The problem of ascertainment for linkage analysis.

It is generally believed that ascertainment corrections are unnecessary in linkage analysis, provided individuals are selected for study solely on the basis of trait phenotype and not on the basis of marker genotype. The theoretical rationale for this is that standard linkage analytic methods involve conditioning likelihoods on all the trait data, which may be viewed as an application of the ascertainment assumption-free (AAF) method of Ewens and Shute. In this paper, we show that when the observed pedigree structure depends on which relatives within a pedigree happen to have been the probands (proband-dependent, or PD, sampling) conditioning on all the trait data is not a valid application of the AAF method and will result in asymptotically biased estimates of genetic parameters (except under single ascertainment). Furthermore, this result holds even if the recombination fraction R is the only parameter of interest. Since the lod score is proportional to the likelihood of the marker data conditional on all the trait data, this means that when data are obtained under PD sampling the lod score will yield asymptotically biased estimates of R, and that so-called mod scores (i.e., lod scores maximized over both R and parameters theta of the trait distribution) will yield asymptotically biased estimates of R and theta. Furthermore, the problem appears to be intractable, in the sense that it is not possible to formulate the correct likelihood conditional on observed pedigree structure. In this paper we do not investigate the numerical magnitude of the bias, which may be small in many situations. On the other hand, virtually all linkage data sets are collected under PD sampling. Thus, the existence of this bias will be the rule rather than the exception in the usual applications.     

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.     

Trait components provide tools to dissect the genetic susceptibility of migraine

The commonly used "end diagnosis" phenotype that is adopted in linkage and association studies of complex traits is likely to represent an oversimplified model of the genetic background of a disease. This is also likely to be the case for common types of migraine, for which no convincingly associated genetic variants have been reported. In headache disorders, most genetic studies have used end diagnoses of the International Headache Society (IHS) classification as phenotypes. Here, we introduce an alternative strategy; we use trait components--individual clinical symptoms of migraine--to determine affection status in genomewide linkage analyses of migraine-affected families. We identified linkage between several traits and markers on chromosome 4q24 (highest LOD score under locus heterogeneity [HLOD] 4.52), a locus we previously reported to be linked to the end diagnosis migraine with aura. The pulsation trait identified a novel locus on 17p13 (HLOD 4.65). Additionally, a trait combination phenotype (IHS full criteria) revealed a locus on 18q12 (HLOD 3.29), and the age at onset trait revealed a locus on 4q28 (HLOD 2.99). Furthermore, suggestive or nearly suggestive evidence of linkage to four additional loci was observed with the traits phonophobia (10q22) and aggravation by physical exercise (12q21, 15q14, and Xp21), and, interestingly, these loci have been linked to migraine in previous studies. Our findings suggest that the use of symptom components of migraine instead of the end diagnosis provides a useful tool in stratifying the sample for genetic studies.     

A two-stage linkage analysis of Chinese schizophrenia pedigrees in 10 target chromosomes

We performed a two-stage linkage scan involving 25 Chinese schizophrenia families, focusing on 10 target chromosomes which have already been the subject of considerable research. We initially genotyped 237 individuals with 186 markers, five candidate regions were then chosen for fine mapping and 49 additional markers were genotyped. In region 1q21-23, a maximum multipoint HLOD (HLOD=2.38) was observed between D1S484 and D1S2705, under the dominant model. In region 5q35, dominant HOLD of 2.36, 2.04, and 2.31 were found at marker D5S2030, D5S408, and D5S2006, respectively. Consistent multipoint results also supported linkage to this region under the same dominant model, with a highest HOLD of 2.47. Furthermore, single-point HLODs (HLOD=1.95 at D22S274, and HLOD=1.91 at D22S1157) were found in region 22q13, under the dominant model. Evidence from these three regions satisfied the criteria for suggestive linkage and should help in identifying schizophrenia susceptibility genes.     

