Mapping quantitative trait loci using both extremely discordant and concordant sib pairs: a unified approach for meta-analysis

Extremely discordant (ED) and concordant (EC) sib pairs are recommended by Risch and Zhang ( 1995, 1996 ) and Zhang and Risch ( 1996 ) for the detection of linkage on the basis of power analysis. They did not, however, include both discordant and concordant sib pairs simultaneously in the test statistic. We construct a new test statistic including both types of sib pairs. The size of the sample needed to identify the sib pairs and parents, who will be genotyped, is reduced substantially by including a hybrid of discordant and concordant sib pairs in the analysis. This mixed design also provides a common parameter that simplifies meta-analysis of sib pair linkage studies.     

Power and robustness of sib-pair linkage tests and extension to larger sibships

We investigate the power and robustness of Haseman and Elstonfs sib-pair test for genetic linkage between a marker locus and a locus affecting a quantitative trait, and compare the test to that of Penrose. The Haseman-Elston test is more powerful than Penrrose's test; its power is acceptable for cases of tight linkage and high heritability due to the hypothesized quantitative trait locus, but is quite low in other situations. Computer simulations indicate that both tests are valid for normally distributed trait values, and that the Haseman-Elston test is robust for a variety of continuous distributions of the trait values. Several linkage tests are developed for sib trios that are much more powerful , for the same total number of sibs, than the test on independent sib pairs. The Haseman-Elston test on all possible sib pairs is suggested for sibships of size larger than three and for samples including sibships of various sizes.     

The universal validity of the possible triangle constraint for affected sib pairs

The authors consider affected‐sib‐pair analysis, in which genetic marker data are collected from families with at least two sibs affected by a disease under investigation. At any locus not linked to the disease gene, a sib pair shares 0, 1 and 2 alleles identical by descent (IBD) with probabilities of 1/4, 1/2 and 1/4, respectively. With linkage, the IBD value increases stochastically. Louis, Payami & Thomson (1987) and Holmans (1993) were the first ones who discovered that the IBD distribution satisfies the “possible triangle constraint” in some situations. Consequently, more powerful statistical procedures can be designed in detecting linkage. It is of statistical and genetical importance to investigate whether the possible triangle constraint remains true under general genetic models. In this paper, the authors introduce a new technique to prove the possible triangle constraint. Their proof is particularly simple for the single disease locus case. The general case is proved by linking IBD distributions between marker loci through a transition probability matrix.     

Modelling paired categorical outcomes in clinical trials

The goal of this paper is to discuss methods for testing the homogeneity of treatment‐induced changes in trials with paired categorical responses. Widely used marginal homogeneity tests ignore the information contained in concordant pairs of observations and become highly underpowered for configurations of parameters encountered in real trials. This paper considers models for paired binary or ordinal outcomes based on both discordant and concordant pairs that provide a natural extension of marginal models. Likelihood‐ratio tests associated with these models are developed and are demonstrated to be at least as powerful as or more powerful than marginal homogeneity tests. The proposed models are easy to fit using standard statistical software. Copyright © 2003 John Wiley & Sons, Ltd.     

An Additive Genetic Gamma Frailty Model for Linkage Analysis of Diseases with Variable Age of Onset Using Nuclear Families

Many late-onset complex diseases exhibit variable age of onset. Efficiently incorporating age of onset information into linkage analysis can potentially increase the power of dissecting complex diseases. In this paper, we treat age of onset as a genetic trait with censored observations. We use multiple markers to infer the inheritance vector at the disease susceptibility (DS) locus in order to extract information about the inheritance pattern of the disease allele in a pedigree. Given the inheritance distribution at the DS locus, we define the genetic frailty for each individual within a nuclear family as the sum of frailties due to a putative major disease gene and a polygenic effect due to any remaining DS loci. Conditioning on these frailties we use the proportional hazards model for the risk of developing disease. We show that a test of linkage can be formulated as a test of zero variance due to a specific locus of the additive gamma frailties. Maximum likelihood estimation, using the EM algorithm, and likelihood ratio tests are employed for parameter estimation and tests of linkage. A simulation study presented indicates that the proposed method is well behaved and can be more powerful than the currently available allele-sharing based linkage methods. A breast cancer data example is used for illustration.     

