Comparison of four sib-pair linkage methods for analyzing sibships with more than two affecteds: Interest of the binomial maximum likelihood approach

Family samples collected for sib-pair linkage studies usually include some sibships with more than two affecteds (multiplex sibships). Several methods have been proposed to take into account these multiplex sibships, and four of them are discussed in this work. Two methods, which are the most widely used, are based on the number of alleles shared by the sib-pairs constitutive of the multiplex sibship, with the first using the total number of these shared alleles (“all possible pairs” method) and the second considering a weighted number of these alleles (weighted method). The two other approaches considered the sibship as a whole, with in particular a likelihood method based on a binomial distribution of parental alleles among affected offspring. We theoretically show that, in the analysis of sibships with two affecteds, this likelihood method is expected to be more powerful than the classical mean test when a common asymptotic type I error is used. The variation of the sibship informativeness (assessed by the proportion of heterozygous parents) according to the number of affected sibs is investigated under various genetic models. Simulations under the null hypothesis of no linkage indicate that the “all possible pairs” is anticonservative, especially for type I errors ≤ 0.001, whereas the weighted method generally provides satisfactory results. The likelihood method shows very consistent results in terms of type I errors, whatever the sample size, and provides power levels similar to those of the other methods. This binomial likelihood approach, which accounts in a natural way for multiplex sibships and provides a simple likelihood-ratio test for linkage involving a single parameter, appears to be a quite interesting alternative to analyze sib-pair studies. Genet. Epidemiol. 15:371–390,1998. © 1998 Wiley-Liss, Inc.     

Efficient use of siblings in testing for linkage and association

Tests of linkage and association between a disease and either a candidate gene or marker allele can be based on sibships with at least one affected and one unaffected sibling. However, specialized techniques are required to account for within-sibship correlation if some sibships contain more than one affected or more than one unaffected sib. In this paper, we propose Within Sibship Paired Resampling (WSPR), a technique that is designed to test the null hypothesis of no linkage or no association, even when sibships contain variable numbers of sibs. One repeatedly generates data subsets based on randomly sampling one affected and one unaffected sibling from each sibship, and each subset is analyzed individually. Then, evidence is combined by averaging results across these resampled data sets, applying a variance expression that implicitly accounts for the correlation among siblings. While the general WSPR procedure allows for numerous testing strategies, we describe two in detail. Simulation results for scenarios with varying degrees of population stratification demonstrate good power for the WSPR testing methods compared to the sib TDT (S-TDT) and the sibship disequilibrium test (SDT).     

Multipoint analysis of quantitative traits

Complete multipoint analysis as implemented by MAPMAKER/SIBS was used to identify the chromosomal regions with the strongest evidence of linkage. Three different quantitative sib-pair methods were compared. For each trait the maximum lod/Z score was used to implicate a chromosomal region. For trait Q5, chromosome 5, the analysis was repeated in a second data set to test for replication of the result from the first data set. The initial screen was carried out using complete parental information and the first sibling pair from each nuclear family. The effect of removing the parental genotypes and the use of multiple independent sibs was examined in the second data set for Q5, chromosome 5. © 1997 Wiley-Liss, Inc.     

The importance of watching our weights: how the choice of weights for non-independent sib pairs can dramatically alter results

Handling non-independent sib pairs in families with multiple affected sibs presents a problem in likelihood-based nonparametric linkage analyses. We contrast the more stable partial-likelihood solution in MAPMAKER/SIBS with the extremely variable partial-likelihood approach used in ASPEX, and the potential inflation of lods when the problem is ignored as in BETA.     

Informative-transmission disequilibrium test (i-TDT): combined linkage and association mapping that includes unaffected offspring as well as affected offspring

To date, there is no test valid for the composite null hypothesis of no linkage or no association that utilizes transmission information from heterozygous parents to their unaffected offspring as well as the affected offspring from ascertained nuclear families. Since the unaffected siblings also provide information about linkage and association, we introduce a new strategy called the informative-transmission disequilibrium test (i-TDT), which uses transmission information from heterozygous parents to all of the affected and unaffected offspring in ascertained nuclear families and provides a valid chi-square test for both linkage and association. The i-TDT can be used in various study designs and can accommodate all types of independent nuclear families with at least one affected offspring. We show that the transmission/disequilibrium test (TDT) (Spielman et al. [1993] Am. J. Hum. Genet. 52:506-516) is a special case of the i-TDT, if the study sample contains only case-parent trios. If the sample contains only affected and unaffected offspring without parental genotypes, the i-TDT is equivalent to the sibship disequilibrium test (SDT) (Horvath and Laird [1998] Am. J. Hum. Genet. 63:1886-1897. In addition, the test statistic of i-TDT is simple, explicit and can be implemented easily without intensive computing. Through computer simulations, we demonstrate that power of the i-TDT can be higher in many circumstances compared to a method that uses affected offspring only. Applying the i-TDT to the Framingham Heart Study data, we found that the apolipoprotein E (APOE) gene is significantly linked and associated with cross-sectional measures and longitudinal changes in total cholesterol.     