Combined analysis of hereditary prostate cancer linkage to 1q24-25: results from 772 hereditary prostate cancer families from the International Consortium for Prostate Cancer Genetics

A previous linkage study provided evidence for a prostate cancer-susceptibility locus at 1q24-25. Subsequent reports in additional collections of families have yielded conflicting results. In addition, evidence for locus heterogeneity has been provided by the identification of other putative hereditary prostate cancer loci on Xq27-28, 1q42-43, and 1p36. The present study describes a combined analysis for six markers in the 1q24-25 region in 772 families affected by hereditary prostate cancer and ascertained by the members of the International Consortium for Prostate Cancer Genetics (ICPCG) from North America, Australia, Finland, Norway, Sweden, and the United Kingdom. Overall, there was some evidence for linkage, with a peak parametric multipoint LOD score assuming heterogeneity (HLOD) of 1.40 (P=.01) at D1S212. The estimated proportion of families (alpha) linked to the locus was.06 (1-LOD support interval.01-.12). This evidence was not observed by a nonparametric approach, presumably because of the extensive heterogeneity. Further parametric analysis revealed a significant effect of the presence of male-to-male disease transmission within the families. In the subset of 491 such families, the peak HLOD was 2.56 (P=.0006) and alpha =.11 (1-LOD support interval.04-.19), compared with HLODs of 0 in the remaining 281 families. Within the families with male-to-male disease transmission, alpha increased with the early mean age at diagnosis (<65 years, alpha =.19, with 1-LOD support interval.06-.34) and the number of affected family members (five or more family members, alpha =.15, with 1-LOD support interval.04-.28). The highest value of alpha was observed for the 48 families that met all three criteria (peak HLOD = 2.25, P=.001, alpha=.29, with 1-LOD support interval.08-.53). These results support the finding of a prostate cancer-susceptibility gene linked to 1q24-25, albeit in a defined subset of prostate cancer families. Although HPC1 accounts for only a small proportion of all families affected by hereditary prostate cancer, it appears to play a more prominent role in the subset of families with several members affected at an early age and with male-to-male disease transmission.     

Linkage Analysis in Familial Non-Lynch Syndrome Colorectal Cancer Families from Sweden

Family history is a major risk factor for colorectal cancer and many families segregate the disease as a seemingly monogenic trait. A minority of familial colorectal cancer could be explained by known monogenic genes and genetic loci. Familial polyposis and Lynch syndrome are two syndromes where the predisposing genes are known but numerous families have been tested without finding the predisposing gene. We performed a genome wide linkage analysis in 121 colorectal families with an increased risk of colorectal cancer. The families were ascertained from the department of clinical genetics at the Karolinska University Hospital in Stockholm, Sweden and were considered negative for Familial Polyposis and Lynch syndrome. In total 600 subjects were genotyped using single nucleotide polymorphism array chips. Parametric- and non-parametric linkage analyses were computed using MERLIN in all and subsets of families. No statistically significant result was seen, however, there were suggestive positive HLODs above two in parametric linkage analysis. This was observed in a recessive model for high-risk families, at locus 9q31.1 (HLOD=2.2, rs1338121) and for moderate-risk families, at locus Xp22.33 (LOD=2.2 and HLOD=2.5, rs2306737). Using families with early-onset, recessive analysis suggested one locus on 4p16.3 (LOD=2.2, rs920683) and one on 17p13.2 (LOD/HLOD=2.0, rs884250). No NPL score above two was seen for any of the families. Our linkage study provided additional support for the previously suggested region on chromosome 9 and suggested additional loci to be involved in colorectal cancer risk. Sequencing of genes in the regions will be done in future studies.     

Comparison of 'model-free' and 'model-based' linkage statistics in the presence of locus heterogeneity: single data set and multiple data set applications

Earlier work [Knapp et al.: Hum Hered 1994;44:44-51] focusing on affected sib pair (ASP) data established the equivalence between the mean test and a test based on a simple recessive lod score, as well as equivalences between certain forms of the maximum likelihood score (MLS) statistic [Risch: Am J Hum Genet 1990;46:242-253] and particular forms of the lod score. Here we extend the results of Knapp et al. [1994] by reconsidering these equivalences for ASP data, but in the presence of locus heterogeneity. We show that Risch's MLS statistic under the possible triangle constraints [Holmans: Am J Hum Genet 1993;52:362-374] is locally equivalent to the ordinary heterogeneity lod score assuming a simple recessive model (HLOD/R); while the one-parameter MLS assuming no dominance variance is locally equivalent to the (homogeneity) recessive lod. The companion paper (this issue, pp 199-208) showed that when considering multiple data sets in the presence of locus heterogeneity, the HLOD can suffer appreciable losses in power. We show here that in ASP data, these equivalences ensure that this same loss in power is incurred by both forms of the MLS statistic as well. The companion paper also introduced an adaptation of the lod, the compound lod score (HLOD/C). We confirm that the HLOD/C maintains higher power than these 'model-free' methods when applied to multiple heterogeneous data sets, even when it is calculated assuming the wrong genetic model.     

