-analysis (MRMA) is an appropriate way for synthesizing data from studies reporting multiple correlated outcomes. In a Bayesian framework, it has great potential for integrating evidence from a variety of sources. In this paper, we propose a Bayesian model for MRMA of mixed outcomes, which extends previously developed bivariate models to the trivariate case and also allows for combination of multiple outcomes that are both continuous and binary. We have constructed informative prior distributions for the correlations by using external evidence. Prior distributions for the within-study correlations were constructed by employing external individual patent data and using a double bootstrap method to obtain the correlations between mixed outcomes. The between-study model of MRMA was parameterized in the form of a product of a series of univariate conditional normal distributions. This allowed us to place explicit prior distributions on the between-study correlations, which were constructed using external summary data. Traditionally, independent ‘vague’ prior distributions are placed on all parameters of the model. In contrast to this approach, we constructed prior distributions for the between-study model parameters in a way that takes into account the inter-relationship between them. This is a flexible method that can be extended to incorporate mixed outcomes other than continuous and binary and beyond the trivariate case. We have applied this model to a motivating example in rheumatoid arthritis with the aim of incorporating all available evidence in the synthesis and potentially reducing uncertainty around the estimate of interest. © 2013 The Authors. Statistics inMedicine Published by John Wiley & Sons, Ltd.

We present new subset scan methods for multivariate event detection in massive space-time datasets. We extend the recently proposed 'fast subset scan' framework from univariate to multivariate data, enabling computationally efficient detection of irregular space-time clusters even when the numbers of spatial locations and data streams are large. For two variants of the multivariate subset scan, we demonstrate that the scan statistic can be efficiently optimized over proximity-constrained subsets of locations and over all subsets of the monitored data streams, enabling timely detection of emerging events and accurate characterization of the affected locations and streams. Using our new fast search algorithms, we perform an empirical comparison of the Subset Aggregation and Kulldorff multivariate subset scans on synthetic data and real-world disease surveillance tasks, demonstrating tradeoffs between the detection and characterization performance of the two methods.

Measures that quantify the impact of heterogeneity in univariate meta-analysis, including the very popular I2 statistic, are now well established. Multivariate meta-analysis, where studies provide multiple outcomes that are pooled in a single analysis, is also becoming more commonly used. The question of how to quantify heterogeneity in the multivariate setting is therefore raised. It is the univariate R2 statistic, the ratio of the variance of the estimated treatment effect under the random and fixed effects models, that generalises most naturally, so this statistic provides our basis. This statistic is then used to derive a multivariate analogue of I2, which we call . We also provide a multivariate H2 statistic, the ratio of a generalisation of Cochran's heterogeneity statistic and its associated degrees of freedom, with an accompanying generalisation of the usual I2 statistic, . Our proposed heterogeneity statistics can be used alongside all the usual estimates and inferential procedures used in multivariate meta-analysis. We apply our methods to some real datasets and show how our statistics are equally appropriate in the context of multivariate meta-regression, where study level covariate effects are included in the model. Our heterogeneity statistics may be used when applying any procedure for fitting the multivariate random effects model. Copyright © 2012 John Wiley & Sons, Ltd.

Multivariate meta-analysis allows the joint synthesis of multiple correlated outcomes from randomised trials, and is an alternative to a separate univariate meta-analysis of each outcome independently. Usually not all trials report all outcomes; furthermore, outcome reporting bias (ORB) within trials, where an outcome is measured and analysed but not reported on the basis of the results, may cause a biased set of the evidence to be available for some outcomes, potentially affecting the significance and direction of meta-analysis results. The multivariate approach, however, allows one to ‘borrow strength’ across correlated outcomes, to potentially reduce the impact of ORB. Assuming ORB missing data mechanisms, we aim to investigate the magnitude of bias in the pooled treatment effect estimates for multiple outcomes using univariate meta-analysis, and to determine whether the ‘borrowing of strength’ from multivariate meta-analysis can reduce the impact of ORB. A simulation study was conducted for a bivariate fixed effect meta-analysis of two correlated outcomes. The approach is illustrated by application to a Cochrane systematic review. Results show that the ‘borrowing of strength’ from a multivariate meta-analysis can reduce the impact of ORB on the pooled treatment effect estimates. We also examine the use of the Pearson correlation as a novel approach for dealing with missing within-study correlations, and provide an extension to bivariate random-effects models that reduce ORB in the presence of heterogeneity. Copyright © 2012 John Wiley & Sons, Ltd.

