Nonparametric Linkage Statistic Research Articles

A comparison of different linkage statistics in small to moderate sized pedigrees with complex diseases

BackgroundIn the last years GWA studies have successfully identified common SNPs associated with complex diseases. However, most of the variants found this way account for only a small portion of the trait variance. This fact leads researchers to focus on rare-variant mapping with large scale sequencing, which can be facilitated by using linkage information. The question arises why linkage analysis often fails to identify genes when analyzing complex diseases. Using simulations we have investigated the power of parametric and nonparametric linkage statistics (KC-LOD, NPL, LOD and MOD scores), to detect the effect of genes responsible for complex diseases using different pedigree structures.ResultsAs expected, a small number of pedigrees with less than three affected individuals has low power to map disease genes with modest effect. Interestingly, the power decreases when unaffected individuals are included in the analysis, irrespective of the true mode of inheritance. Furthermore, we found that the best performing statistic depends not only on the type of pedigrees but also on the true mode of inheritance.ConclusionsWhen applied in a sensible way linkage is an appropriate and robust technique to map genes for complex disease. Unlike association analysis, linkage analysis is not hampered by allelic heterogeneity. So, why does linkage analysis often fail with complex diseases? Evidently, when using an insufficient number of small pedigrees, one might miss a true genetic linkage when actually a real effect exists. Furthermore, we show that the test statistic has an important effect on the power to detect linkage as well. Therefore, a linkage analysis might fail if an inadequate test statistic is employed. We provide recommendations regarding the most favorable test statistics, in terms of power, for a given mode of inheritance and type of pedigrees under study, in order to reduce the probability to miss a true linkage.

New score tests for age-at-onset linkage analysis in general pedigrees

Our aim is to develop methods for mapping genes related to age at onset in general pedigrees. We propose two score tests, one derived from a gamma frailty model with pairwise likelihood and one derived from a log-normal frailty model with approximated likelihood around the null random effect. The score statistics are weighted nonparametric linkage statistics, with weights depending on the age at onset. These tests are correct under the null hypothesis irrespective of the weight used. They are simple, robust, computationally fast, and can be applied to large, complex pedigrees. We apply these methods to simulated data and to the Genetic Analysis Workshop 16 Framingham Heart Study data set. We investigate the time to the first of three events: hard coronary heart disease, diabetes, or death from any cause. We use a two-step procedure. In the first step, we estimate the population parameters under the null hypothesis of no linkage. In the second step, we apply the score tests, using the population parameters estimated in the first step.

Handling linkage disequilibrium in qualitative trait linkage analysis using dense SNPs: a two-step strategy

BackgroundIn affected sibling pair linkage analysis, the presence of linkage disequilibrium (LD) has been shown to lead to overestimation of the number of alleles shared identity-by-descent (IBD) among sibling pairs when parents are ungenotyped. This inflation results in spurious evidence for linkage even when the markers and the disease locus are not linked. In our study, we first theoretically evaluate how inflation in IBD probabilities leads to overestimation of a nonparametric linkage (NPL) statistic under the assumption of linkage equilibrium. Next, we propose a two-step processing strategy in order to systematically evaluate approaches to handle LD. Based on the observed inflation of expected logarithm of the odds ratio (LOD) from our theoretical exploration, we implemented our proposed two-step processing strategy. Step 1 involves three techniques to filter a dense set of markers. In step 2, we use the selected subset of markers from step 1 and apply four different methods of handling LD among dense markers: 1) marker thinning (MT); 2) recursive elimination; 3) SNPLINK; and 4) LD modeling approach in MERLIN. We evaluate relative performance of each method through simulation.ResultsWe observed LOD score inflation only when the parents were ungenotyped. For a given number of markers, all approaches evaluated for each type of LD threshold performed similarly; however, RE approach was the only one that eliminated the LOD score bias. Our simulation results indicate a reduction of approximately 75% to complete elimination of the LOD score inflation while maintaining the information content (IC) when setting a tolerable squared correlation coefficient LD threshold (r2) above 0.3 for or 2 SNPs per cM using MT.ConclusionWe have established a theoretical basis of how inflated IBD information among dense markers overestimates a NPL statistic. The two-step processing strategy serves as a useful framework to systematically evaluate relative performance of different methods to handle LD.