A comparison of sib-pair linkage tests for disease susceptibility loci

An analytical study is conducted of the properties of statistical tests to detect linkage between a disease locus and a very polymorphic marker locus when data on sib pairs are available. In most instances the most powerful test is the test based on the mean number of marker alleles shared identical by descent by the two members of a sib pair, and the most efficient sampling strategy is almost always to sample only pairs with both sibs affected. We show it is valid to use the information from all possible sib pairs as though they came from separate families when data on sibships of size three or larger are available, though more power may be obtained if different weights are given to the different sibship sizes.     

The performance of MIM in comparison with MAPMAKER/SIBS to detect QTLs

This paper summarizes the results of searching for evidence of loci contributing to simulated quantitative traits which are associated with a common genetic disease using two multipoint identity by descent (IBD) sharing methods: MIM and MAPMAKER/SIBS. In brief, by varying the lod-score threshold from 1 to 3, we found that MIM and MAPMAKER/SIBS have similar power to detect linkage, but MAPMAKER/SIBS consistently produces a higher number of false positives. © 1997 Wiley-Liss, Inc.     

Power calculations for likelihood ratio tests for offspring genotype risks, maternal effects, and parent-of-origin (POO) effects in the presence of missing parental genotypes when unaffected siblings are available

Genotype-based likelihood-ratio tests (LRT) of association that examine maternal and parent-of-origin effects have been previously developed in the framework of log-linear and conditional logistic regression models. In the situation where parental genotypes are missing, the expectation-maximization (EM) algorithm has been incorporated in the log-linear approach to allow incomplete triads to contribute to the LRT. We present an extension to this model which we call the Combined_LRT that incorporates additional information from the genotypes of unaffected siblings to improve assignment of incompletely typed families to mating type categories, thereby improving inference of missing parental data. Using simulations involving a realistic array of family structures, we demonstrate the validity of the Combined_LRT under the null hypothesis of no association and provide power comparisons under varying levels of missing data and using sibling genotype data. We demonstrate the improved power of the Combined_LRT compared with the family-based association test (FBAT), another widely used association test. Lastly, we apply the Combined_LRT to a candidate gene analysis in Autism families, some of which have missing parental genotypes. We conclude that the proposed log-linear model will be an important tool for future candidate gene studies, for many complex diseases where unaffected siblings can often be ascertained and where epigenetic factors such as imprinting may play a role in disease etiology.     

Validity, efficiency, and robustness of a family-based test of association

We propose a new test of linkage in the presence of allelic association that uses all available information in a sample of nuclear families, including parental phenotypes, genotypes from both affected and unaffected siblings, and families with homozygous parents. The test is based on the conditional framework developed by Rabinowitz and Laird [2000: Hum Hered 50:211-223] and is thus immune to population stratification and can be applied to families with any pattern of missing information. The test statistic is a conditional likelihood ratio based on a standard two-point linkage model with allelic association, where parameters are estimated from the sample. Through a simulation study, we determined that the proposed test has near optimal power for a wide range of scenarios, outperforming FBAT both when data were complete and when parental genotypes were missing, although differences between the two tests diminish as the genetic effect is reduced. To assess robustness, we also evaluated the performance of the tests under scenarios with population stratification and found that although there is a loss of efficiency, our proposed test remains a strong competitor to FBAT.     

