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author:("CHU, haitian")
1.  Meta-analysis of Proportions of Rare Events–A Comparison of Exact Likelihood Methods with Robust Variance Estimation 
The conventional random effects model for meta-analysis of proportions approximates within-study variation using a normal distribution. Due to potential approximation bias, particularly for the estimation of rare events such as some adverse drug reactions, the conventional method is considered inferior to the exact methods based on binomial distributions. In this paper, we compare two existing exact approaches—beta binomial (B-B) and normal-binomial (N-B)—through an extensive simulation study with focus on the case of rare events that are commonly encountered in medical research. In addition, we implement the empirical (“sandwich”) estimator of variance into the two models to improve the robustness of the statistical inferences. To our knowledge, it is the first such application of sandwich estimator of variance to meta-analysis of proportions. The simulation study shows that the B-B approach tends to have substantially smaller bias and mean squared error than N-B for rare events with occurrences under five percent, while N-B outperforms B-B for relatively common events. Use of the sandwich estimator of variance improves the precision of estimation for both models. We illustrate the two approaches by applying them to two published meta-analysis from the fields of orthopedic surgery and prevention of adverse drug reactions.
doi:10.1080/03610918.2014.911901
PMCID: PMC5010877  PMID: 27605731
2.  The Impact of Excluding Trials from Network Meta-Analyses – An Empirical Study 
PLoS ONE  2016;11(12):e0165889.
Network meta-analysis (NMA) expands the scope of a conventional pairwise meta-analysis to simultaneously compare multiple treatments, which has an inherent appeal for clinicians, patients, and policy decision makers. Two recent reports have shown that the impact of excluding a treatment on NMAs can be substantial. However, no one has assessed the impact of excluding a trial from NMAs, which is important because many NMAs selectively include trials in the analysis. This article empirically examines the impact of trial exclusion using both the arm-based (AB) and contrast-based (CB) approaches, by reanalyzing 20 published NMAs involving 725 randomized controlled trials and 449,325 patients. For the population-averaged absolute risk estimates using the AB approach, the average fold changes across all networks ranged from 1.004 (with standard deviation 0.004) to 1.072 (with standard deviation 0.184); while the maximal fold changes ranged from 1.032 to 2.349. In 12 out of 20 NMAs, a 1.20-fold or larger change is observed in at least one of the population-averaged absolute risk estimates. In addition, while excluding a trial can substantially change the estimated relative effects (e.g., log odds ratios), there is no systematic difference in terms of changes between the two approaches. Changes in treatment rankings are observed in 7 networks and changes in inconsistency are observed in 3 networks. We do not observe correlations between changes in treatment effects, treatment rankings and inconsistency. Finally, we recommend rigorous inclusion and exclusion criteria, logical study selection process, and reasonable network geometry to ensure robustness and generalizability of the results of NMAs.
doi:10.1371/journal.pone.0165889
PMCID: PMC5142775  PMID: 27926924
3.  A Comparison of Primed Low-Frequency Repetitive Transcranial Magnetic Stimulation Treatments In Chronic Stroke 
Brain stimulation  2015;8(6):1074-1084.
Background
Preceding low-frequency repetitive transcranial magnetic stimulation (rTMS) with a bout of high-frequency rTMS called priming potentiates the after-effects of the former in healthy adults. The utility of primed rTMS in stroke remains under-explored despite its theoretical benefits in enhancing cortical excitability and motor function.
Objective
To ascertain the efficacy of priming in chronic stroke by comparing changes in cortical excitability and paretic hand function following three types of primed low-frequency rTMS treatments.
Methods
Eleven individuals with chronic stroke participated in this repeated-measures study receiving three treatments to the contralesional primary motor cortex in randomized order: 6 Hz primed 1 Hz rTMS, 1 Hz primed 1 Hz rTMS, and sham 6 Hz primed active 1 Hz rTMS. Within- and between-treatment differences from baseline in cortical excitability and paretic hand function from baseline were analyzed using mixed effects linear models.
Results
6 Hz primed 1 Hz rTMS produced significant within-treatment differences from baseline in ipsilesional cortical silent period (CSP) duration and short-interval intracortical inhibition. Compared to 1 Hz priming and sham 6 Hz priming of 1 Hz rTMS, active 6 Hz priming generated significantly greater decreases in ipsilesional CSP duration. These heightened effects were not observed for intracortical facilitation or interhemispheric inhibition excitability measures.
