Concordance correlation coefficients estimated by generalized estimating equations and variance components for longitudinal repeated measurements.

The concordance correlation coefficient (CCC) is a commonly accepted measure of agreement between two observers for continuous responses. This paper proposes a generalized estimating equations (GEE) approach allowing dependency between repeated measurements over time to assess intra-agreement for each observer and inter- and total agreement among multiple observers simultaneously. Furthermore, the indices of intra-, inter-, and total agreement through variance components (VC) from an extended three-way linear mixed model (LMM) are also developed with consideration of the correlation structure of longitudinal repeated measurements. Simulation studies are conducted to compare the performance of the GEE and VC approaches for repeated measurements from longitudinal data. An application of optometric conformity study is used for illustration. In conclusion, the GEE approach allowing flexibility in model assumptions and correlation structures of repeated measurements gives satisfactory results with small mean square errors and nominal 95% coverage rates for large data sets, and when the assumption of the relationship between variances and covariances for the extended three-way LMM holds, the VC approach performs outstandingly well for all sample sizes. Copyright © 2017 John Wiley & Sons, Ltd.

Variable selection in Bayesian generalized linear-mixed models: an illustration using candidate gene case-control association studies.

The problem of variable selection in the generalized linear-mixed models (GLMMs) is pervasive in statistical practice. For the purpose of variable selection, many methodologies for determining the best subset of explanatory variables currently exist according to the model complexity and differences between applications. In this paper, we develop a "higher posterior probability model with bootstrap" (HPMB) approach to select explanatory variables without fitting all possible GLMMs involving a small or moderate number of explanatory variables. Furthermore, to save computational load, we propose an efficient approximation approach with Laplace's method and Taylor's expansion to approximate intractable integrals in GLMMs. Simulation studies and an application of HapMap data provide evidence that this selection approach is computationally feasible and reliable for exploring true candidate genes and gene-gene associations, after adjusting for complex structures among clusters.

Concordance correlation coefficients estimated by modified variance components and generalized estimating equations for longitudinal overdispersed Poisson data.

For longitudinal overdispersed Poisson data sets, estimators of the intra-, inter-, and total concordance correlation coefficient through variance components have been proposed. However, biased estimators of quadratic forms are used in concordance correlation coefficient estimation. In addition, the generalized estimating equations approach has been used in estimating agreement for longitudinal normal data and not for longitudinal overdispersed Poisson data. Therefore, this paper proposes a modified variance component approach to develop the unbiased estimators of the concordance correlation coefficient for longitudinal overdispersed Poisson data. Further, the indices of intra-, inter-, and total agreement through generalized estimating equations are also developed considering the correlation structure of longitudinal count repeated measurements. Simulation studies are conducted to compare the performance of the modified variance component and generalized estimating equation approaches for longitudinal Poisson and overdispersed Poisson data sets. An application of corticospinal diffusion tensor tractography study is used for illustration. In conclusion, the modified variance component approach performs outstandingly well with small mean square errors and nominal 95% coverage rates. The generalized estimating equation approach provides in model assumption flexibility of correlation structures for repeated measurements to produce satisfactory concordance correlation coefficient estimation results.

Extended Bayesian model averaging in generalized linear mixed models applied to schizophrenia family data.

The study of disease etiology and the search for susceptible genes of schizophrenia have attracted scientists' attention for decades. Many findings however are inconsistent, possibly due to the higher order interactions involving multi-dimensional genetic and environmental factors or due to the commingling of different ethnic groups. Several studies applied generalized linear mixed models (GLMMs) with family data to identify the genetic contribution to, and environmental influence on, schizophrenia, and to clarify the existence and sources of familial aggregation. Based on an extended Bayesian model averaging (EBMA) procedure, here we estimate the gene-gene (GG) and gene-environment (GE) interactions, and heritability of schizophrenia via variance components of random-effects in GLMMs. Our proposal takes into account the uncertainty in covariates and in genetic model structures, where each competing model includes environmental and genetic covariates, and GE and GG interactions. Simulation studies are conducted to compare the performance of the EBMA approach, permutation test procedure and GEE method. We also illustrate this approach with data from singleton and multiplex schizophrenia families. The results indicate that EBMA is a flexible and stable tool in exploring true candidate genes, and GE and GG interactions, after adjusting for explanatory variables and correlation structures within family members.

