Allowing for uncertainty due to missing data in meta-analysis--part 2: hierarchical models

We propose a hierarchical model for the analysis of data from several randomized trials where some outcomes are missing. The degree of departure from a missing-at-random assumption in each arm of each trial is expressed by an informative missing odds ratio (IMOR). We require a realistic prior for the IMORs, including an assessment of the prior correlation between IMORs in different arms and in different trials. The model is fitted by Monte Carlo Markov Chain techniques. By applying the method in three different data sets, we show that it is possible to appropriately capture the extra uncertainty due to missing data, and we discuss in what circumstances it is possible to learn about the IMOR.     

Estimating cancer incidence using a Bayesian back‐calculation approach

We propose a Bayesian hierarchical model for the calculation of incidence counts from mortality data by a convolution equation that expresses mortality through its relationship with incidence and the survival probability density. The basic idea is to use mortality data together with an estimate of the survival distribution from cancer incidence to cancer mortality to reconstruct the numbers of individuals who constitute previously incident cases that give rise to the observed pattern of cancer mortality. This model is novel because it takes into account the uncertainty from the survival distribution; thus, a Bayesian‐mixture cure model for survival is introduced. Furthermore, projections are obtained starting from a Bayesian age‐period‐cohort model. The main advantage of the proposed approach is its consideration of the three components of the model: the convolution equation, the survival mixture cure model and the age‐period‐cohort projection within a directed acyclic graph model. Furthermore, the estimation are obtained through the Gibbs sampler. We applied the model to cases of women with stomach cancer using six age classes [15–45], [45–55], [55–65], [65–75], [75–85] and [85–95] and validated it by using data from the Tuscany Cancer Registry. The model proposed and the program implemented are convenient because they allow different cancer disease to be analysed because the survival time is modelled by flexible distributions that are able to describe different trends. Copyright © 2014 John Wiley & Sons, Ltd.     

Bayesian hierarchical modeling of drug stability data

Stability data are commonly analyzed using linear fixed or random effect model. The linear fixed effect model does not take into account the batch-to-batch variation, whereas the random effect model may suffer from the unreliable shelf-life estimates due to small sample size. Moreover, both methods do not utilize any prior information that might have been available. In this article, we propose a Bayesian hierarchical approach to modeling drug stability data. Under this hierarchical structure, we first use Bayes factor to test the poolability of batches. Given the decision on poolability of batches, we then estimate the shelf-life that applies to all batches. The approach is illustrated with two example data sets and its performance is compared in simulation studies with that of the commonly used frequentist methods.     

Bayesian multivariate hierarchical transformation models for ROC analysis

A Bayesian multivariate hierarchical transformation model (BMHTM) is developed for receiver operating characteristic (ROC) curve analysis based on clustered continuous diagnostic outcome data with covariates. Two special features of this model are that it incorporates non-linear monotone transformations of the outcomes and that multiple correlated outcomes may be analysed. The mean, variance, and transformation components are all modelled parametrically, enabling a wide range of inferences. The general framework is illustrated by focusing on two problems: (1) analysis of the diagnostic accuracy of a covariate-dependent univariate test outcome requiring a Box-Cox transformation within each cluster to map the test outcomes to a common family of distributions; (2) development of an optimal composite diagnostic test using multivariate clustered outcome data. In the second problem, the composite test is estimated using discriminant function analysis and compared to the test derived from logistic regression analysis where the gold standard is a binary outcome. The proposed methodology is illustrated on prostate cancer biopsy data from a multi-centre clinical trial.     

Bayesian analysis of rare variants in genetic association studies

Recent advances in next-generation sequencing technologies facilitate the detection of rare variants, making it possible to uncover the roles of rare variants in complex diseases. As any single rare variants contain little variation, association analysis of rare variants requires statistical methods that can effectively combine the information across variants and estimate their overall effect. In this study, we propose a novel Bayesian generalized linear model for analyzing multiple rare variants within a gene or genomic region in genetic association studies. Our model can deal with complicated situations that have not been fully addressed by existing methods, including issues of disparate effects and nonfunctional variants. Our method jointly models the overall effect and the weights of multiple rare variants and estimates them from the data. This approach produces different weights to different variants based on their contributions to the phenotype, yielding an effective summary of the information across variants. We evaluate the proposed method and compare its performance to existing methods on extensive simulated data. The results show that the proposed method performs well under all situations and is more powerful than existing approaches.     

