Affecteds-only linkage methods are not a panacea.
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Family↗
Biomedical subjects
S E Hodge
Publications and source records attributed to S E Hodge.
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.
Bias↗
An oliogenic disease displaying weak marker associations: a summary of contributions to problem 1 of GAW9.
Problem 1 consisted of artificial data simulated from an oligogenic (four-locus) disease model. The data set contained 200 nuclear families with at least one affected child and 100 control families with no affected members. Two of the disease loci were intended to be detectable via association analysis but not necessarily via linkage analysis, and the other two were virtually undetectable in this data set. Participants used association analysis, linkage analysis, and segregation analysis to analyze these data. Their findings are summarized, and analysis strategies are discussed.
Chromosome Mapping↗
Genetic analysis workshop 9: development of problem 1.
Problem 1 was designed to involve an oligogenic model with four "disease susceptibility" loci, such that all individuals with at least four "upper-case" alleles were at equal risk to be affected (and those with three or fewer were not at risk). Two of these loci were identical to marker loci, thus giving rise to weak disease-marker associations. The other two were located between marker loci, with no linkage disequilibrium. Participants were given 200 nuclear families with at least one affected child, along with 100 control families with no affected individuals. The first two loci were intended to be detectable via association analysis. The remaining two loci were virtually undetectable in this data set.
Alleles↗
Statistical pitfalls in detecting age-of-onset anticipation: the role of correlation in studying anticipation and detecting ascertainment bias.
Attempts to detect anticipation in datasets have been hampered by two statistical problems: confusion about the role of correlation, and ascertainment bias. We show three things. (1) Correlation and anticipation are two distinct phenomena, such that neither high nor low correlation necessarily reveals anything about anticipation. (2) Nor does correlation analysis (or its cousin, regression analysis) offer a way to detect ascertainment bias, as has been suggested. Demonstration of "regression to the mean" does not necessarily indicate the presence of ascertainment bias, either. (3) Finally, under certain special circumstances, one can test for anticipation without regard for ascertainment bias. However, these circumstances are limited and may prove of little practical value.
Adult↗
Inherent intractability of the ascertainment problem for pedigree data: a general likelihood framework.
The problem of ascertainment in segregation analysis arises when families are selected for study through ascertainment of affected individuals. In this case, ascertainment must be corrected for in data analysis. However, methods for ascertainment correction are not available for many common sampling schemes, e.g., sequential sampling of extended pedigrees (except in the case of "single" selection). Concerns about whether ascertainment correction is even required for large pedigrees, about whether and how multiple probands in the same pedigree can be taken into account properly, and about how to apply sequential sampling strategies have occupied many investigators in recent years. We address these concerns by reconsidering a central issue, namely, how to handle pedigree structure (including size). We introduce a new distinction, between sampling in such a way that observed pedigree structure does not depend on which pedigree members are probands (proband-independent [PI] sampling) and sampling in such a way that observed pedigree structure does depend on who are the probands (proband-dependent [PD] sampling). This distinction corresponds roughly (but not exactly) to the distinction between fixed-structure and sequential sampling. We show that conditioning on observed pedigree structure in ascertained data sets obtained under PD sampling is not in general correct (with the exception of "single" selection), while PI sampling of pedigree structures larger than simple sibships is generally not possible. Yet, in practice one has little choice but to condition on observed pedigree structure. We conclude that the problem of genetic modeling in ascertained data sets is, in most situations, literally intractable. We recommend that future efforts focus on the development of robust approximate approaches to the problem.
Family Characteristics↗
What association analysis can and cannot tell us about the genetics of complex disease.
Human genetics researchers have been intrigued for many years by weak-to-moderate associations between markers and diseases. However, in most cases of association, the cause of this phenomenon is still unknown. Recently, interest has grown in pursuing association studies for complex psychiatric diseases, either instead of or in addition to linkage studies. However, it is one thing to detect association; the next important step is to determine why. Here we consider what a disease-marker association in the weak-to-moderate range (relative risk < 5) can tell us about disease etiology. Two distinct models (not the only possibilities) which could explain such an association are formulated. One is a linkage disequilibrium or major disease gene model, involving tight linkage with a "necessary" major gene. The other is a pure association model, involving a "susceptibility" gene that has only a minor effect on disease state. It will be shown that association analysis cannot distinguish between these two models, and hence cannot elucidate the biological mechanism behind the association. (This statement holds for traditional population-based association tests, as well as for more recent family-based association tests.) The importance of drawing the distinction between these two genetic models and the implications for understanding the genetics of complex human disease will also be discussed.
