A Non‐parametric Conditional Bivariate Reference Region with an Application to Height/Weight Measurements on Normal Girls

A conceptually simple two‐dimensional conditional reference curve is described. The curve gives a decision basis for determining whether a bivariate response from an individual is “normal” or “abnormal” when taking into account that a third (conditioning) variable may influence the bivariate response. The reference curve is not only characterized analytically but also by geometric properties that are easily communicated to medical doctors – the users of such curves. The reference curve estimator is completely non‐parametric, so no distributional assumptions are needed about the two‐dimensional response. An example that will serve to motivate and illustrate the reference is the study of the height/weight distribution of 7–8‐year‐old Danish school girls born in 1930, 1950, or 1970.     

Chronobiological analysis of superimposed period data sets using bivariate cosine series models

The non-linear cosine fit (so-called cosinor method) of chronobiological sets is suited to one-dimensional effect versus time data. Extending the method to multiple components allows one to look for subharmonics or superimposed underlying periods. In more complex two-dimensional chronobiological time series, alternative models may be advantageous to visualise the time structure. Bivariate cosine series and the corresponding numerical surface discussion including first and second partial derivatives may be a suited method to characterise individual maxima or minima. Moreover, the method permits one to define a mean over two periods (bivariate MESOR) of a two-dimensional data set.     

Genetic effects on obesity assessed by bivariate genome scan: the Mexican-American coronary artery disease study

Objective: To identify the genetic determinants of obesity using univariate and bivariate models in a genome scan. Research Methods and Procedures: We evaluated the genetic and environmental effects and performed a genome‐wide linkage analysis of obesity‐related traits in 478 subjects from 105 Mexican‐American nuclear families ascertained through a proband with documented coronary artery disease. The available obesity traits include BMI, body surface area (BSA), waist‐to‐hip ratio (WHR), and trunk fat mass as percentage of body weight. Heritability estimates and multipoint linkage analysis were performed using a variance components procedure implemented in SOLAR software. Results: The heritability estimates were 0.62 for BMI, 0.73 for BSA, 0.40 for WHR, and 0.38 for trunk fat mass as percentage of body weight. Using a bivariate genetic model, we observed significant genetic correlations between BMI and other obesity‐related traits (all p < 0.01). Evidence for univariate linkage was observed at 252 to approximately 267 cM on chromosome 2 for three obesity‐related traits (except for WHR) and at 163 to approximately 167 cM on chromosome 5 for BMI and BSA, with the maximum logarithm of the odds ratio score of 3.12 (empirical p value, 0.002) for BSA on chromosome 2. Use of the bivariate linkage model yielded an additional peak (logarithm of the odds ratio = 3.25, empirical p value, 0.002) at 25 cM on chromosome 7 for the pair of BMI and BSA. Discussion: The evidence for linkage on chromosomes 2q36‐37 and 5q36 is supported both by univariate and bivariate analysis, and an additional linkage peak at 7p15 was identified by the bivariate model. This suggests that use of the bivariate model provides additional information to identify linkage of genes responsible for obesity‐related traits.     

Gravitropic microtubule reorientation can be uncoupled from growth

The causal relationship between gravitropic growth responses and microtubule reorientation has been studied. Growth and microtubule reorientation have been uncoupled during the gravitropic response of maize (Zea mays L.) coleoptiles. Microtubule orientation and growth were measured under three different conditions: (i) a gravitropic stimulation where the growth response was allowed to be expressed (intact seedlings were displaced from the vertical position by 90°), (ii) a gravitropic stimulation where the growth response was suppressed (coleoptiles were attached to microscope slides and kept in a horizontal position), (iii) suppression of growth in the absence of gravitropic stimulation (coleoptiles were attached to microscope slides and kept in a vertical position). It was found that (i) gravitropic stimulation can induce a microtubular reorientation from transverse to longitudinal in the upper (slower growing) flank of the coleoptile, and an inhibition of growth; (ii) the reorientation of microtubules precedes the inhibition of growth; (iii) the gravitropic response of microtubules is weaker, not elevated, when the inhibition of growth is artificially enhanced by attaching the coleoptiles to a slide; and (iv) artificial inhibition of growth in the absence of gravitropic stimulation cannot induce a microtubular response. Thus, the extent of microtubule reorientation is not correlated with the extent of growth inhibition. Moreover, these findings demonstrate that microtubules do not reorient passively after growth changes, but actively in response to gravitropic stimulation. Received: 23 November 1999 / Accepted: 10 May 2000     

