Blinded sample size recalculation in multiple composite population designs with normal data and baseline adjustments

The increasing interest in subpopulation analysis has led to the development of various new trial designs and analysis methods in the fields of personalized medicine and targeted therapies. In this paper, subpopulations are defined in terms of an accumulation of disjoint population subsets and will therefore be called composite populations. The proposed trial design is applicable to any set of composite populations, considering normally distributed endpoints and random baseline covariates. Treatment effects for composite populations are tested by combining p-values, calculated on the subset levels, using the inverse normal combination function to generate test statistics for those composite populations while the closed testing procedure accounts for multiple testing. Critical boundaries for intersection hypothesis tests are derived using multivariate normal distributions, reflecting the joint distribution of composite population test statistics given no treatment effect exists. For sample size calculation and sample size, recalculation multivariate normal distributions are derived which describe the joint distribution of composite population test statistics under an assumed alternative hypothesis. Simulations demonstrate the absence of any practical relevant inflation of the type I error rate. The target power after sample size recalculation is typically met or close to being met.     

Discriminant functions for linear comparisons of means when covariance matrices are unequal

Situations exist, as in the biological example of discriminant analysis for natural hybridization, cited in the text, where (a) not all populations have equal variances, and (b) comparisions based on single degrees of freedom must be planned. This paper presents a statistical methodology of estimating discriminant functions for linear comparisons among k(<2) multivariate normal populations, and of testing their significance, when these populations have unequal covariance matrices.     

Power of three multitrait methods for QTL detection in crossbred populations

The multitrait detections of QTL applied to a mixture of full- and half-sib families require specific strategies. Indeed, the number of parameters estimated by the multivariate methods is excessive compared with the size of the population. Thus, only multitrait methods based on a univariate analysis of a linear combination (LC) of the traits can be extensively performed. We compared three strategies to obtain the LC of the traits. Two linear transformations were performed on the overall population. The last one was performed within each half-sib family. Their powers were compared on simulated data depending on the frequency of the two QTL alleles in each of the grand parental populations of an intercross design. The transformations from the whole population did not lead to a large loss of power even though the frequency of the QTL alleles was similar in the two grand parental populations. In these cases, applying the within-sire family transformation improved the detection when the number of progeny per sire was greater than 100.     

One-Way Classification ANOVA Model for the Mixture of Two Multivariate Normal Populations

When a sample of size n is available from a mixture of two normal populations with different mean vectors and a common covariance matrix, SRIVASTAVA and AWAN (1982) develop one-way ANOVA analysis for testing a certain composite linear hypothesis. They show that the error and hypothesis sum of products matrices have independent noncentral Wishart densities of rank unity each. However, they do not obtain the necessary Wilks' λ for testing the desired hypothesis. The present paper obtains the density of λ. This density is doubly noncentral multivariate beta density. The derivation is based on generalized Sverdrup's lemmas, KABE (1965), (1974).     

新疆哈密拉甫却克墓地人的颅面部测量学特征

新疆地处欧亚大陆东西方交汇处,公元前200年以后的人群迁徙、融合历程能够反映丝绸之路沿线地区不同族群的形成历史和多元文化的互动模式。拉甫却克墓地是东疆哈密地区首次发掘的历史时期墓葬群。本文基于该墓地10例成年人颅面部测量数据,采用多元统计及生物距离的方法来评估拉甫却克墓地的人群结构,并对哈密绿洲地带青铜时代晚期到历史时期的人群变迁进行初步探索。结果显示：1）拉甫却克人群呈现出明显的异质性,既有与欧亚大陆东部人群颅面部特征相近的个体,也有表现出东西方混合特征的个体;2）青铜时代晚期至早期铁器时代（公元前2000年至公元前1000年）,哈密人群在体质特征上存在连续性;而早期铁器时代到历史时期（公元前1000年以后）,随着欧亚大陆东部人群遗传贡献的增加,哈密人群体质特征发生明显变化。结合考古证据和历史记录,新的人骨标本让我们对哈密历史时期的人群迁徙和融合有了初步认识,也使后续可以针对这一问题展开更详细的多学科研究。     