Alcoholism↗
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↗
The application of jackknife statistics to estimates of the recombination fraction.
We develop and evaluate the jackknife statistics [Efron, 1982] for obtaining confidence intervals for the recombination fraction. We consider two cases: (1) a single sibship of size S with phase known parents (one doubly heterozygous and one doubly homozygous) and (2) a sample of 20 nuclear families. We compare the jackknife confidence interval to the -1.00 lod and -0.83 lod intervals. For the first case we compare our intervals with a confidence interval which we develop that has coverage of exactly 95%. For the second case, we do a simulation study and compare the coverage of the intervals and the endpoints of the intervals with the actual 2.5th and 97.5th percentiles. Our results indicate that in case (1) the lod intervals provide closer estimates to the 95% exact interval than does the jackknife approach. However, in case (2), although the lod intervals have better coverage probabilities, the jackknife interval endpoints are closer to the actual percentile points than either of the lod interval endpoints.
Genetic Diseases, Inborn↗
Linkage analysis versus association analysis: distinguishing between two models that explain disease-marker associations.
Human genetics researchers have been intrigued for many years by weak-to-moderate associations between markers and diseases. However, in most cases of association, the cause of this phenomenon is still not known. Recently, interest has grown in pursuing association studies for complex diseases, either instead of or in addition to linkage studies. Hence, it is timely to reconsider what a disease-marker association, particularly in the weak-to-moderate range (relative risk < 10), can tell us about disease etiology. To this end, this study accomplishes three aims: (1) It formulates two different models explaining weak-to-moderate associations and derives the relationship between them. One is a linkage disequilibrium model, and the other is a "susceptibility," or pure association, model. The importance of drawing the distinction between these two models and the implications for our understanding of the genetics of human disease will also be discussed. It will be argued that the linkage disequilibrium model represents true linkage but that the susceptibility model does not. (2) It examines two family-based association tests proposed recently by Parsian et al. and Spielman et al. and derives formulas for their behavior under the two models described above. It demonstrates that these tests yield almost identical results under these two models. It shows that, whereas these tests can confirm an association, they cannot determine whether the association is caused by the linkage disequilibrium model or the susceptibility model. The study also characterizes the probabilities yielded by the family association tests in the presence of weak-to-moderate associations, which will aid researchers using these tests. (3) It proposes two approaches, both based on linkage analysis, which can distinguish between the two models described above. One approach involves a straightforward linkage analysis of the data; the other involves a partitioned association-linkage (PAL) test, as suggested by Greenberg. Formulas are derived for testing identity by descent in affected sib pairs by using both approaches. (4) Finally, the formulas and arguments are illustrated with two examples from the literature and one computer-simulated data set.
Alleles↗
Better data analysis through data exploration.
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Humans↗
Adequacy of single-locus approximations for linkage analyses of oligogenic traits.
When a disease is controlled by two or more mendelian loci acting epistatically, it can be modeled in a linkage analysis as a single-locus mendelian disease with reduced penetrance. However, the reliability of such an approximation has not yet been demonstrated. This study evaluates the adequacy of such single-locus approximations, when the disease under investigation is determined by two loci, one of which is tightly linked to a genetic marker. A wide range of two-locus models were simulated, and analyzed under both the correct two-locus model and under a single-locus approximation to that model. In general, the single-locus approximations yielded lod scores very close to the correct ones, but estimates of theta tended to be upwardly biased. We conclude that a single-locus linkage analysis will, in general, provide an excellent approximation to a correct (two-locus) linkage analysis of epistatic two-locus diseases. This enables researchers to continue to use single-locus linkage analyses when two-locus disease transmission is a possibility, and it validates linkage findings already obtained under single-locus analysis, even if the disease under investigation proves ultimately to be governed by two mendelian loci. We also examine alternative methods for obtaining parameter estimates for the single-locus approximations, and we discuss both generalizations and limitations of our findings.
Chromosome Mapping↗
Do bilineal pedigrees represent a problem for linkage analysis? Basic principles and simulation results for single-gene diseases with no heterogeneity.
