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PubMed1994

Pseudoautosomal region in schizophrenia: linkage analysis of seven loci by sib-pair and lod-score methods.

In a previous study, we reported a nonrandom segregation between schizophrenia and the pseudoautosomal locus DXYS14 in a sample of 33 sibships. That study has been extended by the addition of 16 new sibships from 16 different families. Data from six other loci of the pseudoautosomal region and of the immediately adjacent part of the X specific region have also been analyzed. Two methods of linkage analysis were used: the affected sibling pair (ASP) method and the lod-score method. Lod-score analyses were performed on the basis of three different models--A, B, and C--all shown to be consistent with the epidemiological data on schizophrenia. No clear evidence for linkage was obtained with any of these models. However, whatever the genetic model and the disease classification, maximum lod scores were positive with most of the markers, with the highest scores generally being obtained for the DXYS14 locus. When the ASP method was used, the earlier finding of nonrandom segregation between schizophrenia and the DXYS14 locus was still supported in this larger data set, at an increased level of statistical significance. Findings of ASP analyses were not significant for the other loci. Thus, findings obtained from analyses using the ASP method, but not the lod-score method, were consistent with the pseudoautosomal hypothesis for schizophrenia.

Family↗
PubMed1984

Possible linkage of a breast cancer-susceptibility locus to the ABO locus: sensitivity of LOD scores to a single new recombinant observation.

We present evidence of a pedigree in which a major gene for breast cancer-susceptibility appears to segregate in a dominant fashion. Linkage analysis suggests that the breast cancer-susceptibility locus in this family may be linked to the ABO locus, which is located on band q34 of chromosome 9. At an early stage in the analysis, a LOD score of 3.0 for zero recombination was obtained for linkage between ABO and the susceptibility locus, but a single recombinant reduced the LOD score to 1.72 at a recombination fraction of 0.06. A final observation of a nonrecombinant brings the LOD score for this pedigree to 1.99 at theta = 0.05. We attempt to put these results in perspective by discussing the sensitivity of the LOD score to the next observation. Examples of the volatility of LOD scores are given. These simple calculations show that tight linkage represents the worst case for the interpretation of a LOD score of 3.0. Finally, we discuss the linkage between the breast cancer-susceptibility locus and the ABO blood group and approaches to confirming or denying this result.

ABO Blood-Group System↗
PubMed1996

Conclusion of LOD-score analysis for family data generated under two-locus models.

The power to detect linkage by the LOD-score method is investigated here for diseases that depend on the effects of two genes. The classical strategy is, first, to detect a major-gene (MG) effect by segregation analysis and, second, to seek for linkage with genetic markers by the LOD-score method using the MG parameters. We already showed that segregation analysis can lead to evidence for a MG effect for many two-locus models, with the estimates of the MG parameters being very different from those of the two genes involved in the disease. We show here that use of these MG parameter estimates in the LOD-score analysis may lead to a failure to detect linkage for some two-locus models. For these models, use of the sib-pair method gives a non-negligible increase of power to detect linkage. The linkage-homogeneity test among subsamples differing for the familial disease distribution provides evidence of parameter misspecification, when the MG parameters are used. Moreover, for most of the models, use of the MG parameters in LOD-score analysis leads to a large bias in estimation of the recombination fraction and sometimes also to a rejection of linkage for the true recombination fraction. A final important point is that a strong evidence of an MG effect, obtained by segregation analysis, does not necessarily imply that linkage will be detected for at least one of the two genes, even with the true parameters and with a close informative marker.

Alleles↗
PubMed1999

Comparison of empirical strategies to maximize GENEHUNTER lod scores.

We compare four strategies for finding the settings of genetic parameters that maximize the lod scores reported in GENEHUNTER 1.2. The four strategies are iterated complete factorial designs, iterated orthogonal Latin hypercubes, evolutionary operation, and numerical optimization. The genetic parameters that are set are the phenocopy rate, penetrance, and disease allele frequency; both recessive and dominant models are considered. We selected the optimization of a recessive model on the Collaborative Study on the Genetics of Alcoholism (COGA) data of chromosome 1 for complete analysis. Convergence to a setting producing a local maximum required the evaluation of over 100 settings (for a time budget of 800 minutes on a Pentium II 300 MHz PC). Two notable local maxima were detected, suggesting the need for a more extensive search before claiming that a global maximum had been found. The orthogonal Latin hypercube design was the best strategy for finding areas that produced high lod scores with small numbers of evaluations. Numerical optimization starting from a region producing high lod scores was the strategy that found the highest maximum observed.

