Exact family-based association tests for biallelic data

Family-based study designs have an important role in the search for association between disease phenotypes and genetic markers. Unlike traditional case-control methods, family-based tests use within-family data to avoid identification of spurious associations that may result from population admixture. Many family-based association tests have been proposed to accommodate a variety of ascertainment schemes and patterns of missing data. In this report, we describe exact family-based association tests for biallelic data. Specifically, we discuss test of the null hypotheses "no linkage and no association" and "linkage, but no association". These tests, which are valid under various models for inheritance and patterns of missingness, utilize the procedure proposed by Rabinowitz and Laird [2000: Hum Hered 50:211-223] that provides a unified framework for family based association testing (FBAT). The conditioning approach implemented in FBAT makes an exact test conceptually straightforward, but computationally difficult since the minimum sufficient statistics upon which we condition do not have a conventional form. An exact test may be especially critical when accurate computation of the extreme area of the FBAT statistic is needed, such as when the study design necessitates multiple comparisons adjustments. We describe the exact approach as a useful alternative to the asymptotic test and show that the exact tests for biallelic data may be most useful for the recessive disease model.     

A note on permutation tests for genetic association analysis of quantitative traits when variances are heterogeneous

The genetic dissection of quantitative traits, or endophenotypes, usually involves genetic linkage or association analysis in pedigrees and subsequent fine mapping association analysis in the population. The ascertainment procedure for quantitative traits often results in unequal variance of observations. For example, some phenotypes may be clinically measured whilst others are from self‐reports, or phenotypes may be the average of multiple measures but with the number of measurements varying. The resulting heterogeneity of variance poses no real problem for analysis, as long as it is properly modelled and thereby taken into account. However, if statistical significance is determined using an empirical permutation procedure, it is not obvious what the units of sampling are. We investigated a number of permutation approaches in a simulation study of an association analysis between a quantitative trait and a single nucleotide polymorphism. Our simulations were designed such that we knew the true p‐value of the test statistics. A number of permutation methods were compared from the regression of true on empirical p‐values and the precision of the empirical p‐values. We show that the best procedure involves an implicit adjustment of the original data for the effects in the model before permutation, and that other methods, some of which seemed appropriate a priori, are relatively biased. Genet. Epidemiol. 33:710–716, 2009. © 2009 Wiley‐Liss, Inc.     

A novel mathematical approach for modelling time-dependent musculoskeletal outcomes for office staff

Musculoskeletal disorders are common in prolonged computer use. The dynamics of the relationship between musculoskeletal outcomes and duration of computer use is not easy to model by common statistical methods due to the nonlinearity of the data. The use of inappropriate statistical models increases the likelihood of drawing wrong conclusions. In this paper we present a new mathematical methodology for modelling such a dynamic data set. Data on simultaneous direct measures of computer usage and questionnaire diaries of discomfort ratings were analysed using singular value decomposition as a means to track dominant dynamic trends, which presented the common characteristic of the relationship between computer-related workload and musculoskeletal outcomes over time. The relationship was constructed explicitly as a dose-response functional relationship that was parametrized by body region parameters. Standard statistical software was employed to quantify the variability of the estimates due to the complicated feature involved in the data. A deterministic population model was then developed to simulate the dynamics of computer-related workload and musculoskeletal outcomes. A stochastic model was also proposed to describe the stochastic nature of dynamics for individual subjects. The model was verified by comparison with real data for forecasting purposes. Possibilities for extending the model to accommodate more complicated medical data are discussed. The mathematical model can be served as both a deterministic population model that can project the demographic consequences and a stochastic model that can describe the whole quantity evolution of the study subjects. The proposed methodology is a flexible and broadly applicable one, which can be utilized by a variety of medical research. Copyright (c) 2008 John Wiley & Sons, Ltd.     