Some investigators have expressed concern--especially for psychiatric disorders--that bilineal pedigrees should not be included in linkage studies. This study compares the "informativeness" of bilineal and unilineal families for a homogeneous single-gene disorder. Three approaches were used: (1) simulation studies of three-generation pedigrees, (2) calculation of expected lod scores (ELODs) in nuclear families, and (3) calculation of Fisher's information number I(theta) in nuclear families. The simulation studies in (1) permitted a realistic comparison between bilineal datasets and purely unilineal ones. The calculations in nuclear families in (2) and (3) then made it possible to analyze the sources of information loss in bilineal families. Overall, in datasets of five three-generation pedigrees each, the drop in mean maximum lod score was approximately 50% from purely unilineal datasets to extremely bilineal ones. In less-extreme bilineal datasets, which are closer to most real data than the extremely bilineal ones, the drops in lod score were very small--less than 10% in some, and practically zero in others. The details will vary, depending on size and structure of the pedigree, genetic model, true value of the recombination fraction, and informativeness of the marker. However, these results imply that the information loss due to bilineality is not necessarily very great. The nuclear-family calculations showed that for phase-known matings there is relatively little information loss in bilineal families, but for phase-unknown matings there the loss is much greater. In conclusion, for single-gene disorders with no genetic heterogeneity, whereas bilineal families can be less informative than comparable unilineal families, they are not so much less informative that they should automatically be discarded from linkage datasets. The implications of bilineal pedigrees for linkage studies of heterogeneous disorders are also discussed.
Computer Simulation↗
Linkage analysis of two-locus diseases under single-locus and two-locus analysis models.
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Computer Simulation↗
Inter- and intrafamilial heterogeneity: effective sampling strategies and comparison of analysis methods.
Heterogeneity, both inter- and intrafamilial, represents a serious problem in linkage studies of common complex diseases. In this study we simulated different scenarios with families who phenotypically have identical diseases but who genotypically have two different forms of the disease (both forms genetic). We examined the proportion of families displaying intrafamilial heterogeneity, as a function of mode of inheritance, gene frequency, penetrance, and sampling strategies. Furthermore, we compared two different ways of analyzing linkage in these data sets: a two-locus (2L) analysis versus a one-locus (SL) analysis combined with an admixture test. Data were simulated with tight linkage between one disease locus and a marker locus; the other disease locus was not linked to a marker. Our findings are as follows: (1) In contrast to what has been proposed elsewhere to minimize heterogeneity, sampling only "high-density" pedigrees will increase the proportion of families with intrafamilial heterogeneity, especially when the two forms are relatively close in frequency. (2) When one form is dominant and one is recessive, this sampling strategy will greatly decrease the proportions of families with a recessive form and may therefore make it more difficult to detect linkage to the recessive form. (3) An SL analysis combined with an admixture test achieves about the same lod scores and estimate of the recombination fraction as does a 2L analysis. Also, a 2L analysis of a sample of families with intrafamilial heterogeneity does not perform significantly better than an SL analysis. (4) Bilineal pedigrees have little effect on the mean maximum lod score and mean maximum recombination fraction, and therefore there is little danger that including these families will lead to a false exclusion of linkage.
Computer Simulation↗
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↗
Correction: Hereditary cutaneous malignant melanoma-dysplastic nevus.
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Genetic Markers↗
Twin studies and the genetics of Parkinson's disease--a reappraisal.
Parkinson's disease (PD) has long been regarded as having a hereditary component. However, three recent twin studies have been interpreted as excluding any significant genetic component in the etiology of PD. In this article, we reexamine these twin studies and argue that such a conclusion is premature. We review statistical tests of twin concordance rates, including calculation of G, the coefficient of genetic determination. When variation in a trait is due entirely to genetic factors G = 1, and when variation in a trait is due entirely to nongenetic factors G = 0. We conclude that: (a) low monozygotic concordance rates can be compatible with substantial genetic contribution to etiology; (b) the PD twin study data give substantial optimal values of G (up to 0.78) but the very broad 95% confidence limits for G make it impossible for the twin study data to prove or disprove a substantial genetic component to the etiology of PD; and (c) changing clinical concepts of PD have undermined the assumptions underlying the methodology of the PD twin studies. We review three genetic models that are biologically plausible for PD and are compatible with the low twin concordance rates. Finally, we suggest that further family studies, including linkage studies, are needed to resolve this question.
Diseases in Twins↗