Multipoint Approximations of Identity-by-Descent Probabilities for Accurate Linkage Analysis of Distantly Related Individuals

We propose an analytical approximation method for the estimation of multipoint identity by descent (IBD) probabilities in pedigrees containing a moderate number of distantly related individuals. We show that in large pedigrees where cases are related through untyped ancestors only, it is possible to formulate the hidden Markov model of the Lander-Green algorithm in terms of the IBD configurations of the cases. We use a first-order Markov approximation to model the changes in this IBD-configuration variable along the chromosome. In simulated and real data sets, we demonstrate that estimates of parametric and nonparametric linkage statistics based on the first-order Markov approximation are accurate. The computation time is exponential in the number of cases instead of in the number of meioses separating the cases. We have implemented our approach in the computer program ALADIN (accurate linkage analysis of distantly related individuals). ALADIN can be applied to general pedigrees and marker types and has the ability to model marker-marker linkage disequilibrium with a clustered-markers approach. Using ALADIN is straightforward: It requires no parameters to be specified and accepts standard input files.

A hierarchical model for estimating significance levels of non‐parametric linkage statistics for large pedigrees

The significance level of a non-parametric linkage (NPL) statistic is often found by simulation since the distribution of the test statistic is complex and unknown. Ideally, simulation occurs by randomly assigning founder genotypes and then simulating meiotic events for the descendants in the pedigree, commonly referred to as 'gene dropping'. The missing data pattern in the original pedigree, including lack of phase information (due to unordered genotypes), is then imposed on the simulated pedigree. However, this approach is usually computationally infeasible for larger pedigrees which require Markov chain Monte Carlo (MCMC) techniques to calculate the statistic, as an additional MCMC run is required to estimate the statistic for each gene drop. In this work, we propose a novel method to estimate the significance level of the NPL statistic in large pedigrees. This is accomplished by constructing a hierarchical model, which allows estimation of the NPL statistic variability via separate estimation of the Markov chain and gene dropping variability. The significance level is estimated by fitting a parametric model to the statistic and using the method of moments to obtain parameter estimates. In a simulation study we found our hierarchical model estimates to be very close to the gold standard empirical estimates, and offer substantial improvements over the existing conservative method used by the software SimWalk2. The estimation procedure significantly reduces the computational time relative to the ideal empirical estimate, allowing for an accurate estimate of the significance level in a more manageable amount of time.

Evidence for a colorectal cancer susceptibility locus on chromosome 3q21-q24 from a high-density SNP genome-wide linkage scan

To identify a novel susceptibility gene for colorectal cancer (CRC), we conducted a genome-wide linkage analysis of 69 pedigrees segregating colorectal neoplasia in which involvement of known loci had been excluded, using a high-density single nucleotide polymorphism (SNP) array containing 10,204 markers. Multipoint linkage analyses were undertaken using both non-parametric (model-free) and parametric (model-based) methods. After the removal of SNPs in strong linkage disequilibrium, we obtained a maximum non-parametric linkage statistic of 3.40 (P=0.0003) at chromosomal region 3q21-q24. The same genomic position also yielded the highest multipoint heterogeneity LOD (HLOD) score under a dominant model (HLOD=3.10, genome-wide P=0.038) with 62% of families linked to the locus. We provide evidence for a novel CRC susceptibility gene. Further studies are needed to confirm this localization and to evaluate the contribution of this locus to disease incidence.