Conclusion
Our findings demonstrate the efficacy of 6 Hz primed 1 Hz rTMS in probing homeostatic plasticity mechanisms in the stroke brain as best demonstrated by differences CSP duration and SICI from baseline. Though 6 Hz priming did not universally enhance cortical excitability across measures, our findings pose important implications in non-invasive brain stimulation application in stroke rehabilitation.
doi:10.1016/j.brs.2015.06.007
PMCID: PMC4656059  PMID: 26198365
stroke; priming; repetitive transcranial magnetic stimulation; metaplasticity; homeostatic plasticity
4.  A composite likelihood method for bivariate meta-analysis in diagnostic systematic reviews 
Diagnostic systematic review is a vital step in the evaluation of diagnostic technologies. In many applications, it involves pooling pairs of sensitivity and specificity of a dichotomized diagnostic test from multiple studies. We propose a composite likelihood method for bivariate meta-analysis in diagnostic systematic reviews. This method provides an alternative way to make inference on diagnostic measures such as sensitivity, specificity, likelihood ratios and diagnostic odds ratio. Its main advantages over the standard likelihood method are the avoidance of the non-convergence problem, which is non-trivial when the number of studies are relatively small, the computational simplicity and some robustness to model mis-specifications. Simulation studies show that the composite likelihood method maintains high relative efficiency compared to that of the standard likelihood method. We illustrate our method in a diagnostic review of the performance of contemporary diagnostic imaging technologies for detecting metastases in patients with melanoma.
doi:10.1177/0962280214562146
PMCID: PMC4466215  PMID: 25512146
Bivariate generalized linear mixed effects model; Composite likelihood; Diagnostic accuracy; Diagnostic review; Meta-analysis
5.  A Bayesian missing data framework for generalized multiple outcome mixed treatment comparisons 
Research synthesis methods  2015;7(1):6-22.
Summary
Bayesian statistical approaches to mixed treatment comparisons (MTCs) are becoming more popular due to their flexibility and interpretability. Many randomized clinical trials report multiple outcomes with possible inherent correlations. Moreover, MTC data are typically sparse (though richer than standard meta-analysis, comparing only two treatments) and researchers often choose study arms based upon which treatments emerge as superior in previous trials. In this paper, we summarize existing hierarchical Bayesian methods for MTCs with a single outcome, and introduce novel Bayesian approaches for multiple outcomes simultaneously, rather than in separate MTC analyses. We do this by incorporating partially observed data and its correlation structure between outcomes through contrast- and arm-based parameterizations that consider any unobserved treatment arms as missing data to be imputed. We also extend the model to apply to all types of generalized linear model outcomes, such as count or continuous responses. We offer a simulation study under various missingness mechanisms (e.g., MCAR, MAR, and MNAR) providing evidence that our models outperform existing models in terms of bias, MSE, and coverage probability, then illustrate our methods with a real MTC dataset. We close with a discussion of our results, several contentious issues in MTC analysis, and a few avenues for future methodological development.
doi:10.1002/jrsm.1153
PMCID: PMC4779385  PMID: 26536149
Bayesian hierarchical model; Markov chain Monte Carlo; missingness mechanism; network meta-analysis
7.  A hybrid model for combining case-control and cohort studies in systematic reviews of diagnostic tests 
Systematic reviews of diagnostic tests often involve a mixture of case-control and cohort studies. The standard methods for evaluating diagnostic accuracy only focus on sensitivity and specificity and ignore the information on disease prevalence contained in cohort studies. Consequently, such methods cannot provide estimates of measures related to disease prevalence, such as population averaged or overall positive and negative predictive values, which reflect the clinical utility of a diagnostic test. In this paper, we propose a hybrid approach that jointly models the disease prevalence along with the diagnostic test sensitivity and specificity in cohort studies, and the sensitivity and specificity in case-control studies. In order to overcome the potential computational difficulties in the standard full likelihood inference of the proposed hybrid model, we propose an alternative inference procedure based on the composite likelihood. Such composite likelihood based inference does not suffer computational problems and maintains high relative efficiency. In addition, it is more robust to model mis-specifications compared to the standard full likelihood inference. We apply our approach to a review of the performance of contemporary diagnostic imaging modalities for detecting metastases in patients with melanoma.
