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We develop a new method for classified mixed model prediction (CMMP). The original CMMP method ( Jiang et al., 2018b ) does not incorporate covariate information in matching the class between the new observations and the training data. As a result, the method may not outperform the mixed model prediction (MMP) method in terms of predictive performance. The new CMMP method that we develop utilizes covariate information, and therefore is more accurate in terms of the matching. We show that the new CMMP method outperforms the MMP in terms of the predictive performance. Furthermore, we develop a second-order unbiased estimator of the mean squared prediction error (MSPE) for the new CMMP, which was previously not available for the original CMMP. Theoretical and empirical properties of the proposed new CMMP method as well as the MSPE estimator are studied. A real data application is considered.

Dysbiosis of human gut microbiota has been reported in association with ulcerative colitis (UC) in both children and adults using either 16S rRNA gene or shotgun sequencing data. However, these studies used either 16S rRNA or metagenomic shotgun sequencing but not both. We sequenced feces samples from 19 pediatric UC and 23 healthy children ages between 7 to 21 years using both 16S rRNA and metagenomic shotgun sequencing. The samples were analyzed using three different types of data: 16S rRNA genus level abundance, microbial species and pathway abundance profiles. We demonstrated that (a) the alpha diversity of pediatric UC cases is lower than that of healthy controls; (b) the beta diversity within children with UC is more variable than within the healthy children; (c) several microbial families including Akkermansiaceae, Clostridiaceae, Eggerthellaceae, Lachnospiraceae, and Oscillospiraceae, contain species that are depleted in pediatric UC compared to controls; (d) a few associated species unique to pediatric UC, but not adult UC, were also identified, e.g. some species in the Christensenellaceae family were found to be depleted and some species in the Enterobacteriaceae family were found to be enriched in pediatric UC; and (e) both 16S rRNA and shotgun sequencing data can predict pediatric UC status with area under the receiver operating characteristic curve (AUROC) of close to 0.90 based on cross validation. We showed that 16S rRNA data yielded similar results as shotgun data in terms of alpha diversity, beta diversity, and prediction accuracy. Our study demonstrated that pediatric UC subjects harbor a dysbiotic and less diverse gut microbial population with distinct differences from healthy children. We also showed that 16S rRNA data yielded accurate disease prediction results in comparison to shotgun data, which can be more expensive and laborious. These conclusions were confirmed in an independent data set of 7 pediatric UC cases and 8 controls.

Biological time series data plays an important role in exploring the dynamic changes of biological systems, while the determinate patterns of association between various biological factors can further deepen the understanding of biological system functions and the interactions between them. At present, local trend analysis (LTA) has been commonly conducted in many biological fields, where the biological time series data can be the sequence at either the level of gene expression or OTU abundance, etc., A local trend score can be obtained by taking the similarity degree of the upward, constant or downward trend of time series data as an indicator of the correlation between different biological factors. However, a major limitation facing local trend analysis is that the permutation test conducted to calculate its statistical significance requires a time-consuming process. Therefore, the problem attracting much attention from bioinformatics scientists is to develop a method of evaluating the statistical significance of local trend scores quickly and effectively. In this paper, a new approach is proposed to evaluate the efficient approximation of statistical significance in the local trend analysis of dependent time series, and the effectiveness of the new method is demonstrated through simulation and real data set analysis.

A criterion of optimality in prediction is proposed that requires the predictor to assume the same type of values as the random variable it is predicting. In the case of categorical responses, the method leads to the Bayesian classifier with a uniform prior. However, the method extends to other cases, such as zero-inflated observations, as well. The method, called best look-alike prediction (BLAP), justifies an “usual practice” from a theoretical standpoint. Application of BLAP to small area estimation is considered. A real-data example is discussed.