Properties of case/pseudocontrol analysis for genetic association studies: Effects of recombination, ascertainment, and multiple affected offspring

The case/pseudocontrol approach is a general framework for family-based association analysis, incorporating several previously proposed methods such as the transmission/disequilibrium test and log-linear modelling of parent-of-origin effects. In this report, I examine the properties of methods based on a case/pseudocontrol approach when applied to a linked marker rather than (or in addition to) the true disease locus or loci, and when applied to sibships that have been ascertained on, or that may simply contain, multiple affected sibs. Through simulations and analytical calculations, I show that the expected values of the observed relative risk parameters (estimating quantities such as effects due to a child's own genotype, maternal genotype, and parent-of-origin) depend crucially on the ascertainment scheme used, as well as on whether there is non-negligible recombination between the true disease locus and the locus under study. In the presence of either recombination or ascertainment on multiple affected offspring, methods based on conditioning on parental genotypes are shown to give unbiased genotype relative risk estimates at the true disease locus (or loci) but biased estimates of population genotype relative risks at a linked marker, suggesting that the resulting estimates may be misleading when used to predict the power of future studies. Methods that allow for exchangeability of parental genotypes are shown (in the presence of either recombination or ascertainment on multiple affected offspring) to produce false-positive evidence of maternal genotype effects when there are true parent-of-origin or mother-child interaction effects, even when analyzing the true locus. These results suggest that care should be taken in both the interpretation and application of parameter estimates obtained from family-based genetic association studies.     

Testing linkage and gene x environment interaction: comparison of different affected sib-pair methods

The aim of this study was to compare, under different models of gene-environment (G x E) interaction, the power to detect linkage and G x E interaction of different tests using affected sib-pairs. Methods considered were: 1) the maximum likelihood lod-score (MLS), based on the distribution of parental alleles identical by descent (IBD) in affected sibs; 2) the sum of the MLS (sMLS) calculated in affected sib-pairs with 2, 1, or 0 sibs exposed; 3) the predivided sample test (PST), which compares the IBD distribution between affected sib-pairs with 2, 1, or 0 sibs exposed; 4) the triangle test statistic (TTS), which uses the IBD distribution among discordant affected sib-pairs (one exposed, one unexposed); and 5) the mean interaction test (MIT), based on the regression of the proportion of alleles shared IBD among affected sib-pairs on the exposure among sib-pairs. The MLS, sMLS, and MIT allow detection of linkage. However, the sMLS and MIT account for a possible G x E interaction without testing it. In contrast, the PST and the TTS allow detection of both linkage and G x E interaction. Results showed that when exposure cancels the effect of the gene, or changes the direction of this effect (i.e., the protective allele becomes the risk allele), the PST, sMLS, and MIT may provide, under some models, greater power to detect linkage than the MLS. Under models where exposure changes the direction of the effect of the gene, the TTS test may also be more powerful than the other tests accounting for G x E interaction. Under the other models, the MLS remains the most powerful test to detect linkage. However, only the PST and TTS allow the detection of G x E interaction.     

The Maximum-Likelihood-Binomial method revisited: a robust approach for model-free linkage analysis of quantitative traits in large sibships

Model‐free linkage analysis methods, based on identity‐by‐descent allele sharing, are commonly used for complex trait analysis. The Maximum‐Likelihood‐Binomial (MLB) approach, which is based on the hypothesis that parental alleles are binomially distributed among affected sibs, is particularly popular. An extension of this method to quantitative traits (QT) has been proposed (MLB‐QTL), based on the introduction of a latent binary variable capturing information about the linkage between the QT and the marker. Interestingly, the MLB‐QTL method does not require the decomposition of sibships into constituent sibpairs and requires no prior assumption about the distribution of the QT. We propose a new formulation of the MLB method for quantitative traits (nMLB‐QTL) that explicitly takes advantage of the independence of paternal and maternal allele transmission under the null hypothesis of no linkage. Simulation studies under H₀ showed that the nMLB‐QTL method generated very consistent type I errors. Furthermore, simulations under the alternative hypothesis showed that the nMLB‐QTL method was slightly, but systematically more powerful than the MLB‐QTL method, whatever the genetic model, residual correlation, ascertainment strategy and sibship size considered. Finally, the power of the nMLB‐QTL method is illustrated by a chromosome‐wide linkage scan for a quantitative endophenotype of leprosy infection. Overall, the nMLB‐QTL method is a robust, powerful, and flexible approach for detecting linkage with quantitative phenotypes, particularly in studies of non Gaussian phenotypes in large sibships. Genet. Epidemiol. 35:46–56, 2011. © 2010 Wiley‐Liss, Inc.     

