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At least 19 recordsLinked to original sources
PubMed2006

Distribution and magnitude of type I error of model-based multipoint lod scores: implications for multipoint mod scores.

The multipoint lod score and mod score methods have been advocated for their superior power in detecting linkage. However, little has been done to determine the distribution of multipoint lod scores or to examine the properties of mod scores. In this paper we study the distribution of multipoint lod scores both analytically and by simulation. We also study by simulation the distribution of maximum multipoint lod scores when maximized over different penetrance models. The multipoint lod score is approximately normally distributed with mean and variance that depend on marker informativity, marker density, specified genetic model, number of pedigrees, pedigree structure, and pattern of affection status. When the multipoint lod scores are maximized over a set of assumed penetrances models, an excess of false positive indications of linkage appear under dominant analysis models with low penetrances and under recessive analysis models with high penetrances. Therefore, caution should be taken in interpreting results when employing multipoint lod score and mod score approaches, in particular when inferring the level of linkage significance and the mode of inheritance of a trait.

Chromosome Mapping↗
PubMed2001

The lod score method.

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.

Genetic Linkage↗
PubMed1994

Lods, wrods, and mods: the interpretation of lod scores calculated under different models.

In this paper we examine the relationships among classical lod scores, "wrod" scores (lod scores calculated under the wrong genetic model), and "mod" scores (lod scores maximized over genetic model parameters). We compare the behavior of these scores when the state of nature is linkage to their behavior when the state of nature is no linkage. We describe sufficient conditions for mod scores to be valid and discuss their use to determine the correct genetic model. We show that lod scores represent a likelihood-ratio test for independence. We explain the "ascertainment-assumption-free" aspect of using mod scores to determine mode of inheritance and we set this aspect into a well-established statistical framework. Finally, we summarize practical guidelines for the use of mod scores.

Bias↗
PubMed1998

The power to detect linkage in complex disease by means of simple LOD-score analyses.

Maximum-likelihood analysis (via LOD score) provides the most powerful method for finding linkage when the mode of inheritance (MOI) is known. However, because one must assume an MOI, the application of LOD-score analysis to complex disease has been questioned. Although it is known that one can legitimately maximize the maximum LOD score with respect to genetic parameters, this approach raises three concerns: (1) multiple testing, (2) effect on power to detect linkage, and (3) adequacy of the approximate MOI for the true MOI. We evaluated the power of LOD scores to detect linkage when the true MOI was complex but a LOD score analysis assumed simple models. We simulated data from 14 different genetic models, including dominant and recessive at high (80%) and low (20%) penetrances, intermediate models, and several additive two-locus models. We calculated LOD scores by assuming two simple models, dominant and recessive, each with 50% penetrance, then took the higher of the two LOD scores as the raw test statistic and corrected for multiple tests. We call this test statistic "MMLS-C." We found that the ELODs for MMLS-C are >=80% of the ELOD under the true model when the ELOD for the true model is >=3. Similarly, the power to reach a given LOD score was usually >=80% that of the true model, when the power under the true model was >=60%. These results underscore that a critical factor in LOD-score analysis is the MOI at the linked locus, not that of the disease or trait per se. Thus, a limited set of simple genetic models in LOD-score analysis can work well in testing for linkage.

Chromosome Mapping↗
PubMed2001

Accuracy of a composite score using daily SAPS II and LOD scores for predicting hospital mortality in ICU patients hospitalized for more than 72 h.

