Some Asymptotic Tests for the Equality of the Covariance Matrices of Two Dependent Bivariate Normals

For the problem of testing the equality of the covariance matrices of two dependent bivariate normals, five asymptotic tests are explicitly derived in this paper. Small sample performances of these tests are compared by simulating levels of significance and powers, and recommendation is made of the ones that have good performance. The recommended tests are then applied to real data from a crossover bioequivalence trial. Asymptotically distribution-free versions of the tests derived here are also presented.     

A Fast Incremental Gaussian Mixture Model

This work builds upon previous efforts in online incremental learning, namely the Incremental Gaussian Mixture Network (IGMN). The IGMN is capable of learning from data streams in a single-pass by improving its model after analyzing each data point and discarding it thereafter. Nevertheless, it suffers from the scalability point-of-view, due to its asymptotic time complexity of O(NKD³) for N data points, K Gaussian components and D dimensions, rendering it inadequate for high-dimensional data. In this work, we manage to reduce this complexity to O(NKD²) by deriving formulas for working directly with precision matrices instead of covariance matrices. The final result is a much faster and scalable algorithm which can be applied to high dimensional tasks. This is confirmed by applying the modified algorithm to high-dimensional classification datasets.     

A Stochastic Model of Gene Evolution with Time Dependent Pseudochaotic Mutations

We develop here a new class of stochastic models of gene evolution in which a random subset of the 64 possible trinucleotides mutates at each evolutionary time t according to some time dependent substitution probabilities. Therefore, at each time t, the numbers and the types of mutable trinucleotides are unknown. Thus, the mutation matrix changes at each time t. This pseudochaotic model developed generalizes the standard model in which all the trinucleotides mutate at each time t. It determines the occurrence probabilities at time t of trinucleotides which pseudochaotically mutate according to 3 time dependent substitution parameters associated with the 3 trinucleotide sites. The main result proves that under suitable assumptions, this pseudochaotic model converges to a uniform probability vector identical to that of the standard model. Furthermore, an application of this pseudochaotic model allows an evolutionary study of the 3 circular codes identified in both eukaryotic and prokaryotic genes. A circular code is a particular set of trinucleotides whose main property is the retrieval of the frames in genes locally, i.e., anywhere in genes and particularly without start codons, and automatically with a window of a few nucleotides. After a certain evolutionary time and with particular time dependent functions for the 3 substitution parameters, precisely an exponential decrease in the 1st and 2nd trinucleotide sites and an exponential increase in the 3rd one, this pseudochaotic model retrieves the main statistical properties of the 3 circular codes observed in genes. Furthermore, it leads to a circular code asymmetry stronger than the standard model (nonpseudochaotic) and, therefore, to a better correlation with the genes.     

A Stochastic Model for BOD and DO with Random Initial Conditions and Distance Dependent Velocity

A random differential equation arises in stream pollution models when the initial conditions are stochastic and the stream velocity is distance dependent. The mean squared solution gives the biochemical oxygen demand (BOD) and the dissolved oxygen (DO) at any distance downstream from the pollution source. The probability density function and some of the moments of the BOD and DO are obtained, thus completely characterizing the BOD and DO process. An example illustrates the results and compares them with previous ones.     

Weighted Estimation of the Accelerated Failure Time Model in the Presence of Dependent Censoring

Independent censoring is a crucial assumption in survival analysis. However, this is impractical in many medical studies, where the presence of dependent censoring leads to difficulty in analyzing covariate effects on disease outcomes. The semicompeting risks framework offers one approach to handling dependent censoring. There are two representative estimators based on an artificial censoring technique in this data structure. However, neither of these estimators is better than another with respect to efficiency (standard error). In this paper, we propose a new weighted estimator for the accelerated failure time (AFT) model under dependent censoring. One of the advantages in our approach is that these weights are optimal among all the linear combinations of the previously mentioned two estimators. To calculate these weights, a novel resampling-based scheme is employed. Attendant asymptotic statistical results for the estimator are established. In addition, simulation studies, as well as an application to real data, show the gains in efficiency for our estimator.     