doi:10.1111/rssc.12087
PMCID: PMC4401477  PMID: 25897179
Composite likelihood; Diagnostic accuracy study; Independence likelihood; Meta-analysis; Pseudolikelihood; Systematic review
8.  Bayesian Analysis on Meta-analysis of Case-control Studies Accounting for Within-study Correlation 
In retrospective studies, odds ratio is often used as the measure of association. Under independent beta prior assumption, the exact posterior distribution of odds ratio given a single 2 × 2 table has been derived in the literature. However, independence between risks within the same study may be an oversimplified assumption because cases and controls in the same study are likely to share some common factors and thus to be correlated. Furthermore, in a meta-analysis of case-control studies, investigators usually have multiple 2×2 tables. In this paper, we first extend the published results on a single 2×2 table to allow within study prior correlation while retaining the advantage of closed form posterior formula, and then extend the results to multiple 2 × 2 tables and regression setting. The hyperparameters, including within study correlation, are estimated via an empirical Bayes approach. The overall odds ratio and the exact posterior distribution of the study-specific odds ratio are inferred based on the estimated hyperparameters. We conduct simulation studies to verify our exact posterior distribution formulas and investigate the finite sample properties of the inference for the overall odds ratio. The results are illustrated through a twin study for genetic heritability and a meta-analysis for the association between the N-acetyltransferase 2 (NAT2) acetylation status and colorectal cancer.
doi:10.1177/0962280211430889
PMCID: PMC3683108  PMID: 22143403
Bivariate beta-binomial model; Exact method; Hypergeometric function; Meta-analysis; Odds ratio; Sarmanov family
9.  IsoDOT Detects Differential RNA-isoform Expression/Usage with respect to a Categorical or Continuous Covariate with High Sensitivity and Specificity 
We have developed a statistical method named IsoDOT to assess differential isoform expression (DIE) and differential isoform usage (DIU) using RNA-seq data. Here isoform usage refers to relative isoform expression given the total expression of the corresponding gene. IsoDOT performs two tasks that cannot be accomplished by existing methods: to test DIE/DIU with respect to a continuous covariate, and to test DIE/DIU for one case versus one control. The latter task is not an uncommon situation in practice, e.g., comparing the paternal and maternal alleles of one individual or comparing tumor and normal samples of one cancer patient. Simulation studies demonstrate the high sensitivity and specificity of IsoDOT. We apply IsoDOT to study the effects of haloperidol treatment on the mouse transcriptome and identify a group of genes whose isoform usages respond to haloperidol treatment.
doi:10.1080/01621459.2015.1040880
PMCID: PMC4662594  PMID: 26617424
RNA-seq; isoform; penalized regression; differential isoform expression; differential isoform usage
10.  Joint Modeling of Longitudinal and Survival Data with Missing and Left-Censored Time-Varying Covariates 
Statistics in medicine  2014;33(26):4560-4576.
We propose a joint model for longitudinal and survival data with time-varying covariates subject to detection limits and intermittent missingness at random (MAR). The model is motivated by data from the Multicenter AIDS Cohort Study (MACS), in which HIV+ subjects have viral load and CD4 cell count measured at repeated visits along with survival data. We model the longitudinal component using a normal linear mixed model, modeling the trajectory of CD4 cell count by regressing on viral load and other covariates. The viral load data are subject to both left-censoring due to detection limits (17%) and intermittent missingness (27%). The survival component of the joint model is a Cox model with time-dependent covariates for death due to AIDS. The longitudinal and survival models are linked using the trajectory function of the linear mixed model. A Bayesian analysis is conducted on the MACS data using the proposed joint model. The proposed method is shown to improve the precision of estimates when compared to alternative methods.
doi:10.1002/sim.6242
PMCID: PMC4189992  PMID: 24947785
Detection Limit; Joint Modeling; Missing Data; Multicenter AIDS Cohort Study
11.  Analysis of Cigarette Purchase Task Instrument Data with a Left-Censored Mixed Effects Model 
The drug purchase task is a frequently used instrument for measuring the relative reinforcing efficacy (RRE) of a substance, a central concept in psychopharmacological research. While a purchase task instrument, such as the cigarette purchase task (CPT), provides a comprehensive and inexpensive way to assess various aspects of a drug’s RRE, the application of conventional statistical methods to data generated from such an instrument may not be adequate by simply ignoring or replacing the extra zeros or missing values in the data with arbitrary small consumption values, e.g. 0.001. We applied the left-censored mixed effects model to CPT data from a smoking cessation study of college students and demonstrated its superiority over the existing methods with simulation studies. Theoretical implications of the findings, limitations of the proposed method and future directions of research are also discussed.
doi:10.1037/a0031610
PMCID: PMC4636201  PMID: 23356731
cigarette purchase task; college smoking; demand curve; left-censored mixed effects model; relative reinforcing efficacy
12.  Meta-analysis of randomized trials on the association of prophylactic acyclovir and HIV-1 viral load in individuals coinfected with herpes simplex virus-2 
AIDS (London, England)  2011;25(10):1265-1269.
Objective
To summarize the randomized evidence regarding the association between acyclovir use and HIV-1 replication as measured by plasma HIV-1 RNA viral load among individuals coinfected with herpes simplex virus (HSV)-2.
