On the Optimal Combination of Elliptically Distributed Biomarkers to Improve Diagnostic Accuracy.

Diagnostic biomarkers play a critical role in biomedical research, particularly for the diagnosis and prediction of diseases, etc. To enhance diagnostic accuracy, extensive research about combining multiple biomarkers has been developed based on the multivariate normality, which is often not true in practice, as most biomarkers follow distributions that deviate from normality. While the likelihood ratio combination is recognized to be the optimal approach, it is complicated to calculate. To achieve a more accurate and effective combination of biomarkers, especially when these biomarkers deviate from normality, we propose using a receiver operating characteristic (ROC) curve methodology based on the optimal combination of elliptically distributed biomarkers. In this paper, we derive the ROC curve function for the elliptical likelihood ratio combination. Further, proceeding from the derived best combinations of biomarkers, we propose an efficient technique via nonparametric maximum likelihood estimate (NPMLE) to build empirical estimation. Simulation results show that the proposed elliptical combination method consistently provided better performance, demonstrating its robustness in handling various distribution types of biomarkers. We apply the proposed method to two real datasets: Autism/autism spectrum disorder (ASD) and neural tube defects (NTD). In both applications, the elliptical likelihood ratio combination improves the AUC value compared to the multivariate normal likelihood ratio combination and the best linear combination.

Significance tests for covariates in the diagnostic accuracy index of a biomarker against a continuous gold standard.

Receiver operating characteristic (ROC) curve is a popular tool to describe and compare the diagnostic accuracy of biomarkers when a binary-scale gold standard is available. However, there are many examples of diagnostic tests whose gold standards are continuous. Hence, Several extensions of receiver operating characteristic (ROC) curve are proposed to evaluate the diagnostic potential of biomarkers when the gold standard is continuous-scale. Moreover, in evaluating these biomarkers, it is often necessary to consider the effects of covariates on the diagnostic accuracy of the biomarker of interest. Covariates may include subject characteristics, expertise of the test operator, test procedures or aspects of specimen handling. Applying the covariate adjustment to the case that the gold standard is continuous is challenging and has not been addressed in the literature. To fill the gap, we propose two general testing frameworks to account for the covariates effect on diagnostic accuracy. Simulation studies are conducted to compare the proposed tests. Data from a study that assessed three types of imaging modalities with the purpose of detecting neoplastic colon polyps and cancers are used to illustrate the proposed methods.

Migration and diffusion of unsteady-state flow of volatile organic compounds on activated carbon adsorption beds under reverse ventilation.

Despite increasing attention to the influence of unsteady-state volatile organic compounds (VOCs) on the adsorption of activated carbon, studies in this regard are rare. Therefore, in this study, an investigation into the migration and diffusion of unsteady-state VOCs on activated carbon adsorption beds under reverse ventilation was conducted. Here, reverse clean air was introduced when the activated carbon bed reached the penetration point. The influence of reverse ventilation temperature, reverse superficial gas velocity, activated carbon filling height, and different ventilation modes on the adsorption of unsteady toluene by activated carbon were studied. Our experimental results show that when the reverse ventilation temperature increased from 20 °C to 60 °C, the quasi-first-order desorption rate constant increased from 0.00356 min-1 to 0.00807 min-1, an increase in the reverse superficial gas velocity led to a higher rate constant, and at greater reverse superficial gas velocities, the stripping capacity increased. It was observed that the maximum stripping capacity was achieved at a reverse superficial gas velocity of 0.3 m/s. For different activated carbon filling heights, following reverse ventilation, the stripping capacity of a 5 cm and 30 cm activated carbon bed accounted for 41.43% and 65.85% of the original adsorption capacity, respectively. The study concludes that concentration of toluene first increased and then decreased with time under forward ventilation, whereas the concentration gradually decreased under reverse ventilation.

Analysis of Familial Aggregation Using Recurrence Risk for Complex Survey Data.