Hybrid Mixture Model for Subpopulation Identification

Personalized medicine aims to identify those patients who have good or poor prognosis for overall disease outcomes or therapeutic efficacy for a specific treatment. A well-established approach is to identify a set of biomarkers using statistical methods with a classification algorithm to identify patient subgroups for treatment selection. However, there are potential false positives and false negatives in classification resulting in incorrect patient treatment assignment. In this paper, we propose a hybrid mixture model taking uncertainty in class labels into consideration, where the class labels are modeled by a Bernoulli random variable. An EM algorithm was developed to estimate the model parameters, and a parametric bootstrap method was used to test the significance of the predictive variables that were associated with subgroup memberships. Simulation experiments showed that the proposed method averagely had higher accuracy in identifying the subpopulations than the Naïve Bayes classifier and logistic regression. A breast cancer dataset was analyzed to illustrate the proposed hybrid mixture model.     

A Simple,Flexible Failure Model

A new failure model is introduced in the form of a four-parameter nonlinear differential equation, with failure probability as the dependent variable and failure time as the independent variable. The first parameter characterizes the location, the second the scale, and the other two the shape of the model. The type of the accompanying hazard function is immediately read off the shape parameters. The new model approximates the classical failure models with rather high precision, but also models cases where the failure density is skewed to the left. It can be used to analyze survival data objectively, based on the shape of the failure distribution. The computation of quantiles and moments is easy and fast. Nonlinear regression methods are used to estimate parameter values.     

A Dynamic Logistic Regression Model for Multiple Spell Failure Time Data

The paper deals with discrete-time regression models to analyze multistate-multiepisode failure time data. The covariate process may include fixed and external as well as internal time dependent covariates. The effects of the covariates may differ among different kinds of failures and among successive episodes. A dynamic form of the logistic regression model is investigated and maximum likelihood estimation of the regression coefficients is discussed. In the last section we give an application of the model to the analysis of survival time after breast cancer operation.     

An Equiratio Mixture Model for Non-additive Components: A Case Study for Aspartame/Acesulfame-K Mixtures

The Equiratio Mixture Model predicts the psychophysical functionfor an equiratio mixture type on the basis of the psychophysicalfunctions for the unmixed components. The model reliably estimatesthe sweetness of mixtures of sugars and sugar-alchohols, butis unable to predict intensity for aspartame/sucrose mixtures.In this paper, the sweetness of aspartame/acesulfame-K mixturesin aqueous and acidic solutions is investigated. These two intensivesweeteners probably do not comply with the model's originalassumption of sensory dependency among components. However,they reveal how the Equiratio Mixture Model could be modifiedto describe and predict mixture functions for non-additive substances. To predict equiratio functions for all similar tasting substances,a new Equiratio Mixture Model should yield accurate predictionsfor components eliciting similar intensities at widely differingconcentration levels, and for substances exhibiting hypo- orhyperadditivity. In addition, it should be able to correct violationsof Stevens's power law. These three problems are resolved ina model that uses equi-intense units as the measure of physicalconcentration. An interaction index in the formula for the constantaccounts for the degree of interaction between mixture components.Deviations from the power law are corrected by a nonlinear responseoutput transformation, assuming a two-stage model of psychophysicaljudgment. Chem. Senses 21: 1–11, 1996.     

具有非线性密度制约HollingⅢ类功能反应Predator-Prey系统模型的定性分析

用定性分析的方法讨论了一类具有非线性密度制约的HollingⅢ型功能反应的predator-prey模型,分析了模型平衡点的性态,得出了模型极限环的存在性与惟一性的充分条件.     

A novel Mixture Model Method for identification of differentially expressed genes from DNA microarray data

Background  

The main goal in analyzing microarray data is to determine the genes that are differentially expressed across two types of tissue samples or samples obtained under two experimental conditions. Mixture model method (MMM hereafter) is a nonparametric statistical method often used for microarray processing applications, but is known to over-fit the data if the number of replicates is small. In addition, the results of the MMM may not be repeatable when dealing with a small number of replicates. In this paper, we propose a new version of MMM to ensure the repeatability of the results in different runs, and reduce the sensitivity of the results on the parameters.     