Bayesian mixture modeling of gene‐environment and gene‐gene interactions

With the advent of rapid and relatively cheap genotyping technologies there is now the opportunity to attempt to identify gene‐environment and gene‐gene interactions when the number of genes and environmental factors is potentially large. Unfortunately the dimensionality of the parameter space leads to a computational explosion in the number of possible interactions that may be investigated. The full model that includes all interactions and main effects can be unstable, with wide confidence intervals arising from the large number of estimated parameters. We describe a hierarchical mixture model that allows all interactions to be investigated simultaneously, but assumes the effects come from a mixture prior with two components, one that reflects small null effects and the second for epidemiologically significant effects. Effects from the former are effectively set to zero, hence increasing the power for the detection of real signals. The prior framework is very flexible, which allows substantive information to be incorporated into the analysis. We illustrate the methods first using simulation, and then on data from a case‐control study of lung cancer in Central and Eastern Europe. Genet. Epidemiol. 34:16–25, 2010. © 2009 Wiley‐Liss, Inc.     

A Bayesian hierarchical approach to multirater correlated ROC analysis

In a common ROC study design, several readers are asked to rate diagnostics of the same cases processed under different modalities. We describe a Bayesian hierarchical model that facilitates the analysis of this study design by explicitly modelling the three sources of variation inherent to it. In so doing, we achieve substantial reductions in the posterior uncertainty associated with estimates of the differences in areas under the estimated ROC curves and corresponding reductions in the mean squared error (MSE) of these estimates. Based on simulation studies, both the widths of coverage intervals and MSE of estimates of differences in the area under the curves appear to be reduced by a factor that often exceeds five. Thus, our methodology has important implications for increasing the power of analyses based on ROC data collected from an available study population.     

Bayesian hierarchical modeling of longitudinal glaucomatous visual fields using a two‐stage approach

The Bayesian approach has become increasingly popular because it allows to fit quite complex models to data via Markov chain Monte Carlo sampling. However, it is also recognized nowadays that Markov chain Monte Carlo sampling can become computationally prohibitive when applied to a large data set. We encountered serious computational difficulties when fitting an hierarchical model to longitudinal glaucoma data of patients who participate in an ongoing Dutch study. To overcome this problem, we applied and extended a recently proposed two‐stage approach to model these data. Glaucoma is one of the leading causes of blindness in the world. In order to detect deterioration at an early stage, a model for predicting visual fields (VFs) in time is needed. Hence, the true underlying VF progression can be determined, and treatment strategies can then be optimized to prevent further VF loss. Because we were unable to fit these data with the classical one‐stage approach upon which the current popular Bayesian software is based, we made use of the two‐stage Bayesian approach. The considered hierarchical longitudinal model involves estimating a large number of random effects and deals with censoring and high measurement variability. In addition, we extended the approach with tools for model evaluation. Copyright © 2017 John Wiley & Sons, Ltd.     

Relative rate of change in cognitive score network dynamics via Bayesian hierarchical models reveal spatial patterns of neurodegeneration

The degeneration of the human brain is a complex process, which often affects certain brain regions due to healthy aging or disease. This degeneration can be evaluated on regions of interest (ROI) in the brain through probabilistic networks and morphological estimates. Current approaches for finding such networks are limited to analyses at discrete neuropsychological stages, which cannot appropriately account for connectivity dynamics over the onset of cognitive deterioration, and morphological changes are seldom unified with connectivity networks, despite known dependencies. To overcome these limitations, a probabilistic wombling model is proposed to simultaneously estimate ROI cortical thickness and covariance networks contingent on rates of change in cognitive decline. This proposed model was applied to analyze longitudinal data from healthy control (HC) and Alzheimer's disease (AD) groups and found connection differences pertaining to regions, which play a crucial role in lasting cognitive impairment, such as the entorhinal area and temporal regions. Moreover, HC cortical thickness estimates were significantly higher than those in the AD group across all ROIs. The analyses presented in this work will help practitioners jointly analyze brain tissue atrophy at the ROI-level conditional on neuropsychological networks, which could potentially allow for more targeted therapeutic interventions.     