Phylogenetic analysis of molecular sequences for inferring evolutionary relationships is an essential problem in biology. In this paper, we make an extension of Power Spectrum Moments method based on discrete fractional Fourier transform for phylogenetic analysis. DNA sequences are first converted into numeric sequences, and discrete fractional Fourier transform is then used on these numeric sequences to compute power spectra. By extracting a new j th moment feature based on power spectra, distance matrix is constructed and phylogenetic tree is built. Moreover, we give a guideline for choosing an appropriate order p of discrete fractional Fourier transform through simulation strategy and Friedman test. Our method is tested on three real datasets. Comparing with the Power Spectrum Moments method based on discrete Fourier transform and d 2 ∗ measure, the results of phylogenetic trees demonstrate that our method is more efficient in inferring biological relationships.

Alignment-free sequence comparison is becoming fairly popular in many fields of computational biology due to less requirements for sequence itself and computational efficiency for a large scale of sequence data sets. Especially, the approaches based on k -tuple like D 2 , D 2 S and D 2 ∗ are used widely and effectively. However, these measures treat each k -tuple equally without accounting for the potential importance differences among all k -tuples. In this paper, we take advantage of maximizing deviation method proposed in multiple attribute decision making to evaluate the weights of different k -tuples. We modify D 2 , D 2 S and D 2 ∗ with weights and test them by similarity search and evaluation on functionally related regulatory sequences. The results demonstrate that the newly proposed measures are more efficient and robust compared to existing alignment-free methods.

Appendix. Theoretical approximation of LSA statistical significance for i.i.d. or Markov time series and derivation of the asymptotic distribution of the LS score statistics. (PDF 259 kb)

Figure S1-S6. Power of LSAres and DDLSA for local AR model and bivariate AR model with different time delays(D). (PDF 1115 kb)

Table S1-S3. Type I errors of TLSA, LSAres and DDLSA tests under the AR(1), ARMA(1,1) and ARMA(1,1)-TAR(1) models with time delay Dâ 0, respectively. (PDF 551 kb)

In recent years, a large number of time series microbial community data has been produced in molecular biological studies, especially in metagenomics. Among the statistical methods for time series, local similarity analysis is used in a wide range of environments to capture potential local and time-shifted associations that cannot be distinguished by traditional correlation analysis. Initially, the permutation test is popularly applied to obtain the statistical significance of local similarity analysis. More recently, a theoretical method has also been developed to achieve this aim. However, all these methods require the assumption that the time series are independent and identically distributed. In this paper, we propose a new approach based on moving block bootstrap to approximate the statistical significance of local similarity scores for dependent time series. Simulations show that our method can control the type I error rate reasonably, while theoretical approximation and the permutation test perform less well. Finally, our method is applied to human and marine microbial community datasets, indicating that it can identify potential relationship among operational taxonomic units (OTUs) and significantly decrease the rate of false positives.

The main purpose of this article is to consider the covariate-adjusted regression (CAR) model for time series. The CAR model was initially proposed by Senturk and Muller (2005) for such situations where predictor and response variables are not directly observed, but are distorted by some common observable covariate. Despite CAR being originally designed for independent cross-sectional data, multiple works have extended this method to dependent data setting. In this article, the authors extend CAR to the distorted time series setting. This extension is meaningful in many fields such as econometrics, mathematical finance, and signal processing. The estimates of regression parameters are proposed by establishing connection with functional-coefficient time series model. The consistency and asymptotic normality of the proposed estimates are investigated under the α-mixing conditions. Real data and simulated examples are provided for illustration.

Metagenomics commonly refers to the study of genetic materials directly derived from environments without culturing. Several ongoing large-scale metagenomics projects related to human and marine life, as well as pedology studies, have generated enormous amounts of data, posing a key challenge for efficient analysis, as we try to 1) understand microbial organism assemblage under different conditions, 2) compare different communities, and 3) understand how microbial organisms associate with each other and the environment.To address such questions, investigators are using new sequencing technologies, including Sanger, Illumina Solexa, and Roche 454, to sequence either particular genes, called tag sequences, mostly 16S or 18S ribosomal RNA sequences or other conserved genes, or whole metagenome shotgun sequences of all the genetic materials in a given community. In this paper, we review computational methods used for the analysis of tag sequences.