Alcoholism↗
PubMed1999

Direct power comparisons between simple LOD scores and NPL scores for linkage analysis in complex diseases.

Several methods have been proposed for linkage analysis of complex traits with unknown mode of inheritance. These methods include the LOD score maximized over disease models (MMLS) and the "nonparametric" linkage (NPL) statistic. In previous work, we evaluated the increase of type I error when maximizing over two or more genetic models, and we compared the power of MMLS to detect linkage, in a number of complex modes of inheritance, with analysis assuming the true model. In the present study, we compare MMLS and NPL directly. We simulated 100 data sets with 20 families each, using 26 generating models: (1) 4 intermediate models (penetrance of heterozygote between that of the two homozygotes); (2) 6 two-locus additive models; and (3) 16 two-locus heterogeneity models (admixture alpha = 1.0,.7,.5, and.3; alpha = 1.0 replicates simple Mendelian models). For LOD scores, we assumed dominant and recessive inheritance with 50% penetrance. We took the higher of the two maximum LOD scores and subtracted 0.3 to correct for multiple tests (MMLS-C). We compared expected maximum LOD scores and power, using MMLS-C and NPL as well as the true model. Since NPL uses only the affected family members, we also performed an affecteds-only analysis using MMLS-C. The MMLS-C was both uniformly more powerful than NPL for most cases we examined, except when linkage information was low, and close to the results for the true model under locus heterogeneity. We still found better power for the MMLS-C compared with NPL in affecteds-only analysis. The results show that use of two simple modes of inheritance at a fixed penetrance can have more power than NPL when the trait mode of inheritance is complex and when there is heterogeneity in the data set.

Gene Frequency↗
PubMed1990

Measuring the inflation of the lod score due to its maximization over model parameter values in human linkage analysis.

A computer-simulation method is presented for determining and correcting for the effect of maximizing the lod score over disease definitions, penetrance values, and perhaps other model parameters. The method consists of simulating the complete analysis using marker genotypes randomly generated under the assumption of free recombination. It is applicable as a "post-treatment" to linkage analyses of any trait with an uncertain mode of inheritance and/or disease definition. When the method is applied to a linkage analysis of schizophrenia versus chromosome 5 markers, we find that, in this specific case, the P-value associated with a maximum lod score of 3 is equal to 0.0003. We also find that a lod score of 3.0 should be "deflated" by approximately 0.3 to 1 units, and, by tentative extrapolation, the observed lod score of 6.5 should be "deflated" by 0.7 to 1.5 units.

Chromosomes, Human, Pair 5↗
PubMedDate not supplied

A procedure for combining two-point lod scores into a summary multipoint map.

Multipoint linkage analysis can be extremely demanding in terms of computer time and memory, and these requirements rise exponentially with the number of markers used. A method is described for producing a rapid approximation to a multipoint analysis from the supplied results of two-point analyses with each marker. The method depends on regarding the lod scores as if they were obtained from a number of independent phase-known meioses, and making estimates concerning the proportion of all meioses which are likely to be informative for each marker. It then becomes possible to estimate the amount of information from each marker or pair of markers which is independent of information from other markers. The lod scores arising from independent contributions may then be summed to approximate the true multipoint lod score. The method has been implemented in a computer program called FASTMAP which is freely available. It has been tested on a variety of simulated and real data. In most circumstances it performs well, with a high correlation between the estimated and true multipoint lod score and little bias. However occasionally the results of the estimate deviate markedly from the multipoint lod score, especially at map positions very close to the markers. The overall usefulness of the method will therefore need to be further evaluated, but it does seem adequate at least for building exclusion maps and carrying out preliminary and exploratory analyses.

Bipolar Disorder↗
PubMed1985

Efficiency of lod scores for representing multiple locus linkage data.

