简明生物统计方法

第四讲相关与回归相关与回归是分析两个(或多个)变量之间的关系的方法。譬如说某一特定人群的身高与体重,不仅只分析身高或体重的某一方面(或说指标),而是分析身高与体重两个指标之间有无关联,这便是相关与回归所要分析的内容。当然,相关与回归分析也包括根据样本估计总体     

具有空间自相关残差的回归模型及其应用

提出了具有空间自相关残差的多变量回归问题,这种残差包括单点、局部和区域化三种尺度.文中提出了两种处理空间自相关的方法:把自相关加入残差协方差作参数的改进估计──相邻相关方法和把残差作区域化最优自相关估计──一般空间自相关方法.用森林对舞毒蛾危害敏感性概率的大范围估计为例,比较了传统回归方法和本文方法间的差异,交叉检验结果表明本文的方法明显优于直接回归方法,这说明加入空间自相关对空间回归问题是必要的.     

遗传密码与氨基酸含量的非线性关系

本文利用回归分析方法给出了遗传密码与氨基酸含量之间的相关关系,结果表明;氨基酸的相对含量与遗传密码子数呈四次多项式回归,回归方程的复相关指数高达0.96以上,模型的平均拟合误差在2～7％之间．     

祁连山地甘肃臭草斑块土壤水分的空间自相关分析

用传统统计学方法探讨土壤水分空间分布的前提条件是用于研究的数据在统计上必须独立且均匀分布,但土壤水分在空间上一般存在空间自相关,这些空间自相关包含一些有用信息。本文利用Moran I系数研究了祁连山北坡甘肃臭草(Melica przewalskyi)单优种群斑块浅层剖面(0~30 cm)土壤水分空间自相关关系、空间相关尺度,建立了各层土壤水分影响因子的线性回归模型和空间自回归模型,并比较了2种模型的分析结果。结果表明:各层土壤水分均具有空间正相关性与空间集聚特征,10~20 cm层土壤水分的空间集聚特征较0~10 cm和20~30 cm土层更为明显;土壤水分的Moran I系数随着分析间隔距离的增大而减小,在4 m的范围内各层土壤水分均存在正的空间自相关关系。影响甘肃臭草浅层剖面土壤水分空间分布的因素在不同土层不尽相同;空间自回归模型的LIK值和R2的值比线性回归模型的值要大,从而显示出空间自回归模型的解释能力要优于经典线性回归模型。     

一种新的泛素化-铁死亡相关基因特征用于肝细胞癌患者预后分析

本研究通过筛选泛素化-铁死亡相关基因构建肝细胞癌(hepatocellular carcinoma, HCC)预后模型,并探究泛素化-铁死亡相关基因对HCC预后的影响。使用R包DESeq2对TCGA-LIHC数据集进行差异分析,获取HCC差异表达基因(HCC＿DEGs)。将HCC＿DEGs、泛素化相关基因(ubiquitination related genes, URGs)和铁死亡差异表达基因(ferroptosis＿differentially expressed genes, FERR＿EDGs)取交集获得泛素化和铁死亡相关基因(UBFE＿EDGs),将UBFE＿EDGs依次进行LASSO回归分析、单因素Cox回归分析和多因素Cox回归分析以筛选出最佳独立预后基因用于构建HCC预后模型(ubiquitination and ferroptosis-related prognostic model, UBFE)。由生存曲线、 ROC曲线和校正曲线评估UBFE的预测准确性。单因素Cox回归分析、多因素Cox回归分析评估UBFE风险评分是否为HCC的预后独立危险因素,并构建列线图模型。...     