Sampling of pairs in pairwise likelihood estimation for latent variable models with categorical observed variables

Pairwise likelihood is a limited information estimation method that has also been used for estimating the parameters of latent variable and structural equation models. Pairwise likelihood is a special case of composite likelihood methods that uses lower-order conditional or marginal log-likelihoods instead of the full log-likelihood. The composite likelihood to be maximized is a weighted sum of marginal or conditional log-likelihoods. Weighting has been proposed for increasing efficiency, but the choice of weights is not straightforward in most applications. Furthermore, the importance of leaving out higher-order scores to avoid duplicating lower-order marginal information has been pointed out. In this paper, we approach the problem of weighting from a sampling perspective. More specifically, we propose a sampling method for selecting pairs based on their contribution to the total variance from all pairs. The sampling approach does not aim to increase efficiency but to decrease the estimation time, especially in models with a large number of observed categorical variables. We demonstrate the performance of the proposed methodology using simulated examples and a real application.

     

Asymptotic properties of likelihood ratio test statistics in affected‐sib‐pair analysis

In an affected‐sib‐pair genetic linkage analysis, identical by descent data for affected sib pairs are routinely collected at a large number of markers along chromosomes. Under very general genetic assumptions, the IBD distribution at each marker satisfies the possible triangle constraint. Statistical analysis of IBD data should thus utilize this information to improve efficiency. At the same time, this constraint renders the usual regularity conditions for likelihood‐based statistical methods unsatisfied. In this paper, the authors study the asymptotic properties of the likelihood ratio test (LRT) under the possible triangle constraint. They derive the limiting distribution of the LRT statistic based on data from a single locus. They investigate the precision of the asymptotic distribution and the power of the test by simulation. They also study the test based on the supremum of the LRT statistics over the markers distributed throughout a chromosome. Instead of deriving a limiting distribution for this test, they use a mixture of chi‐squared distributions to approximate its true distribution. Their simulation results show that this approach has desirable simplicity and satisfactory precision.     

Composite conditional likelihood for sparse clustered data

Summary.  Sparse clustered data arise in finely stratified genetic and epidemiologic studies and pose at least two challenges to inference. First, it is difficult to model and interpret the full joint probability of dependent discrete data, which limits the utility of full likelihood methods. Second, standard methods for clustered data, such as pairwise likelihood and the generalized estimating function approach, are unsuitable when the data are sparse owing to the presence of many nuisance parameters. We present a composite conditional likelihood for use with sparse clustered data that provides valid inferences about covariate effects on both the marginal response probabilities and the intracluster pairwise association. Our primary focus is on sparse clustered binary data, in which case the method proposed utilizes doubly discordant quadruplets drawn from each stratum to conduct inference about the intracluster pairwise odds ratios.     

产业关联效应测度理论辨析

基于投入产出模型可以构建多种产业关联效应测度方法,但不同方法间的区别与联系尚未获得足够重视和透彻把握。本文探讨了常规不加权产业关联测度的真实内涵和局限性,并由经济分析入手探讨和论证了相应的加权测度形式;将简单和加权的两种方式归纳为产业关联的相对（边际或平均）测度和绝对（规模）测度,着重辨析其经济内涵的异同点;进而分别采用Leontief和Ghosh模型体系,从需求拉动和供给推动两个角度测度后向和前向产业关联效应。结合我国投入产出数据的实证分析表明,不同测度方法给出的结果均有其经济分析价值;但相对而言,考虑规模因素的加权测度方法在刻画实际的产业关联效应方面显得更为客观、可信。     

Can we recover information from concordant pairs in binary matched pairs?