Design
Meta-analysis of seven randomized trials conducted between 2000 and 2009. Inclusion criteria composed of acyclovir or valacyclovir use as prophylaxis among individuals coinfected with HIV-1 and HSV-2 who were ineligible for highly active antiretroviral therapy. HIV-1 viral load was the outcome.
Methods
Random-effects summarization was used to combine treatment effect estimates. Stratified and meta-regression analyses were used to compare estimated treatment effects by characteristics of trials and participants.
Results
The summary treatment effect estimate was −0.33 (95% confidence interval: −0.56, −0.10, 95% population effects interval: −0.74, 0.08) log10 copies, an approximate halving of plasma viral load. However, there was marked heterogeneity (P < 0.001). Older median age, valacyclovir, higher compliance, earlier publication, and shorter study length were associated with a larger decrease in viral load as compared with their counterparts.
Conclusion
Current evidence suggests a range of favorable effects of acyclovir on plasma HIV-1 viral load among persons coinfected with HSV-2.
doi:10.1097/QAD.0b013e328347fa37
PMCID: PMC4501265  PMID: 21666542
acyclovir; herpes simplex virus; HIV; meta-analysis
13.  A unification of models for meta-analysis of diagnostic accuracy studies without a gold standard 
Biometrics  2014;71(2):538-547.
Several statistical methods for meta-analysis of diagnostic accuracy studies have been discussed in the presence of a gold standard. However, in practice, the selected reference test may be imperfect due to measurement error, non-existence, invasive nature, or expensive cost of a gold standard. It has been suggested that treating an imperfect reference test as a gold standard can lead to substantial bias in the estimation of diagnostic test accuracy. Recently, two models have been proposed to account for imperfect reference test, namely, a multivariate generalized linear mixed model (MGLMM) and a hierarchical summary receiver operating characteristic (HSROC) model. Both models are very flexible in accounting for heterogeneity in accuracies of tests across studies as well as the dependence between tests. In this paper, we show that these two models, although with different formulations, are closely related and are equivalent in the absence of study-level covariates. Furthermore, we provide the exact relations between the parameters of these two models and assumptions under which two models can be reduced to equivalent submodels. On the other hand, we show that some submodels of the MGLMM do not have corresponding equivalent submodels of the HSROC model, and vice versa. With three real examples, we illustrate the cases when fitting the MGLMM and HSROC models leads to equivalent submodels and hence identical inference, and the cases when the inferences from two models are slightly different. Our results generalize the important relations between the bivariate generalized linear mixed model and HSROC model when the reference test is a gold standard.
doi:10.1111/biom.12264
PMCID: PMC4416105  PMID: 25358907
Diagnostic test; Generalized linear mixed model; Hierarchical model; Imperfect reference test; Meta-analysis
14.  Investigation of Efavirenz Discontinuation in Multi-ethnic Populations of HIV-positive Individuals by Genetic Analysis 
EBioMedicine  2015;2(7):706-712.
Background
Efavirenz (EFV) based antiretroviral therapy is expanding worldwide. However discontinuation of EFV containing regimens is common in some patients, particularly black patients, due most often to neuropsychiatric side effects. These adverse drug effects often result in premature drug discontinuation, as well as considerable morbidity.
Methods
We genotyped CYP2A6, CYP2B6 and CYP3A4, which encode enzymes principally involved in EFV metabolism, from patients enrolled in the multinational SMART, FIRST and ESPRIT studies, for whom outcome data of treatment adherence was available. Patients with loss or decrease of function single nucleotide polymorphisms (SNPs) in the above genes were assigned a risk score based upon the number of SNPs present weighted relative to whether CYP2B6 (main metabolism pathway) and/or CYP2A6 and CYP3A4 (accessory pathways) were involved. Cox regression models were used to study the association between high genetic risk and time from initiation to EFV discontinuation. Failure was defined as discontinuation of an antiretroviral regimen other than for virologic failure or protocol determined discontinuation.
Findings
Patients with highest pharmacogenetic risk, as defined by cumulative SNPs in CYP2A6, CYP2B6 and CYP3A4, have an increased risk of discontinuation of EFV containing therapy compared to patients with lower genetic risk scores (adjusted HR 1.9, 95% CI 1.2, 3.1, P = 0.009). High genetic risk score was not associated with an increased risk of discontinuing atazanavir or nevirapine. High genetic risk was present more often in blacks compared to non-blacks (Adjusted OR 4.5, 95% CI: 1.9,10.5), and treatment discontinuation was also increased in blacks overall (Adjusted HR 1.4, 95% CI 1.0, 1.9). However, high genetic risk was more associated with treatment discontinuation than race alone for both blacks (Adjusted OR 1.9, 95% CI 0.8, 4.8) and non-blacks (Adjusted OR 5.3, 95% CI 1.5, 18.0).
