Impact of family structure on the power of linkage tests using sib-pair methods

This analysis sought to determine the impact of specific ascertainment criteria based upon nuclear family affectation structures. Specifically, we evaluated the predicted and observed proportion of alleles shared identical by descent conditional on the number of affected and unaffected siblings in a pedigree, and compared sib-pair method linkage results under two ascertainment schemes, random vs. selected ascertainment, for this simulated complex genetic disease. These results suggest that samples differing in the composition of affected and unaffected siblings in the family will differ in their power to detect linkage. An effect of sampling scheme on power to map using affected-sib-pair methods should be considered when a reported linkage is not found in another study population.     

Extensions to methods of sib-pair linkage analyses.

Sib-pair methods provide simple, robust, easily implemented ways to screen for linkage between a marker locus and a suspected disease susceptibility locus. The basic analysis reflects the idea that, in the presence of linkage, siblings who share more alleles at the marker locus should also tend to be concordant for disease. Available sib-pair methods do not lead directly to estimates of risk associated with nongenetic factors, may not account for a variable age-at-onset, or may require that the age-at-onset distribution be known. In this paper, we propose a method for sib-pair linkage analyses that allows for a variable age-at-onset using a logistic model, easily allows modelling of nongenetic factors, reflects the correlation of sibs within a sibship, and allows for nonzero risk in those without the susceptibility genotype. Based on a limited number of simulations, the method has as good or better power than another recently described method that also allows for a variable age-at-onset.     

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 power of two-locus affected sib-pair linkage analysis to detect interacting disease loci

It has been shown that two-locus linkage analysis can, for some two-locus disease models, be used to detect effects at disease loci that do not reach significance in a genome scan. However, few examples exist where two-locus linkage has been successfully used to map genes. We study the possible gain in power of affected sib-pair nonparametric two-locus linkage analysis for two-locus models which fulfil the two-locus triangle constraints. Using a new parameterization of the two-locus joint identity-by-descent sharing probabilities we can, for fixed marginal sharing at both of two unlinked disease loci, derive a two-locus distribution such that the power of a two-locus analysis is maximized. In a simulation study we look at two test statistics, the two-locus maximum likelihood score and the correlation between nonparametric linkage scores, and study power as a function of marginal sharing. We show that in a best-case scenario two-locus linkage can have considerable power to detect pairs of interacting loci if there is a moderate increase in allele sharing at one of the two loci, even if there is a very small increase in allele sharing at the other locus. But we also show that the power to detect interacting loci in a two-locus analysis decreases as the marginal sharing at the two loci decreases and for any distribution with a small increase in allele sharing at both loci the power of a two-locus analysis is always low.     

Comparison of methods incorporating quantitative covariates into affected sib pair linkage analysis

For complex traits, it may be possible to increase the power to detect linkage if one takes advantage of covariate information. Several statistics have been proposed that incorporate quantitative covariate information into affected sib pair (ASP) linkage analysis. However, it is not clear how these statistics perform under different gene-environment (G x E) interactions. We compare representative statistics to each other on simulated data under three biologically-plausible G x E models. We also compared their performance with a model-free method and with quantitative trait locus (QTL) linkage approaches. The statistics considered here are: (1) mixture model; (2) general conditional-logistic model (LODPAL); (3) multinomial logistic regression models (MLRM); (4) extension of the maximum-likelihood-binomial approach (MLB); (5) ordered-subset analysis (OSA); and (6) logistic regression modeling (COVLINK). In all three G x E models, most of these six statistics perform better when using the covariate C1 associated with a G x E interaction effect than when using the environmental risk factor C2 or the random noise covariate C3. Compared with a model-free method without covariates (S(all)), the mixture model performs the best when using C1, with the high-to-low OSA method also performing quite well. Generally, MLB is the least sensitive to covariate choice. However, most of these statistics do not provide better power than S(all). Thus, while inclusion of the "correct" covariate can lead to increased power, careful selection of appropriate covariates is vital for success.     

