Haplotype-sharing analysis using Mantel statistics for combined genetic effects

We applied a new approach based on Mantel statistics to analyze the Genetic Analysis Workshop 14 simulated data with prior knowledge of the answers. The method was developed in order to improve the power of a haplotype sharing analysis for gene mapping in complex disease. The new statistic correlates genetic similarity and phenotypic similarity across pairs of haplotypes from case-control studies. The genetic similarity is measured as the shared length between haplotype pairs around a genetic marker. The phenotypic similarity is measured as the mean corrected cross-product based on the respective phenotypes. Cases with phenotype P1 and unrelated controls were drawn from the population of Danacaa. Power to detect main effects was compared to the X2-test for association based on 3-marker haplotypes and a global permutation test for haplotype association to test for main effects. Power to detect gene x gene interaction was compared to unconditional logistic regression. The results suggest that the Mantel statistics might be more powerful than alternative tests.     

Detecting genome wide haplotype sharing using SNP or microsatellite haplotype data

Genome wide association studies using high throughput technology are already being conducted despite the significant hurdles that need to be overcome (Nat Rev Genet 6:95–108, 2005; Nat Rev Genet 6:109–118, 2005). Methods for detecting haplotype association signals in genome wide haplotype datasets are as yet very limited. Much methodological research has already been devoted to linkage disequilibrium (LD) fine mapping where the focus is the identification of the disease locus rather than the detection of a disease signal. Applications of these approaches to genome wide scanning are limited by the strong model assumptions of the sharing process, which lead to computational complexity. We describe a new algorithm for the initial identification of disease susceptibility loci in genome wide haplotype association studies. Excess sharing of ancestral haplotypes, which indicates the presence of a disease locus, is detected with a simple, easy to interpret, χ ² based statistic. The method allows genome wide scanning for qualitative traits within reasonable computational timeframes and can serve as a first pass analysis prior to the usage of likelihood based methods, providing candidate regions and inferred susceptibility haplotypes. Our method makes no assumptions regarding the population history or the pattern of background LD. Statistical significance is evaluated with permutation tests. The method is illustrated on simulated and real data where it is applied to simple (cystic fibrosis) and complex disease (multiple sclerosis) examples. The statistic has low type I error and greater power to map disease loci over conventional single marker tests for low to moderate levels of LD.     

Performance of partial statistics in individual‐based landscape genetics

Individual‐based landscape genetic methods have become increasingly popular for quantifying fine‐scale landscape influences on gene flow. One complication for individual‐based methods is that gene flow and landscape variables are often correlated with geography. Partial statistics, particularly Mantel tests, are often employed to control for these inherent correlations by removing the effects of geography while simultaneously correlating measures of genetic differentiation and landscape variables of interest. Concerns about the reliability of Mantel tests prompted this study, in which we use simulated landscapes to evaluate the performance of partial Mantel tests and two ordination methods, distance‐based redundancy analysis (dbRDA) and redundancy analysis (RDA), for detecting isolation by distance (IBD) and isolation by landscape resistance (IBR). Specifically, we described the effects of suitable habitat amount, fragmentation and resistance strength on metrics of accuracy (frequency of correct results, type I/II errors and strength of IBR according to underlying landscape and resistance strength) for each test using realistic individual‐based gene flow simulations. Mantel tests were very effective for detecting IBD, but exhibited higher error rates when detecting IBR. Ordination methods were overall more accurate in detecting IBR, but had high type I errors compared to partial Mantel tests. Thus, no one test outperformed another completely. A combination of statistical tests, for example partial Mantel tests to detect IBD paired with appropriate ordination techniques for IBR detection, provides the best characterization of fine‐scale landscape genetic structure. Realistic simulations of empirical data sets will further increase power to distinguish among putative mechanisms of differentiation.     

POOR STATISTICAL PERFORMANCE OF THE MANTEL TEST IN PHYLOGENETIC COMPARATIVE ANALYSES

The Mantel test, based on comparisons of distance matrices, is commonly employed in comparative biology, but its statistical properties in this context are unknown. Here, we evaluate the performance of the Mantel test for two applications in comparative biology: testing for phylogenetic signal, and testing for an evolutionary correlation between two characters. We find that the Mantel test has poor performance compared to alternative methods, including low power and, under some circumstances, inflated type‐I error. We identify a remedy for the inflated type‐I error of three‐way Mantel tests using phylogenetic permutations; however, this test still has considerably lower power than independent contrasts. We recommend that use of the Mantel test should be restricted to cases in which data can only be expressed as pairwise distances among taxa.     