Interpretation
Premature discontinuation of ART delays the time to effective long term viral suppression, and is associated with significant morbidity. Pharmacogenetic testing may predict those with a high risk of EFV discontinuation, and therefore should be considered in patients in whom initiation of EFV based ART is being considered.
Funding
Funded by NIH.
Highlights
•Efavirenz containing antiretroviral regimens are frequently complicated by premature discontinuation due to adverse drug effects.•Elevated pharmacogenetic risk based on genes for efavirenz-metabolizing enzymes is associated with premature discontinuation of efavirenz.•Pharmacogenetic testing prior to prescribing antiretrovirals may decrease premature discontinuation due to adverse effects.
doi:10.1016/j.ebiom.2015.05.012
PMCID: PMC4534686  PMID: 26288843
HIV; Pharmacogenetics; Efavirenz; Premature discontinuation
15.  Network Meta-analysis of Randomized Clinical Trials: Reporting the Proper Summaries 
Clinical trials (London, England)  2013;11(2):246-262.
Background
In the absence of sufficient data directly comparing two or more treatments, indirect comparisons using network meta-analyses (NMA) across trials can potentially provide useful information to guide the use of treatments. Under current contrast-based methods for NMA of binary outcomes, which do not model the “baseline” risks and focus on modeling the relative treatment effects, the patient-centered measures including the overall treatment-specific event rates and risk differences are not provided, which may create some unnecessary obstacles for patients to comprehensively understand and trade-off efficacy and safety measures. Many NMAs only report odds ratios which are commonly misinterpreted as risk ratios by many physicians, patients and their care givers.
Purpose
We aim to develop network meta-analysis to accurately estimate the overall treatment-specific event rates.
Methods
A novel Bayesian hierarchical model, developed from a missing data perspective, that borrows information across multiple treatment arms, is used to illustrate how treatment-specific event proportions, risk differences (RD) and relative risks (RR) can be computed in NMAs. We first compare our approach to alternative methods using two hypothetical NMAs assuming either a fixe RR or a fixed RD, and then use two published NMAs on new-generation anti-depressants and antimanic drugs to illustrate the improved reporting of NMAs possible with this new approach.
Results
In the hypothetical NMAs, our approach outperforms current contrast-based NMA methods in terms of bias. In the NMAs on new-generation anti-depressants and on antimanic drugs, the outcomes were common with proportions ranging from 0.21 to 0.62. As expected, the RR estimates differ from ORs. In addition, differences in the magnitude of relative treatment effects and the statistical significance of several pairwise comparisons from previous report could lead to different treatment recommendations.
Limitations
First, to facilitate the estimation of overall treatment-specific event proportions, we assume that each study hypothetically compares all treatments, with unstudied arms being missing at random conditional on the observed arms. However, it is plausible that investigators may have selected treatment arms on purpose based on the results of previous trials, which may lead to “nonignorable missingness” and potentially bias our event rate estimation. Second, we have not considered methods to identify and account for potential inconsistency in our missing data network meta-analysis framework. Both methods await further development.
Conclusions
The proposed NMA method can accurately estimate treatment-specific event rates or proportions, RDs, and RRs, and is recommended in practice. Application of this approach can lead to different conclusions, as illustrated here, from current NMA models that only estimate ORs.
doi:10.1177/1740774513498322
PMCID: PMC3972291  PMID: 24096635
network meta-analysis; multiple treatment comparisons; population averaged event rates; Bayesian hierarchical model
16.  Accounting for Outcome Misclassification in Estimates of the Effect of Occupational Asbestos Exposure on Lung Cancer Death 
American Journal of Epidemiology  2013;179(5):641-647.
In studies of the health effects of asbestos, lung cancer death is subject to misclassification. We used modified maximum likelihood to explore the effects of outcome misclassification on the rate ratio of lung cancer death per 100 fiber-years per milliliter of cumulative asbestos exposure in a cohort study of textile workers in Charleston, South Carolina, followed from 1940 to 2001. The standard covariate-adjusted estimate of the rate ratio was 1.94 (95% confidence interval: 1.55, 2.44), and modified maximum likelihood produced similar results when we assumed that the specificity of outcome classification was 0.98. With sensitivity assumed to be 0.80 and specificity assumed to be 0.95, estimated rate ratios were further from the null and less precise (rate ratio = 2.17; 95% confidence interval: 1.59, 2.98). In the present context, standard estimates for the effect of asbestos on lung cancer death were similar to estimates accounting for the limited misclassification. However, sensitivity analysis using modified maximum likelihood was needed to verify the robustness of standard estimates, and this approach will provide unbiased estimates in settings with more misclassification.
doi:10.1093/aje/kwt309
PMCID: PMC3927979  PMID: 24352593
asbestos; bias; sensitivity and specificity
17.  Maximum Likelihood, Profile Likelihood, and Penalized Likelihood: A Primer 
American Journal of Epidemiology  2013;179(2):252-260.