An efficient study design to test parent‐of‐origin effects in family trios

Increasing evidence has shown that genes may cause prenatal, neonatal, and pediatric diseases depending on their parental origins. Statistical models that incorporate parent‐of‐origin effects (POEs) can improve the power of detecting disease‐associated genes and help explain the missing heritability of diseases. In many studies, children have been sequenced for genome‐wide association testing. But it may become unaffordable to sequence their parents and evaluate POEs. Motivated by the reality, we proposed a budget‐friendly study design of sequencing children and only genotyping their parents through single nucleotide polymorphism array. We developed a powerful likelihood‐based method, which takes into account both sequence reads and linkage disequilibrium to infer the parental origins of children's alleles and estimate their POEs on the outcome. We evaluated the performance of our proposed method and compared it with an existing method using only genotypes, through extensive simulations. Our method showed higher power than the genotype‐based method. When either the mean read depth or the pair‐end length was reasonably large, our method achieved ideal power. When single parents’ genotypes were unavailable or parental genotypes at the testing locus were not typed, both methods lost power compared with when complete data were available; but the power loss from our method was smaller than the genotype‐based method. We also extended our method to accommodate mixed genotype, low‐, and high‐coverage sequence data from children and their parents. At presence of sequence errors, low‐coverage parental sequence data may lead to lower power than parental genotype data.     

Examining the effect of linkage disequilibrium between markers on the Type I error rate and power of nonparametric multipoint linkage analysis of two-generation and multigenerational pedigrees in the presence of missing genotype data

Because most multipoint linkage analysis programs currently assume linkage equilibrium between markers when inferring parental haplotypes, ignoring linkage disequilibrium (LD) may inflate the Type I error rate. We investigated the effect of LD on the Type I error rate and power of nonparametric multipoint linkage analysis of two-generation and multigenerational multiplex families. Using genome-wide single nucleotide polymorphism (SNP) data from the Collaborative Study of the Genetics of Alcoholism, we modified the original data set into 30 total data sets in order to consider six different patterns of missing data for five different levels of SNP density. To assess power, we designed simulated traits based on existing marker genotypes. For the Type I error rate, we simulated 1,000 qualitative traits from random distributions, unlinked to any of the marker data. Overall, the different levels of SNP density examined here had only small effects on power (except sibpair data). Missing data had a substantial effect on power, with more completely genotyped pedigrees yielding the highest power (except sibpair data). Most of the missing data patterns did not cause large increases in the Type I error rate if the SNP markers were more than 0.3 cM apart. However, in a dense 0.25-cM map, removing genotypes on founders and/or founders and parents in the middle generation caused substantial inflation of the Type I error rate, which corresponded to the increasing proportion of persons with missing data. Results also showed that long high-LD blocks have severe effects on Type I error rates.     

Tests for genetic association using family data.

We use likelihood-based score statistics to test for association between a disease and a diallelic polymorphism, based on data from arbitrary types of nuclear families. The Nonfounder statistic extends the transmission disequilibrium test (TDT) to accommodate affected and unaffected offspring, missing parental genotypes, phenotypes more general than qualitative traits, such as censored survival data and quantitative traits, and residual correlation of phenotypes within families. The Founder statistic compares observed or inferred parental genotypes to those expected in the general population. Here the genotypes of affected parents and those with many affected offspring are weighted more heavily than unaffected parents and those with few affected offspring. We illustrate the tests by applying them to data on a polymorphism of the SRD5A2 gene in nuclear families with multiple cases of prostate cancer. We also use simulations to compare the power of these family-based statistics to that of the score statistic based on Cox's partial likelihood for censored survival data, and find that the family-based statistics have considerably more power when there are many untyped parents. The software program FGAP for computing test statistics is available at http://www.stanford.edu/dept/HRP/epidemiology/FGAP.     

Comparison of evidence supporting a chromosome 6 alcoholism gene

A whole genome scan has been conducted on 105 families ascertained for probands with a diagnosis of alcoholism by the Collaborative Study on the Genetics of Alcoholism (COGA). To identify chromosomal regions likely to contain genes contributing to the development of this disorder, data from 296 highly polymorphic markers have been analyzed using the MAPMAKER/SIBS [Kruglyak and Lander, 1995] and GENEHUNTER-PLUS [Kruglyak et al., 1996; Kong and Cox, 1997] multipoint linkage programs. Chromosome 6 exhibited lod scores greater than 3.0 and was further tested by two-point linkage analyses at each marker along the chromosome to assess the consistency of results from these allele sharing linkage programs. Two-point linkage was assessed with MAPMAKER/SIBS, GENEHUNTER-PLUS and the SIBPAL subprogram of the SAGE package of genetic epidemiology programs [Elston, 1997].     

Contrasting effects of maternal fertility and birth rank on the occurrence of neural tube defects.