Genetic and environmental correlations between various anthropometric and blood pressure traits among adult Samoans

Shared polygenic effects (i.e., pleiotropy) are assumed to exist for such obesity-related phenotypes as blood pressure and adiposity. It is possible to identify these shared genetic effects through bivariate genetic analyses. This analysis of 1,342 adult Samoans, across 801 pedigrees, indicates that significant heritable components (P < 0.05) ranging from 29-58% exist for weight, height, systolic blood pressure, diastolic blood pressure, triceps skinfold, subscapular skinfold, body mass index, and sum of skinfolds. In general, the anthropometric measurements share additive genetic effects, as do the anthropometric measures, with blood pressure. Heritabilities for central fat distribution are not significant in this population, which could be due to a lack of power. On the other hand, heritabilities have been found in Hispanics; hence the genes responsible for central fat distribution may not be evenly distributed among populations.     

Semiparametric modelling and estimation of covariate-adjusted dependence between bivariate recurrent events

A time-dependent measure, termed the rate ratio, was proposed to assess the local dependence between two types of recurrent event processes in one-sample settings. However, the one-sample work does not consider modeling the dependence by covariates such as subject characteristics and treatments received. The focus of this paper is to understand how and in what magnitude the covariates influence the dependence strength for bivariate recurrent events. We propose the covariate-adjusted rate ratio, a measure of covariate-adjusted dependence. We propose a semiparametric regression model for jointly modeling the frequency and dependence of bivariate recurrent events: the first level is a proportional rates model for the marginal rates and the second level is a proportional rate ratio model for the dependence structure. We develop a pseudo-partial likelihood to estimate the parameters in the proportional rate ratio model. We establish the asymptotic properties of the estimators and evaluate the finite sample performance via simulation studies. We illustrate the proposed models and methods using a soft tissue sarcoma study that examines the effects of initial treatments on the marginal frequencies of local/distant sarcoma recurrence and the dependence structure between the two types of cancer recurrence.     

Pleiotropic Relationships between Cortisol Levels and Adiposity: The HERITAGE Family Study

Objective: To investigate familial basis for the relationship between cortisol adiposity at baseline and their training responses. Research Methods and Procedures: Bivariate correlation and segregation analyses were employed between cortisol and several adiposity measures [body mass index, fat mass (FM), fat-free mass, percentage of body fat (% BF), abdominal visceral fat (AVF), abdominal subcutaneous fat (ASF), and abdominal total fat (ATF)] from 99 white families and 105 black families. Results: In both races, significant inverse phenotypic correlations were generally observed between cortisol and adiposity measures at baseline but not for training responses. Significant cross-trait familial correlations were found for cortisol with abdominal fat (ASF, AVF, ATF) and overall body adiposity (FM, % BF) measures at baseline, which accounted for 14% to 20% of the phenotypic variance in whites. The cross-trait correlations were not significant for baseline phenotypes in blacks, perhaps because of the small sample size. A bivariate segregation analysis showed evidence of polygenic pleiotropy for cortisol with both abdominal fat and overall adiposity measures that accounted for 14% to 17% of the phenotypic covariance, but major gene pleiotropy was not suggested in whites. However, when ASF, AVF, and ATF were additionally adjusted for FM, no familial cross-trait correlations or polygenic pleiotropy between cortisol and the abdominal fat measures remained. Discussion: Evidence was found for polygenic pleiotropy but not for pleiotropic major gene effects between cortisol and overall adiposity in whites. However, the covariation of cortisol with abdominal fat phenotypes is dependent on concomitant polygenic factors for total-body fat.     