The method of maximum likelihood is widely used in epidemiology, yet many epidemiologists receive little or no education in the conceptual underpinnings of the approach. Here we provide a primer on maximum likelihood and some important extensions which have proven useful in epidemiologic research, and which reveal connections between maximum likelihood and Bayesian methods. For a given data set and probability model, maximum likelihood finds values of the model parameters that give the observed data the highest probability. As with all inferential statistical methods, maximum likelihood is based on an assumed model and cannot account for bias sources that are not controlled by the model or the study design. Maximum likelihood is nonetheless popular, because it is computationally straightforward and intuitive and because maximum likelihood estimators have desirable large-sample properties in the (largely fictitious) case in which the model has been correctly specified. Here, we work through an example to illustrate the mechanics of maximum likelihood estimation and indicate how improvements can be made easily with commercial software. We then describe recent extensions and generalizations which are better suited to observational health research and which should arguably replace standard maximum likelihood as the default method.
doi:10.1093/aje/kwt245
PMCID: PMC3873110  PMID: 24173548
epidemiologic methods; maximum likelihood; modeling; penalized estimation; regression; statistics
18.  Statistical Methods for Multivariate Meta-analysis of Diagnostic Tests: An Overview and Tutorial 
Statistical methods in medical research  2013;10.1177/0962280213492588.
Summary
In this article, we present an overview and tutorial of statistical methods for meta-analysis of diagnostic tests under two scenarios: 1) when the reference test can be considered a gold standard; and 2) when the reference test cannot be considered a gold standard. In the first scenario, we first review the conventional summary receiver operating characteristics (ROC) approach and a bivariate approach using linear mixed models (BLMM). Both approaches require direct calculations of study-specific sensitivities and specificities. We next discuss the hierarchical summary ROC curve approach for jointly modeling positivity criteria and accuracy parameters, and the bivariate generalized linear mixed models (GLMM) for jointly modeling sensitivities and specificities. We further discuss the trivariate GLMM for jointly modeling prevalence, sensitivities and specificities, which allows us to assess the correlations among the three parameters. These approaches are based on the exact binomial distribution and thus do not require an ad hoc continuity correction. Last, we discuss a latent class random effects model for meta-analysis of diagnostic tests when the reference test itself is imperfect for the second scenario. A number of case studies with detailed annotated SAS code in procedures MIXED and NLMIXED are presented to facilitate the implementation of these approaches.
doi:10.1177/0962280213492588
PMCID: PMC3883791  PMID: 23804970
meta-analysis; diagnostic test; gold standard; generalized linear mixed models
19.  Change-Point Models to Estimate the Limit of Detection 
Statistics in medicine  2013;32(28):4995-5007.
In many biological and environmental studies, measured data is subject to a limit of detection. The limit of detection is generally defined as the lowest concentration of analyte that can be differentiated from a blank sample with some certainty. Data falling below the limit of detection is left-censored, falling below a level that is easily quantified by a measuring device. A great deal of interest lies in estimating the limit of detection for a particular measurement device. In this paper we propose a change-point model to estimate the limit of detection using data from an experiment with known analyte concentrations. Estimation of the limit of detection proceeds by a two-stage maximum likelihood method. Extensions are considered that allow for censored measurements and data from multiple experiments. A simulation study is conducted demonstrating that in some settings the change-point model provides less biased estimates of the limit of detection than conventional methods. The proposed method is then applied to data from an HIV pilot study.
doi:10.1002/sim.5872
PMCID: PMC3858526  PMID: 23784922
change point; limit of detection; linear calibration curve; two-stage maximum likelihood
20.  A trivariate meta-analysis of diagnostic studies accounting for prevalence and non-evaluable subjects: re-evaluation of the meta-analysis of coronary CT angiography studies 
Background
A recent paper proposed an intent-to-diagnose approach to handle non-evaluable index test results and discussed several alternative approaches, with an application to the meta-analysis of coronary CT angiography diagnostic accuracy studies. However, no simulation studies have been conducted to test the performance of the methods.
Methods
We propose an extended trivariate generalized linear mixed model (TGLMM) to handle non-evaluable index test results. The performance of the intent-to-diagnose approach, the alternative approaches and the extended TGLMM approach is examined by extensive simulation studies. The meta-analysis of coronary CT angiography diagnostic accuracy studies is re-evaluated by the extended TGLMM.
