The null distribution of the heterogeneity lod score does depend on the assumed genetic model for the trait.

It is well known that the asymptotic null distribution of the homogeneity lod score (LOD) does not depend on the genetic model specified in the analysis. When appropriately rescaled, the LOD is asymptotically distributed as 0.5 chi(2)(0) + 0.5 chi(2)(1), regardless of the assumed trait model. However, because locus heterogeneity is a common phenomenon, the heterogeneity lod score (HLOD), rather than the LOD itself, is often used in gene mapping studies. We show here that, in contrast with the LOD, the asymptotic null distribution of the HLOD does depend upon the genetic model assumed in the analysis. In affected sib pair (ASP) data, this distribution can be worked out explicitly as (0.5 - c)chi(2)(0) + 0.5chi(2)(1) + cchi(2)(2), where c depends on the assumed trait model. E.g., for a simple dominant model (HLOD/D), c is a function of the disease allele frequency p: for p = 0.01, c = 0.0006; while for p = 0.1, c = 0.059. For a simple recessive model (HLOD/R), c = 0.098 independently of p. This latter (recessive) distribution turns out to be the same as the asymptotic distribution of the MLS statistic under the possible triangle constraint, which is asymptotically equivalent to the HLOD/R. The null distribution of the HLOD/D is close to that of the LOD, because the weight c on the chi(2)(2) component is small. These results mean that the cutoff value for a test of size alpha will tend to be smaller for the HLOD/D than the HLOD/R. For example, the alpha = 0.0001 cutoff (on the lod scale) for the HLOD/D with p = 0.05 is 3.01, while for the LOD it is 3.00, and for the HLOD/R it is 3.27. For general pedigrees, explicit analytical expression of the null HLOD distribution does not appear possible, but it will still depend on the assumed genetic model.     

Weighting improves the "new Haseman-Elston" method

Elston et al. [Genet Epidemiol, in press] apply the results of Wright [Am J Hum Genet 1997;60:740-742] and Drigalenko [Am J Hum Genet 1998;63:1242-1245] to extend the traditional Haseman-Elston regression scheme [Haseman and Elston, Behav Genet 1972;2:3-19] to include not only linkage information contained in the sib pair's squared difference, but also information in their mean-corrected squared sum. The new algorithm detects linkage to a quantitative trait locus by modelling sib pair trait covariance as a function of identity-by-descent status. We demonstrate why this new estimator is suboptimal and can in some cases be inferior to the original Haseman-Elston method. We also describe a simple approach to estimation which improves on this new Haseman-Elston method by incorporating variance-based weights into the test statistic while staying within the linear modelling framework. In support of our theoretical claim, we conduct both a sib pair simulation and an application to GAW 10 sib pair data showing that our new estimator is superior to both the old and new Haseman-Elston schemes currently implemented in the analysis package S.A.G.E. 4.0.     

Heterogeneity in IBD allele sharing among covariate-defined subgroups: issues and findings for affected relatives

OBJECTIVES: Modelling of variation in identical-by-descent (IBD) allele sharing using covariates can increase power to detect linkage, identify covariate-defined subgroups linked to particular marker regions, and improve the design of subsequent studies to localize genes and characterize their effects. In this report, we highlight issues that arise in studies of families with affected relatives. METHODS: Mirea et al. [Genet Epidemiol 2003, in press] extended linear and exponential linkage likelihood models [Kong and Cox, Am J Hum Genet 1997;61: 1179-1188] to model variation in NPL scores among covariate-defined groups of families, and proposed likelihood ratio (LR) and t statistics to detect differences in allele sharing between groups defined by a binary covariate. Here we evaluate factors affecting the power of these tests analytically and by example, as well as effects of constraints, nuisance parameters, and incomplete data on test validity by simulation of locus heterogeneity in families with affected siblings or affected cousins. RESULTS: Provided constraints on the parameters are avoided, these tests are particularly useful when one subgroup has less than expected IBD sharing. The distribution of the LR statistic depends on the extent of linkage, particularly in the presence of constraints. The t statistic may be biased by group differences in information content. CONCLUSIONS: We recommend that constraints be applied cautiously, and covariate effects in IBD allele sharing models interpreted with care.     