Bivariate random‐effects meta‐analysis models for diagnostic test accuracy studies using arcsine‐based transformations

Diagnostic or screening tests are widely used in medical fields to classify patients according to their disease status. Several statistical models for meta‐analysis of diagnostic test accuracy studies have been developed to synthesize test sensitivity and specificity of a diagnostic test of interest. Because of the correlation between test sensitivity and specificity, modeling the two measures using a bivariate model is recommended. In this paper, we extend the current standard bivariate linear mixed model (LMM) by proposing two variance‐stabilizing transformations: the arcsine square root and the Freeman–Tukey double arcsine transformation. We compared the performance of the proposed methods with the standard method through simulations using several performance measures. The simulation results showed that our proposed methods performed better than the standard LMM in terms of bias, root mean square error, and coverage probability in most of the scenarios, even when data were generated assuming the standard LMM. We also illustrated the methods using two real data sets.     

Climatic Control on Forests and Tree Species Distribution in the Forest Region of Northeast China

North-east （NE） China covers considerable climatic gradients and all major forests types of NE Asia. in the present study, 10 major forest types across the forest region of NE China were sampled to Investigate forest distribution in relation to climate. Canonical correspondence analysis （CCA） revealed that growing season precipitation and energy availability were primary climatic factors for the overall forest pattern of NE China, accounting for 66% of the explanatory power of CCA. Conversely, annual precipitation and winter coldness had minor effects. Generalized additive models revealed that tree species responded to climatic gradients differently and showed three types of response curve： （i） monotonous decline; （ii） monotonous Increase; and （iii） a unimodai pattern. Furthermore, tree species showed remarkable differences in limiting climatic factors for their distribution. The power of climate in explaining species distribution declined significantly with decreasing species dominance, suggesting that the distribution of dominant species was primarily controlled by climate, whereas that of subordinate species was more affected by competition from other species.     

Simultaneous confidence corridors for mean functions in functional data analysis of imaging data

Motivated by recent work involving the analysis of biomedical imaging data, we present a novel procedure for constructing simultaneous confidence corridors for the mean of imaging data. We propose to use flexible bivariate splines over triangulations to handle an irregular domain of the images that is common in brain imaging studies and in other biomedical imaging applications. The proposed spline estimators of the mean functions are shown to be consistent and asymptotically normal under some regularity conditions. We also provide a computationally efficient estimator of the covariance function and derive its uniform consistency. The procedure is also extended to the two-sample case in which we focus on comparing the mean functions from two populations of imaging data. Through Monte Carlo simulation studies, we examine the finite sample performance of the proposed method. Finally, the proposed method is applied to analyze brain positron emission tomography data in two different studies. One data set used in preparation of this article was obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database.     

A bivariate median test

A bivariate median test is proposed which makes use of the geometric median or mediancentre. Simulations have shown that the resulting test statistic is X²-distributed. The test may be extended to more than two groups, but not to more than two variates.     

A Modified Chi-squared Approach for Fitting WEIBULL Models to Synthetic Life Tables1

WEIBULL models are fitted to synthetic life table data by applying weighted least squares analysis to log log functions which are constructed from appropriate underlying contingency tables. As such, the resulting estimates and test statistics are based on the linearized minimum modified X²₁-criterion and thus have satisfactory properties in moderately large samples. The basic methodology is illustrated in terms of an example which is bivariate in the sense of involving two simultaneous, but non-competing, vital events. For this situation, the estimation of WEIBULL model parameters is described for both marginal as well as certain conditional distributions either individually or jointly.     

Trimmed Weighted Simes' Test for Two One‐Sided Hypotheses With Arbitrarily Correlated Test Statistics