A Novel MiRNA-Based Predictive Model for Biochemical Failure Following Post-Prostatectomy Salvage Radiation Therapy

Purpose

To develop a microRNA (miRNA)-based predictive model for prostate cancer patients of 1) time to biochemical recurrence after radical prostatectomy and 2) biochemical recurrence after salvage radiation therapy following documented biochemical disease progression post-radical prostatectomy.

Methods

Forty three patients who had undergone salvage radiation therapy following biochemical failure after radical prostatectomy with greater than 4 years of follow-up data were identified. Formalin-fixed, paraffin-embedded tissue blocks were collected for all patients and total RNA was isolated from 1mm cores enriched for tumor (>70%). Eight hundred miRNAs were analyzed simultaneously using the nCounter human miRNA v2 assay (NanoString Technologies; Seattle, WA). Univariate and multivariate Cox proportion hazards regression models as well as receiver operating characteristics were used to identify statistically significant miRNAs that were predictive of biochemical recurrence.

Results

Eighty eight miRNAs were identified to be significantly (p<0.05) associated with biochemical failure post-prostatectomy by multivariate analysis and clustered into two groups that correlated with early (≤ 36 months) versus late recurrence (>36 months). Nine miRNAs were identified to be significantly (p<0.05) associated by multivariate analysis with biochemical failure after salvage radiation therapy. A new predictive model for biochemical recurrence after salvage radiation therapy was developed; this model consisted of miR-4516 and miR-601 together with, Gleason score, and lymph node status. The area under the ROC curve (AUC) was improved to 0.83 compared to that of 0.66 for Gleason score and lymph node status alone.

Conclusion

miRNA signatures can distinguish patients who fail soon after radical prostatectomy versus late failures, giving insight into which patients may need adjuvant therapy. Notably, two novel miRNAs (miR-4516 and miR-601) were identified that significantly improve prediction of biochemical failure post-salvage radiation therapy compared to clinico-histopathological factors, supporting the use of miRNAs within clinically used predictive models. Both findings warrant further validation studies.     

A Genomewide Screen for Autism Susceptibility Loci

We report the analysis of 335 microsatellite markers genotyped in 110 multiplex families with autism. All families include at least two "affected" siblings, at least one of whom has autism; the remaining affected sibs carry diagnoses of either Asperger syndrome or pervasive developmental disorder. Affected sib-pair analysis yielded multipoint maximum LOD scores (MLS) that reach the accepted threshold for suggestive linkage on chromosomes 5, X, and 19. Nominal evidence for linkage (point-wise P<.05) was obtained on chromosomes 2, 3, 4, 8, 10, 11, 12, 15, 16, 18, and 20, and secondary loci were found on chromosomes 5 and 19. Analysis of families sharing alleles at the putative X chromosomal linked locus and one or more other putative linked loci produced an MLS of 3.56 for the DXS470-D19S174 marker combination. In an effort to increase power to detect linkage, scan statistics were used to evaluate the significance of peak LOD scores based on statistical evidence at adjacent marker loci. This analysis yielded impressive evidence for linkage to autism and autism-spectrum disorders with significant genomewide P values <.05 for markers on chromosomes 5 and 8 and with suggestive linkage evidence for a marker on chromosome 19.     

具状态依赖时滞单种群模型周期正解的存在性

用重合度论的连续性定理,本文获得如下具状态依赖时滞的单种群增长模型周期正解的存在性x(t)=x(t)[a(t)+b(t)xp(t-τ(t,x(t)))-c(t)xq(t-τ(t,x(t)))]这里a,b,c∈C((0,∞),R)是周期为ω(ω>0)的连续函数,且a>0,c>0.m,p,q为正整数且q>p.     