Power to detect linkage based on multiple sets of data in the presence of locus heterogeneity: comparative evaluation of model-based linkage methods for affected sib pair data

The development of rigorous methods for evaluating the overall strength of evidence for genetic linkage based on multiple sets of data is becoming increasingly important in connection with genomic screens for complex disorders. We consider here what happens when we attempt to increase power to detect linkage by pooling multiple independently collected sets of families under conditions of variable levels of locus heterogeneity across samples. We show that power can be substantially reduced in pooled samples when compared to the most informative constituent subsamples considered alone, in spite of the increased sample size afforded by pooling. We demonstrate that for affected sib pair data, a simple adaptation of the lod score (which we call the compound lod), which allows for intersample admixture differences can afford appreciably higher power than the ordinary heterogeneity lod; and also, that a statistic we have proposed elsewhere, the posterior probability of linkage, performs at least as well as the compound lod while having considerable computational advantages. The companion paper (this issue, pp 217-225) shows further that in application to multiple data sets, familiar model-free methods are in some sense equivalent to ordinary lod scores based on data pooling, and that they therefore will also suffer dramatic losses in power for pooled data in the presence of locus heterogeneity and other complicating factors.     

Comments on the entropy-based transmission/disequilibrium test

It has recently been claimed in this journal (Zhao et al. in Hum Genet 121:357–367, 2007) that a so-called “entropy-based” TDT test has improved power over the standard TDT test of Spielman et al. (Am J Hum Genet 52:506–516, 1993). We show that this claim is contradicted by standard statistical theory as well as by our simulation results. We show that the incorrect claim arises because of inappropriate assumptions, and also show that the entropy-based statistic has various undesirable properties.     

The score statistic of the LD-lod analysis: detecting linkage adaptive to linkage disequilibrium

We study the properties of a modified lod score method for testing linkage that incorporates linkage disequilibrium (LD-lod). By examination of its score statistic, we show that the LD-lod score method adaptively combines two sources of information: (a) the IBD sharing score which is informative for linkage regardless of the existence of LD and (b) the contrast between allele-specific IBD sharing scores which is informative for linkage only in the presence of LD. We also consider the connection between the LD-lod score method and the transmission-disequilibrium test (TDT) for triad data and the mean test for affected sib pair (ASP) data. We show that, for triad data, the recessive LD-lod test is asymptotically equivalent to the TDT; and for ASP data, it is an adaptive combination of the TDT and the ASP mean test. We demonstrate that the LD-lod score method has relatively good statistical efficiency in comparison with the ASP mean test and the TDT for a broad range of LD and the genetic models considered in this report. Therefore, the LD-lod score method is an interesting approach for detecting linkage when the extent of LD is unknown, such as in a genome-wide screen with a dense set of genetic markers.     

Mapping of a gene determining tuberous sclerosis to human chromosome 11q14-11q23

Tuberous sclerosis (TSC) is a dominantly inherited disorder characterized by hamartomas and hamartias in one or more organs, most often in skin, brain, and kidneys. Analysis of the basic genetic defect in tuberous sclerosis would be greatly expedited by definitive determination of the chromosomal location of the TSC gene or genes. We have carried out genetic linkage studies in 15 TSC families, using 34 polymorphic markers including protein markers and DNA markers. Pairwise lod scores were calculated using LIPED, and multipoint analyses were carried out using MENDEL. In the pairwise linkage analysis, using a penetrance value of 90%, a significant positive lod score was obtained with MCT128.1 (D11S144), 11q22-11q23, Zmax 3.26 at theta = 0.08. The tyrosinase probe TYR (11q14-11q22) gave a maximum lod score of 2.88 at theta = 0. In the multipoint analyses the most likely order is (TYR,TSC)-MCT128.1-HHH172. Homogeneity analysis was carried out using the USERM9 subprogram of MENDEL, which conducts the admixture test of C. Smith (1963, Ann. Hum. Genet. 27: 175-182). This test provided no evidence for genetic heterogeneity (that is, non-11-linked families) in this data set.     