When possible values of a response variable are limited, distributional assumptions about random effects may not be checkable. This may cause a distribution-robust estimator, such as the conditional maximum likelihood estimator to be recommended; however, it does not utilize all the information in the data. We show how, with binary matched pairs, the hierarchical likelihood can be used to recover information from concordant pairs, giving an improvement over the conditional maximum likelihood estimator without losing distribution-robustness.     

INFERENCE FOR CENSORED MATCHED PAIRS USING SIGNED RANKS

Using the marginal likelihood based on the signed ranks derived from matched pairs data, inferences are made for regression parameters. Both members of a given pair are subject to the same censoring time, while different pairs are subject to different censoring times. Censoring is independent of the response and on the right. Easily calculated logistic density scores are used to provide an approximate analysis so that inferences can be made about a regression parameter in the presence of a difference within the matched pairs. Inference for the survival times of matched skin grafts is considered.     

A SEMIPARAMETRIC MIXTURE MODEL FOR THE ANALYSIS OF COMPETING RISKS DATA

This paper deals with the regression analysis of failure time data when there are censoring and multiple types of failures. We propose a semiparametric generalization of a parametric mixture model of Larson & Dinse (1985), for which the marginal probabilities of the various failure types are logistic functions of the covariates. Given the type of failure, the conditional distribution of the time to failure follows a proportional hazards model. A marginal like lihood approach to estimating regression parameters is suggested, whereby the baseline hazard functions are eliminated as nuisance parameters. The Monte Carlo method is used to approximate the marginal likelihood; the resulting function is maximized easily using existing software. Some guidelines for choosing the number of Monte Carlo replications are given. Fixing the regression parameters at their estimated values, the full likelihood is maximized via an EM algorithm to estimate the baseline survivor functions. The methods suggested are illustrated using the Stanford heart transplant data.     

Mixture models for matched pairs

Mixture models for matched pairs arise when the pair-specific parameter is assumed to be a random quantity. We explore the use of semiparametric maximum-likelihood methods for a family of mixture models for matched pairs. The geometry of mixture likelihoods provides insight into the properties of these models.     

Exact tests for matched pairs:studies with covariates

In prospective or retrospective studies with matched pairs one often wishes to control for covariates other than those used in the matching process.Large sample procedures assuming a logistic model are available for this problem.The present paper presents some exact permutation tests which are uniformly most powerful unbiased within a large class of tests.     

Estimation of Sib–Sib Correlation via a Kotz-Type Density Function

We estimate sib–sib correlation by maximizing the log-likelihood of a Kotz-type distribution. Using extensive simulations we conclude that estimating sib–sib correlation using the proposed method has many advantages. Results are illustrated on a real life data set due to Galton. Testing of hypothesis about this correlation is also discussed using the three likelihood based tests and a test based on Srivastava's estimator. It is concluded that score test derived using Kotz-type density performs the best.     

A marginal regression model for multivariate failure time data with a surviving fraction

A marginal regression approach for correlated censored survival data has become a widely used statistical method. Examples of this approach in survival analysis include from the early work by Wei et al. (J Am Stat Assoc 84:1065–1073, 1989) to more recent work by Spiekerman and Lin (J Am Stat Assoc 93:1164–1175, 1998). This approach is particularly useful if a covariate’s population average effect is of primary interest and the correlation structure is not of interest or cannot be appropriately specified due to lack of sufficient information. In this paper, we consider a semiparametric marginal proportional hazard mixture cure model for clustered survival data with a surviving or “cure” fraction. Unlike the clustered data in previous work, the latent binary cure statuses of patients in one cluster tend to be correlated in addition to the possible correlated failure times among the patients in the cluster who are not cured. The complexity of specifying appropriate correlation structures for the data becomes even worse if the potential correlation between cure statuses and the failure times in the cluster has to be considered, and thus a marginal regression approach is particularly attractive. We formulate a semiparametric marginal proportional hazards mixture cure model. Estimates are obtained using an EM algorithm and expressions for the variance–covariance are derived using sandwich estimators. Simulation studies are conducted to assess finite sample properties of the proposed model. The marginal model is applied to a multi-institutional study of local recurrences of tonsil cancer patients who received radiation therapy. It reveals new findings that are not available from previous analyses of this study that ignored the potential correlation between patients within the same institution.     