Familial or family aggregation of a disease is important for studying possible genetic etiology of a disease. A popular and useful measure of family aggregation is recurrence risk. Household health surveys with (family) network sampling, which surveyed individuals report about disease status of themselves and specified relatives, has been shown to be useful for estimating prevalence of diseases and more recently for estimating recurrence risk of disease using nonparametric classical survey methods. Because these surveys have complex sample designs with sample weighting for differential sample selection rates, this paper extends the composite-likelihood estimation and hypothesis of parameters of the quadratic exponential model (QEM) for simple random samples to data from these complex sample designs. In addition, the QEM is extended to simultaneously estimate and test parameters and recurrence risk for multiple family relationships, for comparing recurrence risk across family-level covariates (e.g., race) and utilizing propensity score weighting to adjust for confounding by individual-level covariates (e.g., age). Simulations are used to study the finite sample properties of the parameter estimation, variance estimation and level and power of hypothesis testing based on derived Wald and Quasi-Score tests for these extended QEMs. Finally, our methods are illustrated using the 1976 National Health Interview Survey diabetes data set.

The motivations of Chinese firms in response to the Carbon Disclosure Project.

Through an analysis of data gathered from Chinese firms surveyed by the Carbon Disclosure Project (CDP), this paper studies the motivations of Chinese firms to respond to the CDP. The results indicate that (1) Chinese firms are more inclined to respond to the CDP survey for the sense-making motivation; (2) Chinese firms are less inclined to respond to the CDP survey due to the existence of proprietary costs for information disclosure; (3) self-interested political motivation is a negative motivation for Chinese firms to respond to the CDP survey; state-owned enterprises (SOEs) are less inclined to respond to the CDP survey than are non-SOEs; and (4) Chinese firms did not consider a financing motivation when deciding whether to respond to the CDP survey. However, the results of our further research show that if firms actively respond to the CDP survey, their financing constraints can be significantly reduced. This paper studies the four motivations for Chinese firms to respond to the CDP survey, contributing to the research of carbon emission disclosure. This paper highlights the importance of corporate carbon awareness for carbon emission disclosure, builds an understanding of the internal driving forces of response to the CDP survey among Chinese firms, and thus promotes the increase of Chinese corporate disclosure of carbon emission.

Repeated significance tests of linear combinations of sensitivity and specificity of a diagnostic biomarker.

A sequential design is proposed to test whether the accuracy of a binary diagnostic biomarker meets the minimal level of acceptance. The accuracy of a binary diagnostic biomarker is a linear combination of the marker's sensitivity and specificity. The objective of the sequential method is to minimize the maximum expected sample size under the null hypothesis that the marker's accuracy is below the minimal level of acceptance. The exact results of two-stage designs based on Youden's index and efficiency indicate that the maximum expected sample sizes are smaller than the sample sizes of the fixed designs. Exact methods are also developed for estimation, confidence interval and p-value concerning the proposed accuracy index upon termination of the sequential testing. Published 2016. This article is a U.S. Government work and is in the public domain in the USA.

A two-phase procedure for non-normal quantitative trait genetic association study.

BACKGROUND: The nonparametric trend test (NPT) is well suitable for identifying the genetic variants associated with quantitative traits when the trait values do not satisfy the normal distribution assumption. If the genetic model, defined according to the mode of inheritance, is known, the NPT derived under the given genetic model is optimal. However, in practice, the genetic model is often unknown beforehand. The NPT derived from an uncorrected model might result in loss of power. When the underlying genetic model is unknown, a robust test is preferred to maintain satisfactory power. RESULTS: We propose a two-phase procedure to handle the uncertainty of the genetic model for non-normal quantitative trait genetic association study. First, a model selection procedure is employed to help choose the genetic model. Then the optimal test derived under the selected model is constructed to test for possible association. To control the type I error rate, we derive the joint distribution of the test statistics developed in the two phases and obtain the proper size. CONCLUSIONS: The proposed method is more robust than existing methods through the simulation results and application to gene DNAH9 from the Genetic Analysis Workshop 16 for associated with Anti-cyclic citrullinated peptide antibody further demonstrate its performance.

Estimation of ROC curve with complex survey data.