Pairwise rank-based likelihood for estimation and inference on the mixture proportion

We consider the problem of estimation and inference on the mixture parameter in the two-sample problem when sample data from the two distributions as well as from a third population consisting of a mixture of the two are used. Under a general nonparametric model, where the relationship between the two populations is unspecified, we develop a pairwise rank-based likelihood. Simultaneous inference on the mixture proportion and a parameter representing the probability an observation from one population is greater than an observation from the other population is based on this likelihood. Under some regularity conditions, it is shown that the maximum pairwise rank likelihood estimator is consistent and has an asymptotic normal distribution. Simulation results indicate that the performance of this statistic is satisfactory. The methodology is demonstrated on a data set in prostate cancer.     

Canonical functions for dispersal-induced synchrony

Two processes are universally recognized for inducing spatial synchrony in abundance: dispersal and correlated environmental stochasticity. In the present study we seek the expected relationship between synchrony and distance in populations that are synchronized by density-independent dispersal. In the absence of dispersal, synchrony among populations with simple dynamics has been shown to echo the correlation in the environment. We ask what functional form we may expect between synchrony and distance when dispersal is the synchronizing agent. We formulate a continuous-space, continuous-time model that explicitly represents the time evolution of the spatial covariance as a function of spatial distance. Solving this model gives us two simple canonical functions for dispersal-induced covariance in spatially extended populations. If dispersal is rare relative to birth and death, then covariances between nearby points will follow the dispersal distance distribution. At long distances, however, the covariance tails off according to exponential or Bessel functions (depending on whether the population moves in one or two dimensions). If dispersal is common, then the covariances will follow the mixture distribution that is approximately Gaussian around the origin and with an exponential or Bessel tail. The latter mixture results regardless of the original dispersal distance distribution. There are hence two canonical functions for dispersal-induced synchrony     

Epicuticular wax variability of Juniperus deltoides R.P. Adams from the central Balkan – Ecology and chemophenetics

Juniperus deltoides R.P.Adams is a prickly, evergreen shrub that grows in the East Mediterranean on dry hills and mountains. Needle-like leaves have a thick cuticular layer on the surface, which serves as the ultimate barrier for prevention of water loss. n-Alkanes comprise the biggest part of this hydrophobic wax mixture. These compounds are studied as chemophenetic characters due to their chemical and physiological stability, and strong genetic control. Six central Balkan populations were studied and compared to one eastern and one western. Fifteen n-alkanes were identified, with C33 being dominant in all samples. Univariate and multivariate statistical analyses separated western population from all central Balkan populations, while the eastern Balkan population showed high similarity with the central ones. Climatic, orographic and pedological characteristics of the studied localities were also taken into account.     

Anthropometry and the biological structure of the Hvar population

Biological structure of the population of the island of Hvar was investigated by using the data on anthropometric variation among nine village populations; 24 body and 14 head dimensions were analysed from 487 male and 437 female adult subjects. Univariate and multivariate analyses revealed heterogeneity among the populations, which says much for the strength of the isolating factors on the island. Using correlations of anthropometric and geographic distance, the observed patterns of variation among villages were closely related to geography, suggesting migration to be an important factor in the formation of the island's population structure. Populations of the examined villages were further grouped to form the population of the eastern part and the population of the western part of the island, which have an ethnodemographic and sociocultural basis. The analyses revealed heterogeneity between the populations and thus provided evidence to support the hypothesis about the existence of the genetically different groups living in the same biotope.     

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.     

Proposal of k Sample Tests for Bivariate Censored Data for Nondecreasing Ordered Alternatives

Tests are introduced which are designed to test for a nondecreasing ordered alternative among the survival functions of k populations consisting of multiple observations on each subject. Some of the observations could be right censored. A simulation study is conducted comparing the proposed tests on the basis of estimated power when the underlying distributions are multivariate normal. Equal sample sizes of 20 with 25% censoring, and 40 with both 25% and 50% censoring are considered for 3 and 4 populations. All of the tests hold their α‐values well. A recommendation is made as to the best overall test for the situations considered.     

