Statistical method for prediction of gait kinematics with Gaussian process regression

We propose a novel methodology for predicting human gait pattern kinematics based on a statistical and stochastic approach using a method called Gaussian process regression (GPR). We selected 14 body parameters that significantly affect the gait pattern and 14 joint motions that represent gait kinematics. The body parameter and gait kinematics data were recorded from 113 subjects by anthropometric measurements and a motion capture system. We generated a regression model with GPR for gait pattern prediction and built a stochastic function mapping from body parameters to gait kinematics based on the database and GPR, and validated the model with a cross validation method. The function can not only produce trajectories for the joint motions associated with gait kinematics, but can also estimate the associated uncertainties. Our approach results in a novel, low-cost and subject-specific method for predicting gait kinematics with only the subject's body parameters as the necessary input, and also enables a comprehensive understanding of the correlation and uncertainty between body parameters and gait kinematics.     

Unsupervised assessment of microarray data quality using a Gaussian mixture model

Background  

Quality assessment of microarray data is an important and often challenging aspect of gene expression analysis. This task frequently involves the examination of a variety of summary statistics and diagnostic plots. The interpretation of these diagnostics is often subjective, and generally requires careful expert scrutiny.     

A Bayesian generalized random regression model for estimating heritability using overdispersed count data

Background

Faecal egg counts are a common indicator of nematode infection and since it is a heritable trait, it provides a marker for selective breeding. However, since resistance to disease changes as the adaptive immune system develops, quantifying temporal changes in heritability could help improve selective breeding programs. Faecal egg counts can be extremely skewed and difficult to handle statistically. Therefore, previous heritability analyses have log transformed faecal egg counts to estimate heritability on a latent scale. However, such transformations may not always be appropriate. In addition, analyses of faecal egg counts have typically used univariate rather than multivariate analyses such as random regression that are appropriate when traits are correlated. We present a method for estimating the heritability of untransformed faecal egg counts over the grazing season using random regression.

Results

Replicating standard univariate analyses, we showed the dependence of heritability estimates on choice of transformation. Then, using a multitrait model, we exposed temporal correlations, highlighting the need for a random regression approach. Since random regression can sometimes involve the estimation of more parameters than observations or result in computationally intractable problems, we chose to investigate reduced rank random regression. Using standard software (WOMBAT), we discuss the estimation of variance components for log transformed data using both full and reduced rank analyses. Then, we modelled the untransformed data assuming it to be negative binomially distributed and used Metropolis Hastings to fit a generalized reduced rank random regression model with an additive genetic, permanent environmental and maternal effect. These three variance components explained more than 80 % of the total phenotypic variation, whereas the variance components for the log transformed data accounted for considerably less. The heritability, on a link scale, increased from around 0.25 at the beginning of the grazing season to around 0.4 at the end.

Conclusions

Random regressions are a useful tool for quantifying sources of variation across time. Our MCMC (Markov chain Monte Carlo) algorithm provides a flexible approach to fitting random regression models to non-normal data. Here we applied the algorithm to negative binomially distributed faecal egg count data, but this method is readily applicable to other types of overdispersed data.     

A robust two-way semi-linear model for normalization of cDNA microarray data

Background  

Normalization is a basic step in microarray data analysis. A proper normalization procedure ensures that the intensity ratios provide meaningful measures of relative expression values.     

Group normalization for genomic data

Data normalization is a crucial preliminary step in analyzing genomic datasets. The goal of normalization is to remove global variation to make readings across different experiments comparable. In addition, most genomic loci have non-uniform sensitivity to any given assay because of variation in local sequence properties. In microarray experiments, this non-uniform sensitivity is due to different DNA hybridization and cross-hybridization efficiencies, known as the probe effect. In this paper we introduce a new scheme, called Group Normalization (GN), to remove both global and local biases in one integrated step, whereby we determine the normalized probe signal by finding a set of reference probes with similar responses. Compared to conventional normalization methods such as Quantile normalization and physically motivated probe effect models, our proposed method is general in the sense that it does not require the assumption that the underlying signal distribution be identical for the treatment and control, and is flexible enough to correct for nonlinear and higher order probe effects. The Group Normalization algorithm is computationally efficient and easy to implement. We also describe a variant of the Group Normalization algorithm, called Cross Normalization, which efficiently amplifies biologically relevant differences between any two genomic datasets.     

Evaluation of microarray data normalization procedures using spike-in experiments

Background  

Recently, a large number of methods for the analysis of microarray data have been proposed but there are few comparisons of their relative performances. By using so-called spike-in experiments, it is possible to characterize the analyzed data and thereby enable comparisons of different analysis methods.     

Standard data model representation for taxonomic information

The names used by biologists to label the observations they make are imprecise. This is an issue as workers increasingly seek to exploit data gathered from multiple, unrelated sources on line. Even when the international codes of nomenclature are followed strictly the resulting names (Taxon Names) do not uniquely identify the taxa (Taxon Concepts) that have been described by taxonomists but merely groups of type specimens. A standard data model for exchange of taxonomic information is described. It addresses this issue by facilitating explicit communication of information about Taxon Concepts and their associated names. A representation of this model as a XML Schema is introduced and the implications of the use of Globally Unique Identifiers discussed.     

