The equivalence of two tests and models for HLA data with no observed double blanks

Gart and Nam (1984, Biometrics 40, 887-894) consider the analysis of an ABO-like model based on the Hardy-Weinberg law in the commonly occurring case of human leukocyte antigen (HLA) data where there are no double blanks, that is, no recessive homozygotes. They derive a score test, based on the truncated likelihood, of the hypothesis that the true recessive gene (or allele) frequency is zero. Yasuda (1968, Biometrics 24, 915-935) considers a similar codominant system wherein the true recessive gene frequency is assumed zero, but the Hardy-Weinberg law does not hold. In particular, he considers the possibility of a nonzero inbreeding coefficient. We show that the two models are equivalent; each likelihood can be shown to be a reparameterization of the other. Furthermore, the score test of the zero gene frequency in Gart and Nam is identical to the score test for a zero inbreeding coefficient given by Yasuda. The results are applied to an example wherein it appears that the Hardy-Weinberg model is appropriate. Thus, it is not possible in this population to identify homozygous individuals without error from phenotypic data alone.     

A program for maximum likelihood estimation and likelihood ratio tests in one-locus ABO-like systems based upon population phenotype data.

Phenotypes in an ABO-like system of a number of genetically-independent persons from a number of populations are supposed to be observed. The program which is written in FORTRAN calculates maximum likelihood estimates of gene frequencies and their standard errors in each population and in the populations taken together. Furthermore the program calculates expected values and likelihood ratio and goodness of fit chi-square tests of Hardy-Weinberg equilibrium. If several subpopulations are pooled together a likelihood ratio test of homogeneity is performed.     

On two tests of fit for HLA data with no double blanks.

Stevens suggests a test of fit, based on Bernstein's estimators, of the Hardy-Weinberg law for the ABO system. Nam and Gart extend this test to the generalized ABO-like system and apply it to HLA data. When the recessive gene is rare, Huether and Murphy recall Haldane's point that its Bernstein's estimator is negatively biased and go on to suggest novel corrected versions of it. With the identification of more HLA antigens, it is not uncommon to find, in certain populations, that the sample data contain no double blanks; that is, every individual reacts to at least one antigen for a given locus. Gart and Nam give a simple score test of a zero true recessive-gene frequency for such situations. Here we examine the extended test of Stevens as a test of this hypothesis. We find that it is fully efficient for two codominant alleles but that when the number exceeds two its efficiency may be 50% or lower or as high as 100%, depending on the number of alleles and the pattern of gene frequencies. The tests are applied to a set of HLA data.     

Mutagenicity testing and risk estimation with mammals

Mammalian test systems are currently used for mutagenicity screening. The necessity and the limitations of standardizing these methods are discussed for the dominant-lethal assay. In addition to the refinement of standard methods, the development of new systems in mammals is emphasized. One promising approach is the detection of presumed somatic mutations. Another new development takes advantage of electrophoretic methods for detecting induced structural alterations of gene products. Mammalian experiments will be essential for the assessment of risks from chemical mutagens. The development of standards for the controlled use of chemical mutagens should be guided by the experience accumulated in radiation genetics. Two methods, the measurement of specific-locus mutation rates in mice and the direct determination fo the phenotypic damage of dominant genes affecting the skeleton of mice, are recommended for the assessment of the hazard of chemical mutagens.     

Normalization, testing, and false discovery rate estimation for RNA-sequencing data

We discuss the identification of genes that are associated with an outcome in RNA sequencing and other sequence-based comparative genomic experiments. RNA-sequencing data take the form of counts, so models based on the Gaussian distribution are unsuitable. Moreover, normalization is challenging because different sequencing experiments may generate quite different total numbers of reads. To overcome these difficulties, we use a log-linear model with a new approach to normalization. We derive a novel procedure to estimate the false discovery rate (FDR). Our method can be applied to data with quantitative, two-class, or multiple-class outcomes, and the computation is fast even for large data sets. We study the accuracy of our approaches for significance calculation and FDR estimation, and we demonstrate that our method has potential advantages over existing methods that are based on a Poisson or negative binomial model. In summary, this work provides a pipeline for the significance analysis of sequencing data.     

Genetic heterogeneity of residual variance - estimation of variance components using double hierarchical generalized linear models

Background

The sensitivity to microenvironmental changes varies among animals and may be under genetic control. It is essential to take this element into account when aiming at breeding robust farm animals. Here, linear mixed models with genetic effects in the residual variance part of the model can be used. Such models have previously been fitted using EM and MCMC algorithms.

Results

We propose the use of double hierarchical generalized linear models (DHGLM), where the squared residuals are assumed to be gamma distributed and the residual variance is fitted using a generalized linear model. The algorithm iterates between two sets of mixed model equations, one on the level of observations and one on the level of variances. The method was validated using simulations and also by re-analyzing a data set on pig litter size that was previously analyzed using a Bayesian approach. The pig litter size data contained 10,060 records from 4,149 sows. The DHGLM was implemented using the ASReml software and the algorithm converged within three minutes on a Linux server. The estimates were similar to those previously obtained using Bayesian methodology, especially the variance components in the residual variance part of the model.

Conclusions

We have shown that variance components in the residual variance part of a linear mixed model can be estimated using a DHGLM approach. The method enables analyses of animal models with large numbers of observations. An important future development of the DHGLM methodology is to include the genetic correlation between the random effects in the mean and residual variance parts of the model as a parameter of the DHGLM.     

The fitting of dynamic models to observed data

The question of how to fit a general cubic model of a multicomponent, interactive growth system to observed data is addressed. A multidimensional-polynomial type of regression analysis is used, with a least-squares criterion. By testing the scheme on a problem with known solution, the way in which the accuracy of the results varies with the number of datum points used is investigated in an heuristic manner.     

Flexible modeling via a hybrid estimation scheme in generalized mixed models for longitudinal data

To circumvent the computational complexity of likelihood inference in generalized mixed models that assume linear or more general additive regression models of covariate effects, Laplace's approximations to multiple integrals in the likelihood have been commonly used without addressing the issue of adequacy of the approximations for individuals with sparse observations. In this article, we propose a hybrid estimation scheme to address this issue. The likelihoods for subjects with sparse observations use Monte Carlo approximations involving importance sampling, while Laplace's approximation is used for the likelihoods of other subjects that satisfy a certain diagnostic check on the adequacy of Laplace's approximation. Because of its computational tractability, the proposed approach allows flexible modeling of covariate effects by using regression splines and model selection procedures for knot and variable selection. Its computational and statistical advantages are illustrated by simulation and by application to longitudinal data from a fecundity study of fruit flies, for which overdispersion is modeled via a double exponential family.     

Bayesian estimation and testing of gene frequencies

This article explains estimation of gene frequencies from a Bayesian viewpoint using prior information. How to obtain Bayes estimators and the highest posterior density credible sets (Bayesian counterpart to classical confidence intervals) for gene frequencies is described. Tests of hypotheses are also discussed. A readily available mathematical application package is used to demonstrate the mathematical computations.     

The production,testing, and utility of double congenic mouse strains

Two new double congenic strains, B10-H-2 ^a H-7 ^b /Wts and B10-H-2 ^d H-7 ^b /Wts, were selected to differ from B10.A and B10.D2/o, respectively, at theH-7 locus. The survival time ofH-7-incompatible skin grafts is dependent upon theH-2 haplotype of recipient and donor.