Results
Simulation studies showed that the intent-to-diagnose approach under-estimate sensitivity and specificity. Under the missing at random (MAR) assumption, the TGLMM gives nearly unbiased estimates of test accuracy indices and disease prevalence. After applying the TGLMM approach to re-evaluate the coronary CT angiography meta-analysis, overall median sensitivity is 0.98 (0.967, 0.993), specificity is 0.875 (0.827, 0.923) and disease prevalence is 0.478 (0.379, 0.577).
Conclusions
Under MAR assumption, the intent-to-diagnose approach under-estimate both sensitivity and specificity, while the extended TGLMM gives nearly unbiased estimates of sensitivity, specificity and prevalence. We recommend the extended TGLMM to handle non-evaluable index test subjects.
doi:10.1186/1471-2288-14-128
PMCID: PMC4280699  PMID: 25475705
Meta-analysis; Diagnostic test; Non-evaluable subjects
21.  A Bayesian approach to strengthen inference for case-control studies with multiple error-prone exposure assessments 
Statistics in medicine  2013;32(25):4426-4437.
In case-control studies, exposure assessments are almost always error-prone. In the absence of a gold standard, two or more assessment approaches are often used to classify people with respect to exposure. Each imperfect assessment tool may lead to misclassification of exposure assignment; the exposure misclassification may be differential with respect to case status or not; and, the errors in exposure classification under the different approaches may be independent (conditional upon the true exposure status) or not. Although methods have been proposed to study diagnostic accuracy in the absence of a gold standard, these methods are infrequently used in case-control studies to correct exposure misclassification that is simultaneously differential and dependent. In this paper, we proposed a Bayesian method to estimate the measurement-error corrected exposure-disease association, accounting for both differential and dependent misclassification. The performance of the proposed method is investigated using simulations, which show that the proposed approach works well, as well as an application to a case-control study assessing the association between asbestos exposure and mesothelioma.
doi:10.1002/sim.5842
PMCID: PMC3788843  PMID: 23661263
Case-control study; gold standard; misclassification; dependent; differential
22.  DNA methylation profiling in the Carolina Breast Cancer Study defines cancer subclasses differing in clinicopathologic characteristics and survival 
Introduction
Breast cancer is a heterogeneous disease, with several intrinsic subtypes differing by hormone receptor (HR) status, molecular profiles, and prognosis. However, the role of DNA methylation in breast cancer development and progression and its relationship with the intrinsic tumor subtypes are not fully understood.
Methods
A microarray targeting promoters of cancer-related genes was used to evaluate DNA methylation at 935 CpG sites in 517 breast tumors from the Carolina Breast Cancer Study, a population-based study of invasive breast cancer.
Results
Consensus clustering using methylation (β) values for the 167 most variant CpG loci defined four clusters differing most distinctly in HR status, intrinsic subtype (luminal versus basal-like), and p53 mutation status. Supervised analyses for HR status, subtype, and p53 status identified 266 differentially methylated CpG loci with considerable overlap. Genes relatively hypermethylated in HR+, luminal A, or p53 wild-type breast cancers included FABP3, FGF2, FZD9, GAS7, HDAC9, HOXA11, MME, PAX6, POMC, PTGS2, RASSF1, RBP1, and SCGB3A1, whereas those more highly methylated in HR-, basal-like, or p53 mutant tumors included BCR, C4B, DAB2IP, MEST, RARA, SEPT5, TFF1, THY1, and SERPINA5. Clustering also defined a hypermethylated luminal-enriched tumor cluster 3 that gene ontology analysis revealed to be enriched for homeobox and other developmental genes (ASCL2, DLK1, EYA4, GAS7, HOXA5, HOXA9, HOXB13, IHH, IPF1, ISL1, PAX6, TBX1, SOX1, and SOX17). Although basal-enriched cluster 2 showed worse short-term survival, the luminal-enriched cluster 3 showed worse long-term survival but was not independently prognostic in multivariate Cox proportional hazard analysis, likely due to the mostly early stage cases in this dataset.
Conclusions
This study demonstrates that epigenetic patterns are strongly associated with HR status, subtype, and p53 mutation status and may show heterogeneity within tumor subclass. Among HR+ breast tumors, a subset exhibiting a gene signature characterized by hypermethylation of developmental genes and poorer clinicopathologic features may have prognostic value and requires further study. Genes differentially methylated between clinically important tumor subsets have roles in differentiation, development, and tumor growth and may be critical to establishing and maintaining tumor phenotypes and clinical outcomes.