Robust multipoint simultaneous identical-by-descent mapping for two linked loci

A challenging issue in genetic mapping of complex human diseases is localizing disease susceptibility genes when the genetic effects are small to moderate. There are greater complexities when multiple loci are linked to a chromosomal region. Liang et al. [Hum Hered 2001;51:64-78] proposed a robust multipoint method that can simultaneously estimate both the position of a trait locus and its effect on disease status by using affected sib pairs (ASPs). Based on the framework of generalized estimating equations (GEEs), the estimate and standard error of the position of a trait locus are robust to different genetic models. To utilize other relative pairs collected in pedigree data, Schaid et al. [Am J Hum Genet 2005;76:128-138] extended Liang's method to various types of affected relative pairs (ARPs) by two approaches: unconstrained and constrained methods. However, the above methods are limited to situations in which only one trait locus exists on the chromosome of interest. The mean functions are no longer correctly specified when there are multiple causative loci linked to a chromosomal region. To overcome this, Biernacka et al. [Genet Epidemiol 2005;28:33-47] considered the multipoint methods for ASPs to allow for two linked disease genes. We further generalize the approach to cover other types of ARPs. To reflect realistic situations for complex human diseases, we set modest sizes of genetic effects in our simulation. Our results suggest that several hundred independent pedigrees are needed, and markers with high information, to provide reliable estimates of trait locus positions and their confidence intervals. Bootstrap resampling can correct the downward bias of the robust variance for location estimates. These methods are applied to a prostate cancer linkage study on chromosome 20 and compared with the results for the one-locus model [Am J Hum Genet 2005;76:128-138]. We have implemented the multipoint IBD mapping for one and two linked loci in our software GEEARP, which allows analyses for five general types of ARPs.     

A new statistic for the analysis of association between trait and polymorphic marker loci

Inference for detecting the existence of an association between a diallelic marker and a trait locus is based on the chi-squared statistic with one degree of freedom. For polymorphic markers with m alleles (2), three approaches are mainly used in practice. First, one may use Pearson's chi-squared statistic with m-1 degrees of freedom (d.f.) but this leads to a loss in test power. Second, one can select an allele to be the most associated and then collapse the other allele categories into a single class. This reduces in a biased way, the locus to a diallelic system. Third, one may use the Terwilliger [J.D. Terwilliger, Am. J. Hum. Genet. 56 (1995) 777] likelihood ratio statistic which has a non-standard unknown limiting probability distribution. In this paper, we propose a new statistic, L(D), based on the second testing approach. We derive the asymptotic probability distribution of L(D) in an easy way. Simulation studies show that L(D) is more powerful than Pearson's chi-squared statistic with m-1 d.f.     

A second-generation genomic screen for multiple sclerosis

Multiple sclerosis (MS) is a debilitating neuroimmunological and neurodegenerative disorder. Despite substantial evidence for polygenic inheritance of the disease, the major histocompatibility complex is the only region that clearly and consistently demonstrates linkage and association in MS studies. The goal of this study was to identify additional chromosomal regions that harbor susceptibility genes for MS. With a panel of 390 microsatellite markers genotyped in 245 U.S. and French multiplex families (456 affected relative pairs), this is the largest genomic screen for MS conducted to date. Four regions met both of our primary criteria for further interest (heterogeneity LOD [HLOD] and Z scores >2.0): 1q (HLOD=2.17; Z=3.38), 6p (HLOD=4.21; Z=2.26), 9q (HLOD; Z=2.71), and 16p (HLOD=2.64; Z=2.05). Two additional regions met only the Z score criterion: 3q (Z=2.39) and 5q (Z=2.17). Further examination of the data by country (United States vs. France) identified one additional region demonstrating suggestive linkage in the U.S. subset (18p [HLOD=2.39]) and two additional regions generating suggestive linkage in the French subset (1p [HLOD=2.08] and 22q [HLOD=2.06]). Examination of the data by human leukocyte antigen (HLA)-DR2 stratification identified four additional regions demonstrating suggestive linkage: 2q (HLOD=3.09 in the U.S. DR2- families), 6q (HLOD=3.10 in the French DR2- families), 13q (HLOD=2.32 in all DR2+ families and HLOD=2.17 in the U.S. DR2+ families), and 16q (HLOD=2.32 in all DR2+ families and HLOD=2.13 in the U.S. DR2+ families). These data suggest several regions that warrant further investigation in the search for MS susceptibility genes.     