An epidemiologic study of tooth retention after nonsurgical endodontic treatment in a large population in Taiwan.

In this study, tooth retention and untoward events were assessed over a 5-year follow-up period for 1,557,547 teeth receiving nonsurgical root canal treatment (NSRCT) in Taiwan in 1998. We found that 1,446,199 (92.9%) of teeth receiving NSRCT were retained in the oral cavity 5 years after treatment and that a total of 111,348 (7.1%) of the studied teeth were extracted. Untoward events occurred in 159,680 (10.3%) teeth during the 5-year follow-up period. Of this small subpopulation, nonsurgical retreatment was performed for 50,587 teeth (31.7%), apical surgery was performed on 4,502 (2.8%) teeth, and extractions were performed on 104,591 (65.5%) teeth. Approximately 40% of the nonsurgical retreatments and 81% of the apical surgeries occurred in the first follow-up year. However, the yearly incidence of tooth extractions was nearly even within the 5-year study period. We conclude that NSRCT is a valuable dental procedure because of the high rate (92.9%) of tooth retention 5 years after NSRCTs in Taiwan.

Haplotype association analysis of combining unrelated case-control and triads with consideration of population stratification.

Combining data when data are collected under different study designs, such as family trios and unrelated case-control samples, gains more power and is cost-effective than analyzing each data separately. However, a potential concern is population stratification (PS) among unrelated case-control samples and analyses integrating data should address this confounding effect. In this paper, we develop a simpler method, haplotype generalized linear model (HGLM), that tests and estimates haplotype effects on disease risk and allows for modification against PS for combining data. We proposed to combine information across aggregations of haplotype weighted-counts estimated from population case-control data and trio data separately, and to perform subsequent GLM analysis. Furthermore, we present a framework of analysis of variance based on haplotype weighted-counts for detecting whether it is appropriate to combine two data sources, as well as the modified HGLM with clustering methods for addressing PS. We evaluate the statistical properties in terms of the accuracy, false positive rate (FPR) and empirical power using simulated data with regard to various disease risks, sample sizes, multi-SNP haplotypes and the presence of PS. Our simulation results indicate that HGLM performs comparably well with the likelihood-based haplotype association analysis, particularly when the haplotype effects are moderate, but may not perform well when dealing with lengthy haplotypes for small sample sizes. In the presence of PS, the modified HGLM remains valid and has satisfactory nominal level and small bias. Overall, HGLM appears to be successful in combining data and is simple to implement in standard statistical software.

Reproducibility of corticospinal diffusion tensor tractography in normal subjects and hemiparetic stroke patients.

PURPOSE: The reproducibility of corticospinal diffusion tensor tractography (DTT) for a guideline is important before longitudinal monitoring of the therapy effects in stroke patients. This study aimed to establish the reproducibility of corticospinal DTT indices in healthy subjects and chronic hemiparetic stroke patients. MATERIALS AND METHODS: Written informed consents were obtained from 10 healthy subjects (mean age 25.8 ± 6.8 years), who underwent two scans in one session plus the third scan one week later, and from 15 patients (mean age 47.5 ± 9.1 years, 6-60 months after the onset of stroke, NIHSS scores between 9 and 20) who were scanned thrice on separate days within one month. Diffusion-tensor imaging was performed at 3T with 25 diffusion directions. Corticospinal tracts were reconstructed using fiber assignment by continuous tracking without and with motion/eddy-current corrections. Intra- and inter-rater as well as intra- and inter-session variations of the DTT derived indices (fiber number, apparent diffusion coefficient (ADC), and fractional anisotropy (FA)) were assessed. RESULTS: Intra-session and inter-session coefficients of variations (CVs) are small for FA (1.13-2.09%) and ADC (0.45-1.64%), but much larger for fiber number (8.05-22.4%). Inter-session CVs in the stroke side of patients (22.4%) are higher than those in the normal sides (18.0%) and in the normal subjects (14.7%). Motion/eddy-current correction improved inter-session reproducibility only for the fiber number of the infarcted corticospinal tract (CV reduced from 22.4% to 14.1%). CONCLUSION: The fiber number derived from corticospinal DTT shows substantially lower precision than ADC and FA, with infarcted tracts showing lower reproducibility than the healthy tissues.