Epistasis can increase multivariate trait diversity in haploid non-recombining populations

We evaluate the effect of epistasis on genetically-based multivariate trait variation in haploid non-recombining populations. In a univariate setting, past work has shown that epistasis reduces genetic variance (additive plus epistatic) in a population experiencing stabilizing selection. Here we show that in a multivariate setting, epistasis also reduces total genetic variation across the entire multivariate trait in a population experiencing stabilizing selection. But, we also show that the pattern of variation across the multivariate trait can be more even when epistasis occurs compared to when epistasis is absent, such that some character combinations will have more genetic variance when epistasis occurs compared to when epistasis is absent. In fact, a measure of generalized multivariate trait variation can be increased by epistasis under weak to moderate stabilizing selection conditions, as well as neutral conditions. Likewise, a measure of conditional evolvability can be increased by epistasis under weak to moderate stabilizing selection and neutral conditions. We investigate the nature of epistasis assuming a multivariate-normal model genetic effects and investigate the nature of epistasis underlying the biophysical properties of RNA. Increased multivariate diversity occurs for populations that are infinite in size, as well as populations that are finite in size. Our model of finite populations is explicitly genealogical and we link our findings about the evenness of eigenvalues with epistasis to prior work on the genealogical mapping of epistatic effects.     

A nonparametric approach to analyzing large human populations.

There are many statistical techniques that require the assumption that the population being studied is normally distributed--regression analysis, multivariate analysis, time series analysis, and so on. Unfortunately, as the development of survey sampling has long acknowledged, large human populations are usually stratified into several different subpopulations. Since the boundaries between the strata are somewhat blurred, they are not independent, so the overall distribution of the population tends to be multimodal rather than normal. In this paper, a technique is developed to find these multimodal techniques using nonparametric density estimation. Its effectiveness is demonstrated by means of an example.     

Geographical variation in the cranial and external characters of the little tube-nosed bat,Murina silvatica in the Japanese archipelago

The distribution ofMurina silvatica (Yoshiyuki, 1983) in the Japanese archipelago extends over about 2000 km from north to south. Specimens were obtained from populations in Hokkaido and Yakushima, which are at the northern and southern ends of the range, and from two intermediate locations in Honshu. Measurements of cranial and external morphology were examined for evidence of geographical variation. The results of both multivariate analysis of variance and cluster analysis showed that there was no distinct cline in skull morphology among the Hokkaido, Tohoku and Chubu populations. However, the results of multivariate analysis of variance showed that all measures were significantly greater for the Yakushima population than for the others. Similarly, in a dendrogram of cluster analysis, the Yakushima population formed a cluster that was distinct from the other populations. However, as the difference between the Yakushima population and the other populations was less than the variation found within the Hokkaido, Tohoku and Chubu populations, morphological divergence of the Yakushima population was attributable to intraspecific variation. The island of Yakushima is the most isolated of the four locations and the morphological divergence of this population may be associated with its relative geographic isolation.     

Excursions along the Interface between Disruptive and Stabilizing Selection

When a polygenic character is exposed to natural selection in which the curve giving fitness as a function of phenotype is a mixture of two Gaussian (normal) curves, the population may respond either by evolving to a specialized phenotype near one of the two optimum phenotypes, or by evolving to a generalized phenotype between them. Using approximate multivariate normal distribution methods, it is demonstrated that the condition for selection to result in a specialized phenotype is that the curve of fitness as a function of breeding value be bimodal. This implies that a specialized phenotype is more likely to result the higher is the heritability of the character. Numerical iterations of four-locus models and algebraic analysis of a symmetric two-locus model generally support the conclusions of the normal approximation.     

A sequential approach to the counting of plankton organisms

A counting strategy is described by means of which it is possible to decide, after carrying out a few counts, whether a sampled plankton population can be considered homogeneously distributed. The time saving of the proposed strategy lies in the fact that if the underlying population is homogeneously distributed only one count, i.e., the one of the mixture of aliquots taken from all individual samples collected, would be necessary to characterize the population sufficiently. The count of this mixture may be considered as a ‘mean value’ equivalent to the mean obtained from the counts of all individual samples.With some experience in predicting where homogeneously and where heterogeneously distributed populations are sampled, it is possible to mix large numbers of samples and thus save a great amount of effort in the analysis of plankton populations. The samples may be collected during a survey in any way desired, e.g., in normal hydrographie casts, with pumps, with the air bubble lift etc. A numerical example is given in the Appendix illustrating the method.     