Genome association studies of complex diseases by case-control designs

One way to perform linkage-disequilibrium (LD) mapping of genetic traits is to use single markers. Since dense marker maps-such as single-nucleotide polymorphism and high-resolution microsatellite maps-are available, it is natural and practical to generalize single-marker LD mapping to high-resolution haplotype or multiple-marker LD mapping. This article investigates high-resolution LD-mapping methods, for complex diseases, based on haplotype maps or microsatellite marker maps. The objective is to explore test statistics that combine information from haplotype blocks or multiple markers. Based on two coding methods, genotype coding and haplotype coding, Hotelling's T2 statistics TG and TH are proposed to test the association between a disease locus and two haplotype blocks or two markers. The validity of the two T2 statistics is proved by theoretical calculations. A statistic TC, an extension of the traditional chi2 method of comparing haplotype frequencies, is introduced by simply adding the chi2 test statistics of the two haplotype blocks together. The merit of the three methods is explored by calculation and comparison of power and of type I errors. In the presence of LD between the two blocks, the type I error of TC is higher than that of TH and TG, since TC ignores the correlation between the two blocks. For each of the three statistics, the power of using two haplotype blocks is higher than that of using only one haplotype block. By power comparison, we notice that TC has higher power than that of TH, and TH has higher power than that of TG. In the absence of LD between the two blocks, the power of TC is similar to that of TH and higher than that of TG. Hence, we advocate use of TH in the data analysis. In the presence of LD between the two blocks, TH takes into account the correlation between the two haplotype blocks and has a lower type I error and higher power than TG. Besides, the feasibility of the methods is shown by sample-size calculation.     

Haplotype-based linkage disequilibrium mapping via direct data mining

MOTIVATION: With the availability of large-scale, high-density single-nucleotide polymorphism markers and information on haplotype structures and frequencies, a great challenge is how to take advantage of haplotype information in the association mapping of complex diseases in case-control studies. RESULTS: We present a novel approach for association mapping based on directly mining haplotypes (i.e. phased genotype pairs) produced from case-control data or case-parent data via a density-based clustering algorithm, which can be applied to whole-genome screens as well as candidate-gene studies in small genomic regions. The method directly explores the sharing of haplotype segments in affected individuals that are rarely present in normal individuals. The measure of sharing between two haplotypes is defined by a new similarity metric that combines the length of the shared segments and the number of common alleles around any marker position of the haplotypes, which is robust against recent mutations/genotype errors and recombination events. The effectiveness of the approach is demonstrated by using both simulated datasets and real datasets. The results show that the algorithm is accurate for different population models and for different disease models, even for genes with small effects, and it outperforms some recently developed methods.     

Nonlinear tests for genomewide association studies

As millions of single-nucleotide polymorphisms (SNPs) have been identified and high-throughput genotyping technologies have been rapidly developed, large-scale genomewide association studies are soon within reach. However, since a genomewide association study involves a large number of SNPs it is therefore nearly impossible to ensure a genomewide significance level of 0.05 using the available statistics, although the multiple-test problems can be alleviated, but not sufficiently, by the use of tagging SNPs. One strategy to circumvent the multiple-test problem associated with genome-wide association tests is to develop novel test statistics with high power. In this report, we introduce several nonlinear tests, which are based on nonlinear transformation of allele or haplotype frequencies. We investigate the power of the nonlinear test statistics and demonstrate that under certain conditions, some nonlinear test statistics have much higher power than the standard chi2-test statistic. Type I error rates of the nonlinear tests are validated using simulation studies. We also show that a class of similarity measure-based test statistics is based on the quadratic function of allele or haplotype frequencies, and thus they belong to nonlinear tests. To evaluate their performance, the nonlinear test statistics are also applied to three real data sets. Our study shows that nonlinear test statistics have great potential in association studies of complex diseases.     

Statistical models for haplotype sharing in case-parent trio data

BACKGROUND: Haplotype sharing statistics have been introduced in an ad-hoc way, often relying heavily on permutation testing. As a result, applying these approaches to whole genome association studies or to evaluate their properties in extensive simulation experiments is problematic. Further, permutation testing may be inappropriate in the presence of phase ambiguity and population stratification. AIMS: To present a simple framework for a class of haplotype sharing statistics useful for association mapping in case-parent trio data. This framework allows derivation of novel haplotype sharing tests as well as simple variance estimators and asymptotic distributions for haplotype sharing tests. RESULTS AND CONCLUSIONS: We validated that our approach is appropriately sized using simulated data, and illustrate the methodology by analyzing a Crohn's disease dataset. We find that haplotype-based analyses are much more powerful than single-locus analyses for these data.     