Bayesian methods for the design and interpretation of clinical trials in very rare diseases

This paper considers the design and interpretation of clinical trials comparing treatments for conditions so rare that worldwide recruitment efforts are likely to yield total sample sizes of 50 or fewer, even when patients are recruited over several years. For such studies, the sample size needed to meet a conventional frequentist power requirement is clearly infeasible. Rather, the expectation of any such trial has to be limited to the generation of an improved understanding of treatment options. We propose a Bayesian approach for the conduct of rare‐disease trials comparing an experimental treatment with a control where patient responses are classified as a success or failure. A systematic elicitation from clinicians of their beliefs concerning treatment efficacy is used to establish Bayesian priors for unknown model parameters. The process of determining the prior is described, including the possibility of formally considering results from related trials. As sample sizes are small, it is possible to compute all possible posterior distributions of the two success rates. A number of allocation ratios between the two treatment groups can be considered with a view to maximising the prior probability that the trial concludes recommending the new treatment when in fact it is non‐inferior to control. Consideration of the extent to which opinion can be changed, even by data from the best feasible design, can help to determine whether such a trial is worthwhile. © 2014 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd.     

Epigenetic change detection and pattern recognition via Bayesian hierarchical hidden Markov models

Epigenetics is the study of changes to the genome that can switch genes on or off and determine which proteins are transcribed without altering the DNA sequence. Recently, epigenetic changes have been linked to the development and progression of disease such as psychiatric disorders. High‐throughput epigenetic experiments have enabled researchers to measure genome‐wide epigenetic profiles and yield data consisting of intensity ratios of immunoprecipitation versus reference samples. The intensity ratios can provide a view of genomic regions where protein binding occur under one experimental condition and further allow us to detect epigenetic alterations through comparison between two different conditions. However, such experiments can be expensive, with only a few replicates available. Moreover, epigenetic data are often spatially correlated with high noise levels. In this paper, we develop a Bayesian hierarchical model, combined with hidden Markov processes with four states for modeling spatial dependence, to detect genomic sites with epigenetic changes from two‐sample experiments with paired internal control. One attractive feature of the proposed method is that the four states of the hidden Markov process have well‐defined biological meanings and allow us to directly call the change patterns based on the corresponding posterior probabilities. In contrast, none of existing methods can offer this advantage. In addition, the proposed method offers great power in statistical inference by spatial smoothing (via hidden Markov modeling) and information pooling (via hierarchical modeling). Both simulation studies and real data analysis in a cocaine addiction study illustrate the reliability and success of this method. Copyright © 2012 John Wiley & Sons, Ltd.     

Bayesian mixture models for the incorporation of prior knowledge to inform genetic association studies

In the last decade, numerous genome‐wide linkage and association studies of complex diseases have been completed. The critical question remains of how to best use this potentially valuable information to improve study design and statistical analysis in current and future genetic association studies. With genetic effect size for complex diseases being relatively small, the use of all available information is essential to untangle the genetic architecture of complex diseases. One promising approach to incorporating prior knowledge from linkage scans, or other information, is to up‐ or down‐weight P‐values resulting from genetic association study in either a frequentist or Bayesian manner. As an alternative to these methods, we propose a fully Bayesian mixture model to incorporate previous knowledge into on‐going association analysis. In this approach, both the data and previous information collectively inform the association analysis, in contrast to modifying the association results (P‐values) to conform to the prior knowledge. By using a Bayesian framework, one has flexibility in modeling, and is able to comprehensively assess the impact of model specification on posterior inferences. We illustrate the use of this method through a genome‐wide linkage study of colorectal cancer, and a genome‐wide association study of colorectal polyps. Genet. Epidemiol. 34:418–426, 2010. © 2010 Wiley‐Liss, Inc.     

Analysis of ulcer data using hierarchical generalized linear models

In multi-centre clinical trials, heterogeneities in individual hospital treatment effects can be modelled as random effects. Estimates of the individual hospital treatment effects and estimate of the mean treatment effect, allowing for the presence of overall hospital differences, are required, together with some measure of their uncertainty. Systematic inferences from the hierarchical-likelihood are now possible, using hierarchical generalized linear models. We show how to construct profile likelihoods for the treatment effects of individual hospitals.     

