-
Advances in Genetics 2001The lod score method originated in a seminal article by Newton Morton in 1955. The method is broadly concerned with issues of power and the posterior probability of... (Review)
Review
The lod score method originated in a seminal article by Newton Morton in 1955. The method is broadly concerned with issues of power and the posterior probability of linkage, ensuring that a reported linkage has a high probability of being a true linkage. In addition, the method is sequential, so that pedigrees or lod curves may be combined from published reports to pool data for analysis. This approach has been remarkably successful for 50 years in identifying disease genes for Mendelian disorders. After discussing these issues, we consider the situation for complex disorders, where the maximum lod score (MLS) statistic shares some of the advantages of the traditional lod score approach but is limited by unknown power and the lack of sharing of the primary data needed to optimally combine analytic results. We may still learn from the lod score method as we explore new methods in molecular biology and genetic analysis to utilize the complete human DNA sequence and the cataloging of all human genes.
Topics: Genetic Linkage; Humans; Lod Score; Mathematical Computing; Meta-Analysis as Topic; Probability Theory; Quantitative Trait, Heritable; Research Design
PubMed: 11037316
DOI: 10.1016/s0065-2660(01)42017-7 -
Advances in Genetics 2001In 1955 Morton proposed the lod score method both for testing linkage between loci and for estimating the recombination fraction between them. If a disease is controlled... (Review)
Review
In 1955 Morton proposed the lod score method both for testing linkage between loci and for estimating the recombination fraction between them. If a disease is controlled by a gene at one of these loci, the lod score computation requires the prior specification of an underlying model that assigns the probabilities of genotypes from the observed phenotypes. To address the case of linkage studies for diseases with unknown mode of inheritance, we suggested (Clerget-Darpoux et al., 1986) extending the lod score function to a so-called mod score function. In this function, the variables are both the recombination fraction and the disease model parameters. Maximizing the mod score function over all these parameters amounts to maximizing the probability of marker data conditional on the disease status. Under the absence of linkage, the mod score conforms to a chi-square distribution, with extra degrees of freedom in comparison to the lod score function (MacLean et al., 1993). The mod score is asymptotically maximum for the true disease model (Clerget-Darpoux and Bonaïti-Pellié, 1992; Hodge and Elston, 1994). Consequently, the power to detect linkage through mod score will be highest when the space of models where the maximization is performed includes the true model. On the other hand, one must avoid overparametrization of the model space. For example, when the approach is applied to affected sibpairs, only two constrained disease model parameters should be used (Knapp et al., 1994) for the mod score maximization. It is also important to emphasize the existence of a strong correlation between the disease gene location and the disease model. Consequently, there is poor resolution of the location of the susceptibility locus when the disease model at this locus is unknown. Of course, this is true regardless of the statistics used. The mod score may also be applied in a candidate gene strategy to model the potential effect of this gene in the disease. Since, however, it ignores the information provided both by disease segregation and by linkage disequilibrium between the marker alleles and the functional disease alleles, its power of discrimination between genetic models is weak. The MASC method (Clerget-Darpoux et al., 1988) has been designed to address more efficiently the objectives of a candidate gene approach.
Topics: Female; Genetic Diseases, Inborn; Human Genome Project; Humans; Linkage Disequilibrium; Lod Score; Male; Mathematical Computing; Models, Genetic; Pedigree
PubMed: 11037317
DOI: 10.1016/s0065-2660(01)42018-9 -
Nature Aug 1988
Topics: Genetic Linkage; Lod Score; Probability; Terminology as Topic
PubMed: 3405297
DOI: 10.1038/334477b0 -
Advances in Genetics 2001Strengths and weaknesses of the lod score method for human genetic linkage analysis are discussed. The main weakness is its requirement for the specification of a... (Review)
Review
Strengths and weaknesses of the lod score method for human genetic linkage analysis are discussed. The main weakness is its requirement for the specification of a detailed inheritance model for the trait. Various strengths are identified. For example, the lod score (likelihood) method has optimality properties when the trait to be studied is known to follow a Mendelian mode of inheritance. The ELOD is a useful measure for information content of the data. The lod score method can emulate various "nonparametric" methods, and this emulation is equivalent to the nonparametric methods. Finally, the possibility of building errors into the analysis will prove to be essential for the large amount of linkage and disequilibrium data expected in the near future.
Topics: Disease Transmission, Infectious; Genetic Linkage; Humans; Lod Score; Nuclear Family; Quantitative Trait, Heritable
PubMed: 11037318
DOI: 10.1016/s0065-2660(01)42019-0 -
Human Heredity 2001We 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...
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.