Multivariate longitudinal data with mixed continuous and discrete responses with the possibility of non-ignorable missingness are often common in follow-up medical studies and their analysis needs to be developed. Standard methods of analysis based on the strong and the unverifiable assumption of missing at random (MAR) mechanism could be highly misleading. A way out of this problem is to start with methods that simultaneously allow modelling non-ignorable mechanism, which includes somehow troubling computations that are often time consuming, then we can use a sensitivity analysis, in which one estimates models under a range of assumptions about non-ignorability parameters to study the impact of these parameters on key inferences. A general index of sensitivity to non-ignorability (ISNI) to measure sensitivity of key inferences in a neighborhood of MAR model without fitting a complicated not MAR (NMAR) model for univariate generalized linear models and for models used for univariate longitudinal normal and non-Gaussian data with potentially NMAR dropout are well presented in the literature. In this paper we extend ISNI methodology to analyze multivariate longitudinal mixed data subject to non-ignorable dropout in which the non-ignorable dropout model could be dependent on the mixed responses. The approach is illustrated by analyzing a longitudinal data set in which the general substantive goal of the study is to better understand the relations between parental assessment of child's antisocial behavior and child's reading recognition skill.

When global techniques, based on fractional polynomials (FPs), are employed for modeling potentially nonlinear effects of several continuous covariates on a response, accessible model equations are obtained. However, local features might be missed. Therefore, a procedure is introduced, which systematically checks model fits, obtained by the multivariable fractional polynomial (MFP) approach, for overlooked local features. Statistically significant local polynomials are then parsimoniously added. This approach, called MFP + L, is seen to result in an effective control of the Type I error with respect to the addition of local components in a small simulation study with univariate and multivariable settings. Prediction performance is compared with that of a penalized regression spline technique. In a setting unfavorable for FPs, the latter outperforms the MFP approach, if there is much information in the data. However, the addition of local features reduces this performance difference. There is only a small detrimental effect in settings where the MFP approach performs better. In an application example with children's respiratory health data, fits from the spline-based approach indicate many local features, but MFP + L adds only few significant features, which seem to have good support in the data. The proposed approach may be expected to be superior in settings with local features, but retains the good properties of the MFP approach in a large number of settings where global functions are sufficient.

To evaluate globally the average bioequivalence of a test drug to a reference drug in a pharmacokinetic (PK) study under a 2 x 2 crossover design, we consider directly comparing the associated drug concentration-time curves. Statistical models for the drug concentrations are suggested when the concentrations measured at different time points are distributed according to a generalized gamma distribution and the mean concentrations over time is described by a one-compartment PK model. A multiple test based on the supreme distance between the two curves over the time interval under study is then proposed for testing the equivalence of the two drug concentration-time curves. The results of a Monte Carlo study suggest that, comparative to the conventional univariate and bivariate tests, the proposed test is more powerful for detecting the global bioequivalence and superior on maintaining its level when the global bioequivalence is violated. The application of the proposed tests is finally illustrated by using the data in a PK study involving two brands of benzbromarone tablets for reducing the uric acid.

This paper discusses further advances in making robust predictions with the Holt-Winters forecasts for a variety of syndromic time series behaviors and introduces a control-chart detection approach based on these forecasts. Using three collections of time series data, we compare biosurveillance alerting methods with quantified measures of forecast agreement, signal sensitivity, and time-to-detect. The study presents practical rules for initialization and parameterization of biosurveillance time series. Several outbreak scenarios are used for detection comparison. We derive an alerting algorithm from forecasts using Holt-Winters-generalized smoothing for prospective application to daily syndromic time series. The derived algorithm is compared with simple control-chart adaptations and to more computationally intensive regression modeling methods. The comparisons are conducted on background data from both authentic and simulated data streams. Both types of background data include time series that vary widely by both mean value and cyclic or seasonal behavior. Plausible, simulated signals are added to the background data for detection performance testing at signal strengths calculated to be neither too easy nor too hard to separate the compared methods. Results show that both the sensitivity and the timeliness of the Holt-Winters-based algorithm proved to be comparable or superior to that of the more traditional prediction methods used for syndromic surveillance.