Electronic supplementary material
The online version of this article (doi:10.1186/s13058-014-0450-6) contains supplementary material, which is available to authorized users.
doi:10.1186/s13058-014-0450-6
PMCID: PMC4303129  PMID: 25287138
23.  An Empirical Bayes Method for Multivariate Meta-analysis with an Application in Clinical Trials 
We propose an empirical Bayes method for evaluating overall and study-specific treatment effects in multivariate meta-analysis with binary outcome. Instead of modeling transformed proportions or risks via commonly used multivariate general or generalized linear models, we directly model the risks without any transformation. The exact posterior distribution of the study-specific relative risk is derived. The hyperparameters in the posterior distribution can be inferred through an empirical Bayes procedure. As our method does not rely on the choice of transformation, it provides a flexible alternative to the existing methods and in addition, the correlation parameter can be intuitively interpreted as the correlation coefficient between risks.
doi:10.1080/03610926.2012.700379
PMCID: PMC4115294  PMID: 25089070
Bivariate beta-binomial model; Exact method; Hypergeometric function; Meta-analysis; Relative risk; Sarmanov family
24.  Graduated driver licensing and motor vehicle crashes involving teenage drivers: an exploratory age-stratified meta-analysis 
Objective
Graduated Driver Licensing (GDL) has been implemented in Australia, Canada, New Zealand, USA and Israel. We conducted an exploratory summary of available data to estimate whether GDL effects varied with age.
Methods
We searched MEDLINE and other sources from 1991–2011. GDL evaluation studies with crashes resulting in injuries or deaths were eligible. They had to provide age-specific incidence rate ratios with CI or information for calculating these quantities. We included studies from individual states or provinces, but excluded national studies. We examined rates based on person-years, not license-years.
Results
Of 1397 papers, 144 were screened by abstract and 47 were reviewed. Twelve studies from 11 US states and one Canadian province were selected for meta-analysis for age 16, eight were selected for age 17, and four for age 18. Adjusted rate ratios were pooled using random effects models. The pooled adjusted rate ratios for the association of GDL presence with crash rates was 0.78 (95% CI 0.72 to 0.84) for age 16 years, 0.94 (95% CI 0.93 to 0.96) for 17 and 1.00 (95% CI 0.95 to 1.04) for 18. The difference between these three rate ratios was statistically significant: p<0.001.
Conclusions
GDL policies were associated with a 22% reduction in crash rates among 16-year-old drivers, but only a 6% reduction for 17-year-old drivers. GDL showed no association with crashes among 18-year-old drivers. Because we had few studies to summarise, particularly for older adolescents, our findings should be considered exploratory.
doi:10.1136/injuryprev-2012-040474
PMCID: PMC4103686  PMID: 23211352
25.  Nitrogen Dioxide and Allergic Sensitization in the 2005–2006 National Health and Nutrition Examination Survey 
Respiratory medicine  2013;107(11):1763-1772.
Background
Allergic sensitization is a risk factor for asthma and allergic diseases. The relationship between ambient air pollution and allergic sensitization is unclear.
Objective
To investigate the relationship between ambient air pollution and allergic sensitization in a nationally representative sample of the US population.
Methods
We linked annual average concentrations of nitrogen dioxide (NO2), particulate matter ≤ 10 µm (PM10), particulate matter ≤ 2.5 µm (PM25), and summer concentrations of ozone (O3), to allergen-specific immunoglobulin E (IgE) data for participants in the 2005–2006 National Health and Nutrition Examination Survey (NHANES). In addition to the monitor-based air pollution estimates, we used the Community Multiscale Air Quality (CMAQ) model to increase the representation of rural participants in our sample. Logistic regression with population-based sampling weights was used to calculate adjusted prevalence odds ratios per 10 ppb increase in O3 and NO2, per 10 µg/m3 increase in PM10, and per 5 µg/m3 increase in PM2.5 adjusting for race, gender, age, socioeconomic status, smoking, and urban/rural status.
Results
Using CMAQ data, increased levels of NO2 were associated with positive IgE to any (OR 1.15, 95% CI 1.04, 1.27), inhalant (OR 1.17, 95% CI 1.02, 1.33), and outdoor (OR 1.16, 95% CI 1.03, 1.31) allergens. Higher PM2.5 levels were associated with positivity to indoor allergen-specific IgE (OR 1.24, 95% CI 1.13, 1.36). Effect estimates were similar using monitored data.
Conclusions
Increased ambient NO2 was consistently associated with increased prevalence of allergic sensitization.
doi:10.1016/j.rmed.2013.08.010
PMCID: PMC4071349  PMID: 24045117
air pollution; allergic; sensitization; epidemiology; NHANES; IgE

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