Mutation Discovery in Regions of Segmental Cancer Genome Amplifications with CoNAn-SNV: A Mixture Model for Next Generation Sequencing of Tumors

Next generation sequencing has now enabled a cost-effective enumeration of the full mutational complement of a tumor genome-in particular single nucleotide variants (SNVs). Most current computational and statistical models for analyzing next generation sequencing data, however, do not account for cancer-specific biological properties, including somatic segmental copy number alterations (CNAs)-which require special treatment of the data. Here we present CoNAn-SNV (Copy Number Annotated SNV): a novel algorithm for the inference of single nucleotide variants (SNVs) that overlap copy number alterations. The method is based on modelling the notion that genomic regions of segmental duplication and amplification induce an extended genotype space where a subset of genotypes will exhibit heavily skewed allelic distributions in SNVs (and therefore render them undetectable by methods that assume diploidy). We introduce the concept of modelling allelic counts from sequencing data using a panel of Binomial mixture models where the number of mixtures for a given locus in the genome is informed by a discrete copy number state given as input. We applied CoNAn-SNV to a previously published whole genome shotgun data set obtained from a lobular breast cancer and show that it is able to discover 21 experimentally revalidated somatic non-synonymous mutations in a lobular breast cancer genome that were not detected using copy number insensitive SNV detection algorithms. Importantly, ROC analysis shows that the increased sensitivity of CoNAn-SNV does not result in disproportionate loss of specificity. This was also supported by analysis of a recently published lymphoma genome with a relatively quiescent karyotype, where CoNAn-SNV showed similar results to other callers except in regions of copy number gain where increased sensitivity was conferred. Our results indicate that in genomically unstable tumors, copy number annotation for SNV detection will be critical to fully characterize the mutational landscape of cancer genomes.     

Likelihood-Based Approach to Gene Set Enrichment Analysis with a Finite Mixture Model

In this paper, we study a parametric modeling approach to gene set enrichment analysis. Existing methods have largely relied on nonparametric approaches employing, e.g., categorization, permutation or resampling-based significance analysis methods. These methods have proven useful yet might not be powerful. By formulating the enrichment analysis into a model comparison problem, we adopt the likelihood ratio-based testing approach to assess significance of enrichment. Through simulation studies and application to gene expression data, we will illustrate the competitive performance of the proposed method.     

Cryptococcus neoformans: The Model Organism for Yeast Antifungal Drug Susceptibility Testing

We describe an approach to antifungal susceptibility testing of the yeast Cryptococcus neoformans that shows promise for predicting the mycological response in patients to treatment. Quantitative cultures of the cerebrospinal fluid provide a direct measure of the patient's mycological response to treatment and have been used in multiple studies to identify the most promising antifungal drugs for subsequent testing in larger clinical studies. Using these quantitative measures of response, a modified macrobroth dilution assay system shows the potential for predicting the response of an individual patient to treatment with amphotericin B, fluconazole, or the combination of amphotericin B plus flucytosine. We describe this modified macrobroth dilution assay method, the statistical approach for assessing susceptibility, and the clinical decisions that can be guided by this in vitro antifungal drug susceptibility testing.     

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).     

A General Model of Negative Frequency Dependent Selection Explains Global Patterns of Human ABO Polymorphism

The ABO locus in humans is characterized by elevated heterozygosity and very similar allele frequencies among populations scattered across the globe. Using knowledge of ABO protein function, we generated a simple model of asymmetric negative frequency dependent selection and genetic drift to explain the maintenance of ABO polymorphism and its loss in human populations. In our models, regardless of the strength of selection, models with large effective population sizes result in ABO allele frequencies that closely match those observed in most continental populations. Populations must be moderately small to fall out of equilibrium and lose either the A or B allele (N_e ≤ 50) and much smaller (N_e ≤ 25) for the complete loss of diversity, which nearly always involved the fixation of the O allele. A pattern of low heterozygosity at the ABO locus where loss of polymorphism occurs in our model is consistent with small populations, such as Native American populations. This study provides a general evolutionary model to explain the observed global patterns of polymorphism at the ABO locus and the pattern of allele loss in small populations. Moreover, these results inform the range of population sizes associated with the recent human colonization of the Americas.