The problem of compact, fully efficient representation of multilocus data has not yet been solved. Lod scores can be used to map multilocus data, but because of certain statistical problems, this method loses some information. However, simulation studies show that for distances less than 10 or 20 cMo, where there is little danger of huge overestimates of distance, the lod score method yields estimators just as good as maximum likelihood (ML). Since short distances are the most important, the lod method is quite efficient. Its main drawback is misrepresentation of the likelihood under wrong gene orders. This problem can be ameliorated with a single multipoint calculation under each order. Thus, representation of multipoint data with lod scores can be very practical.

Biometry↗
PubMed2004

A quantitative trait locus mixture model that avoids spurious LOD score peaks.

In standard interval mapping of quantitative trait loci (QTL), the QTL effect is described by a normal mixture model. At any given location in the genome, the evidence of a putative QTL is measured by the likelihood ratio of the mixture model compared to a single normal distribution (the LOD score). This approach can occasionally produce spurious LOD score peaks in regions of low genotype information (e.g., widely spaced markers), especially if the phenotype distribution deviates markedly from a normal distribution. Such peaks are not indicative of a QTL effect; rather, they are caused by the fact that a mixture of normals always produces a better fit than a single normal distribution. In this study, a mixture model for QTL mapping that avoids the problems of such spurious LOD score peaks is presented.

Genetic Techniques↗
PubMed2003

LOD score exclusion analyses for candidate QTLs using random population samples.

While extensive analyses have been conducted to test for, no formal analyses have been conducted to test against, the importance of candidate genes as putative QTLs using random population samples. Previously, we developed an LOD score exclusion mapping approach for candidate genes for complex diseases. Here, we extend this LOD score approach for exclusion analyses of candidate genes for quantitative traits. Under this approach, specific genetic effects (as reflected by heritability) and inheritance models at candidate QTLs can be analyzed and if an LOD score is < or = -2.0, the locus can be excluded from having a heritability larger than that specified. Simulations show that this approach has high power to exclude a candidate gene from having moderate genetic effects if it is not a QTL and is robust to population admixture. Our exclusion analysis complements association analysis for candidate genes as putative QTLs in random population samples. The approach is applied to test the importance of Vitamin D receptor (VDR) gene as a potential QTL underlying the variation of bone mass, an important determinant of osteoporosis.

Bone Density↗
PubMed1980

Application of the lod score method to detection of linkage between HLA and juvenile insulin-dependent diabetes.

The lod score method has been applied to 28 informative families with at least one child suffering from juvenile insulin-dependent diabetes (JIDD), assuming autosomal recessive inheritance, for detection of linkage between HLA and a susceptibility locus for this disease. These 28 families were pooled with 21 other families from the literature. The maximum lod scores were obtained for recombination fractions from 4 to 16%, according to the level of penetrance (10 to 90%). These high estimates of the recombination fraction are not in agreement with the hypothesis that the association between JIDD and specific HLA haplotypes is due to a simple linkage disequilibrium between the HLA region and a susceptibility locus for JIDD.

Chromosome Mapping↗
PubMed1992

Effect of heterogeneity and assumed mode of inheritance on lod scores.

Heterogeneity is a major factor in many common, complex diseases and can confound linkage analysis. Using computer-simulated heterogeneous data we tested what effect unlinked families have on a linkage analysis when heterogeneity is not taken into account. We created 60 data sets of 40 nuclear families each with different proportions of linked and unlinked families and with different modes of inheritance. The ascertainment probability was 0.05, the disease had a penetrance of 0.6, and the recombination fraction for the linked families was zero. For the analysis we used a variety of assumed modes of inheritance and penetrances. Under these conditions we looked at the effect of the unlinked families on the lod score, the evaluation of the mode of inheritance, and the estimate of penetrance and of the recombination fraction in the linked families. 1. When the analysis was done under the correct mode of inheritance for the linked families, we found that the mode of inheritance of the unlinked families had minimal influence on the highest maximum lod score (MMLS) (i.e., we maximized the maximum lod score with respect to penetrance). Adding sporadic families decreased the MMLS less than adding recessive or dominant unlinked families. 2. The mixtures of dominant linked families with unlinked families always led to a higher MMLS when analyzed under the correct (dominant) mode of inheritance than when analyzed under the incorrect mode of inheritance. In the mixtures with recessive linked families, assuming the correct mode of inheritance generally led to a higher MMLS, but we observed broad variation.(ABSTRACT TRUNCATED AT 250 WORDS)

Genetic Linkage↗
PubMed2001

Effect of misspecification of gene frequency on the two-point LOD score.