(0──1)变量与定量、定性变量间的相关分析

本文介绍了经验Logistic回归及列联表检验的基本思想,探讨了用经验Logistic回归及列联表检验研究（0-1）变量与定量、定性变量相关的方法,并举例作了说明。     

中值温度和干燥度指数计算及其应用的简便方法

利用合肥2003年逐日温度资料进行相关分析和回归分析,发现中值温度与最低、最高及平均温度之间存在极显著的相关性,回归模型的拟合优度均在96．8％以上。依据合肥多年逐日中值温度和平均温度的回归分析,建立了一元回归方程Y=1．0026x-0．4683,并通过了α=0.001水平检验;对其他地区资料进行分析也发现有同样规律,这充分表明了日中值温度与日平均温度之间存在极显著回归关系。另外,根据合肥多年气象资料,对“蒸降比”与积温干燥度指数进行相关分析和回归分析,建立了干燥度指数计算的新公式E=0．282054＋0．552118E／r。方法可直接利用蒸发量和降水量常规气象数据,简便地计算出各年份干燥度指数;也可用在低于10℃期间,以便计算年内各季节或月份干燥度指数;经分析验证,效果良好。     

由胸骨长度估算中国北方成年人身高的回归方程

调查了中国北方28具(男15、女13)汉族成年人尸体身高、胸骨全长、胸骨柄长和胸骨体长的均值,并计算了胸骨的长度与身高的相关系数。除男性胸骨全长高度相关外,其余皆为中度相关。由胸骨全长推算身高的回归方程式,较由胸骨柄长和胸骨体长推算身高的回归方程式,有较高的相关系数和较低的标准估计误差。由胸骨体长推算也较由胸骨柄长推算为佳。     

TRIA处理西葫芦的聚类分析及对早期产量影响的回归分析

本文以TRIA的6个浓度梯度对西葫芦进行处理,通过聚类分析及对早期产量的回归分析．结果表明：TRIA的适宜处理浓度范围为0.10～1.O0ppm,其中以0.50ppm效果最好,拟合的模型为Y=0.17＋0.82X-0.57X~2,有显著相关的非线性回归．     

结合自噬相关基因表达谱和临床因素的肺腺癌预后预测模型

对肺腺癌自噬相关基因进行生物信息学分析,结合多基因预后标志和临床参数构建能够预测肺腺癌患者预后的模型。首先,对TCGA肺腺癌数据中的938个自噬相关基因进行差异分析,获得了82个差异自噬相关基因,使用单因素Cox比例风险回归模型从差异自噬相关基因中筛选出候选基因,通过 lasso回归进一步筛选出预后相关基因,分别是ARNTL2、NAPSA、ATG9B、CAPN12、MAP1LC3C和KRT81。通过多因素Cox回归分析以构建风险评分模型,根据最优cutoff值将患者分为高低风险组,生存曲线显示高低风险组之间生存差异显著,ROC曲线显示风险评分的预测能力良好,并在内、外验证集中得到验证。同时对传统的临床因素进行单因素和多因素Cox回归分析,结果显示Stage、复发和风险评分能够独立预测预后,结合这三个独立的预后参数以构建列线图模型,使用一致性指数、校准曲线评估列线图的预测能力,结果显示预测结果与实际结果之间具有良好的一致性。通过与Stage和风险评分的比较发现,列线图的预测能力表现最佳。基于肺腺癌相关的自噬基因和临床参数构建了一个列线图模型来预测肺腺癌患者的预后生存,这可能为临床医生提供了一种可靠的预后评估工具。     

Bayesian models for the analysis of genetic structure when populations are correlated

MOTIVATION: Population allele frequencies are correlated when populations have a shared history or when they exchange genes. Unfortunately, most models for allele frequency and inference about population structure ignore this correlation. Recent analytical results show that among populations, correlations can be very high, which could affect estimates of population genetic structure. In this study, we propose a mixture beta model to characterize the allele frequency distribution among populations. This formulation incorporates the correlation among populations as well as extending the model to data with different clusters of populations. RESULTS: Using simulated data, we show that in general, the mixture model provides a good approximation of the among-population allele frequency distribution and a good estimate of correlation among populations. Results from fitting the mixture model to a dataset of genotypes at 377 autosomal microsatellite loci from human populations indicate high correlation among populations, which may not be appropriate to neglect. Traditional measures of population structure tend to overestimate the amount of genetic differentiation when correlation is neglected. Inference is performed in a Bayesian framework. CONTACT: fur@ohsu.edu.     