Using lod-score differences to determine mode of inheritance: a simple, robust method even in the presence of heterogeneity and reduced penetrance.

Determining the mode of inheritance is often difficult under the best of circumstances, but when segregation analysis is used, the problems of ambiguous ascertainment procedures, reduced penetrance, heterogeneity, and misdiagnosis make mode-of-inheritance determinations even more unreliable. The mode of inheritance can also be determined using a linkage-based method (maximized maximum lod score or mod score) and association-based methods, which can overcome many of these problems. In this work, we determined how much information is necessary to reliably determine the mode of inheritance from linkage data when heterogeneity and reduced penetrance are present in the data set. We generated data sets under both dominant and recessive inheritance with reduced penetrance and with varying fractions of linked and unlinked families. We then analyzed those data sets, assuming reduced penetrance, both dominant and recessive inheritance, and no heterogeneity. We investigated the reliability of two methods for determining the mode of inheritance from the linkage data. The first method examined the difference (delta) between the maximum lod scores calculated under the two mode-of-inheritance assumptions. We found that if delta was > 1.5, then the higher of the two maximum lod scores reflected the correct mode of inheritance with high reliability and that a delta of 2.5 appeared to practically guarantee a correct mode-of-inheritance inference. Furthermore, this reliability appeared to be virtually independent of alpha, the fraction of linked families in the data set, although the reliability decreased slightly as alpha fell below .50.(ABSTRACT TRUNCATED AT 250 WORDS)     

Colorectal cancer linkage on chromosomes 4q21, 8q13, 12q24, and 15q22

A substantial proportion of familial colorectal cancer (CRC) is not a consequence of known susceptibility loci, such as mismatch repair (MMR) genes, supporting the existence of additional loci. To identify novel CRC loci, we conducted a genome-wide linkage scan in 356 white families with no evidence of defective MMR (i.e., no loss of tumor expression of MMR proteins, no microsatellite instability (MSI)-high tumors, or no evidence of linkage to MMR genes). Families were ascertained via the Colon Cancer Family Registry multi-site NCI-supported consortium (Colon CFR), the City of Hope Comprehensive Cancer Center, and Memorial University of Newfoundland. A total of 1,612 individuals (average 5.0 per family including 2.2 affected) were genotyped using genome-wide single nucleotide polymorphism linkage arrays; parametric and non-parametric linkage analysis used MERLIN in a priori-defined family groups. Five lod scores greater than 3.0 were observed assuming heterogeneity. The greatest were among families with mean age of diagnosis less than 50 years at 4q21.1 (dominant HLOD?=?4.51, α?=?0.84, 145.40 cM, rs10518142) and among all families at 12q24.32 (dominant HLOD?=?3.60, α?=?0.48, 285.15 cM, rs952093). Among families with four or more affected individuals and among clinic-based families, a common peak was observed at 15q22.31 (101.40 cM, rs1477798; dominant HLOD?=?3.07, α?=?0.29; dominant HLOD?=?3.03, α?=?0.32, respectively). Analysis of families with only two affected individuals yielded a peak at 8q13.2 (recessive HLOD?=?3.02, α?=?0.51, 132.52 cM, rs1319036). These previously unreported linkage peaks demonstrate the continued utility of family-based data in complex traits and suggest that new CRC risk alleles remain to be elucidated.     