Tests for Monotonic Trend from Case‐Control Data: Cochran‐Armitage‐Mantel Trend Test,Isotonic Regression and Single and Multiple Contrast Tests

Tests for a monotonic trend between an ordered categorical exposure and disease status are routinely carried out from case‐control data using the Mantel‐extension trend test or the asymptotically equivalent Cochran‐Armitage test. In this study, we considered two alternative tests based on isotonic regression, namely an order‐restricted likelihood ratio test and an isotonic modification of the Mantel‐extension test extending the recent proposal by Mancuso, Ahn and Chen (2001) to case‐control data. Furthermore, we considered three tests based on contrasts, namely a single contrast (SC) test based on Schaafsma's coefficients, the Dosemeci and Benichou (DB) test, a multiple contrast (MC) test based on the Helmert, reverse‐Helmert and linear contrasts and we derived their case‐control versions. Using simulations, we compared the statistical properties of these five alternative tests to those of the Mantel‐extension test under various patterns including no relationship, as well as monotonic and non‐monotonic relationships between exposure and disease status. In the case of no relationship, all tests had close to nominal type I error except in situations combining a very unbalanced exposure distribution and small sample size, where the asymptotic versions of the three tests based on contrasts were highly anticonservative. The use of bootstrap instead of asymptotic versions corrected this anticonservatism. For monotonic patterns, all tests had close powers. For non monotonic patterns, the DB‐test showed the most favourable results as it was the least powerful test. The two tests based on isotonic regression were the most powerful tests and the Mantel‐extension test, the SC‐ and MC‐tests had in‐between powers. The six tests were applied to data from a case‐control study investigating the relationship between alcohol consumption and risk of laryngeal cancer in Turkey. In situations with no evidence of a monotonic relationship between exposure and disease status, the three tests based on contrasts did not conclude in favour of a significant trend whereas all the other tests did. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Linkage disequilibrium mapping via cladistic analysis of single-nucleotide polymorphism haplotypes

We present a novel approach to disease-gene mapping via cladistic analysis of single-nucleotide polymorphism (SNP) haplotypes obtained from large-scale, population-based association studies, applicable to whole-genome screens, candidate-gene studies, or fine-scale mapping. Clades of haplotypes are tested for association with disease, exploiting the expected similarity of chromosomes with recent shared ancestry in the region flanking the disease gene. The method is developed in a logistic-regression framework and can easily incorporate covariates such as environmental risk factors or additional unlinked loci to allow for population structure. To evaluate the power of this approach to detect disease-marker association, we have developed a simulation algorithm to generate high-density SNP data with short-range linkage disequilibrium based on empirical patterns of haplotype diversity. The results of the simulation study highlight substantial gains in power over single-locus tests for a wide range of disease models, despite overcorrection for multiple testing.     

On the identification of disease mutations by the analysis of haplotype similarity and goodness of fit

The observation that haplotypes from a particular region of the genome differ between affected and unaffected individuals or between chromosomes transmitted to affected individuals versus those not transmitted is sound evidence for a disease-liability mutation in the region. Tests for differentiation of haplotype distributions often take the form of either Pearson's chi(2) statistic or tests based on the similarity among haplotypes in the different populations. In this article, we show that many measures of haplotype similarity can be expressed in the same quadratic form, and we give the general form of the variance. As we describe, these methods can be applied to either phase-known or phase-unknown data. We investigate the performance of Pearson's chi(2) statistic and haplotype similarity tests through use of evolutionary simulations. We show that both approaches can be powerful, but under quite different conditions. Moreover, we show that the power of both approaches can be enhanced by clustering rare haplotypes from the distributions before performing a test.     

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.     