UNLABELLED: In most databases used to build general severity scores the median duration of intensive care unit (ICU) stay is less than 3 days. Consequently, these scores are not the most appropriate tools for measuring prognosis in studies dealing with ICU patients hospitalized for more than 72 h. PURPOSE: To develop a new prognostic model based on a general severity score (SAPS II), an organ dysfunction score (LOD) and evolution of both scores during the first 3 days of ICU stay. DESIGN: Prospective multicenter study. SETTING: Twenty-eight intensive care units (ICUs) in France. PATIENTS: A training data-set was created with four ICUs during an 18-month period (893 patients). Seventy percent of the patients were medical (628) aged 66 years. The median SAPS II was 38. The ICU and hospital mortality rates were 22.7% and 30%, respectively. Forty-seven percent (420 patients) were transferred from hospital wards. In this population, the calibration (Hosmer-Lemeshow chi-square: 37.4, P = 0.001) and the discrimination [area under the ROC curves: 0.744 (95 % CI: 0.714-0.773)] of the original SAPS II were relatively poor. A validation data set was created with a random panel of 24 French ICUs during March 1999 (312 patients). MEASUREMENTS AND MAIN RESULTS: The LOD and SAPS II scores were calculated during the first (SAPS1, LOD1), second (SAPS2, LOD2), and third (SAPS3, LOD3) calendar days. The LOD and SAPS scores alterations were assigned the value "1" when scores increased with time and "0" otherwise. A multivariable logistic regression model was used to select variables measured during the first three calendar days, and independently associated with death. Selected variables were: SAPS II at admission [OR: 1.04 (95 % CI: 1.027-1.053) per point], LOD [OR: 1.16 (95 % CI: 1.085-1.253) per point], transfer from ward [OR: 1.74 (95 % CI: 1.25-2.42)], as well as SAPS3-SAPS2 alterations [OR: 1.516 (95 % CI: 1.04-2.22)], and LOD3-LOD2 alterations [OR: 2.00 (95 % CI: 1.29-3.11)]. The final model has good calibration and discrimination properties in the training data set [area under the ROC curve: 0.794 (95 % CI: 0.766-0.820), Hosmer-Lemeshow C statistic: 5.56, P = 0.7]. In the validation data set, the model maintained good accuracy [area under the ROC curve: 0.826 (95 % CI: 0.780-0.867), Hosmer-Lemeshow C statistic: 7.14, P = 0.5]. CONCLUSIONS: The new model using SAPS II and LOD and their evolution during the first calendar days has good discrimination and calibration properties. We propose its use for benchmarking and evaluating the over-risk of death associated with ICU-acquired nosocomial infections.

APACHE↗
PubMed2001

Extension of the lod score: the mod score.

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.

Female↗
PubMed2001

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.

Chromosome Mapping↗
PubMed1986

Effects of misspecifying genetic parameters in lod score analysis.

The lod score method is widely used to test linkage and to estimate the recombination fraction between a disease locus and a marker locus. The parameters (gene frequency, penetrance, and degree of dominance) are assumed to be known at each locus. This condition may not be fulfilled at the disease locus. In this paper, we evaluate the errors due to the use of wrong parameters. The power of the linkage test is sensitive to the degree of dominance, and slightly to the penetrance, but not to the gene frequency. In contrast, the estimation of the recombination fraction may be strongly affected by an error on any genetic parameter.

Alleles↗
PubMed1992

Sensitivity of lod scores to changes in diagnostic status.

This paper investigates effects on lod scores when one individual in a data set changes diagnostic or recombinant status. First we examine the situation in which a single offspring in a nuclear family changes status. The nuclear-family situation, in addition to being of interest in its own right, also has general theoretical importance, since nuclear families are "transparent"; that is, one can track genetic events more precisely in nuclear families than in complex pedigrees. We demonstrate that in nuclear families log10 [(1-theta)/theta] gives an upper limit on the impact that a single offspring's change in status can have on the lod score at that recombination fraction (theta). These limits hold for a fully penetrant dominant condition and fully informative marker, in either phase-known or phase-unknown matings. Moreover, log10 [(1-theta)/theta] (where theta denotes the value of theta at which Zmax occurs) gives an upper limit on the impact of a single offspring's status change on the maximum lod score (Zmax). In extended pedigrees, in contrast to nuclear families, no comparable limit can be set on the impact of a single individual on the lod score. Complex pedigrees are subject to both stabilizing and destabilizing influences, and these are described. Finally, we describe a "sensitivity analysis," in which, after all linkage analysis is completed, every informative individual in the data set is changed, one at a time, to see the effect which each separate change has on the lod scores. The procedure includes identifying "critical individuals," i.e., those who would have the greatest impact on the lod scores, should their diagnostic status in fact change. To illustrate use of the sensitivity analysis, we apply it to the large bipolar pedigree reported by Egeland et al. and Kelsoe et al. We show that the changes in lod scores observed there, on the order of 1.1-1.2 per person, are not unusual. We recommend that investigators include a sensitivity analysis as a standard part of reporting the results of a linkage analysis.

Female↗
PubMed1989

Inferring mode of inheritance by comparison of lod scores.

One usually must assume a mode of inheritance when using lod scores for linkage analysis. In this study, we asked the question, "If one assumed mode of inheritance in a linkage analysis gives a higher lod score than another, does that indicate that the mode of inheritance that led to the higher lod score is more 'correct' than the other?" We simulated data under a variety of penetrances, assuming either dominant or recessive inheritance. We then analyzed those simulated data under the correct mode of inheritance, assuming a range of penetrance values, and under the incorrect model, also assuming a range of penetrance values. We found that, if there was enough information for a maximum lod score of at least 3.0, assuming the correct penetrance value or mode of inheritance in the analysis led to a higher lod score than assuming the incorrect penetrance or the incorrect mode of inheritance. These results cannot yet be generalized outside of the specific modes of inheritance and penetrance combinations that we have modeled. Also, penetrance was modeled as "random." The effect of "reduced penetrance" caused by other genetic factors has not yet been tested. We also tested the effect of non-standard ascertainment on drawing conclusions about mode of inheritance from linkage data. Even when families were ascertained only if the family was multiplex (i.e., more than one affected sib), assuming the correct mode of inheritance gave a higher lod score than assuming the incorrect mode of inheritance. This method has the promise of both simplifying and expanding the application of linkage analysis.(ABSTRACT TRUNCATED AT 250 WORDS)

Female↗
PubMed2001

Major strengths and weaknesses of the lod score method.