Advances in statistical human genetics over the last 25 years

The past 25 years has seen an explosion in the number of genetic markers that can be measured on DNA samples at an ever decreasing cost. Although basic statistical methods for analysing such data gathered on samples of either independent individuals or family members, one or two markers at a time, were already well developed before this explosion occurred, there has been a corresponding burst in activity to develop multiple marker models to find disease-causing gene variants, capitalizing on the data that have become available, to increase the power of such methods. This has required the concomitant development of faster algorithms to speed up the computation of various likelihoods. For linkage analysis, to obtain the approximate locations for genes of interest, Mendelian segregation models have been extended to be more realistic and statistical models that do not assume specific modes of inheritance have been extended to allow for the analysis of larger pedigree structures. For association analysis, to obtain more precise locations for genes of interest, the recent completion of the first stage of the HapMap project has spurred the development, still underway, of novel experimental designs and analytical methods to combat the curse of dimensionality and the resulting multiple testing problem. Perhaps the greatest current challenge concerns how best to gather and synthesize the many lines of evidence possible in order to discover the genetic determinants underlying complex diseases.     

Analyzing sequentially randomized trials based on causal effect models for realistic individualized treatment rules

In this paper, we argue that causal effect models for realistic individualized treatment rules represent an attractive tool for analyzing sequentially randomized trials. Unlike a number of methods proposed previously, this approach does not rely on the assumption that intermediate outcomes are discrete or that models for the distributions of these intermediate outcomes given the observed past are correctly specified. In addition, it generalizes the methodology for performing pairwise comparisons between individualized treatment rules by allowing the user to posit a marginal structural model for all candidate treatment rules simultaneously. This is particularly useful if the number of such rules is large, in which case an approach based on individual pairwise comparisons would be likely to suffer from too much sampling variability to provide an informative answer. In addition, such causal effect models represent an interesting alternative to methods previously proposed for selecting an optimal individualized treatment rule in that they immediately give the user a sense of how the optimal outcome is estimated to change in the neighborhood of the identified optimum. We discuss an inverse-probability-of-treatment-weighted (IPTW) estimator for these causal effect models, which is straightforward to implement using standard statistical software, and develop an approach for constructing valid asymptotic confidence intervals based on the influence curve of this estimator. The methodology is illustrated in two simulation studies that are intended to mimic an HIV/AIDS trial.     

CLUMPHAP: a simple tool for performing haplotype-based association analysis

The completion of the HapMap Project and the development of high-throughput single nucleotide polymorphism genotyping technologies have greatly enhanced the prospects of identifying and characterizing the genetic variants that influence complex traits. In principle, association analysis of haplotypes rather than single nucleotide polymorphisms may better capture an underlying causal variant, but the multiple haplotypes can lead to reduced statistical power due to the testing of (and need to correct for) a large number of haplotypes. This paper presents a novel method based on clustering similar haplotypes to address this issue. The method, implemented in the CLUMPHAP program, is an extension of the CLUMP program designed for the analysis of multi-allelic markers (Sham and Curtis [1995] Ann. Hum. Genet. 59(Pt1):97-105). CLUMPHAP performs a hierarchical clustering of the haplotypes and then computes the chi(2) statistic between each haplotype cluster and disease; the statistical significance of the largest of the chi(2) statistics is obtained by permutation testing. A significant result suggests that the presence of a disease-causing variant in the haplotype cluster is over-represented in cases. Using simulation studies, we have compared CLUMPHAP and more widely used approaches in terms of their statistical power to identify an untyped susceptibility locus. Our results show that CLUMPHAP tends to have greater power than the omnibus haplotype test and is comparable in power to multiple regression locus-coding approaches.     

Genotype relative-risks and association tests for nuclear families with missing parental data

The development of a new method for testing the association of genetic markers with disease is presented. This approach is applicable when sampling nuclear families with one or more affected siblings and when neither, one, or both parents are missing marker genotype data. All siblings, affected and not affected, are used to probabilistically infer the missing parental marker data. A likelihood ratio statistic, which treats marker allele frequencies as nuisance parameters, is presented to test whether all marker relative risks are equal to one (i.e., no marker association). This approach offers a solution to test for marker associations when parents are difficult to obtain. © 1997 Wiley-Liss, Inc.     