Topics: Genetic Linkage; Humans; Likelihood Functions; Linkage Disequilibrium; Lod Score; Models, Genetic; Sample Size
PubMed: 11474209
DOI: 10.1159/000053359 -
Human Heredity 1996For a phase-unknown nuclear family, we show that the likelihood and lod score are unimodal, and we describe conditions under which the maximum occurs at recombination...
For a phase-unknown nuclear family, we show that the likelihood and lod score are unimodal, and we describe conditions under which the maximum occurs at recombination fraction theta = 0, theta = 1/2, and 0 < theta < 1/2. These simply stated necessary and sufficient conditions seem to have escaped the notice of previous statistical geneticists.
Topics: Female; Genetic Linkage; Humans; Lod Score; Male; Mathematical Computing; Models, Genetic; Pedigree
PubMed: 8825464
DOI: 10.1159/000154326 -
Genetica Nov 2003While 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... (Comparative Study)
Comparative Study
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.
Topics: Bone Density; Computer Simulation; Female; Genotype; Humans; Lod Score; Male; Models, Genetic; Quantitative Trait Loci; Quantitative Trait, Heritable; Receptors, Calcitriol; Sample Size; Spine
PubMed: 14686609
DOI: 10.1023/b:gene.0000003827.86624.ac -
Annals of Human Genetics Jul 2008The maximum LOD score statistic is extremely powerful for gene mapping when calculated using the correct genetic parameter value. When the mode of genetic transmission... (Comparative Study)
Comparative Study
The maximum LOD score statistic is extremely powerful for gene mapping when calculated using the correct genetic parameter value. When the mode of genetic transmission is unknown, the maximum of the LOD scores obtained using several genetic parameter values is reported. This latter statistic requires higher critical value than the maximum LOD score statistic calculated from a single genetic parameter value. In this paper, we compare the power of maximum LOD scores based on three fixed sets of genetic parameter values with the power of the LOD score obtained after maximizing over the entire range of genetic parameter values. We simulate family data under nine generating models. For generating models with non-zero phenocopy rates, LOD scores maximized over the entire range of genetic parameters yielded greater power than maximum LOD scores for fixed sets of parameter values with zero phenocopy rates. No maximum LOD score was consistently more powerful than the others for generating models with a zero phenocopy rate. The power loss of the LOD score maximized over the entire range of genetic parameters, relative to the maximum LOD score calculated using the correct genetic parameter value, appeared to be robust to the generating models.
Topics: Computer Simulation; Family; Genotype; Humans; Lod Score; Models, Genetic; Models, Statistical; Population Groups
PubMed: 18410472
DOI: 10.1111/j.1469-1809.2008.00442.x -
Human Heredity 2001It 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...
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.
Topics: Chromosome Mapping; Data Interpretation, Statistical; Genetic Heterogeneity; Genetic Linkage; Humans; Lod Score; Mathematics; Models, Genetic; Models, Statistical; Quantitative Trait, Heritable
PubMed: 11713418
DOI: 10.1159/000053379 -
Annals of Human Genetics Oct 1984Genetic epidemiology deals with the interaction of environmental and genetic determinants in common diseases. Linkage analysis is an important branch of this field. The...
Genetic epidemiology deals with the interaction of environmental and genetic determinants in common diseases. Linkage analysis is an important branch of this field. The current practice of claiming linkage between two genetic loci when the maximum lod score z(theta) exceeds 3 has not received theoretical justification, whether considered as a sequential or as a fixed sample size test. Within the framework of significance testing, Wald's (1947) formulae are not applicable to allow this procedure a sequential interpretation. Considered as a fixed sample size test, we find that a chi 2 approximation would instead be very adequate. Since repeated significance testing is performed on linkage data, the nominal significance level should be more stringent for each test than the overall level. Some recent developments in group sequential trials by Pocock (1977) and in repeated significance testing by Woodroofe (1979) seem to indicate that the critical value of the maximum lod score should lie roughly between 0.9 and 3.3, depending on the maximum number of repetitions anticipated, on whether the significance level is desired to be 0.05, 0.01 or 0.001, and on whether the test is derived from a one-sided or a two-sided consideration. In terms of the group sequential approach, if a maximum of twenty repetitions is allowed, if z(theta) greater than log10 A is considered as a one-sided test and assumed to be symmetric when linkage is absent, then the type I error is approximately given by 1/A. We also treat the confidence interval approach for exclusion of unlikely recombination values.
Topics: Genetic Linkage; Humans; Lod Score; Methods; Statistics as Topic
PubMed: 6497351
DOI: 10.1111/j.1469-1809.1984.tb00849.x