Common and unique susceptibility loci in Graves and Hashimoto diseases: results of whole-genome screening in a data set of 102 multiplex families

The autoimmune thyroid diseases (AITDs), comprising Graves disease (GD) and Hashimoto thyroiditis (HT), develop as a result of a complex interaction between predisposing genes and environmental triggers. Previously, we identified six loci that showed evidence for linkage with AITD in a data set of 56 multiplex families. The goals of the present study were to replicate/reject the previously identified loci before fine mapping and sequencing the candidate genes in these regions. We performed a whole-genome linkage study in an expanded data set of 102 multiplex families with AITD (540 individuals), through use of 400 microsatellite markers. Seven loci showed evidence for linkage to AITD. Three loci, on chromosomes 6p, 8q, and 10q, showed evidence for linkage with both GD and HT (maximum multipoint heterogeneity LOD scores [HLOD] 2.0, 3.5, and 4.1, respectively). Three loci showed evidence for linkage with GD: on 7q (HLOD 2.3), 14q (HLOD 2.1), and 20q (LOD 3.3, in a subset of the families). One locus on 12q showed evidence of linkage with HT, giving an HLOD of 3.4. Comparison with the results obtained in the original data set showed that the 20q (GD-2) and 12q (HT-2) loci continued to show evidence for linkage in the expanded data set; the 6p and 14q loci were located within the same region as the previously identified 6p and 14q loci (AITD-1 and GD-1, respectively), but the Xq (GD-3) and 13q (HT-1) loci were not replicated in the expanded data set. These results demonstrated that multiple genes may predispose to GD and HT and that some may be common to both diseases and some are unique. The loci that continue to show evidence for linkage in the expanded data set represent serious candidate regions for gene identification.     

The future is now - will the real disease gene please stand up?

The transmission/disequilibrium test (TDT) [Spielman et al.: Am J Hum Genet 1993;52:506-516] has been postulated as the future of gene mapping for complex diseases, provided one is able to genotype a dense enough map of markers across the genome. Risch and Merikangas [Science 1996;273:1516-1517] suggested a million-marker screen in affected sibpair (ASP) families, demonstrating that the TDT is a more powerful test of linkage than traditional linkage tests based on allele-sharing when there is also association between marker and disease alleles. While the future of genotyping has arrived, successes in family-based association studies have been modest. This is often attributed to excessive false positives in candidate gene studies. This problem is only exacerbated by the increasing numbers of whole genome association (WGA) screens. When applied in ASPs, the TDT statistic, which assumes transmissions to siblings are independent, is not expected to have a constant variance in the presence of variable linkage. This results in generally more extreme statistics, hence will further aggravate the problem of having a large number of positive results to sort through. So an important question is how many positive TDT results will show up on a chromosome containing a disease gene due only to linkage, and will they obfuscate the true disease gene location. To answer this question we combined theory and computer simulations. These studies show that in ASPs the normal version of the TDT statistic has a mean of 0 and a variance of 1 in unlinked regions, but has a variance larger than 1 in linked regions. In contrast, the pedigree disequilibrium test (PDT) statistic adjusts for correlation between siblings due to linkage and maintains a constant variance of 1 at unassociated markers irrespective of linkage. The TDT statistic is generally larger than the PDT statistic across linked regions. This is true for unassociated as well as associated markers. To compare the two tests we ranked both statistics at the disease locus, or an associated marker, among statistics at all other markers. The TDT did better job than PDT placing the score of the associated marker near the top. Though, strictly speaking, the TDT in ASPs should be interpreted as a test of linkage and not a test of association, there is a good chance that if a marker stands out, the marker is associated as well as linked. In conclusion, our results suggest that TDT is an effective screening tool for WGA studies, especially in multiplex families.     

Inter- and intrafamilial heterogeneity: effective sampling strategies and comparison of analysis methods.