SNP selection for predicting a quantitative trait

Molecular markers combined with powerful statistical tools have made it possible to detect and analyze multiple loci on the genome that are responsible for the phenotypic variation in quantitative traits. The objectives of the study presented in this paper are to identify a subset of single nucleotide polymorphism (SNP) markers that are associated with a particular trait and to construct a model that can best predict the value of the trait given the genotypic information of the SNPs using a three-step strategy. In the first step, a genome-wide association test is performed to screen SNPs that are associated with the quantitative trait of interest. SNPs with p-values of less than 5% are then analyzed in the second step. In the second step, a large number of randomly selected models, each consisting of a fixed number of randomly selected SNPs, are analyzed using the least angle regression method. This step will further remove redundant SNPs due to the complicated association among SNPs. A subset of SNPs that are shown to have a significant effect on the response trait more often than by chance are considered for the third step. In the third step, two alternative methods are considered: the least angle shrinkage and selection operation and sparse partial least squares regression. For both methods, the predictive ability of the fitted model is evaluated by an independent test set. The performance of the proposed method is illustrated by the analysis of a real data set on Canadian Holstein cattle.     

Large sample interval mapping method for genetic trait loci in finite regression mixture models

This article investigates the large sample interval mapping method for genetic trait loci (GTL) in a finite non-linear regression mixture model. The general model includes most commonly used kernel functions, such as exponential family mixture, logistic regression mixture and generalized linear mixture models, as special cases. The populations derived from either the backcross or intercross design are considered. In particular, unlike all existing results in the literature in the finite mixture models, the large sample results presented in this paper do not require the boundness condition on the parametric space. Therefore, the large sample theory presented in this article possesses general applicability to the interval mapping method of GTL in genetic research. The limiting null distribution of the likelihood ratio test statistics can be utilized easily to determine the threshold values or p-values required in the interval mapping. The limiting distribution is proved to be free of the parameter values of null model and free of the choice of a kernel function. Extension to the multiple marker interval GTL detection is also discussed. Simulation study results show favorable performance of the asymptotic procedure when sample sizes are moderate.     

A practical sampling approach for a Bayesian mixture model with unknown number of components

Recently, mixture distribution becomes more and more popular in many scientific fields. Statistical computation and analysis of mixture models, however, are extremely complex due to the large number of parameters involved. Both EM algorithms for likelihood inference and MCMC procedures for Bayesian analysis have various difficulties in dealing with mixtures with unknown number of components. In this paper, we propose a direct sampling approach to the computation of Bayesian finite mixture models with varying number of components. This approach requires only the knowledge of the density function up to a multiplicative constant. It is easy to implement, numerically efficient and very practical in real applications. A simulation study shows that it performs quite satisfactorily on relatively high dimensional distributions. A well-known genetic data set is used to demonstrate the simplicity of this method and its power for the computation of high dimensional Bayesian mixture models.     

Mixture cure model with an application to interval mapping of quantitative trait loci

When censored time-to-event data are used to map quantitative trait loci (QTL), the existence of nonsusceptible subjects entails extra challenges. If the heterogeneous susceptibility is ignored or inappropriately handled, we may either fail to detect the responsible genetic factors or find spuriously significant locations. In this article, an interval mapping method based on parametric mixture cure models is proposed, which takes into consideration of nonsusceptible subjects. The proposed model can be used to detect the QTL that are responsible for differential susceptibility and/or time-to-event trait distribution. In particular, we propose a likelihood-based testing procedure with genome-wide significance levels calculated using a resampling method. The performance of the proposed method and the importance of considering the heterogeneous susceptibility are demonstrated by simulation studies and an application to survival data from an experiment on mice infected with Listeria monocytogenes.