Covariate-based linkage analysis: application of a propensity score as the single covariate consistently improves power to detect linkage

Successful identification of genetic risk loci for complex diseases has relied on the ability to minimize disease and genetic heterogeneity to increase the power to detect linkage. One means to account for disease heterogeneity is by incorporating covariate data. However, the inclusion of each covariate will add one degree of freedom to the allele sharing based linkage test, which may in fact decrease power. We explore the application of a propensity score, which is typically used in causal inference to combine multiple covariates into a single variable, as a means of allowing for multiple covariates with the addition of only one degree of freedom. In this study, binary trait data, simulated under various models involving genetic and environmental effects, were analyzed using a nonparametric linkage statistic implemented in LODPAL. Power and type I error rates were evaluated. Results suggest that the use of the propensity score to combine multiple covariates as a single covariate consistently improves the power compared to an analysis including no covariates, each covariate individually, or all covariates simultaneously. Type I error rates were inflated for analyses with covariates and increased with increasing number of covariates, but reduced to nominal rates with sample sizes of 1000 families. Therefore, we recommend using the propensity score as a single covariate in the linkage analysis of a trait suspected to be influenced by multiple covariates because of its potential to increase the power to detect linkage, while controlling for the increase in the type I error.

False Disease Region Identification From Identity-By-Descent Haplotype Sharing in the Presence of Phenocopies

Linkage analysis (either parametric or nonparametric) is commonly applied to identify chromosomal regions using related individuals affected by disease. In complex disease the incomplete relationship between phenotype and genotype can be modeled using a phenocopy parameter, the probability that an individual is affected given they do not carry the disease mutation of interest, and a nonpenetrance parameter, the probability that an individual is not affected given they do carry the disease mutation of interest. If the linkage phase between multiple markers and a putative disease locus is known, then haplotypes carrying the mutation can, in principle, be identified by comparing the chromosome segments that are shared identical-by-descent (IBD) across affected individuals. We consider here the effect of a nonzero phenocopy rate on the linkage peak and hence upon the identification of disease haplotypes that are shared IBD between affected individuals. We show, by theory and computer simulation, that in diseases for which there is a nonzero phenocopy rate, the chromosomal regions identified may not include the true disease locus. We utilize a LOD-1 confidence interval for a widely used nonparametric linkage statistic. We find that in small/moderate samples this confidence interval may be inappropriate. We give specific examples where the phenocopy rates are nonnegligible in some complex diseases. The success of further work to identify the causal mutations underlying the linkage peaks in these diseases will depend on researchers allowing for the presence of phenocopies by examining appropriately wide regions around the initial positive linkage finding.

False Disease Region Identification From Identity-By-Descent Haplotype Sharing in the Presence of Phenocopies

AbstractLinkage analysis (either parametric or nonparametric) is commonly applied to identify chromosomal regions using related individuals affected by disease. In complex disease the incomplete relationship between phenotype and genotype can be modeled using a phenocopy parameter, the probability that an individual is affected given they do not carry the disease mutation of interest, and a nonpenetrance parameter, the probability that an individual is not affected given they do carry the disease mutation of interest. If the linkage phase between multiple markers and a putative disease locus is known, then haplotypes carrying the mutation can, in principle, be identified by comparing the chromosome segments that are shared identical-by-descent (IBD) across affected individuals. We consider here the effect of a nonzero phenocopy rate on the linkage peak and hence upon the identification of disease haplotypes that are shared IBD between affected individuals. We show, by theory and computer simulation, that in diseases for which there is a nonzero phenocopy rate, the chromosomal regions identified may not include the true disease locus. We utilize a LOD-1 confidence interval for a widely used nonparametric linkage statistic. We find that in small/moderate samples this confidence interval may be inappropriate. We give specific examples where the phenocopy rates are nonnegligible in some complex diseases. The success of further work to identify the causal mutations underlying the linkage peaks in these diseases will depend on researchers allowing for the presence of phenocopies by examining appropriately wide regions around the initial positive linkage finding.

Genetic studies in familial ankylosing spondylitis susceptibility.