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.

Disease Transmission, Infectious↗
PubMed2004

Percentiles of the null distribution of 2 maximum lod score tests.

We here consider the null distribution of the maximum lod score (LOD-M) obtained upon maximizing over transmission model parameters (penetrance values, dominance, and allele frequency) as well as the recombination fraction. Also considered is the lod score maximized over a fixed choice of genetic model parameters and recombination-fraction values set prior to the analysis (MMLS) as proposed by Hodge et al. The objective is to fit parametric distributions to MMLS and LOD-M. Our results are based on 3,600 simulations of samples of n = 100 nuclear families ascertained for having one affected member and at least one other sibling available for linkage analysis. Each null distribution is approximately a mixture p(2)(0) + (1 - p)(2)(v). The values of MMLS appear to fit the mixture 0.20(2)(0) + 0.80chi(2)(1.6). The mixture distribution 0.13(2)(0) + 0.87chi(2)(2.8). appears to describe the null distribution of LOD-M. From these results we derive a simple method for obtaining critical values of LOD-M and MMLS.

Alleles↗
PubMed1999

Further evidence for the increased power of LOD scores compared with nonparametric methods.

In genetic analysis of diseases in which the underlying model is unknown, "model free" methods-such as affected sib pair (ASP) tests-are often preferred over LOD-score methods, although LOD-score methods under the correct or even approximately correct model are more powerful than ASP tests. However, there might be circumstances in which nonparametric methods will outperform LOD-score methods. Recently, Dizier et al. reported that, in some complex two-locus (2L) models, LOD-score methods with segregation analysis-derived parameters had less power to detect linkage than ASP tests. We investigated whether these particular models, in fact, represent a situation that ASP tests are more powerful than LOD scores. We simulated data according to the parameters specified by Dizier et al. and analyzed the data by using a (a) single locus (SL) LOD-score analysis performed twice, under a simple dominant and a recessive mode of inheritance (MOI), (b) ASP methods, and (c) nonparametric linkage (NPL) analysis. We show that SL analysis performed twice and corrected for the type I-error increase due to multiple testing yields almost as much linkage information as does an analysis under the correct 2L model and is more powerful than either the ASP method or the NPL method. We demonstrate that, even for complex genetic models, the most important condition for linkage analysis is that the assumed MOI at the disease locus being tested is approximately correct, not that the inheritance of the disease per se is correctly specified. In the analysis by Dizier et al., segregation analysis led to estimates of dominance parameters that were grossly misspecified for the locus tested in those models in which ASP tests appeared to be more powerful than LOD-score analyses.

Genes, Dominant↗
PubMed2001

Lod scores for gene mapping in the presence of marker map uncertainty.

Multipoint lod scores are typically calculated for a grid of locus positions, moving the putative disease locus across a fixed map of genetic markers. Changing the order of a set of markers and/or the distances between the markers can make a substantial difference in the resulting lod score curve and the location and height of its maximum. The typical approach of using the best maximum likelihood marker map is not easily justified if other marker orders are nearly as likely and give substantially different lod score curves. To deal with this problem, we propose three weighted multipoint lod score statistics that make use of information from all plausible marker orders. In each of these statistics, the information conditional on a particular marker order is included in a weighted sum, with weight equal to the posterior probability of that order. We evaluate the type 1 error rate and power of these three statistics on the basis of results from simulated data, and compare these results to those obtained using the best maximum likelihood map and the map with the true marker order. We find that the lod score based on a weighted sum of maximum likelihoods improves on using only the best maximum likelihood map, having a type 1 error rate and power closest to that of using the true marker order in the simulation scenarios we considered.

Bias↗
PubMed2005

A new method of linkage analysis using LOD scores for quantitative traits supports linkage of monoamine oxidase activity to D17S250 in the Collaborative Study on the Genetics of Alcoholism pedigrees.