Heterogeneity, both inter- and intrafamilial, represents a serious problem in linkage studies of common complex diseases. In this study we simulated different scenarios with families who phenotypically have identical diseases but who genotypically have two different forms of the disease (both forms genetic). We examined the proportion of families displaying intrafamilial heterogeneity, as a function of mode of inheritance, gene frequency, penetrance, and sampling strategies. Furthermore, we compared two different ways of analyzing linkage in these data sets: a two-locus (2L) analysis versus a one-locus (SL) analysis combined with an admixture test. Data were simulated with tight linkage between one disease locus and a marker locus; the other disease locus was not linked to a marker. Our findings are as follows: (1) In contrast to what has been proposed elsewhere to minimize heterogeneity, sampling only "high-density" pedigrees will increase the proportion of families with intrafamilial heterogeneity, especially when the two forms are relatively close in frequency. (2) When one form is dominant and one is recessive, this sampling strategy will greatly decrease the proportions of families with a recessive form and may therefore make it more difficult to detect linkage to the recessive form. (3) An SL analysis combined with an admixture test achieves about the same lod scores and estimate of the recombination fraction as does a 2L analysis. Also, a 2L analysis of a sample of families with intrafamilial heterogeneity does not perform significantly better than an SL analysis. (4) Bilineal pedigrees have little effect on the mean maximum lod score and mean maximum recombination fraction, and therefore there is little danger that including these families will lead to a false exclusion of linkage.     

Genome-wide meta-analysis for rheumatoid arthritis

Meta-analysis is being increasingly used as a tool for integrating data from different studies of complex phenotypes, because the power of any one study to identify causal loci is limited. We applied a novel meta-analytical approach (Loesgen et al. in Genet Epidemiol 21(Suppl 1):S142–S147, 2001) in compiling results from four studies of rheumatoid arthritis in Caucasians including two studies from NARAC (Jawaheer et al. in Am J Hum Genet 68:927–936, 2001; Jawaheer et al. in Arthritis Rheum 48:906–916, 2003), one study from the UK (MacKay et al. in Arthritis Rheum 46:632–639, 2001) and one from France (Cornelis et al. in Proc Natl Acad Sci USA 95:10746–10750, 1998). For each study, we obtained NPL scores by performing interval mapping (2 cM intervals) using GeneHunter2 (Kruglyak et al. in Am J Hum Genet 58:1347–1363, 1996; Markianos et al. in Am J Hum Genet 68:963–977, 2001). The marker maps differed among the three consortium groups, therefore, the marker maps were aligned after the interval mapping was completed and the NPL scores that were within 1 cM of each other were combined using the method of Loesgen et al. (Genet Epidemiol 21(Suppl 1):S142–S147, 2001) by calculating the weighted average of the NPL score. This approach avoids some problems in analysis encountered by using GeneHunter2 when some markers in the sample are not genotyped. This procedure provided marginal evidence (P<0.05) of linkage on chromosome 1, 2, 5 and 18, strong evidence (P<0.01) on chromosomes 8 and 16, and overwhelming evidence in the HLA region of chromosome 6.     

A method for evaluating the results of Bayesian model selection: application to linkage analyses of attributes determined by two or more genes

OBJECTIVES: We apply and evaluate the intrinsic Bayes factor (IBF) of Berger and Pericchi [J Am Stat Assoc 1996;91:109-122; Bayesian Statistics, Oxford University Press, vol 5, 1996] to linkage analyses done using the stochastic search variable selection (SSVS) method of George and McCulloch [J Am Stat Assoc 1993;88:881-889] as proposed by Suh et al. [Genet Epidemiol 2001;21(suppl 1):S706-S711]. METHODS: We consider 20 simulations of linkage data obtained under two different generating models. The SSVS is applied to a multiple regression extension [Genet Epidemiol 2001;21(suppl 1): S706-S711] of the Haseman-Elston [Behav Genet 1972;2:3-19; Genet Epidemiol 2000;19:1-17] methods. Four prior distributions are considered. We apply the IBF criterion to those samples where different prior distributions result in different top models. RESULTS: In those samples where three different models were obtained using the four priors, application of the IBFs eliminated one of the two wrong models in 4 out of 5 situations. Further elimination using the IBF criterion for situations with two different subsets did not serve as well. CONCLUSIONS: When different priors result in three or more different subsets of markers, one can use the IBF to get this number down to two for consideration. When two subsets result we recommend that both be considered.     