The two‐sided Simes test is known to control the type I error rate with bivariate normal test statistics. For one‐sided hypotheses, control of the type I error rate requires that the correlation between the bivariate normal test statistics is non‐negative. In this article, we introduce a trimmed version of the one‐sided weighted Simes test for two hypotheses which rejects if (i) the one‐sided weighted Simes test rejects and (ii) both p‐values are below one minus the respective weighted Bonferroni adjusted level. We show that the trimmed version controls the type I error rate at nominal significance level α if (i) the common distribution of test statistics is point symmetric and (ii) the two‐sided weighted Simes test at level 2α controls the level. These assumptions apply, for instance, to bivariate normal test statistics with arbitrary correlation. In a simulation study, we compare the power of the trimmed weighted Simes test with the power of the weighted Bonferroni test and the untrimmed weighted Simes test. An additional result of this article ensures type I error rate control of the usual weighted Simes test under a weak version of the positive regression dependence condition for the case of two hypotheses. This condition is shown to apply to the two‐sided p‐values of one‐ or two‐sample t‐tests for bivariate normal endpoints with arbitrary correlation and to the corresponding one‐sided p‐values if the correlation is non‐negative. The Simes test for such types of bivariate t‐tests has not been considered before. According to our main result, the trimmed version of the weighted Simes test then also applies to the one‐sided bivariate t‐test with arbitrary correlation.     

Gene-based association analysis for bivariate time-to-event data through functional regression with copula models

Several gene-based association tests for time-to-event traits have been proposed recently to detect whether a gene region (containing multiple variants), as a set, is associated with the survival outcome. However, for bivariate survival outcomes, to the best of our knowledge, there is no statistical method that can be directly applied for gene-based association analysis. Motivated by a genetic study to discover the gene regions associated with the progression of a bilateral eye disease, age-related macular degeneration (AMD), we implement a novel functional regression (FR) method under the copula framework. Specifically, the effects of variants within a gene region are modeled through a functional linear model, which then contributes to the marginal survival functions within the copula. Generalized score test statistics are derived to test for the association between bivariate survival traits and the genetic region. Extensive simulation studies are conducted to evaluate the type I error control and power performance of the proposed approach, with comparisons to several existing methods for a single survival trait, as well as the marginal Cox FR model using the robust sandwich estimator for bivariate survival traits. Finally, we apply our method to a large AMD study, the Age-related Eye Disease Study, and to identify the gene regions that are associated with AMD progression.     

Quantitative characterization of virus-like particles by asymmetrical flow field flow fractionation, electrospray differential mobility analysis, and transmission electron microscopy

Here we characterize virus-like particles (VLPs) by three very distinct, orthogonal, and quantitative techniques: electrospray differential mobility analysis (ES-DMA), asymmetric flow field-flow fractionation with multi-angle light scattering detection (AFFFF-MALS) and transmission electron microscopy (TEM). VLPs are biomolecular particles assembled from viral proteins with applications ranging from synthetic vaccines to vectors for delivery of gene and drug therapies. VLPs may have polydispersed, multimodal size distributions, where the size distribution can be altered by subtle changes in the production process. These three techniques detect subtle size differences in VLPs derived from the non-enveloped murine polyomavirus (MPV) following: (i) functionalization of the surface of VLPs with an influenza viral peptide fragment; (ii) packaging of foreign protein internally within the VLPs; and (iii) packaging of genomic DNA internally within the VLPs. These results demonstrate that ES-DMA and AFFFF-MALS are able to quantitatively determine VLP size distributions with greater rapidity and statistical significance than TEM, providing useful technologies for product development and process analytics.     

中国中生代鸟类的体重估计及其演化趋势

体重是一项重要的生物学指标,生物的体重受到发育、繁殖和进化等诸多因素的影响。对于灭绝生物体重的估计有助于进一步恢复它们的各种生物学信息。本研究采用统计学的方法,对422件现生鸟类(分属于21目229种)的体重和18项骨骼量度指标分别进行一元回归分析,结果显示判定系数的分布范围在0.5～0.91之间,多数指标的判定系数均集中在0.8～0.9之间。采用另外64件测量有体重数据和骨骼量度的鸟样本对回归方程的估算准确率进行检验,发现前肢中肱骨长度和尺骨宽度以及后肢中胫跗骨宽度3项指标的估算准确率高于其他指标。分析结果还表明前肢两项指标对于估算鸣禽、猛禽和攀禽类等树栖鸟类的体重准确率较后肢显著;后肢指标对于估算陆禽类等地栖鸟类体重的准确率高于前肢指标。这一结果反映出与体重相关程度较高的骨骼量度指标在不同习性的鸟类当中存在着一定的差异。对于化石鸟类的体重估计,采用估算准确率较高并且便于测量的肱骨长度和胫跗骨宽度两项回归方程加以计算。通过对中国中生代鸟类的体重进行估算,结果显示中生代鸟类在系统发育过程中,反鸟类经历了体重逐渐减轻的过程,而今鸟类的体重开始不断增大并且出现显著的分异。     