The receiver operating characteristic (ROC) curve can be utilized to evaluate the performance of diagnostic tests. The area under the ROC curve (AUC) is a widely used summary index for comparing multiple ROC curves. Both parametric and nonparametric methods have been developed to estimate and compare the AUCs. However, these methods are usually only applicable to data collected from simple random samples and not surveys and epidemiologic studies that use complex sample designs such as stratified and/or multistage cluster sampling with sample weighting. Such complex samples can inflate variances from intra-cluster correlation and alter the expectations of test statistics because of the use of sample weights that account for differential sampling rates. In this paper, we modify the nonparametric method to incorporate sampling weights to estimate the AUC and employ leaving-one-out jackknife methods along with the balanced repeated replication method to account for the effects of the complex sampling in the variance estimation of our proposed estimators of the AUC. The finite sample properties of our methods are evaluated using simulations, and our methods are illustrated by comparing the estimated AUC for predicting overweight/obesity using different measures of body weight and adiposity among sampled children and adults in the US Hispanic Health and Nutrition Examination Survey.

Genetic association with multiple traits in the presence of population stratification.

Testing association between a genetic marker and multiple-dependent traits is a challenging task when both binary and quantitative traits are involved. The inverted regression model is a convenient method, in which the traits are treated as predictors although the genetic marker is an ordinal response. It is known that population stratification (PS) often affects population-based association studies. However, how it would affect the inverted regression for pleiotropic association, especially with the mixed types of traits (binary and quantitative), is not examined and the performance of existing methods to correct for PS using the inverted regression analysis is unknown. In this paper, we focus on the methods based on genomic control and principal component analysis, and investigate type I error of pleiotropic association using the inverted regression model in the presence of PS with allele frequencies and the distributions (or disease prevalences) of multiple traits varying across the subpopulations. We focus on common alleles but simulation results for a rare variant are also reported. An application to the HapMap data is used for illustration.

SEQUENTIAL TESTING OF MEASUREMENT ERRORS IN INTER-RATER RELIABILITY STUDIES.

Inter-rater reliability is usually assessed by means of the intraclass correlation coefficient. Using two-way analysis of variance to model raters and subjects as random effects, we derive group sequential testing procedures for the design and analysis of reliability studies in which multiple raters evaluate multiple subjects. Compared with the conventional fixed sample procedures, the group sequential test has smaller average sample number. The performance of the proposed technique is examined using simulation studies and critical values are tabulated for a range of two-stage design parameters. The methods are exemplified using data from the Physician Reliability Study for diagnosis of endometriosis.

Testing for Hardy Weinberg Equilibrium in national household surveys that collect family-based genetic data.

In population-based household surveys, for example, the National Health and Nutrition Examination Survey (NHANES), blood-related individuals are often sampled from the same household. Therefore, genetic data collected from national household surveys are often correlated due to two levels of clustering (correlation) with one induced by the multistage geographical cluster sampling, and the other induced by biological inheritance among multiple participants within the same sampled household. In this paper, we develop efficient statistical methods that consider the weighting effect induced by the differential selection probabilities in complex sample designs, as well as the clustering (correlation) effects described above. We examine and compare the magnitude of each level of clustering effects under different scenarios and identify the scenario under which the clustering effect induced by one level dominates the other. The proposed method is evaluated via Monte Carlo simulation studies and illustrated using the Hispanic Health and Nutrition Survey (HHANES) with simulated genotype data.

Influence of population stratification on population-based marker-disease association analysis.

Population-based genetic association analysis may suffer from the failure to control for confounders such as population stratification (PS). There has been extensive study on the influence of PS on candidate gene-disease association analysis, but much less attention has been paid to its influence on marker-disease association analysis. In this paper, we focus on the Pearson chi(2) test and the trend test for marker-disease association analysis. The mean and variance of the test statistics are derived under presence of PS, so that the power and inflated type I error rate can be evaluated. It is shown that the bias and the variance distortion are not zero in the presence of both PS and penetrance heterogeneity (PH). Unlike candidate gene-disease association analysis, when PS is present, the bias is not zero no matter whether PH is present or not. This work generalises the published results, where only the fully recessive penetrance model is considered and only the bias is calculated. It is shown that candidate gene-disease association analysis can be treated as a special case of marker-disease association analysis. Consequently, our results extend previous studies on candidate gene-disease association analysis. A simulation study confirms the theoretical findings.