To define the genetic basis of susceptibility to ankylosing spondylitis (AS), especially non-major histocompatibility complex (MHC) genes. The study group comprised 244 affected sibling pairs from 180 pedigrees of primarily European ancestry. Sibling pairs were concordant for AS by the modified New York criteria and had available sacroiliac radiographs. The subjects were genotyped for 400 markers in ABI PRISM linkage map MD-10 and for 17 additional markers on chromosomes 6p, 6q, and 11q (including HLA-B, DRB1, DQA1, DQB1, and DPB1 alleles). Two-point and multipoint nonparametric linkage (NPL) analyses were conducted using the NPL statistic and 1-parameter allele-sharing model logarithm of odds (LOD) scores, calculated using the Allele-Sharing Model (ASM) computer program. Linkage of the MHC region was supported by both 2-point and multipoint analyses, with the strongest peak (45.90 cM) in the MHC at the HLA-DRB1 locus (NPL score 8.720, ASM LOD score 20.49; P = 6.8 x 10(-20) for 2-point analysis). A second region was found to have positive linkage at the q arm of chromosome 6 (D6S441) in 2-point analysis; this was supported by a 39.13-cM region (135.58-174.71 cM) in multipoint analysis, with the smallest P value (4.2 x 10(-3)) at 166.39 cM. A third region was found on chromosome 11q, with the strongest evidence for linkage for D11S4094 at 123 cM (NPL score 2.235, ASM LOD score 1.939) and, on transmission disequilibrium test analysis, D11S4090 at 105.74 cM (P = 6.2 x 10(-5)). Linkage in this area was supported by multipoint analysis, spanning 22.19 cM continuously from 101.68 cM to 123.87 cM, with the strongest peak at 112.33 cM (P = 0.014); this was confirmed by subsequent fine mapping studies. Thus, this genome-wide scan implicates, in addition to the MHC, regions outside the MHC in AS susceptibility, especially on chromosomes 6q and 11q.

Genome scan of venous thrombosis in a pedigree with protein C deficiency

Kindred Vermont II has a high frequency of venous thrombosis, occurring primarily in pedigree members with type I protein C deficiency due to a 3363 inserted (Ins) C mutation in exon 6 of the protein C gene. However, only a subset of 3363 InsC carriers have suffered thrombotic episodes, suggesting that the increased risk of thrombosis results upon the co-occurrence of 3363 InsC with a second, unknown, thrombophilic mutation that segregates independently within the pedigree. To test this hypothesis and to localize the co-occurring gene, we performed a genome scan of venous thrombosis in Kindred Vermont II. Non-parametric linkage statistics identified three potential gene locations, on chromosomes 11q23 (nominal P < 0.0001), 18p11.2-q11.2 (P < 0.0007), and 10p12 (P < 0.0003), supporting the presence of at least one additional thrombophilic mutation in the pedigree. Identification of the unknown mutation(s) promises to reveal a new genetic risk factor for thrombophilia, contribute to our understanding of the blood clotting mechanism, and expand our knowledge of the diversity of oligogenic disease.

Bias toward the Null Hypothesis in Model-Free Linkage Analysis Is Highly Dependent on the Test Statistic Used

Recently, it has been suggested that traditional nonparametric multipoint-linkage procedures can show a "bias" toward the null hypothesis of no effect when there is incomplete information about allele sharing at genotyped marker loci (or at positions in between marker loci). Here, I investigate the extent of this bias for a variety of test statistics commonly used in qualitative- ("affecteds only") and quantitative-trait linkage analysis. Through simulation and analytical derivation, I show that many of the test statistics available in standard linkage analysis packages (such as Genehunter, Merlin, and Allegro) are, in fact, not affected by this bias problem. A few test statistics--most notably the nonparametric linkage statistic and, to a lesser extent, the Aspex-MLS and Haseman-Elston statistics--are affected by the bias. Variance-components procedures, although unbiased, can show inflation or deflation of the test statistic attributable to the inclusion of pairs with incomplete identity-by-descent information. Results obtained--for instance, in genome scans--using these methods might therefore be worth revisiting to see if greater power can be obtained by use of an alternative statistic or by eliminating or downweighting uninformative relative pairs.