Phenotypic integration and plastic correlations in Phlox drummondii (Polemoniaceae)

Clones from two populations of Phlox drummondii were grown in three different nutrient environments to determine the extent to which the overall level and pattern of correlation among traits within an environment changes across environments. With one exception, the level of phenotypic correlation in both populations was the same across environments. Plants from Lexington, Texas exhibited a significantly lower level of phenotypic correlation when grown at a high nutrient concentration. The two populations did not differ from one another in their levels of phenotypic correlation when compared within environments. The pattern of correlation was homogenous both within populations across environments and among populations within environments. Tests of a priori hypotheses regarding the associations among functionally or developmentally related traits suggest that the correlations among traits are higher in traits that share a common function or developmental origin. We also compared the level and pattern of plasticity correlations among populations for three different components of the plastic response. We found that the level and pattern of plastic correlation for the average, linear, and nonlinear components of the plastic response did not differ among the two populations. With only one exception, the relationships among the plastic responses of different traits fit our model of functional and developmental integration. The results from our analyses of phenotypic and plastic correlations support the hypothesis that plastic correlations determine the extent to which phenotypic correlations are environment-dependent.     

Correlations of amino acids in proteins

A correlation analysis among 20 amino acids is performed for four protein structural classes (, β, /β, and +β) in a total of 204 proteins. The correlation relationships among amino acids can be classified into the following four types: (1) strong positive correlation, (2) strong negative correlation, (3) weak correlation, and (4) no correlation. The correlation relationships are different for different proteins and are correlated with the features of their structural classes. The amino acids with the weak correlation relationship can be treated as the independent basis functions for the space where proteins are defined. The amino acids with large correlation coefficients are linear correlative with each other and they are not independent. The strong correlation among amino acids reflects their mutual constrained relationship, as exhibited by their relevant structural features. The information obtained through the correlation analysis is used for predicting protein structural classes and a better prediction quality is obtained than that by the simple geometry distance methods without taking into account the correlation effects.     

Quantitative genetics of skeletal nonmetric traits in the rhesus macaques on Cayo Santiago. II. Phenotypic,genetic, and environmental correlations between traits

The general lack of phenotypic correlation among skeletal nonmetric traits has been interpreted as indicating a lack of genetic correlation among these traits. Nonmetric traits scored on animals in the skeletal collection of rhesus macaques from Cayo Santiago are used to calculate phenotypic, genetic, and environmental correlations between traits. The results show that even when phenotypic correlations are low, there may be large, significant genetic correlations among these traits. The genetic correlation pattern suggests that genes which affect nonmetric trait variation act primarily at a local level in the cranium, even though there are genes with pleiotropic effects on skeletal nonmetric traits throughout the cranium. Environmental and phenotypic correlations do not show this neighborhood pattern of correlation.     

HETEROZYGOSITY AND GROWTH IN MARINE BIVALVES: FURTHER DATA AND POSSIBLE EXPLANATIONS

In a natural population of two-year-old mussels, shell length was correlated with degree of heterozygosity. There was no correlation between an individual's glycogen level and its degree of heterozygosity, but when individuals were grouped in heterozygosity classes a near-significant correlation was observed between degree of heterozygosity and mean glycogen level corrected for the effects of sex and stage of gonad development. There was no correlation between degree of heterozygosity and index of gonad development. Such a correlation would have provided support for the hypothesis (Zouros and Foltz, 1984) that dependence of time of spawning on heterozygosity may explain the observed heterozygote-deficiency. The causes of heterozygote-deficiency, a common phenomenon in populations of marine bivalves, remain obscure. The observed heterozygosity-growth correlation is examined in the light of the controversy of whether allozymes act as markers in linkage association with genetic conditions that are responsible for the differences in growth among individuals or are themselves the agents of the correlation. The observations that 1) the contributions of individual loci to the correlation vary among populations, 2) the correlation is observed in samples from natural populations but not among progeny from pair matings, and 3) the correlation is nearly always accompanied with heterozygote-deficiency in the population are more compatible with the first explanation and suggest that the growth-heterozygosity correlation results mostly from associative overdominance and to a lesser extent from the direct contributions of scored loci to growth.     

Geochemistry of Lake Biwa sediments revisited

Extensive chemical data for the Lake Biwa sediments were examined with statistical factor analysis to find any correlation patterns among elements and among samples. Based on those patterns, a series of x-y correlation plots of the concentrations of selected elements was constructed to see in detail how the concentrations of elements vary among different sample groups and explain the observed variation patterns.     