Weighted averaging,logistic regression and the Gaussian response model

The indicator value and ecological amplitude of a species with respect to a quantitative environmental variable can be estimated from data on species occurrence and environment. A simple weighted averaging (WA) method for estimating these parameters is compared by simulation with the more elaborate method of Gaussian logistic regression (GLR), a form of the generalized linear model which fits a Gaussian-like species response curve to presence-absence data. The indicator value and the ecological amplitude are expressed by two parameters of this curve, termed the optimum and the tolerance, respectively. When a species is rare and has a narrow ecological amplitude — or when the distribution of quadrats along the environmental variable is reasonably even over the species' range, and the number of quadrats is small — then WA is shown to approach GLR in efficiency. Otherwise WA may give misleading results. GLR is therefore preferred as a practical method for summarizing species' distributions along environmental gradients. Formulas are given to calculate species optima and tolerances (with their standard errors), and a confidence interval for the optimum from the GLR output of standard statistical packages.Nomenclature follows Heukels-van der Meijden (1983).We would like to thank Drs I. C. Prentice, N. J. M. Gremmen and J. A. Hoekstra for comments on the paper. We are grateful to Ir. Th. A. de Boer (CABO, Wageningen) for permission to use the data of the first example.     

Two-stage normalization using background intensities in cDNA microarray data

Background  

In the microarray experiment, many undesirable systematic variations are commonly observed. Normalization is the process of removing such variation that affects the measured gene expression levels. Normalization plays an important role in the earlier stage of microarray data analysis. The subsequent analysis results are highly dependent on normalization. One major source of variation is the background intensities. Recently, some methods have been employed for correcting the background intensities. However, all these methods focus on defining signal intensities appropriately from foreground and background intensities in the image analysis. Although a number of normalization methods have been proposed, no systematic methods have been proposed using the background intensities in the normalization process.     

Tests of significance using regression models for ordered categorical data

Regression models of the type proposed by McCullagh (1980, Journal of the Royal Statistical Society, Series B 42, 109-142) are a general and powerful method of analyzing ordered categorical responses, assuming categorization of an (unknown) continuous response of a specified distribution type. Tests of significance with these models are generally based on likelihood-ratio statistics that have asymptotic chi 2 distributions; therefore, investigators with small data sets may be concerned with the small-sample behavior of these tests. In a Monte Carlo sampling study, significance tests based on the ordinal model are found to be powerful, but a modified test procedure (using an F distribution with a finite number of degrees of freedom for the denominator) is suggested such that the empirical significance level agrees more closely with the nominal significance level in small-sample situations. We also discuss the parallels between an ordinal regression model assuming underlying normality and conventional multiple regression. We illustrate the model with two data sets: one from a study investigating the relationship between phosphorus in soil and plant-available phosphorus in corn grown in that soil, and the other from a clinical trial comparing analgesic drugs.     

Evaluation of normalization methods for microarray data

Background

Microarray technology allows the monitoring of expression levels for thousands of genes simultaneously. This novel technique helps us to understand gene regulation as well as gene by gene interactions more systematically. In the microarray experiment, however, many undesirable systematic variations are observed. Even in replicated experiment, some variations are commonly observed. Normalization is the process of removing some sources of variation which affect the measured gene expression levels. Although a number of normalization methods have been proposed, it has been difficult to decide which methods perform best. Normalization plays an important role in the earlier stage of microarray data analysis. The subsequent analysis results are highly dependent on normalization.

Results

In this paper, we use the variability among the replicated slides to compare performance of normalization methods. We also compare normalization methods with regard to bias and mean square error using simulated data.

Conclusions

Our results show that intensity-dependent normalization often performs better than global normalization methods, and that linear and nonlinear normalization methods perform similarly. These conclusions are based on analysis of 36 cDNA microarrays of 3,840 genes obtained in an experiment to search for changes in gene expression profiles during neuronal differentiation of cortical stem cells. Simulation studies confirm our findings.

     

Kernel-imbedded Gaussian processes for disease classification using microarray gene expression data

Background  

Designing appropriate machine learning methods for identifying genes that have a significant discriminating power for disease outcomes has become more and more important for our understanding of diseases at genomic level. Although many machine learning methods have been developed and applied to the area of microarray gene expression data analysis, the majority of them are based on linear models, which however are not necessarily appropriate for the underlying connection between the target disease and its associated explanatory genes. Linear model based methods usually also bring in false positive significant features more easily. Furthermore, linear model based algorithms often involve calculating the inverse of a matrix that is possibly singular when the number of potentially important genes is relatively large. This leads to problems of numerical instability. To overcome these limitations, a few non-linear methods have recently been introduced to the area. Many of the existing non-linear methods have a couple of critical problems, the model selection problem and the model parameter tuning problem, that remain unsolved or even untouched. In general, a unified framework that allows model parameters of both linear and non-linear models to be easily tuned is always preferred in real-world applications. Kernel-induced learning methods form a class of approaches that show promising potentials to achieve this goal.     

A semiparametric model for regression analysis of interval-censored failure time data

Left-, right-, and interval-censored response time data arise in a variety of settings, including the analyses of data from laboratory animal carcinogenicity experiments, clinical trials, and longitudinal studies. For such incomplete data, the usual regression techniques such as the Cox (1972, Journal of the Royal Statistical Society, Series B 34, 187-220) proportional hazards model are inapplicable. In this paper, we present a method for regression analysis which accommodates interval-censored data. We present applications of this methodology to data sets from a study of breast cancer patients who were followed for cosmetic response to therapy, a small animal tumorigenicity study, and a clinical trial.