Exact tests for the analysis of case-control studies of genetic markers

OBJECTIVES: The association of a candidate gene with disease can be evaluated by a case-control study in which the genotype distribution is compared for diseased cases and unaffected controls. Usually, the data are analyzed with Armitage's test using the asymptotic null distribution of the test statistic. Since this test does not generally guarantee a type I error rate less than or equal to the significance level alpha, tests based on exact null distributions have been investigated. METHODS: An algorithm to generate the exact null distribution for both Armitage's test statistic and a recently proposed modification of the Baumgartner-Weiss-Schindler statistic is presented. I have compared the tests in a simulation study. RESULTS: The asymptotic Armitage test is slightly anticonservative whereas the exact tests control the type I error rate. The exact Armitage test is very conservative, but the exact test based on the modification of the Baumgartner-Weiss-Schindler statistic has a type I error rate close to alpha. The exact Armitage test is the least powerful test; the difference in power between the other two tests is often small and the comparison does not show a clear winner. CONCLUSION: Simulation results indicate that an exact test based on the modification of the Baumgartner-Weiss-Schindler statistic is preferable for the analysis of case-control studies of genetic markers.     

Expected Error Rates for Logistic Regression Versus Normal Discriminant Analysis

The expected error rates associated with using the allocation rule based on logistic regression are derived in the context of two multivariate normal populations with a common covariance matrix and compared with the corresponding error rates of the classical rule based on this normality assumption. It is shown in terms of the actual sizes of the asymptotic expected error rates that the performance of the logistic procedure does not fall far short of the normality based method, even for widely separated populations. This latter result is not obvious from previously available work on the asymptotic relative efficiency of the logistic procedure.     

Combined linkage and association mapping of quantitative trait loci by multiple markers

Using multiple diallelic markers, variance component models are proposed for high-resolution combined linkage and association mapping of quantitative trait loci (QTL) based on nuclear families. The objective is to build a model that may fully use marker information for fine association mapping of QTL in the presence of prior linkage. The measures of linkage disequilibrium and the genetic effects are incorporated in the mean coefficients and are decomposed into orthogonal additive and dominance effects. The linkage information is modeled in variance-covariance matrices. Hence, the proposed methods model both association and linkage in a unified model. On the basis of marker information, a multipoint interval mapping method is provided to estimate the proportion of allele sharing identical by descent (IBD) and the probability of sharing two alleles IBD at a putative QTL for a sib-pair. To test the association between the trait locus and the markers, both likelihood-ratio tests and F-tests can be constructed on the basis of the proposed models. In addition, analytical formulas of noncentrality parameter approximations of the F-test statistics are provided. Type I error rates of the proposed test statistics are calculated to show their robustness. After comparing with the association between-family and association within-family (AbAw) approach by Abecasis and Fulker et al., it is found that the method proposed in this article is more powerful and advantageous based on simulation study and power calculation. By power and sample size comparison, it is shown that models that use more markers may have higher power than models that use fewer markers. The multiple-marker analysis can be more advantageous and has higher power in fine mapping QTL. As an application, the Genetic Analysis Workshop 12 German asthma data are analyzed using the proposed methods.     

Nonparametric simulation-based statistics for detecting linkage in general pedigrees.

We present here four nonparametric statistics for linkage analysis that test whether pairs of affected relatives share marker alleles more often than expected. These statistics are based on simulating the null distribution of a given statistic conditional on the unaffecteds' marker genotypes. Each statistic uses a different measure of marker sharing: the SimAPM statistic uses the simulation-based affected-pedigree-member measure based on identity-by-state (IBS) sharing. The SimKIN (kinship) measure is 1.0 for identity-by-descent (IBD) sharing, 0.0 for no IBD status sharing, and the kinship coefficient when the IBD status is ambiguous. The simulation-based IBD (SimIBD) statistic uses a recursive algorithm to determine the probability of two affecteds sharing a specific allele IBD. The SimISO statistic is identical to SimIBD, except that it also measures marker similarity between unaffected pairs. We evaluated our statistics on data simulated under different two-locus disease models, comparing our results to those obtained with several other nonparametric statistics. Use of IBD information produces dramatic increases in power over the SimAPM method, which uses only IBS information. The power of our best statistic in most cases meets or exceeds the power of the other nonparametric statistics. Furthermore, our statistics perform comparisons between all affected relative pairs within general pedigrees and are not restricted to sib pairs or nuclear families.     