An adaptive bivariate kernel smoothing method for determining instars of Austrosimulium tillyardianum (Diptera: Simuliidae) larvae

1. In insects, instar determination is generally based on the frequency distribution of sclerotised body part measurements. Commonly used univariate methods, such as histograms and univariate kernel smoothing, are not sufficient to reflect the distribution of the measurements, because development of sclerotised body parts is multidimensional. 2. This study used an adaptive bivariate kernel smoothing method, based on 10 pairs of separating variables, to differentiate instars of Austrosimulium tillyardianum (Diptera: Simuliidae) larvae in two‐dimensional space. A variable bandwidth matrix was used and separation lines between instars were defined. Using the Crosby growth ratio, Brooks' rule and the new standard recently proposed, larvae were separated into nine instars. It was found that, using the bivariate kernel smoothing method, the clustering accuracy and determination of separation lines as instar class limits were higher than those associated with the univariate kernel smoothing method. With the exceptions of the paired separating variables, head capsule length and antennal segment 3 length (AS3L), the mean probabilities of correct classifications was > 85%. The pair of separating variables that yielded the greatest classification accuracy comprised mandible length (ML) and AS3L, which had mean probabilities of 0.8984. The clustering accuracy was higher for early‐ and late‐instar larvae, but lower for instars 6 and 7. The adaptive bivariate kernel smoothing method was better than univariate methods for instar determination, especially in the detection of divisions between instars and identification of a larval instar.     

Testing for ordered group effects in binary and continuous outcomes

A likelihood ratio test is proposed for the detection of an ordered group effect on bivariate responses where one response is binary and the other is continuous. The procedure is based on a conditional logistic model for the binary response given the continuous outcome. We also develop a likelihood ratio test for simultaneously determining the goodness of fit of the ordering assumption on both responses. Our approach is motivated by a particular toxicity study application involving laboratory animals that focused on the effect of a food color additive on the development of reticuloendothelial (RE) tumors. A brief discussion on extensions to the methodology introduced here is also given, along with a comparison of the approach with a marginal strategy where the presence of an ordered group effect is assessed independently for each of the two responses.     

Bivariate association analysis for quantitative traits using generalized estimation equation

Quantitative traits often underlie risk for complex diseases. Many studies collect multiple correlated quantitative phenotypes and perform univariate analyses on each of them respectively. However, this strategy may not be powerful and has limitations to detect plei- otropic genes that may underlie correlated quantitative traits. In addition, testing multiple traits individually will exacerbate perplexing problem of multiple testing. In this study, generalized estimating equation 2 （GEE2） is applied to association mapping of two correlated quantitative traits. We suppose that a quantitative trait locus is located in a chromosome region that exerts pleiotropic effects on multiple quantitative traits. In that region, multiple SNPs are genotyped. Genotypes of these SNPs and the two quantitative traits affected by a causal SNP were simulated under various parameter values： residual correlation coefficient between two traits, causal SNP heritability, minor allele frequency of the causal SNP, extent of linkage disequilibrium with the causal SNP, and the test sample size. By power ana- lytical analyses, it is showed that the bivariate method is generally more powerful than the univariate method. This method is robust and yields false-positive rates close to the pre-set nominal significance level. Our real data analyses attested to the usefulness of the method.     

On the Modified and Inflated Discrete Distributions

Firstly, a modified bivariate discrete distribution is considered where a set of counts are misreported as another set of counts with different modification rates. Variances and covariances are put in the closed form and for the case when all modification rates are the same, these variances and covariances are expressed as parabolic functions and they are actually evaluated for the bivariate negative binomial. Regarding the asymptotic distributions of the estimates, elements of variance-covariance matrix are obtained. Next, a multivariate inflated discrete distribution is taken up. For the case of inflated multivariate negative binomial, Bayesian estimates of inflation as well as those of parameters are given.