Genome-wide high-density SNP-based linkage analysis of infantile hypertrophic pyloric stenosis identifies loci on chromosomes 11q14-q22 and Xq23

Infantile hypertrophic pyloric stenosis (IHPS) has an incidence of 1-8 per 1000 live births and is inherited as a complex sex-modified multifactorial trait with a striking male preponderance. Syndromic and monogenic forms exist, and two loci have been identified. Infants present with vomiting due to gastric-outlet obstruction caused by hypertrophy of the smooth muscle of the pylorus. A genome-wide SNP-based high-density linkage scan was carried out on 81 IHPS pedigrees. Nonparametric and parametric linkage analysis identified loci on chromosomes 11q14-q22 (Z(max) = 3.9, p < 0.0001; HLOD(max) = 3.4, alpha = 0.34) and Xq23 (Z(max) = 4.3, p < 0.00001; HLOD(max) = 4.8, alpha = 0.56). The two linked chromosomal regions each harbor functional candidate genes that are members of the canonical transient receptor potential (TRPC) family of ion channels and have a potential role in smooth-muscle control and hypertrophy.     

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.     

Detection of linkage for heterogeneous disorders by using multipoint linkage analysis.

We have compared the efficiency of the lod score test which assumes heterogeneity (lod2) to the standard lod score test which assumes homogeneity (lod1) when three-point linkage analysis is used in successive map intervals. If it is assumed that a gene located midway between two linked marker loci is responsible for a proportion of disease cases, then the lod1 test loses power relative to the lod2 test, as the proportion of linked families decreases, as the flanking markers are more closely linked, and as more map intervals are tested. Moreover, when multipoint analysis is used, linkage for a disease gene is more likely to be incorrectly excluded from a complete and dense linkage map if true genetic heterogeneity is ignored. We thus conclude that, in general, the lod2 linkage test is more efficient for detecting a true linkage when a complete genetic marker map is screened for a heterogeneous disorder.     

An alternative foundation for the planning and evaluation of linkage analysis. I. Decoupling "error probabilities" from "measures of evidence"

The lod score, which is based on the likelihood ratio (LR), is central to linkage analysis. Users interpret lods by translating them into standard statistical concepts such as p values, alpha levels and power. An alternative statistical paradigm, the Evidential Framework, in contrast, works directly with the LR. A key feature of this paradigm is that it decouples error probabilities from measures of evidence. We describe the philosophy behind and the operating characteristics of this paradigm--based on new, alternatively-defined error probabilities. We then apply this approach to linkage studies of a genetic trait for: I. fully informative gametes, II. double backcross sibling pairs, and III. nuclear families. We consider complete and incomplete penetrance for the disease model, as well as using an incorrect penetrance. We calculate the error probabilities (exactly for situations I and II, via simulation for III), over a range of recombination fractions, sample sizes, and linkage criteria. We show how to choose linkage criteria and plan linkage studies, such that the probabilities of being misled by the data (i.e. concluding either that there is strong evidence favouring linkage when there is no linkage, or that there is strong evidence against linkage when there is linkage) are low, and the probability of observing strong evidence in favour of the truth is high. We lay the groundwork for applying this paradigm in genetic studies and for understanding its implications for multiple tests.     

Two-locus models of disease: comparison of likelihood and nonparametric linkage methods.

The power to detect linkage for likelihood and nonparametric (Haseman-Elston, affected-sib-pair, and affected-pedigree-member) methods is compared for the case of a common, dichotomous trait resulting from the segregation of two loci. Pedigree data for several two-locus epistatic and heterogeneity models have been simulated, with one of the loci linked to a marker locus. Replicate samples of 20 three-generation pedigrees (16 individuals/pedigree) were simulated and then ascertained for having at least 6 affected individuals. The power of linkage detection calculated under the correct two-locus model is only slightly higher than that under a single locus model with reduced penetrance. As expected, the nonparametric linkage methods have somewhat lower power than does the lod-score method, the difference depending on the mode of transmission of the linked locus. Thus, for many pedigree linkage studies, the lod-score method will have the best power. However, this conclusion depends on how many times the lod score will be calculated for a given marker. The Haseman-Elston method would likely be preferable to calculating lod scores under a large number of genetic models (i.e., varying both the mode of transmission and the penetrances), since such an analysis requires an increase in the critical value of the lod criterion. The power of the affected-pedigree-member method is lower than the other methods, which can be shown to be largely due to the fact that marker genotypes for unaffected individuals are not used.     