On the estimation of the binomial probability in multistage clinical trials

Due to the optional sampling effect in a sequential design, the maximum likelihood estimator (MLE) following sequential tests is generally biased. In a typical two-stage design employed in a phase II clinical trial in cancer drug screening, a fixed number of patients are enrolled initially. The trial may be terminated for lack of clinical efficacy of treatment if the observed number of treatment responses after the first stage is too small. Otherwise, an additional fixed number of patients are enrolled to accumulate additional information on efficacy as well as on safety. There have been numerous suggestions for design of such two-stage studies. Here we establish that under the two-stage design the sufficient statistic, i.e. stopping stage and the number of treatment responses, for the parameter of the binomial distribution is also complete. Then, based on the Rao-Blackwell theorem, we derive the uniformly minimum variance unbiased estimator (UMVUE) as the conditional expectation of an unbiased estimator, which in this case is simply the maximum likelihood estimator based only on the first stage data, given the complete sufficient statistic. Our results generalize to a multistage design. We will illustrate features of the UMVUE based on two-stage phase II clinical trial design examples and present results of numerical studies on the properties of the UMVUE in comparison to the usual MLE.     

X chromosome association testing in genome wide association studies

Genome wide association studies (GWAS) have revealed many fascinating insights into complex diseases even from simple, single-marker statistical tests. Most of these tests are designed for testing of associations between a phenotype and an autosomal genotype and are therefore not applicable to X chromosome data. Testing for association on the X chromosome raises unique challenges that have motivated the development of X-specific statistical tests in the literature. However, to date there has been no study of these methods under a wide range of realistic study designs, allele frequencies and disease models to assess the size and power of each test. To address this, we have performed an extensive simulation study to investigate the effects of the sex ratios in the case and control cohorts, as well as the allele frequencies, on the size and power of eight test statistics under three different disease models that each account for X-inactivation. We show that existing, but under-used, methods that make use of both male and female data are uniformly more powerful than popular methods that make use of only female data. In particular, we show that Clayton's one degree of freedom statistic [Clayton, 2008] is robust and powerful across a wide range of realistic simulation parameters. Our results provide guidance on selecting the most appropriate test statistic to analyse X chromosome data from GWAS and show that much power can be gained by a more careful analysis of X chromosome GWAS data.     

Biology‐Driven Gene‐Gene Interaction Analysis of Age‐Related Cataract in the eMERGE Network

Bioinformatics approaches to examine gene‐gene models provide a means to discover interactions between multiple genes that underlie complex disease. Extensive computational demands and adjusting for multiple testing make uncovering genetic interactions a challenge. Here, we address these issues using our knowledge‐driven filtering method, Biofilter, to identify putative single nucleotide polymorphism (SNP) interaction models for cataract susceptibility, thereby reducing the number of models for analysis. Models were evaluated in 3,377 European Americans (1,185 controls, 2,192 cases) from the Marshfield Clinic, a study site of the Electronic Medical Records and Genomics (eMERGE) Network, using logistic regression. All statistically significant models from the Marshfield Clinic were then evaluated in an independent dataset of 4,311 individuals (742 controls, 3,569 cases), using independent samples from additional study sites in the eMERGE Network: Mayo Clinic, Group Health/University of Washington, Vanderbilt University Medical Center, and Geisinger Health System. Eighty‐three SNP‐SNP models replicated in the independent dataset at likelihood ratio test P < 0.05. Among the most significant replicating models was rs12597188 (intron of CDH1)–rs11564445 (intron of CTNNB1). These genes are known to be involved in processes that include: cell‐to‐cell adhesion signaling, cell‐cell junction organization, and cell‐cell communication. Further Biofilter analysis of all replicating models revealed a number of common functions among the genes harboring the 83 replicating SNP‐SNP models, which included signal transduction and PI3K‐Akt signaling pathway. These findings demonstrate the utility of Biofilter as a biology‐driven method, applicable for any genome‐wide association study dataset.     