OBJECTIVE: Although LOD score methods have been applied to diseases with complex modes of inheritance, linkage analysis of quantitative traits has tended to rely on non-parametric methods based on regression or variance components analysis. Here, we describe a new method for LOD score analysis of quantitative traits which does not require specification of a mode of inheritance. METHODS: The technique is derived from the MFLINK method for dichotomous traits. A range of plausible transmission models is constructed, constrained to yield the correct population mean and variance for the trait but differing with respect to the contribution to the variance due to the locus under consideration. Maximized LOD scores under homogeneity and admixture are calculated, as is a model-free LOD score which compares the maximized likelihoods under admixture assuming linkage and no linkage. These LOD scores have known asymptotic distributions and hence can be used to provide a statistical test for linkage. The method has been implemented in a program called QMFLINK. It was applied to data sets simulated using a variety of transmission models and to a measure of monoamine oxidase activity in 105 pedigrees from the Collaborative Study on the Genetics of Alcoholism. RESULTS: With the simulated data, the results showed that the new method could detect linkage well if the true allele frequency for the trait was close to that specified. However, it performed poorly on models in which the true allele frequency was much rarer. For the Collaborative Study on the Genetics of Alcoholism data set only a modest overlap was observed between the results obtained from the new method and those obtained when the same data were analysed previously using regression and variance components analysis. Of interest is that D17S250 produced a maximized LOD score under homogeneity and admixture of 2.6 but did not indicate linkage using the previous methods. However, this region did produce evidence for linkage in a separate data set, suggesting that QMFLINK may have been able to detect a true linkage which was not picked up by the other methods. CONCLUSION: The application of model-free LOD score analysis to quantitative traits is novel and deserves further evaluation of its merits and disadvantages relative to other methods.

Alcoholism↗
PubMed1993

LODVIEW: a computer program for the graphical evaluation of lod score results in exclusion mapping of human disease genes.

For linkage analysis projects aimed at mapping hereditary disease genes in humans, hundreds of highly polymorphic microsatellite markers which can be typed by PCR (PCR markers) have become available. With this technical improvement, the availability of a technique allowing for transparency in the handling of rapidly generated lod score data is becoming important. We present a computer program LODVIEW for the graphical representation of lod score data. It is designed for the input of lod score data generated with the LINKAGE package or similar programs. LODVIEW consists of 24 preformatted files, one for each chromosome. Each file contains a table for the input of lod score data and a file for the graphical representation of the data, which will show automatically any entry that is made in the respective input table. The program provides the user with published PCR marker information pre-entered into a table and graph at the correct positions corresponding to the genetic distances between markers. The graphical display of LODVIEW allows for the rapid evaluation of lod score results calculated from PCR markers on each chromosome. The following information can be obtained from the graphical display at one glance: (i) Regions of exclusion (Z(theta) < -2) and nonexclusion, (ii) markers with positive lod scores, (iii) the distribution of positive and negative lod scores among the families examined (indication of genetic heterogeneity), (iv) multipoint lod scores, and (v) the availability of PCR markers in regions of interest. The program is continually updated for novel PCR marker information from the literature. The program will help to efficiently monitor and direct the progress of exclusion mapping projects.

Chromosome Mapping↗
PubMed1995

Posterior probability of linkage and maximal lod score.

To detect linkage between a trait and a marker, Morton (1955) proposed to calculate the lod score z(theta 1) at a given value theta 1 of the recombination fraction. If z(theta 1) reaches +3 then linkage is concluded. However, in practice, lod scores are calculated for different values of the recombination fraction between 0 and 0.5 and the test is based on the maximum value of the lod score Zmax. The impact of this deviation of the test on the probability that in fact linkage does not exist, when linkage was concluded, is documented here. This posterior probability of no linkage can be derived by using Bayes' theorem. It is less than 5% when the lod score at a predetermined theta 1 is used for the test. But, for a Zmax of +3, we showed that it can reach 16.4%. Thus, considering a composite alternative hypothesis instead of a single one decreases the reliability of the test. The reliability decreases rapidly when Zmax is less than +3. Given a Zmax of +2.5, there is a 33% chance that linkage does not exist. Moreover, the posterior probability depends not only on the value of Zmax but also jointly on the family structures and on the genetic model. For a given Zmax, the chance that linkage exists may then vary.

Genetic Markers↗
PubMed1993

Distribution of lod scores under uncertain mode of inheritance.

We consider probability distributions of alternative lod statistics, differing in their treatment of segregation parameters when mode of inheritance is uncertain. A particular pedigree structure and a dominant genetic system displaying incomplete penetrance are analyzed. Lod scores calculated assuming an incorrect segregation model appear to conform quite well to the chi 2 distribution in the absence of linkage. In the presence of linkage, some power is lost. However, if lod scores are calculated under several different segregation models and the best one is accepted, opportunity for chance occurrence of high lod scores is enhanced. The distribution is still chi 2, but with extra degrees of freedom. These results hold over a wide range of sample sizes and segregation models, including small samples and low levels of penetrance.

Chi-Square Distribution↗