Use of response functions in selecting lodgepole pine populations for future climates

Although growth response functions have previously been developed for lodgepole pine (Pinus contorta Dougl. ex Loud.) populations in British Columbia, new analyses were conducted: (1) to demonstrate the merit of a new local climate model in genecological analysis; (2) to highlight new methods for deriving response functions; and (3) to evaluate the impacts of management options for existing geographically defined seed planning units (SPUs) for reforestation. Results of this study suggest that new methods for anchoring population response functions, and a multivariate approach for incorporating climate variables into a single model, considerably improve the reliability of these functions. These functions identified a small number of populations in central areas of the species distribution with greater growth potential over a wide range of mean annual temperature (MAT). Average productivity of lodgepole pine is predicted to increase (up to 7%) if moderate warming (～2°C MAT) occurs in the next few decades as predicted, although productivity would substantially decline in some SPUs in southern BC. Severe global warming (>3°C MAT) would result in either a drastic decline in productivity or local populations being extirpated in southern SPUs. New deployment strategies using the best seed sources for future reforestation may not only be able to mitigate the negative impact of global warming, but may even be able to increase productivity in some areas.     

A measure of sexual dimorphism in populations which are univariate normal mixtures

Measures of sexual dimorphism have been used extensively to predict the social organization and ecology of animal and human populations. There is, however, no universally accepted measure of phenotypic differences between the sexes. Most indices of sexual dimorphism fail to incorporate all of the information contained in a random data set. In an attempt to have a better alternative, an index is proposed to measure sexual dimorphism in populations that are distributed according to a probabilistic mixture model with two normal components. The index calculates the overlap between two functions that represent the contribution of each sex in the mixture. In order to assess such an index, sample means, variances and sizes of each sex are needed. As a consequence, the sample information used is greater than that used by other indices that take intrasexual variability into account. By evaluating some examples, our proposed index appears to be a more realistic measure of sexual dimorphism than other measures currently used.     

Integrating stable isotopes,parasite, and ring‐reencounter data to quantify migratory connectivity—A case study with Barn Swallows breeding in Switzerland,Germany, Sweden,and Finland

Ecosystems around the world are connected by seasonal migration. The migrant animals themselves are influenced by migratory connectivity through effects on the individual and the population level. Measuring migratory connectivity is notoriously difficult due to the simple requirement of data conveying information about the nonbreeding distribution of many individuals from several breeding populations. Explicit integration of data derived from different methods increases the precision and the reliability of parameter estimates. We combine ring‐reencounter, stable isotope, and blood parasite data of Barn Swallows Hirundo rustica in a single integrated model to estimate migratory connectivity for three large scale breeding populations across a latitudinal gradient from Central Europe to Scandinavia. To this end, we integrated a non‐Markovian multistate mark‐recovery model for the ring‐reencounter data with normal and binomial mixture models for the stable isotope and parasite data. The integration of different data sources within a mark‐recapture modeling framework enables the most precise quantification of migratory connectivity on the given broad spatial scale. The results show that northern‐breeding populations and Southern Africa as well as southern‐breeding populations and Western–Central Africa are more strongly connected through Barn Swallow migration than central European breeding populations with any of the African wintering areas. The nonbreeding distribution of Barn Swallows from central European breeding populations seems to be a mixture of those populations breeding further north and south, indicating a migratory divide.     

Elevated esterase activity in resistant tufted apple bud moth, Platynota idaeusalis (Walker) (Lepidoptera: Tortricidae).

1. Esterase activity in the tufted apple bud moth was measured spectrophotometrically by the hydrolysis of alpha-naphthyl acetate. 2. Resistant populations from both laboratory and field exhibited significantly greater esterase activity than did the respective susceptible populations. 3. The resistant laboratory population had significantly higher esterase activity than the resistant field population, suggesting that this field population contained a mixture of resistant and susceptible individuals.