The relationships between the occurrence of anencephalus and spina bifida, sibship size and birth rank were examined, using linked records for births in British Columbia. Comparison of 414 sibships in which at least one infant had a neural tube defect with 1362 randomly chosen unaffected sibships showed that the affected sibships were larger. There were both more births than expected after the affected birth, and shorter intervals between births before the affected birth. Within sibships, the risk of anencephalus or spina bifida decreased strongly with increasing birth rank. No associations were seen with maternal age at first birth.     

Some effects of selection strategies on linkage analysis

A study was designed to address the relative merits of different sampling strategies for detecting linkage. Genotypes of pedigree members were generated by the use of a single genetic model, and the pedigrees were subdivided into dominant-appearing, recessive-appearing, and "interesting" subsets. An investigator blind to how the data had been generated applied two different selection rules to determine which individuals in each pedigree would be "typed" for linkage analysis. Linkage analyses were then conducted on these pedigree subsets, as well as on the combined data, by the use of three autosomal dominant models, three autosomal recessive models, and the generating (i.e., "true") model. Results suggest (1) that linkage is likely to be detected even in the absence of knowledge of the mode of transmission, if a range of models can be examined; (2) that false evidence for heterogeneity will not necessarily result when pedigrees are selected according to apparent mode of transmission for analysis; (3) that recessive-appearing pedigrees (i.e., those with multiplex sibships) may be particularly useful for detecting linkage; and (4) that including information on unaffected second-degree relatives adds little to linkage studies of affected individuals and their first-degree relatives.     

Analyzing sibship correlations in birth weight using large sibships from Norway

Data from the Medical Birth Registry of Norway were used to estimate sibship correlations in large sibships (each with ≥5 infants among singleton live births surviving the first year of life), while adjusting for covariates such as infant gender, gestational age, maternal age, parity, and time since last pregnancy. This sample of 12,356 full sibs in 2,462 sibships born in Norway between 1968 and 1989 was selected to maximize the information on parity, and a robust approach to estimating both regression coefficients and the sibship correlation using generalized estimating equations (GEE) was employed. In concordance with previous studies, these data showed a high overall correlation in birth weight among full sibs (0.48 ± 0.01), but this sibship correlation was influenced by parity. In particular, the correlation between the firstborn infant and a subsequent infant was slightly lower than between two subsequent sibs (0.44 ± 0.01 vs. 0.50 ± 0.01, respectively). The effect of time between pregnancies was statistically significant, but its predicted impact was modest over the period in which most of these large families were completed. While these data cannot discriminate whether factors influencing birth weight are maternal or fetal in nature, this analysis does illustrate how robust statistical models can be used to estimate sibship correlations while adjusting for covariates in family studies. Genet. Epidemiol. 14:423–433,1997. © 1997 Wiley-Liss, Inc.     

Detection of major genes underlying several quantitative traits associated with a common disease using different ascertainment schemes

Using the Problem 2A data sets of GAW10, we assessed the power of four ascertainment schemes to localize major genes underlying a disease trait; the schemes were based on disease or quantitative trait status of nuclear families. MAPMAKER/SIBS was used to perform sib-pair analysis for all four data sets using marker data from three chromosomes, 4,5 and 8. Each scheme varied in power to identify major genes underlying the quantitative traits depending on the genetic architecture of the data set. Three different methods, Haseman-Elston quantitative trait locus (QTL) regression analysis, maximum likelihood variance estimation and a non-parametric method, were used to assess the strength of linkage in all four data sets. False positive mappings localizing to the same region of the genome, verifiable across all three methods did not occur. Two major genes, MG1 and MG2, were successfully assigned to chromosomes 5 and 8, respectively, by at least one of the ascertainment schemes. MG1 was localized under two schemes, selection of families with exactly two affected sibs and selection of families with two sibs who had extremely discordant values for Q1. Additional weak evidence of the location of MG1 was also obtained under the other two ascertainment schemes. MG2 could not be detected by analyzing data sets ascertained either by affected sib pairs or by sib pairs with extremely discordant values for Q1. In the data set ascertained by a third strategy, selection of families with sib pairs extremely discordant for Q2, MG2 could be mapped to chromosome 8. A random ascertainment scheme yielded a data set in which we could find weak evidence for MG1 and no evidence for MG2. Thus our ability to detect major genes underlying the QTL depended on several factors which included the ascertainment scheme, the population allelle frequencies, linkage and epistasis. © 1997 Wiley-Liss, Inc.