A powerful association test of multiple genetic variants using a random‐effects model

There is an emerging interest in sequencing‐based association studies of multiple rare variants. Most association tests suggested in the literature involve collapsing rare variants with or without weighting. Recently, a variance‐component score test [sequence kernel association test (SKAT)] was proposed to address the limitations of collapsing method. Although SKAT was shown to outperform most of the alternative tests, its applications and power might be restricted and influenced by missing genotypes. In this paper, we suggest a new method based on testing whether the fraction of causal variants in a region is zero. The new association test, T _REM, is derived from a random‐effects model and allows for missing genotypes, and the choice of weighting function is not required when common and rare variants are analyzed simultaneously. We performed simulations to study the type I error rates and power of four competing tests under various conditions on the sample size, genotype missing rate, variant frequency, effect directionality, and the number of non‐causal rare variant and/or causal common variant. The simulation results showed that T _REM was a valid test and less sensitive to the inclusion of non‐causal rare variants and/or low effect common variants or to the presence of missing genotypes. When the effects were more consistent in the same direction, T _REM also had better power performance. Finally, an application to the Shanghai Breast Cancer Study showed that rare causal variants at the FGFR2 gene were detected by T _REM and SKAT, but T _REM produced more consistent results for different sets of rare and common variants. Copyright © 2013 John Wiley & Sons, Ltd.     

A Bayesian mixture of semiparametric mixed‐effects joint models for skewed‐longitudinal and time‐to‐event data

In longitudinal studies, it is of interest to investigate how repeatedly measured markers in time are associated with a time to an event of interest, and in the mean time, the repeated measurements are often observed with the features of a heterogeneous population, non‐normality, and covariate measured with error because of longitudinal nature. Statistical analysis may complicate dramatically when one analyzes longitudinal–survival data with these features together. Recently, a mixture of skewed distributions has received increasing attention in the treatment of heterogeneous data involving asymmetric behaviors across subclasses, but there are relatively few studies accommodating heterogeneity, non‐normality, and measurement error in covariate simultaneously arose in longitudinal–survival data setting. Under the umbrella of Bayesian inference, this article explores a finite mixture of semiparametric mixed‐effects joint models with skewed distributions for longitudinal measures with an attempt to mediate homogeneous characteristics, adjust departures from normality, and tailor accuracy from measurement error in covariate as well as overcome shortages of confidence in specifying a time‐to‐event model. The Bayesian mixture of joint modeling offers an appropriate avenue to estimate not only all parameters of mixture joint models but also probabilities of class membership. Simulation studies are conducted to assess the performance of the proposed method, and a real example is analyzed to demonstrate the methodology. The results are reported by comparing potential models with various scenarios. Copyright © 2015 John Wiley & Sons, Ltd.     

Assessment of rare BRCA1 and BRCA2 variants of unknown significance using hierarchical modeling

Current evidence suggests that the genetic risk of breast cancer may be caused primarily by rare variants. However, while classification of protein-truncating mutations as deleterious is relatively straightforward, distinguishing as deleterious or neutral the large number of rare missense variants is a difficult on-going task. In this article, we present one approach to this problem, hierarchical statistical modeling of data observed in a case-control study of contralateral breast cancer (CBC) in which all the participants were genotyped for variants in BRCA1 and BRCA2. Hierarchical modeling permits leverage of information from observed correlations of characteristics of groups of variants with case-control status to infer with greater precision the risks of individual rare variants. A total of 181 distinct rare missense variants were identified among the 705 cases with CBC and the 1,398 controls with unilateral breast cancer. The model identified three bioinformatic hierarchical covariates, align-GV, align-GD, and SIFT scores, each of which was modestly associated with risk. Collectively, the 11 variants that were classified as adverse on the basis of all the three bioinformatic predictors demonstrated a stronger risk signal. This group included five of six missense variants that were classified as deleterious at the outset by conventional criteria. The remaining six variants can be considered as plausibly deleterious, and deserving of further investigation (BRCA1 R866C; BRCA2 G1529R, D2665G, W2626C, E2663V, and R3052W). Hierarchical modeling is a strategy that has promise for interpreting the evidence from future association studies that involve sequencing of known or suspected cancer genes.     

The use of hierarchical models for estimating relative risks of individual genetic variants: an application to a study of melanoma

For major genes known to influence the risk of cancer, an important task is to determine the risks conferred by individual variants, so that one can appropriately counsel carriers of these mutations. This is a challenging task, since new mutations are continually being identified, and there is typically relatively little empirical evidence available about each individual mutation. Hierarchical modeling offers a natural strategy to leverage the collective evidence from these rare variants with sparse data. This can be accomplished when there are available higher-level covariates that characterize the variants in terms of attributes that could distinguish their association with disease. In this article, we explore the use of hierarchical modeling for this purpose using data from a large population-based study of the risks of melanoma conferred by variants in the CDKN2A gene. We employ both a pseudo-likelihood approach and a Bayesian approach using Gibbs sampling. The results indicate that relative risk estimates tend to be primarily influenced by the individual case-control frequencies when several cases and/or controls are observed with the variant under study, but that relative risk estimates for variants with very sparse data are more influenced by the higher-level covariate values, as one would expect. The analysis offers encouragement that we can draw strength from the aggregating power of hierarchical models to provide guidance to medical geneticists when they offer counseling to patients with rare or even hitherto unobserved variants. However, further research is needed to validate the application of asymptotic methods to such sparse data.     