We consider the problem of variable selection using Bayesian method in high-dimensional linear models, where the number of explanatory variables K n is possibly much larger than the sample size n. In particular, the true regression coefficients vector β* is required sparsity in the sense of , which describes a general situation when all explanatory variables are relevant, but most of them have very small effects. According to Bayesian inference of Wasserman (1998), given a proper prior to propose joint densities f(y, x) of response y and explanatory variables vector x, the posterior-proposed densities are often close to the true density f 0(y, x), for large n. It's the so-called “density consistency”. We aim to prove that in linear models, density consistency can induce regression function consistency, which ensures good performance of variable selection. Especially in the special case of , when some regression coefficients are bounded away from zero while the rest are exactly zero, our method would ident...

A method is proposed to detect the number, locations and heights of jump points of the derivative in the regressive modeli = f(� i )+ � i, by checking if the empirical indirect wavelet coe4cients of data have signi!cantly large absolute values across !ne scale levels. The consistency of the estimators is established and practical implementation is discussed. Some simulationexamples are givento test our method. c 2001 Elsevier Science B.V. All rights reserved

High-resolution fetal electrocardiogram (FECG) plays an important role in assisting physicians to detect fetal changes in the womb and to make clinical decisions. However, in real situations, clear FECG is difficult to extract because it is usually overwhelmed by the dominant maternal ECG and other contaminated noise such as baseline wander, high-frequency noise. In this paper, we proposed a novel integrated adaptive algorithm based on independent component analysis (ICA), ensemble empirical mode decomposition (EEMD), and wavelet shrinkage (WS) denoising, denoted as ICA-EEMD-WS, for FECG separation and noise reduction. First, ICA algorithm was used to separate the mixed abdominal ECG signal and to obtain the noisy FECG. Second, the noise in FECG was reduced by a three-step integrated algorithm comprised of EEMD, useful subcomponents statistical inference and WS processing, and partial reconstruction for baseline wander reduction. Finally, we evaluate the proposed algorithm using simulated data sets. The results indicated that the proposed ICA-EEMD-WS outperformed the conventional algorithms in signal denoising.

First, good performance of Bayesian variable selection (BVS for short) in a variety of applications is introduced. Then, we will give a theoretical explanation why BVS works so well in linear models. We assume the true regression coefficients vector of the linear model is sparsity, in a sense that some regression coefficients are bounded from zero while the rest are exactly zero. In this case, under some conditions, BVS will show it can select the true model by means of giving a consistent estimate of the true regression coefficients vector.

We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size increases to infinity. Furthermore, we show that the limiting estimator is consistent and asymptotically efficient, as expected. The method applies to semiparametric regression models with unspecified covariances among the observations. In the special case of linear models, the procedure reduces to iterative reweighted least squares. Finite sample performance of the procedure is studied by simulations, and compared with other methods. A numerical example from a medical study is considered to illustrate the application of the method., Published in at http://dx.doi.org/10.1214/009053607000000208 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

One important problem in genomic research is to identify genomic features such as gene expression data or DNA single nucleotide polymorphisms (SNPs) that are related to clinical phenotypes. Often these genomic data can be naturally divided into biologically meaningful groups such as genes belonging to the same pathways or SNPs within genes. In this paper, we propose group additive regression models and a group gradient descent boosting procedure for identifying groups of genomic features that are related to clinical phenotypes. Our simulation results show that by dividing the variables into appropriate groups, we can obtain better identification of the group features that are related to the phenotypes. In addition, the prediction mean square errors are also smaller than the component-wise boosting procedure. We demonstrate the application of the methods to pathway-based analysis of microarray gene expression data of breast cancer. Results from analysis of a breast cancer microarray gene expression data set indicate that the pathways of metalloendopeptidases (MMPs) and MMP inhibitors, as well as cell proliferation, cell growth, and maintenance are important to breast cancer-specific survival.