In this study, we used computer simulation of simple and complex models to ask: (1) What is the penalty in evidence for linkage when the assumed gene frequency is far from the true gene frequency? (2) If the assumed model for gene frequency and inheritance are misspecified in the analysis, can this lead to a higher maximum LOD score than that obtained under the true parameters? Linkage data simulated under simple dominant, recessive, dominant and recessive with reduced penetrance, and additive models, were analysed assuming a single locus with both the correct and incorrect dominance model and assuming a range of different gene frequencies. We found that misspecifying the analysis gene frequency led to little penalty in maximum LOD score in all models examined, especially if the assumed gene frequency was lower than the generating one. Analysing linkage data assuming a gene frequency of the order of 0.01 for a dominant gene, and 0.1 for a recessive gene, appears to be a reasonable tactic in the majority of realistic situations because underestimating the gene frequency, even when the true gene frequency is high, leads to little penalty in the LOD score.

Computer Simulation↗
PubMed1994

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)

Female↗
PubMed1995

An extension of the Maximum Lod Score method to X-linked loci.

The Maximum Lod Score method for affected relative-pair analysis, introduced by Risch, is a powerful method for detecting linkage between an autosomal marker locus and disease. In order to use the method to detect linkage to markers on the X-chromosome, some modification is necessary. Here we extend the method to be applicable to X-chromosomal data, and derive genetic restrictions on the haplotype-sharing probabilities analogous to the 'possible triangle' restrictions described by Holmans for the autosomal case. Size criteria are derived using asymptotic theory and simulation, and the power is calculated for a number of possible underlying models. The method is applied to data from 284 type 1 diabetic families and evidence is found for the presence of one or more diabetogenic loci on the X-chromosome.

Alleles↗
PubMed2001

Distribution of lod scores in oligogenic linkage analysis.

In variance component oligogenic linkage analysis it can happen that the residual additive genetic variance bounds to zero when estimating the effect of the ith quantitative trait locus. Using quantitative trait Q1 from the Genetic Analysis Workshop 12 simulated general population data, we compare the observed lod scores from oligogenic linkage analysis with the empirical lod score distribution under a null model of no linkage. We find that zero residual additive genetic variance in the null model alters the usual distribution of the likelihood-ratio statistic.

Chromosome Mapping↗
PubMed2001

LOD score exclusion analyses for candidate genes using random population samples.

While extensive analyses have been conducted to test for, no formal analyses have been conducted to test against, the importance of candidate genes with random population samples. We develop a LOD score approach for exclusion analyses of candidate genes with random population samples. Under this approach, specific genetic effects and inheritance models at candidate genes can be analysed and if a LOD score is < or = - 2.0, the locus can be excluded from having an effect larger than that specified. Computer simulations show that, with sample sizes often employed in association studies, this approach has high power to exclude a gene from having moderate genetic effects. In contrast to regular association analyses, population admixture will not affect the robustness of our analyses; in fact, it renders our analyses more conservative and thus any significant exclusion result is robust. Our exclusion analysis complements association analysis for candidate genes in random population samples and is parallel to the exclusion mapping analyses that may be conducted in linkage analyses with pedigrees or relative pairs. The usefulness of the approach is demonstrated by an application to test the importance of vitamin D receptor and estrogen receptor genes underlying the differential risk to osteoporotic fractures.

Alleles↗
PubMedDate not supplied

Linkage analysis in nuclear families. 2: Relationship between affected sib-pair tests and lod score analysis.

It is believed that the main advantage of affected sib-pair tests is that their application requires no information about the underlying genetic mechanism of the disease. However, here it is proved that the mean test, which can be considered the most prominent of the affected sib-pair tests, is equivalent to lod score analysis for an assumed recessive mode of inheritance, irrespective of the true mode of the disease. Further relationships of certain sib-pair tests and lod score analysis under specific assumed genetic modes are investigated.

Data Interpretation, Statistical↗