Differentiation among populations with migration, mutation, and drift: implications for genetic inference

Populations may become differentiated from one another as a result of genetic drift. The amounts and patterns of differentiation at neutral loci are determined by local population sizes, migration rates among populations, and mutation rates. We provide exact analytical expressions for the mean, variance, and covariance of a stochastic model for hierarchically structured populations subject to migration, mutation, and drift. In addition to the expected correlation in allele frequencies among populations in the same geographic region, we demonstrate that there is a substantial correlation in allele frequencies among regions at the top level of the hierarchy. We propose a hierarchical Bayesian model for inference of Wright's F-statistics in a two-level hierarchy in which we estimate the among-region correlation in allele frequencies by substituting replication across loci for replication across time. We illustrate the approach through an analysis of human microsatellite data, and we show that approaches ignoring the among-region correlation in allele frequencies underestimate the amount of genetic differentiation among major geographic population groups by approximately 30%. Finally, we discuss the implications of these results for the use and interpretation of F-statistics in evolutionary studies.     

猕猴桃(Actinidia Lindl.)叶片与果实维生素C含量的相关性研究

以猕猴桃属中华猕猴桃（Actinidia chinensis）32个品种和1个种间杂交后代群体为研究对象,对猕猴桃属植物叶片与果实维生素C含量的相关性进行了研究。结果表明,在中华猕猴桃种内水平上,幼果与成熟果实的果肉维生素C含量间存在极显著的正相关关系;在种间杂交后代群体中成熟叶片和成熟果实的维生素C含量存在极显著正相关关系,为利用早期相关性状开展猕猴桃育种的可行性提供了理论依据。此外,对15个常见中华猕猴桃品种的果实维生素C含量进行了多重比较,为人工杂交时的亲本选择提供了依据。     

A comparison of phenotypic variation and covariation patterns and the role of phylogeny, ecology, and ontogeny during cranial evolution of new world monkeys

Similarity of genetic and phenotypic variation patterns among populations is important for making quantitative inferences about past evolutionary forces acting to differentiate populations and for evaluating the evolution of relationships among traits in response to new functional and developmental relationships. Here, phenotypic co variance and correlation structure is compared among Platyrrhine Neotropical primates. Comparisons range from among species within a genus to the superfamily level. Matrix correlation followed by Mantel's test and vector correlation among responses to random natural selection vectors (random skewers) were used to compare correlation and variance/covariance matrices of 39 skull traits. Sampling errors involved in matrix estimates were taken into account in comparisons using matrix repeatability to set upper limits for each pairwise comparison. Results indicate that covariance structure is not strictly constant but that the amount of variance pattern divergence observed among taxa is generally low and not associated with taxonomic distance. Specific instances of divergence are identified. There is no correlation between the amount of divergence in covariance patterns among the 16 genera and their phylogenetic distance derived from a conjoint analysis of four already published nuclear gene datasets. In contrast, there is a significant correlation between phylogenetic distance and morphological distance (Mahalanobis distance among genus centroids). This result indicates that while the phenotypic means were evolving during the last 30 millions years of New World monkey evolution, phenotypic covariance structures of Neotropical primate skulls have remained relatively consistent. Neotropical primates can be divided into four major groups based on their feeding habits (fruit-leaves, seed-fruits, insect-fruits, and gum-insect-fruits). Differences in phenotypic covariance structure are correlated with differences in feeding habits, indicating that to some extent changes in interrelationships among skull traits are associated with changes in feeding habits. Finally, common patterns and levels of morphological integration are found among Platyrrhine primates, suggesting that functional/developmental integration could be one major factor keeping covariance structure relatively stable during evolutionary diversification of South American monkeys.     

Effects of dependence in high-dimensional multiple testing problems

Background  

We consider effects of dependence among variables of high-dimensional data in multiple hypothesis testing problems, in particular the False Discovery Rate (FDR) control procedures. Recent simulation studies consider only simple correlation structures among variables, which is hardly inspired by real data features. Our aim is to systematically study effects of several network features like sparsity and correlation strength by imposing dependence structures among variables using random correlation matrices.