Linkage analysis with sequential imputation.

Multilocus calculations, using all available information on all pedigree members, are important for linkage analysis. Exact calculation methods in linkage analysis are limited in either the number of loci or the number of pedigree members they can handle. In this article, we propose a Monte Carlo method for linkage analysis based on sequential imputation. Unlike exact methods, sequential imputation can handle large pedigrees with a moderate number of loci in its current implementation. This Monte Carlo method is an application of importance sampling, in which we sequentially impute ordered genotypes locus by locus, and then impute inheritance vectors conditioned on these genotypes. The resulting inheritance vectors, together with the importance sampling weights, are used to derive a consistent estimator of any linkage statistic of interest. The linkage statistic can be parametric or nonparametric; we focus on nonparametric linkage statistics. We demonstrate that accurate estimates can be achieved within a reasonable computing time. A simulation study illustrates the potential gain in power using our method for multilocus linkage analysis with large pedigrees. We simulated data at six markers under three models. We analyzed them using both sequential imputation and GENEHUNTER. GENEHUNTER had to drop between 38-54% of pedigree members, whereas our method was able to use all pedigree members. The power gains of using all pedigree members were substantial under 2 of the 3 models. We implemented sequential imputation for multilocus linkage analysis in a user-friendly software package called SIMPLE.

The power and statistical behaviour of allele-sharing statistics when applied to models with two disease loci.

We have evaluated the power for detecting a common trait determined by two loci, using seven statistics, of which five are implemented in the computer program SimWalk2, and two are implemented in GENEHUNTER. Unlike most previous reports which involve evaluations of the power of allele-sharing statistics for a single disease locus, we have used a simulated data set of general pedigrees in which a two-locus disease is segregating and evaluated several nonparametric linkage statistics implemented in the two programs. We found that the power for detecting linkage using the S(all) statistic in GENEHUNTER (GH, version 2.1), implemented as statistic E in SimWalk2 (version 2.82), is different in the two. The P values associated with statistic E output by SimWalk2 are consistently more conservative than those from GENEHUNTER except when the underlying model includes heterogeneity at a level of 50% where the P values output are very comparable. On the other hand, when the thresholds are determined empirically under the null hypothesis, S(all) in GENEHUNTER and statistic E have similar power.

A New Essential Hypertension Susceptibility Locus on Chromosome 2p24-p25, Detected by Genomewide Search

Essential hypertension (EH) is a complex disorder that results from the interaction of a number of susceptibility genes and environmental factors. We studied an isolated Sardinian village (Talana) in which the prevalence of hypertension is comparable to that in most Western populations. Talana exhibits features, such as slow demographic growth, high inbreeding, a low number of founders, stable lifestyle and culture, and accurate genealogical records, that make it suitable for the study of complex disorders. Clinical assessment of the entire adult population (N= approximately 1,000) identified approximately 100 hypertensive subjects. For our study, we selected the individuals with the most-severe EH (i.e., diastolic blood pressure >100 mm Hg), belonging to a single deep-rooted pedigree (12 generations), whose common ancestors lived in the 17th century. We performed a three-stage genomewide search using 36 affected individuals, by means of parametric linkage and allele-sharing approaches. LOD scores >1 were observed on chromosomes 1, 2, 13, 15, 17, and 19 (stage I). The most striking result was found in a 7.57-cM region on chromosome 2p24-p25. All five nonparametric linkage statistics estimated by the SimWalk2 program lie above the significance threshold of P<.008 for the whole region. Similar significance was obtained for 2p24-25 when parametric linkage (LOD score 1.99) and linkage disequilibrium mapping (P=.00006) were used, suggesting that a hypertension-susceptibility locus is located between D2S2278 and D2S168. This finding is strengthened by a recent report of linkage with marker D2S168 in a hypertensive sib-pair sample from China.