Impact of population substructure on trend tests for genetic case-control association studies.

Hidden population substructure in case-control data has the potential to distort the performance of Cochran-Armitage trend tests (CATTs) for genetic associations. Three possible scenarios that may arise are investigated here: (i) heterogeneity of genotype frequencies across unidentified subpopulations (PSI), (ii) heterogeneity of genotype frequencies and disease risk across unidentified subpopulations (PSII), and (iii) cryptic correlations within unidentified subpopulations. A unified approach is presented for deriving the bias and variance distortion under the three scenarios for any CATT in a general family. Using these analytical formulas, we evaluate the excess type I errors of the CATTs numerically in the presence of population substructure. Our results provide insight into the properties of some proposed corrections for bias and variance distortion and show why they may not fully correct for the effects of population substructure.

Trend tests for genetic association using population-based cross-sectional complex survey data.

Genetic data collected from surveys such as the Third National Health and Nutrition Examination Survey (NHANES III) enable researchers to investigate the association between wide varieties of health factors and genetic variation for the US population. Tests for trend in disease with increasing number of alleles have been developed for simple random samples. However, surveys such as the NHANES III have complex sample designs involving multistage cluster sampling and sample weighting. These types of sample designs can affect Type I error and power properties of statistical tests based on simple random samples. In order to address these issues, we have derived tests of trend based on Wald and quasi-score statistics, with and without assuming a genetic model, that account for the complex sampling design. The finite-sample properties of the proposed test procedures are evaluated via Monte Carlo simulation studies. We make recommendations about the choice of the test statistic depending on whether or not the underlying genetic model is known. Proposed test statistics are applied to NHANES III data to test for associations between the locus ADRB2 (rs1042713) and obesity, between VDR (rs2239185) and high blood lead level, and between TGFB1 (rs1982073) and asthma.

Testing Hardy-Weinberg equilibrium using family data from complex surveys.

Genetic data collected during the second phase of the Third National Health and Nutrition Examination Survey (NHANES III) enable us to investigate the association of a wide variety of health factors with regard to genetic variation. The classic question when looking into the genetic variations in a population is whether the population is in the state of Hardy-Weinberg Equilibrium (HWE). Our objective was to develop test procedures using family data from complex surveys such as NHANES III. We developed six Pearson chi(2) based tests for a diallelic locus of autosomal genes. The finite sample properties of the proposed test procedures were evaluated via Monte Carlo simulation studies and the Rao-Scott first order corrected test was recommended. Test procedures were applied to three loci from NHANES III genetic databases, i.e., ADRB2, TGFB1, and VDR. HWE was shown to hold at 0.05 level for all three loci when only families with genotypic information available for two parents and for one or more children were used in the analysis.

MAX-rank: a simple and robust genome-wide scan for case-control association studies.

In genome-wide association studies (GWAS), single-marker analysis is usually employed to identify the most significant single nucleotide polymorphisms (SNPs). The trend test has been proposed for analysis of case-control association. Three trend tests, optimal for the recessive, additive and dominant models respectively, are available. When the underlying genetic model is unknown, the maximum of the three trend test results (MAX) has been shown to be robust against genetic model misspecification. Since the asymptotic distribution of MAX depends on the allele frequency of the SNP, using the P-value of MAX for ranking may be different from using the MAX statistic. Calculating the P-value of MAX for 300,000 (300 K) or more SNPs is computationally intensive and the software and program to obtain the P-value of MAX are not widely available. On the other hand, the MAX statistic is very easy to calculate without complex computer programs. Thus, we study whether or not one could use the MAX statistic instead of its P-value to rank SNPs in GWAS. The approaches using the MAX and its P-value to rank SNPs are referred to as MAX-rank and P-rank. By applying MAX-rank and P-rank to simulated and four real datasets from GWAS, we found the ranks of SNPs with true association are very similar using both approaches. Thus, we recommend to use MAX-rank for genome-wide scans. After the top-ranked SNPs are identified, their P-values based on MAX can be calculated and compared with the significance level.