Estimation of heritability in myopic twin studies.

PURPOSE: To examine the genetic and environmental factors for myopia at the family level, as well as risk factors such as ocular measurements and environmental covariates at the individual level, by analysis of myopic twin data. METHODS: A myopic twin study was conducted on participants from the 2000 Guinness World Records for twins in Taiwan. A total of 130 participants comprising 58 twin pairs and 13 siblings were recruited. The generalized estimating equation approach was used to evaluate the covariate effects. A Bayesian linear mixed model was then used to estimate the heritability. RESULTS: Pearson's intrapairwise correlation coefficients for ocular refraction and its components were higher among monozygotic twins than among dizygotic twins. The significance of sex suggested that women are more myopic than men. Both axial length and anterior chamber depth were significant factors associated with myopia. The results also showed that people with higher education levels were more likely to have a higher degree of myopia. After accounting for genetic and environmental effects and other covariates, the estimate of heritability of myopia was as high as 0.306. CONCLUSIONS: After adjusting for environmental covariates, heritability still plays a decisive genetic role in the development of myopia.

Maximum number of live births per donor in artificial insemination.

BACKGROUND: The maximal number of live births (k) per donor was usually determined by cultural and social perspective. It was rarely decided on the basis of scientific evidence or discussed from mathematical or probabilistic viewpoint. METHODS AND RESULTS: To recommend a value for k, we propose three criteria to evaluate its impact on consanguinity and disease incidence due to artificial insemination by donor (AID). The first approach considers the optimization of k under the criterion of fixed tolerable number of consanguineous mating due to AID. The second approach optimizes k under fixed allowable average coefficient of inbreeding. This approach is particularly helpful when assessing the impact on the public, is of interest. The third criterion considers specific inheritance diseases. This approach is useful when evaluating the individual's risk of genetic diseases. When different diseases are considered, this criterion can be easily adopted. All these derivations are based on the assumption of shortage of gamete donors due to great demand and insufficient supply. CONCLUSIONS: Our results indicate that strong degree of assortative mating, small population size and insufficient supply in gamete donors will lead to greater risk of consanguinity. Recommendations under other settings are also tabulated for reference. A web site for calculating the limit for live births per donor is available.

Inference of nested variance components in a longitudinal myopia intervention trial.

This paper was motivated by a double-blind randomized clinical trial of myopia intervention. In addition to the primary goal of comparing treatment effects, we are concerned with the modelling of correlation that may come from two possible sources, one among the longitudinal observations and the other between measurements taken from both eyes per subject. The data are nested repeated measurements. We suggest three models for analysis. Each one expresses the correlation differently in various covariance structures. We articulate their differences and describe the implementations in estimation using commercial statistical software. The computer output can be further utilized to perform model selection with Schwarz criterion. Simulation studies are conducted to evaluate the performance under each model. Data of the myopia intervention trial are reanalysed with these models for illustration. The results indicate that atropine is more effective in reducing the progression rate, the rates are homogeneous across subjects, and, among the suggested models, the one with independent random effects of two eyes fits best. We conclude that model selection is a crucial step before making inference with estimates; otherwise the correlation may be attributed incorrectly to a different mechanism. The same conclusion applies to other variance components as well.