In functional genomics, one important problem is to relate the microarray gene expression profiles to various clinical phenotypes from patients. The success has been demonstrated in molecular classification of cancer in which gene expression data serve as predictors and different types of cancer are the binary or multi-categorical outcome variable. However, there has been less research in linking gene expression profiles to other types of phenotypes, in particular, the censored survival data such as patients' overall survival or cancer relapse times. In the paper, we develop a kernel Cox regression model for relating gene expression profiles to censored phenotypes in the framework the penalization method in terms of function estimation in reproducing kernel Hilbert spaces. To circumvent the problem of censoring, we use the negative partial likelihood as a loss function in the estimation procedure. The functional combinations of the original gene expression data identified by the method are highly correlated with the patients' survival times and at the same time account for the variability in the gene expression levels. We apply our method to data sets from diffuse large B-cell lymphoma, lung adenocarcinoma and breast carcinoma studies to verify its effectiveness. The results from these analyses indicate that the proposed method works very well in identifying subgroups of patients with different risks of death or relapse and in predicting the risk of relapse or death based on the gene expression profiles measured from the tumor samples taken from the patients.

Since many biological systems or regulatory networks are dynamic systems, gene expression levels measured over different time points during a given biological process can often provide more insights about the underlying system. These gene expression data measured over time are often called the time-course gene expression data. One unique feature of such data is the time dependency of the gene expression levels for a given gene at different times or between two different genes. Statistical analysis needs to account for such dependency in order to make valid inferences. This paper presents several statistical methods for analyzing such time-course gene expression data, including the time-lagged correlation coefficient for analyzing the relationship between genes, a mixed-effects model with splines for clustering genes and for estimating missing gene expression data, and a new method for aligning gene expression profiles obtained under two experimental conditions and for identifying gene clusters that show significant changes between two experimental conditions. We used the yeast cell cycle gene expression data sets to illustrate these methods and obtained the biologically meaningful conclusions from these analyses.

BackgroundMany aspects of biological functions can be modeled by biological networks, such as protein interaction networks, metabolic networks, and gene coexpression networks. Studying the statistical properties of these networks in turn allows us to infer biological function. Complex statistical network models can potentially more accurately describe the networks, but it is not clear whether such complex models are better suited to find biologically meaningful subnetworks.ResultsRecent studies have shown that the degree distribution of the nodes is not an adequate statistic in many molecular networks. We sought to extend this statistic with 2nd and 3rd order degree correlations and developed a pseudo-likelihood approach to estimate the parameters. The approach was used to analyze the MIPS and BIOGRID yeast protein interaction networks, and two yeast coexpression networks. We showed that 2nd order degree correlation information gave better predictions of gene interactions in both protein interaction and gene coexpression networks. However, in the biologically important task of predicting functionally homogeneous modules, degree correlation information performs marginally better in the case of the MIPS and BIOGRID protein interaction networks, but worse in the case of gene coexpression networks.ConclusionOur use of dK models showed that incorporation of degree correlations could increase predictive power in some contexts, albeit sometimes marginally, but, in all contexts, the use of third-order degree correlations decreased accuracy. However, it is possible that other parameter estimation methods, such as maximum likelihood, will show the usefulness of incorporating 2nd and 3rd degree correlations in predicting functionally homogeneous modules.

The main purpose of this paper is to investigate the detection of jump points of a discontinuous function in the presence of a noise by the wavelet approach. A computing algorithm of our method is proposed and then applied to the daily exchange rate of US Dollar against Deutsche Mark. All the points detected by our method reflect very strong economic and political impacts. Other statistical methods to detect jump points have also been applied to the same exchange rate data. Our proposed method has produced more convincing empirical results than others.