Point and interval estimation of accuracies of a binary medical diagnostic test following group sequential testing.

When hypotheses concerning the sensitivity and specificity of a binary medical diagnostic test are simultaneously tested using a group sequential procedure, constructing point and interval estimates of the parameters is challenging because there is no unique way to order sample points in the two-dimensional space. In this paper, upon termination of a group sequential procedure, we compare the bias and mean squared errors of the maximum-likelihood and Rao-Blackwell unbiased estimators of sensitivity and specificity. Confidence intervals (CIs) of the two parameters were constructed using normal approximation and Woodroofe's pivot methods based on maximum-likelihood and Rao-Blackwell unbiased estimates. The coverage probability and the expected length of CIs for the parameters were compared by simulation studies.

Efficient approximation of P-value of the maximum of correlated tests, with applications to genome-wide association studies.

Genome-wide association study (GWAS), typically involving 100,000 to 500,000 single-nucleotide polymorphisms (SNPs), is a powerful approach to identify disease susceptibility loci. In a GWAS, single-marker analysis, which tests one SNP at a time, is usually used as the first stage to screen SNPs across the genome in order to identify a small fraction of promising SNPs with relatively low p-values for further and more focused studies. For single-marker analysis, the trend test derived for an additive genetic model is often used. This may not be robust when the additive assumption is not appropriate for the true underlying disease model. A robust test, MAX, based on the maximum of three trend test statistics derived for recessive, additive, and dominant models, has been proposed recently for GWAS. But its p-value has to be evaluated through a resampling-based procedure, which is computationally challenging for the analysis of GWAS. Obtaining the p-value for MAX with adjustment for the covariates can be even more time-consuming. In this article, we provide a simple approximation for the p-value of the MAX test with or without adjusting for the covariates. The new method avoids resampling steps and thus makes the MAX test readily applicable to GWAS. We use simulation studies as well as real datasets on 17 confirmed disease-associated SNPs to assess the accuracy of the proposed method. We also apply the method to the GWAS of coronary artery disease.

Two-stage group sequential robust tests in family-based association studies: controlling type I error.

In family-based association studies, an optimal test statistic with asymptotic normal distribution is available when the underlying genetic model is known (e.g., recessive, additive, multiplicative, or dominant). In practice, however, genetic models for many complex diseases are usually unknown. Using a single test statistic optimal for one genetic model may lose substantial power when the model is mis-specified. When a family of genetic models is scientifically plausible, the maximum of several tests, each optimal for a specific genetic model, is robust against the model mis-specification. This robust test is preferred over a single optimal test. Recently, cost-effective group sequential approaches have been introduced to genetic studies. The group sequential approach allows interim analyses and has been applied to many test statistics, but not to the maximum statistic. When the group sequential method is applied, type I error should be controlled. We propose and compare several approaches of controlling type I error rates when group sequential analysis is conducted with the maximum test for family-based candidate-gene association studies. For a two-stage group sequential robust procedure with a single interim analysis, two critical values for the maximum tests are provided based on a given alpha spending function to control the desired overall type I error.

Inference of haplotype effects in case-control studies using unphased genotype and environmental data.

A retrospective likelihood-based approach was proposed to test and estimate the effect of haplotype on disease risk using unphased genotype data with adjustment for environmental covariates. The proposed method was also extended to handle the data in which the haplotype and environmental covariates are not independent. Likelihood ratio tests were constructed to test the effects of haplotype and gene-environment interaction. The model parameters such as haplotype effect size was estimated using an Expectation Conditional-Maximization (ECM) algorithm developed by Meng and Rubin (1993). Model-based variance estimates were derived using the observed information matrix. Simulation studies were conducted for three different genetic effect models, including dominant effect, recessive effect, and additive effect. The results showed that the proposed method generated unbiased parameter estimates, proper type I error, and true beta coverage probabilities. The model performed well with small or large sample sizes, as well as short or long haplotypes.