Inclusion of biological knowledge in a Bayesian shrinkage model for joint estimation of SNP effects

With the aim of improving detection of novel single‐nucleotide polymorphisms (SNPs) in genetic association studies, we propose a method of including prior biological information in a Bayesian shrinkage model that jointly estimates SNP effects. We assume that the SNP effects follow a normal distribution centered at zero with variance controlled by a shrinkage hyperparameter. We use biological information to define the amount of shrinkage applied on the SNP effects distribution, so that the effects of SNPs with more biological support are less shrunk toward zero, thus being more likely detected. The performance of the method was tested in a simulation study (1,000 datasets, 500 subjects with ～200 SNPs in 10 linkage disequilibrium (LD) blocks) using a continuous and a binary outcome. It was further tested in an empirical example on body mass index (continuous) and overweight (binary) in a dataset of 1,829 subjects and 2,614 SNPs from 30 blocks. Biological knowledge was retrieved using the bioinformatics tool Dintor, which queried various databases. The joint Bayesian model with inclusion of prior information outperformed the standard analysis: in the simulation study, the mean ranking of the true LD block was 2.8 for the Bayesian model versus 3.6 for the standard analysis of individual SNPs; in the empirical example, the mean ranking of the six true blocks was 8.5 versus 9.3 in the standard analysis. These results suggest that our method is more powerful than the standard analysis. We expect its performance to improve further as more biological information about SNPs becomes available.     

层次贝叶斯模型在校正低估以估计慢性病患病率中的应用

目的 探讨层次贝叶斯模型中在慢性病患病率估计研究中的应用,以校正低估的计数数据从而获得潜在的真实患病率。 方法 基于真实的患者人数服从Poisson分布,建档登记的患者人数服从二项分布的假设,考虑与疾病患病水平及建档过程相关的影响因素,建立层次贝叶斯模型对某地17个县(市)2018—2020年建档登记的高血压患者人数进行校正,并对影响患病及建档过程的相关因素的效应进行了估计。 结果 校正之后该地总的高血压患病率为25.62%(95%CI: 22.66%～28.58%),而建档登记的患病率为10.85%。在该地的17个县(市)中,建档率最高为17.70%(95%CI: 14.65%～20.74%),最低为12.96%(95%CI: 8.09%～17.82%)。老龄化率与高血压患病率呈现正相关关系。城镇化率、当地老龄人口的规范化管理率、已建档高血压患者的规范化管理率与高血压患者建档率呈正相关关系。 结论 层次贝叶斯模型在校正低估数据,估计真实的患病率中效果优良,在校正低估从而获得真实的患病人数方面具有潜在的应用价值。     

Bayesian analysis of nonlinear mixed‐effects mixture models for longitudinal data with heterogeneity and skewness

It is a common practice to analyze complex longitudinal data using nonlinear mixed‐effects (NLME) models with normality assumption. The NLME models with normal distributions provide the most popular framework for modeling continuous longitudinal outcomes, assuming individuals are from a homogeneous population and relying on random‐effects to accommodate inter‐individual variation. However, the following two issues may standout: (i) normality assumption for model errors may cause lack of robustness and subsequently lead to invalid inference and unreasonable estimates, particularly, if the data exhibit skewness and (ii) a homogeneous population assumption may be unrealistically obscuring important features of between‐subject and within‐subject variations, which may result in unreliable modeling results. There has been relatively few studies concerning longitudinal data with both heterogeneity and skewness features. In the last two decades, the skew distributions have shown beneficial in dealing with asymmetric data in various applications. In this article, our objective is to address the simultaneous impact of both features arisen from longitudinal data by developing a flexible finite mixture of NLME models with skew distributions under Bayesian framework that allows estimates of both model parameters and class membership probabilities for longitudinal data. Simulation studies are conducted to assess the performance of the proposed models and methods, and a real example from an AIDS clinical trial illustrates the methodology by modeling the viral dynamics to compare potential models with different distribution specifications; the analysis results are reported. Copyright © 2014 John Wiley & Sons, Ltd.