Diagnostic tests are increasingly evaluated with systematic reviews and this has lead to the recent developments of statistical methods to analyse such data. The most commonly used method is the summary receiver operating characteristic (SROC) curve, which can be fitted with a non-linear bivariate random-effects model. This paper focuses on the practical problems of interpreting and presenting data from such analyses. First, many meta-analyses may be underpowered to obtain reliable estimates of the SROC parameters. Second, the SROC model may be inappropriate. In these situations, a summary with two univariate meta-analyses of the true and false positive rates (TPRs and FPRs) may be more appropriate. We characterize the type of problems that can occur in fitting these models and present an algorithm to guide the analyst of such studies, with illustrations from analyses of published data. A set of R functions, freely available to perform these analyses, can be downloaded from (www.diagmeta.info).

A common situation in the biological and social sciences is to have data on one or more variables measured longitudinally on a sample of individuals. A problem of growing interest in these areas is the grouping of individuals into one of two or more clusters according to their longitudinal behavior. Recently, methods have been proposed to deal with cases where individuals are classified into clusters through a linear model of mixed univariate effects deriving from a longitudinally measured variable. The method proposed in the current work deals with the case of clustering and then classification based on two or more variables measured longitudinally, through the fitting of non-linear multivariate mixed effect models, and with consideration given to parameter estimation for balanced and unbalanced data using an EM algorithm. The application of the method is illustrated with an example in which the clusters are identified and the classification into clusters is compared with the true membership of individuals in one of two groups, which is known at the end of the follow-up period.

To estimate the multivariate regression model from multiple individual studies, it would be challenging to obtain results if the input from individual studies only provide univariate or incomplete multivariate regression information. Samsa et al. (J. Biomed. Biotechnol. 2005; 2:113–123) proposed a simple method to combine coefficients from univariate linear regression models into a multivariate linear regression model, a method known as synthesis analysis. However, the validity of this method relies on the normality assumption of the data, and it does not provide variance estimates. In this paper we propose a new synthesis method that improves on the existing synthesis method by eliminating the normality assumption, reducing bias, and allowing for the variance estimation of the estimated parameters.

Multivariate outcomes measured longitudinally over time are common in medicine, public health, psychology and sociology. The typical (saturated) longitudinal multivariate regression model has a separate set of regression coefficients for each outcome. However, multivariate outcomes are often quite similar and many outcomes can be expected to respond similarly to changes in covariate values. Given a set of outcomes likely to share common covariate effects, we propose the clustered outcome common predictor effect model and offer a two step iterative algorithm to fit the model using available software for univariate longitudinal data. Outcomes that share predictor effects need not be chosen a priori; we propose model selection tools to let the data select outcome clusters. We apply the proposed methods to psychometric data from adolescent children of HIV+ parents.

In clinical studies, dependent bivariate continuous responses may approach equilibrium over time. We propose an autoregressive linear mixed effects model for bivariate longitudinal data in which the current responses are regressed on the previous responses of both variables, fixed effects, and random effects. The equilibria are modeled using fixed and random effects. This model is a bivariate extension of the model for univariate longitudinal data given by Funatogawa et al. (Statist. Med. 2007; 26:2113-2130). As an illustration of the approach we analyze parathyroid hormone and serum calcium measurements in the treatment of secondary hyperparathyroidism in chronic hemodialysis patients.

We analyze data obtained from a study designed to evaluate training effects on the performance of certain motor activities of Parkinson's disease patients. Maximum likelihood methods were used to fit beta-binomial/Poisson regression models tailored to evaluate the effects of training on the numbers of attempted and successful specified manual movements in 1 min periods, controlling for disease stage and use of the preferred hand. We extend models previously considered by other authors in univariate settings to account for the repeated measures nature of the data. The results suggest that the expected number of attempts and successes increase with training, except for patients with advanced stages of the disease using the non-preferred hand.

The use of standard univariate fixed- and random-effects models in meta-analysis has become well known in the last 20 years. However, these models are unsuitable for meta-analysis of clinical trials that present multiple survival estimates (usually illustrated by a survival curve) during a follow-up period. Therefore, special methods are needed to combine the survival curve data from different trials in a meta-analysis. For this purpose, only fixed-effects models have been suggested in the literature. In this paper, we propose a multivariate random-effects model for joint analysis of survival proportions reported at multiple time points and in different studies, to be combined in a meta-analysis. The model could be seen as a generalization of the fixed-effects model of Dear (Biometrics 1994; 50:989-1002). We illustrate the method by using a simulated data example as well as using a clinical data example of meta-analysis with aggregated survival curve data. All analyses can be carried out with standard general linear MIXED model software. Copyright (c) 2008 John Wiley & Sons, Ltd.