广州市儿童少年全血锌铜正常值探讨

为了解广州市儿童少年血锌、铜含量的水平，我们测定了本市355名中小学生的全血锌、铜值，探讨了血锌、铜的正常值范围．血锌值属偏态分布，以百分位数法P95下限确定各年龄组的正常值下限为；6～9岁3．46μg／ml，10～13岁3.56μg／ml．14～18岁423μg／ml，血铜属正态分布，以正态分布法确定各年龄组正常值范围为：6～9岁0.77～1.09μg／ml．10～13岁0.68～0.94μg／ml，14～18岁0.63～0.89μg／ml．     

Estimators of annual probability of infection for quantitative microbial risk assessment

Four estimators of annual infection probability were compared pertinent to Quantitative Microbial Risk Analysis (QMRA). A stochastic model, the Gold Standard, was used as the benchmark. It is a product of independent daily infection probabilities which in turn are based on daily doses. An alternative and commonly-used estimator, here referred to as the Naïve, assumes a single daily infection probability from a single value of daily dose. The typical use of this estimator in stochastic QMRA involves the generation of a distribution of annual infection probabilities, but since each of these is based on a single realisation of the dose distribution, the resultant annual infection probability distribution simply represents a set of inaccurate estimates. While the medians of both distributions were within an order of magnitude for our test scenario, the 95th percentiles, which are sometimes used in QMRA as conservative estimates of risk, differed by around one order of magnitude. The other two estimators examined, the Geometric and Arithmetic, were closely related to the Naïve and use the same equation, and both proved to be poor estimators. Lastly, this paper proposes a simple adjustment to the Gold Standard equation accommodating periodic infection probabilities when the daily infection probabilities are unknown.     

A fast collapsed data method for estimating haplotype frequencies from pooled genotype data with applications to the study of rare variants

Haplotype information could lead to more powerful tests of genetic association than single‐locus analyses but it is not easy to estimate haplotype frequencies from genotype data due to phase ambiguity. The challenge is compounded when individuals are pooled together to save costs or to increase sample size, which is crucial in the study of rare variants. Existing expectation–maximization type algorithms are slow and cannot cope with large pool size or long haplotypes. We show that by collapsing the total allele frequencies of each pool suitably, the maximum likelihood estimates of haplotype frequencies based on the collapsed data can be calculated very quickly regardless of pool size and haplotype length. We provide a running time analysis to demonstrate the considerable savings in time that the collapsed data method can bring. The method is particularly well suited to estimating certain union probabilities useful in the study of rare variants. We provide theoretical and empirical evidence to suggest that the proposed estimation method will not suffer much loss in efficiency if the variants are rare. We use the method to analyze re‐sequencing data collected from a case control study involving 148 obese persons and 150 controls. Focusing on a region containing 25 rare variants around the MGLL gene, our method selects three rare variants as potentially causal. This is more parsimonious than the 12 variants selected by a recently proposed covering method. From another set of 32 rare variants around the FAAH gene, we discover an interesting potential interaction between two of them. Copyright © 2012 John Wiley & Sons, Ltd.     

Novel Likelihood Ratio Tests for Screening Gene‐Gene and Gene‐Environment Interactions With Unbalanced Repeated‐Measures Data

There has been extensive literature on modeling gene‐gene interaction (GGI) and gene‐environment interaction (GEI) in case‐control studies with limited literature on statistical methods for GGI and GEI in longitudinal cohort studies. We borrow ideas from the classical two‐way analysis of variance literature to address the issue of robust modeling of interactions in repeated‐measures studies. While classical interaction models proposed by Tukey and Mandel have interaction structures as a function of main effects, a newer class of models, additive main effects and multiplicative interaction (AMMI) models, do not have similar restrictive assumptions on the interaction structure. AMMI entails a singular value decomposition of the cell residual matrix after fitting the additive main effects and has been shown to perform well across various interaction structures. We consider these models for testing GGI and GEI from two perspectives: likelihood ratio test based on cell means and a regression‐based approach using individual observations. Simulation results indicate that both approaches for AMMI models lead to valid tests in terms of maintaining the type I error rate, with the regression approach having better power properties. The performance of these models was evaluated across different interaction structures and 12 common epistasis patterns. In summary, AMMI model is robust with respect to misspecified interaction structure and is a useful screening tool for interaction even in the absence of main effects. We use the proposed methods to examine the interplay between the hemochromatosis gene and cumulative lead exposure on pulse pressure in the Normative Aging Study.