Model-free sib-pair linkage analysis: combining full-sib and half-sib pairs

When sampling full-sibs for linkage studies, half-sibs are often available. Not only are half-sibs convenient to sample, but they can sometimes offer greater power than full-sibs. We propose a method to combine the information from full-sibs and half-sibs into a single test for linkage. This method is based on the Haseman and Elston [1972] method of regressing the squared trait-difference for a pair of sibs (either full- or half-sibs) on the estimated proportion of alleles shared identical by descent. To approximate the distribution of the test statistic, we propose a correction factor that considers the correlation among sibs, and demonstrate by simulations that this approximation works well in many situations, although there are some conditions for which the statistic can have an inflated Type-I error rate. The main appeal of our proposed method is the speed at which it can be computed, offering a rapid way to perform genome-wide linkage screens.     

Multipoint linkage mapping using sibpairs: non-parametric estimation of trait effects with quantitative covariates

Multipoint linkage analysis using sibpair designs remains a common approach to help investigators to narrow chromosomal regions for traits (either qualitative or quantitative) of interest. Despite its popularity, the success of this approach depends heavily on how issues such as genetic heterogeneity, gene-gene, and gene-environment interactions are properly handled. If addressed properly, the likelihood of detecting genetic linkage and of efficiently estimating the location of the trait locus would be enhanced, sometimes drastically. Previously, we have proposed an approach to deal with these issues by modeling the genetic effect of the target trait locus as a function of covariates pertained to the sibpairs. Here the genetic effect is simply the probability that a sibpair shares the same allele at the trait locus from their parents. Such modeling helps to divide the sibpairs into more homogeneous subgroups, which in turn helps to enhance the chance to detect linkage. One limitation of this approach is the need to categorize the covariates so that a small and fixed number of genetic effect parameters are introduced. In this report, we take advantage of the fact that nowadays multiple markers are readily available for genotyping simultaneously. This suggests that one could estimate the dependence of the generic effect on the covariates nonparametrically. We present an iterative procedure to estimate (1) the genetic effect nonparametrically and (2) the location of the trait locus through estimating functions developed by Liang et al. ([2001a] Hum Hered 51:67-76). We apply this new method to the linkage study of schizophrenia to illustrate how the onset ages of each sibpair may help to address the issue of genetic heterogeneity. This analysis sheds new light on the dependence of the trait effect on onset ages from affected sibpairs, an observation not revealed previously. In addition, we have carried out some simulation work, which suggests that this method provides accurate inference for estimating the location of quantitative trait loci.     

Effects of marker information on sib-pair linkage analysis of a rare disease

Model-free sib-pair linkage analysis was used to screen the GAW9 - Problem 1 data set for evidence of linkage of a rare disease to any of 360 highly polymorphic marker loci. Negative regressions nominally significant at the α = 0.05 level were obtained for 44 markers; however all of these proved to be Type I errors. None of the four disease loci were detected by sib-pair linkage, which was not surprising, given the particular model and sampling scheme used to generate these data. Neither deleting parental marker genotypic information nor misspecifying marker allele frequency estimates substantially increased the Type I error rate. A two-stage testing procedure using a 10 or 20 cM map and a liberal first stage significance level gave the same overall results as a one-stage 2 cM map but required only about 42% or 22% as many markers, respectively. ©1995 Wiley-Liss, Inc.     

Affected sib-pair tests for linkage: Type I errors with dependent sib-pairs

We compared the robustness of affected-sib-pair (ASP) tests for multiple-affected sibships. Forming all possible pairs increases the type I errors only slightly whereas the most used weighting procedures decrease the efficiency of the tests. Another weighting procedure accounting for the reduction of variance of the weighted identical by descent (IBD) information appears robust. Missing parental marker data leads to a decrease of type I errors in all cases. © 1997 Wiley-Liss, Inc.     