Robust score statistics for QTL linkage analysis

The traditional variance components approach for quantitative trait locus (QTL) linkage analysis is sensitive to violations of normality and fails for selected sampling schemes. Recently, a number of new methods have been developed for QTL mapping in humans. Most of the new methods are based on score statistics or regression-based statistics and are expected to be relatively robust to non-normality of the trait distribution and also to selected sampling, at least in terms of type I error. Whereas the theoretical development of these statistics is more or less complete, some practical issues concerning their implementation still need to be addressed. Here we study some of these issues such as the choice of denominator variance estimates, weighting of pedigrees, effect of parameter misspecification, effect of non-normality of the trait distribution, and effect of incorporating dominance. We present a comprehensive discussion of the theoretical properties of various denominator variance estimates and of the weighting issue and then perform simulation studies for nuclear families to compare the methods in terms of power and robustness. Based on our analytical and simulation results, we provide general guidelines regarding the choice of appropriate QTL mapping statistics in practical situations.     

Cluster Randomization Trials: A Simulation Study

A simulation study is conducted to compare several methods that test the common log odds ratio in multiple 2 × 2 tables when the data are correlated within clusters. Allowing cluster size to vary within each table, we evaluate the unadjusted Mantel‐Haenszel chi‐square statistic (χ²_MH), the adjusted Mantel‐Haenszel chi‐square statistics of Rao and Scott using both an unpooled design effect (χ²_RSN) and a pooled design effect (χ²_RSP), the adjusted Mantel‐Haenszel chi‐square statistic of Donald and Donner (χ²_DD), the chi‐square statistic using the GEE approach (χ²_GEE), the adjusted Mantel‐Haenszel chi‐square statistic of Begg (χ²_B), the Wald (χ²_W), the robust Wald (χ²_RW), the score (χ²_S), the robust score (χ²_RS), and the adjusted Mantel‐Haenszel chi‐square statistics of Zhang and Boos (χ²_ZBP and χ²_ZBN). The test statistics above are compared in terms of empirical significance levels and empirical power levels. The robust score statistic χ²_RS and the adjusted Mantel‐Haenszel chi‐square statistics of Zhang and Boos (χ²_ZBP and χ²_ZBN) generally have empirical significance levels closer to the nominal value than the other statistics. These three statistics have similar empirical power levels when the intracluster correlation is zero or the cluster sizes are balanced. χ²_RS performs better in terms of empirical power levels when a positive intracluster correlation exists in the imbalance setting.     

Testing the non-unity of rate ratio under inverse sampling

Inverse sampling is considered to be a more appropriate sampling scheme than the usual binomial sampling scheme when subjects arrive sequentially, when the underlying response of interest is acute, and when maximum likelihood estimators of some epidemiologic indices are undefined. In this article, we study various statistics for testing non-unity rate ratios in case-control studies under inverse sampling. These include the Wald, unconditional score, likelihood ratio and conditional score statistics. Three methods (the asymptotic, conditional exact, and Mid-P methods) are adopted for P-value calculation. We evaluate the performance of different combinations of test statistics and P-value calculation methods in terms of their empirical sizes and powers via Monte Carlo simulation. In general, asymptotic score and conditional score tests are preferable for their actual type I error rates are well controlled around the pre-chosen nominal level, and their powers are comparatively the largest. The exact version of Wald test is recommended if one wants to control the actual type I error rate at or below the pre-chosen nominal level. If larger power is expected and fluctuation of sizes around the pre-chosen nominal level are allowed, then the Mid-P version of Wald test is a desirable alternative. We illustrate the methodologies with a real example from a heart disease study.     

Confidence interval for rate ratio in a 2 x 2 table with structural zero: an application in assessing false-negative rate ratio when combining two diagnostic tests

In this article, we consider problems with correlated data that can be summarized in a 2 x 2 table with structural zero in one of the off-diagonal cells. Data of this kind sometimes appear in infectious disease studies and two-step procedure studies. Lui (1998, Biometrics54, 706-711) considered confidence interval estimation of rate ratio based on Fieller-type, Wald-type, and logarithmic transformation statistics. We reexamine the same problem under the context of confidence interval construction on false-negative rate ratio in diagnostic performance when combining two diagnostic tests. We propose a score statistic for testing the null hypothesis of nonunity false-negative rate ratio. Score test-based confidence interval construction for false-negative rate ratio will also be discussed. Simulation studies are conducted to compare the performance of the new derived score test statistic and existing statistics for small to moderate sample sizes. In terms of confidence interval construction, our asymptotic score test-based confidence interval estimator possesses significantly shorter expected width with coverage probability being close to the anticipated confidence level. In terms of hypothesis testing, our asymptotic score test procedure has actual type I error rate close to the pre-assigned nominal level. We illustrate our methodologies with real examples from a clinical laboratory study and a cancer study.