The importance of modelling heterogeneity in complex disease: application to NIMH Schizophrenia Genetics Initiative data

As for other complex diseases, linkage analyses of schizophrenia (SZ) have produced evidence for numerous chromosomal regions, with inconsistent results reported across studies. The presence of locus heterogeneity appears likely and may reduce the power of linkage analyses if homogeneity is assumed. In addition, when multiple heterogeneous datasets are pooled, inter-sample variation in the proportion of linked families () may diminish the power of the pooled sample to detect susceptibility loci, in spite of the larger sample size obtained. We compare the significance of linkage findings obtained using allele-sharing LOD scores (LOD_exp)—which assume homogeneity—and heterogeneity LOD scores (HLOD) in European American and African American NIMH SZ families. We also pool these two samples and evaluate the relative power of the LOD_exp and two different heterogeneity statistics. One of these (HLOD-P) estimates the heterogeneity parameter only in aggregate data, while the second (HLOD-S) determines separately for each sample. In separate and combined data, we show consistently improved performance of HLOD scores over LOD_exp. Notably, genome-wide significant evidence for linkage is obtained at chromosome 10p in the European American sample using a recessive HLOD score. When the two samples are combined, linkage at the 10p locus also achieves genome-wide significance under HLOD-S, but not HLOD-P. Using HLOD-S, improved evidence for linkage was also obtained for a previously reported region on chromosome 15q. In linkage analyses of complex disease, power may be maximised by routinely modelling locus heterogeneity within individual datasets, even when multiple datasets are combined to form larger samples.     

Phenotypic homogeneity provides increased support for linkage on chromosome 2 in autistic disorder

Autistic disorder (AutD) is a neurodevelopmental disorder characterized by significant disturbances in social, communicative, and behavioral functioning. A two-stage genomic screen analysis of 99 families with AutD revealed suggestive evidence for linkage to chromosome 2q (D2S116 nonparametric sib-pair LOD score [MLS] 1.12 at 198 cM). In addition, analysis of linkage disequilibrium for D2S116 showed an allele-specific P value of <.01. Recently, linkage to the same region of 2q was reported in an independent genome screen. This evidence for linkage increased when analysis was restricted to the subset of patients with AutD who had delayed onset (>36 mo) of phrase speech (PSD). We similarly classified our data set of 82 sib pairs with AutD, identifying 45 families with AutD and PSD. Analysis of this PSD subset increased our support for linkage to 2q (MLS 2.86 and HLOD 2.12 for marker D2S116). These data support evidence for a gene on chromosome 2 contributing to risk of AutD, and they suggest that phenotypic homogeneity increases the power to find susceptibility genes for AutD.     

Joint linkage of multiple loci for a complex disorder.

Many investigators who have been searching for linkage to complex diseases have by now accumulated a drawer full of negative results. If disease is actually caused by genes at several loci, these data might contain multiple-locus system (MLS) information that the investigator does not realize. Trying to obtain this information formally, through the MLS likelihood, leads to severe computational and statistical difficulties. Therefore, we propose a scheme of inference based on single-locus (SL) statistics, considered jointly. By simulation, we find that the MLS lod score is closely approximated by the sum of SL lod scores. However, we also find that for moderately large systems, say three of four loci, both MLS and SL lod scores are likely to be inconclusive. Nonetheless, MLS can often be detected through the correlation of individual pedigree SL lod scores. Significant correlation is itself evidence of an MLS, because, in the absence of linkage, false-positive lod scores are necessarily random. Under epistasis SL lod scores tend to be positively correlated among pedigrees, while under independent action SL lod scores from high-density samples tend to be negatively correlated.