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.     

Incorporation of covariates into genome scanning using sib-pair analysis in bipolar affective disorder

Assessing heterogeneity in affected relative pair linkage analysis can help control type I error or identify important subgroups. We develop a method to incorporate covariates into sib-pair analysis, and hence are able to test for covariate effects on allele sharing in sib pairs. We propose a way of combining the five bipolar data sets to do a joint analysis of chromosome 18 data using this new method. Our results from a limited set of analyses do not show significant heterogeneity, and do not confirm the linkage previously identified on chromosome 18. © 1997 Wiley-Liss, Inc.     

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 method of sib-pair linkage analysis in context of case-control design

We used sib-pair linkage analysis as part of an epidemiologic approach to solving Problem 2 of the GAW10 data set of nuclear families. We recoded the quantitative trait Q1 into a dichotomous trait using Q1 ≥ 40 as the cut-point. In a case-control design of sib-pair analysis, the affected siblings of the proband were the case subjects and the unaffected siblings were the control subjects. Case and control subjects were compared with respect to the number of alleles at one or more loci (0,1,2) that were identical-by-descent (IBD) with those of the proband. Odds ratios (Ors) and 95% confidence intervals (95% CI) were then computed with subjects sharing no alleles (share-0) serving as the reference group. Significantly high ORs were taken as indication of linkage between a marker locus and a suspected disease-susceptibility locus. The case-control sib-pair analysis identified marker D5G15 as associated with disease susceptibility (OR of sharing two alleles [share-2] = 7.7 [95% CI 2.5-23.9]). Our results were consistent with the results from Kruglyak and Lander's method of complete multipoint sib-pair analysis for linkage. For the marker (D5G15) identified through sib-pair analysis, we examined the effects of other covariates and evaluated gene-environment interaction using conditional logistic regression. © 1997 Wiley-Liss, Inc.     

Interval mapping of quantitative trait loci using a sib-pair linkage method

Fulker and Cardon's interval mapping extension of Haseman and Elston's sib-pair linkage method was used to map loci affecting the quantitative phenotypes presented as part of Problem 2, both adjusted and not adjusted for covariates: Q1 was adjusted for age and the environmental factor (EF); Q2 and Q3 for EF; and Q4 for age, sex, and EF. Adjusted Q2 and Q4 were also log-transformed. The effect of candidate locus C5 (D5G28) on Q1 was detected by a test of association – apparently, allele 1 of C5 is protective (leading to lower values of Q1), allele 2 has no effect, and allele 3 contributes to elevated levels of Q1. C5 accounted for 5.2% of the variation in Q1; it was included as an additional concomitant in the adjustment procedure. Analysis of the correlational structure among the variables revealed that Q4 was not associated with either affected status or Q1 after controlling for the effects of age, and we concluded that Q4 probably does not itself play a role in the etiology of the disease. Mapping studies using a significance level of 0.05 lead to the detection of all the genes, but also resulted in a high frequency of false positive results. On the other hand, using a 0.0005 significance level resulted in the detection of D2G10-11 for both Q1 and Q3, and D1G2 was detected for Q2. One false positive was detected using this significance level and the effects of D1G2 on Q1 and D5G22-23 on Q4 were missed. There was no systematic effect of adjustment for covariates on the detection of loci, although in general, analysis of adjusted phenotypes yielded substantially higher rates of false positives. Finally, this mapping approach correctly located D1G2 and D2G10-11 for Q1 using the nonadjusted phenotype, and D1G10-11 for Q3 using the adjusted phenotype. The maximum difference between the estimated map location from the true location was 1.5 cM. It would be important to estimate the error interval around these inferred locations in order to assess the utility of this method for fine mapping over small (e.g., 2 cM) intervals. © 1995 Wiley-Liss, Inc.     