Model-free linkage analysis using likelihoods.

Misspecification of transmission model parameters can produce artifactually negative lod scores at small recombination fractions and in multipoint analysis. To avoid this problem, we have tried to devise a test that aims to detect a genetic effect at a particular locus, rather than attempting to estimate the map position of a locus with specified effect. Maximizing likelihoods over transmission model parameters, as well as linkage parameters, can produce seriously biased parameter estimates and so yield tests that lack power for the detection of linkage. However, constraining the transmission model parameters to produce the correct population prevalence largely avoids this problem. For computational convenience, we recommend that the likelihoods under linkage and non-linkage are independently maximized over a limited set of transmission models, ranging from Mendelian dominant to null effect and from null effect to Mendelian recessive. In order to test for a genetic effect at a given map position, the likelihood under linkage is maximized over admixture, the proportion of families linked. Application to simulated data for a wide range of transmission models in both affected sib pairs and pedigrees demonstrates that the new method is well behaved under the null hypothesis and provides a powerful test for linkage when it is present. This test requires no specification of transmission model parameters, apart from an approximate estimate of the population prevalence. It can be applied equally to sib pairs and pedigrees, and, since it does not diminish the lod score at test positions very close to a marker, it is suitable for application to multipoint data.     

Evidence for linkage of migraine in Rolandic epilepsy to known 1q23 FHM2 and novel 17q22 genetic loci

Migraine headaches are a common comorbidity in Rolandic epilepsy (RE) and familial aggregation of migraine in RE families suggests a genetic basis not mediated by seizures. We performed a genome‐wide linkage analysis of the migraine phenotype in 38 families with RE to localize potential genetic contribution, with a follow‐up in an additional 21 families at linked loci. We used two‐point and multipoint LOD (logarithm of the odds) score methods for linkage, maximized over genetic models. We found evidence of linkage to migraine at chromosome 17q12‐22 [multipoint HLOD (heterogeneity LOD) 4.40, recessive, 99% penetrance], replicated in the second dataset (HLOD 2.61), and suggestive evidence at 1q23.1‐23.2, centering over the FHM2 locus (two‐point LOD 3.00 and MP HLOD 2.52). Sanger sequencing in 14 migraine‐affected individuals found no coding mutations in the FHM2 gene ATP1A2. There was no evidence of pleiotropy for migraine and either reading or speech disorder, or the electroencephalographic endophenotype of RE when the affected definition was redefined as those with migraine or the comorbid phenotype, and pedigrees were reanalyzed for linkage. In summary, we report a novel migraine susceptibility locus at 17q12‐22, and a second locus that may contribute to migraine in the general population at 1q23.1‐23.2. Comorbid migraine in RE appears genetically influenced, but we did not obtain evidence that the identified susceptibility loci are consistent with pleiotropic effects on other comorbidities in RE. Loci identified here should be fine‐mapped in individuals from RE families with migraine, and prioritized for analysis in other types of epilepsy‐associated migraine.     

Power of maximum HLOD tests to detect linkage to obesity genes

Background

We investigate the power of heterogeneity LOD test to detect linkage when a trait is determined by several major genes using Genetic Analysis Workshop 13 simulated data. We consider three traits, two of which are disease-causing traits: 1) the rate of change in body mass index (BMI); and 2) the maximum BMI; and 3) the disease itself (hypertension). Of interest is the power of "HLOD2", the maximum heterogeneity LOD obtained upon maximizing over the two genetic models.

Results

Using a trait phenotype Obesity Slope, we observe that the power to detect the two markers closest to the two genes (S1, S2) at the 0.05 level using HLOD2 is 13% and 10%. The power of HLOD2 for Max BMI phenotype is 12% and 9%. The corresponding values for the Hypertension phenotype are 8% and 6%.

Conclusion

The power to detect linkage to the slope genes is quite low. But the power using disease-related traits as a phenotype is greater than the power using the disease (hypertension) phenotype.