A more powerful robust sib-pair test of linkage for quantitative traits

A more powerful robust test for linkage is developed from the methodology of Haseman and Elston [Behav Genet 2(1):3-19, 1972]. This new robust test uses weighted least-squares (WLS) methods to detect linkage between a quantitative trait and a polymorphic marker. For comparison, the characteristics of a test for linakge that uses known trait genotypes for the parents are also studied. Sample sizes needed to detect linkage, calculated using asymptotic results, are compared for 1) the usual Haseman-Elston method, 2) the WLS method, and 3) the method that uses parental trait genotype data. The WLS method needs at most twice the number of sib pairs as does the method that uses information on the trait genotypes of the parents. The small sample properties of the Haseman-Elston (H-E) and WLS tests are investigated by simulation. The power calculations for the H-E method are found to be accurate. The power of the WLS method is overestimated when fewer than 300 sib pairs are studied, but the WLS method is nonetheless more powerful than the usual H-E method. In samples of fewer than 300 sib pairs, the WLS test tends to be anticonservative. Treating all sib pairs from sibships of size 3 or 5 as independent does not increase the significance of the tests.     

Familial effects on survival after myocardial infarction: a registry-based sib-pair study

The chance of surviving an acute myocardial infarction (MI) has increased greatly but many persons still die as a consequence of MI. We assessed the familiality of suffering fatal MI using Swedish registry data. All 4,239 sib-pairs (n = 8,478) where both siblings had suffered an MI and who were born 1932 or later were identified by matching the Swedish National Patient-, Cause of Death and Multi-Generation registries. The Cox proportional hazards model was used to estimate the association between survival times between sibling who had, or not had, a sibling who died within 28 days of their first MI. The risk estimate was adjusted for year of infarction, age at infarction, sex and county for both siblings. The mortality rate was increased the first 28 days after infarction amongst patients who had a sibling who also died within 28 days of infarction (adjusted Hazard ratio (HR) [95 % confidence interval [95 % CI]: 1.44 [1.18–1.75]). These patients also have a worse long-term survival (adjusted HR [95 % CI]: 1.65 [1.24–2.21]). There appears to be familial effects that influence MI survival. This may have important implications for MI prevention strategies but further studies are required to determine if these effects are due to genetic or environmental factors.     

Detection of vulnerability loci by association and sib-pair methods

A haplotype-based haplotype relative risk (HHRR) analysis of simulated data for 200 affected offspring and their parents (Genetic Analysis Workshop 9, Problem 1) detected linkage disequilibrium at 2 of 360 marker loci. An additive model was suggested but not proven by haplotypes of affected vs. unaffected offspring. These findings were consistent with the generating model. Affected sib pair analysis failed to detect additional loci. Discussion among workshop participants suggested that the chi-square test used here (2 [transmitted vs. nontransmitted] x n [alleles] for each locus) was invalid because of the nonindependence of proportions of transmitted alleles. In post-workshop analyses, transmission disequilibrium tests (TDTs) for each allele at each locus detected only the true associations if p values were corrected by one of two methods: Bonferroni correction for 2,035 TDTs, or correcting each test for n (number of tests at the locus) minus 1 and then for the number of loci tested. Screening loci for linkage disequilibrium requires careful attention to correction for multiple comparisons. ©1995 Wiley-Liss, Inc.     

Comparison of sib-pair and variance-components methods for genomic screening

The statistical properties of sib-pair and variance-components linkage methods were compared using the nuclear family data from Problem 2. Overall, the power to detect linkage was not high for either method. The variance-components method had better power for detection of linkage, particularly when covariates were included in the model. Type I error rates were similar to nominal error rates for both methods. © 1997 Wiley-Liss, Inc.     

A novel polylocus method for linkage analysis using the lod-score or affected sib-pair method

A novel approach to combining data from multiple linked loci is proposed that can provide substantial increases in power over normal two-point linkage analysis or sib-pair analysis, with a substantial saving in computing time over traditional multipoint methods. © 1993 Wiley-Liss, Inc.