     

Family-based tests of association and linkage that use unaffected sibs, covariates, and interactions

We extend the methodology for family-based tests of association and linkage to allow for both variation in the phenotypes of subjects and incorporation of covariates into general-score tests of association. We use standard association models for a phenotype and any number of predictors. We then construct a score statistic, using likelihoods for the distribution of phenotype, given genotype. The distribution of the score is computed as a function of offspring genotypes, conditional on parental genotypes and trait values for offspring and parents. This approach provides a natural extension of the transmission/disequilibrium test to any phenotype and to multiple genes or environmental factors and allows the study of gene-gene and gene-environment interaction. When the trait varies among subjects or when covariates are included in the association model, the score statistic depends on one or more nuisance parameters. We suggest two approaches for obtaining parameter estimates: (1) choosing the estimate that minimizes the variance of the test statistic and (2) maximizing the statistic over a nuisance parameter and using a corrected P value. We apply our methods to a sample of families with attention-deficit/hyperactivity disorder and provide examples of how covariates and gene-environment and gene-gene interactions can be incorporated.     

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)     

Determining the sample size for co-dominant molecular marker-assisted linkage detection for a monogenic qualitative trait by controlling the type-I and type-II errors in a segregating F2 population

Tests for linkage are usually performed using the lod score method. A critical question in linkage analyses is the choice of sample size. The appropriate sample size depends on the desired type-I error and power of the test. This paper investigates the exact type-I error and power of the lod score method in a segregating F(2) population with co-dominant markers and a qualitative monogenic dominant-recessive trait. For illustration, a disease-resistance trait is considered, where the susceptible allele is recessive. A procedure is suggested for finding the appropriate sample size. It is shown that recessive plants have about twice the information content of dominant plants, so the former should be preferred for linkage detection. In some cases the exact alpha-values for a given nominal alpha may be rather small due to the discrete nature of the sampling distribution in small samples. We show that a gain in power is possible by using exact methods.     

Linkage analysis of the apolipoprotein C2 gene and myotonic dystrophy on human chromosome 19 reveals linkage disequilibrium in a French-Canadian population.

The gene for human apolipoprotein C2 (APOC2), situated on the proximal long arm of chromosome 19, is closely linked to the gene for the most common form of adult muscular dystrophy, myotonic dystrophy (DM). Six APOC2 RFLPs (TaqI, BglI, BanI, BamHI, NcoI, and AvaII) have been identified to date. We have conducted a comprehensive DM linkage study utilizing all six RFLPs and involving 50 families and 372 individuals. The most informative RFLPs are, in descending order, NcoI (lod = 6.64, theta = 0.05), BglI (lod = 6.12, theta = 0.05), AvaII (lod = 6.02, theta = 0.03), BanI (lod = 5.76, theta = 0.04), TaqI (lod = 4.29, theta = 0.06), and BamHI (lod = 1.75, theta = 0.01). A substantial increase in the lod scores over those seen with the individual RFLPs was obtained when the linkage of the entire APOC2 haplotype (composed of the six RFLPs) was studied (lod = 17.87, theta = 0.04). We have observed significant inter-APOC2 RFLP linkage disequilibrium. Consequently, the three most informative RFLPs have been found to be BanI, TaqI, and either BglI, AvaII, or NcoI polymorphisms. We also demonstrate linkage disequilibrium between DM and APOC2 in our French-Canadian population (standardized disequilibrium constant phi = .22, chi 2 = 5.12, df = 1, P less than 0.04). This represents the first evidence of linkage disequilibrium between APOC2 and the DM locus.     

Estimating the power of a proposed linkage study for a complex genetic trait.

Many genetic traits have complex modes of inheritance; they may exhibit incomplete or age-dependent penetrance or fail to show any clear Mendelian inheritance pattern. As primary linkage maps for the human genome near completion, it is becoming increasingly possible to map these traits. Prior to undertaking a linkage study, it is important to consider whether the pedigrees available for the proposed study are likely to provide sufficient information to demonstrate linkage, assuming a linked marker is tested. In the current paper, we describe a computer simulation method to estimate the power of a proposed study to detect linkage for a complex genetic trait, given a hypothesized genetic model for the trait. Our method simulates trait locus genotypes consistent with observed trait phenotypes, in such a way that the probability to detect linkage can be estimated by sample statistics of the maximum lod score distribution. The method uses terms available when calculating the likelihood of the trait phenotypes for the pedigree and is applicable to any trait determined by one or a few genetic loci; individual-specific environmental effects can also be dealt with. Our method provides an objective answer to the question, Will these pedigrees provide sufficient information to map this complex genetic trait?