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In linkage studies, independent replication of positive findings is crucial in order to distinguish between true positives and false positives. Recently, the following question has arisen in linkage studies of complex traits: at what distance do we reject the hypothesis that two location estimates in a genomic region represent the same gene? Here we attempt to address this question. Sampling distributions for location estimates were constructed by computer simulation. The conditions for simulation were chosen to reflect features of "typical" complex traits, including incomplete penetrance, phenocopies, and genetic heterogeneity. Our findings, which bear on what is considered a replication in linkage studies of complex traits, suggest that, even with relatively large numbers of multiplex families, chance variation in the location estimate is substantial. In addition, we report evidence that, for the conditions studied here, the standard error of a location estimate is a function of the magnitude of the expected LOD score.

Objective: This study was an attempt to replicate evidence for a vulnerability locus for schizophrenia and associated disorders in the 8p22-21 region reported by Pulver and colleagues., Method: The linkage sample of the Irish Study of High-Density Schizophrenia Families consists of 265 multiplex families containing 1,408 individuals. Fifteen markers covering 30 centimorgans on chromosome 8p were tested. Three statistical methods were used: two-point and multipoint heterogeneity lod scores and a multipoint nonparametric test., Results: According to two-point heterogeneity lod scores, the strongest evidence for linkage was found for markers D8S1731 (maximum lod score = 2.00), D8S1715 (maximum lod score = 2.52), and D8S133 (maximum lod score = 2.08) by assuming a phenotypic definition of all psychiatric illness and a range of genetic models. According to multipoint heterogeneity lod scores, the strongest evidence for linkage (maximum lod score = 2.34), found by using a dominant genetic model and a broad definition of the schizophrenia spectrum, extended over a 10-cM region between markers D8S1715 and D8S1739. Multipoint nonparametric linkage found the strongest evidence (maximum z = 2.51) over a broader region when either a diagnosis of core schizophrenia or a narrow definition of the schizophrenia spectrum was used. This putative vulnerability locus was segregating in 10%-25% of the families studied., Conclusions: This study supports the existence of a vulnerability locus for schizophrenia on chromosome 8p. In this sample, this locus appears to influence the risk of illness in only a modest proportion of families and predisposes to a range of schizophrenia spectrum and possibly nonspectrum disorders.

Large samples of multiplex pedigrees will probably be needed to detect susceptibility loci for schizophrenia by linkage analysis. Standardized ascertainment of such pedigrees from culturally and ethnically homogeneous populations may improve the probability of detection and replication of linkage. The Irish Study of High-Density Schizophrenia Families (ISHDSF) was formed from standardized ascertainment of multiplex schizophrenia families in 39 psychiatric facilities covering over 90% of the population in Ireland and Northern Ireland. We here describe a phenotypic sample and a subset thereof, the linkage sample. Individuals were included in the phenotypic sample if adequate diagnostic information, based on personal interview and/or hospital record, was available. Only individuals with available DNA were included in the linkage sample. Inclusion of a pedigree into the phenotypic sample required at least two first, second, or third degree relatives with non-affective psychosis (NAP), one whom had schizophrenia (S) or poor-outcome schizo-affective disorder (PO-SAD). Entry into the linkage sample required DNA samples on at least two individuals with NAP, of whom at least one had S or PO-SAD. Affection was defined by narrow, intermediate, and broad criteria. The phenotypic sample contained 277 pedigrees and 1,770 individuals and the linkage sample 265 pedigrees and 1,408 individuals. Using the intermediate definition of affection, the phenotypic sample contained 837 affected individuals and 526 affected sibling pairs. Parallel figures for the linkage sample were 700 and 420. Individuals with schizophrenia from these multiplex pedigrees resembled epidemiologically sampled cases with respect to age at onset, gender distribution, and most clinical symptoms, although they were more thought-disordered and had a poorer outcome. Power analyses based on the model of linkage heterogeneity indicated that the ISHDSF should be able to detect a major locus that influences susceptibility to schizophrenia in as few as 20% of families. Compared to first-degree relatives of epidemiologically sampled schizophrenic probands, first-degree relatives of schizophrenic members from the ISHDSF had a similar risk for schizotypal personality disorder, affective illness, alcoholism, and anxiety disorder. With sufficient resources, large-scale ascertainment of multiplex schizophrenia pedigrees is feasible, especially in countries with catchmented psychiatric care and stable populations. Although somewhat more severely ill, schizophrenic members of such pedigrees appear to clinically resemble typical schizophrenic patients. Our ascertainment process for multiplex schizophrenia families did not select for excess familial risk for affective illness or alcoholism. With its large sample ascertained in a standardized manner from a relatively homogeneous population, the ISHDSF provides considerable power to detect susceptibility loci for schizophrenia.

In 265 Irish pedigrees, with linkage analysis we find evidence for a vulnerability locus for schizophrenia in region 6p24-22. The greatest lod score, assuming locus heterogeneity, is 3.51 (P = 0.0002) with D6S296. Another test, the C test, also supported linkage, the strongest results being obtained with D6S296 (P = 0.00001), D6S274 (P = 0.004) and D6S285 (P = 0.006). Non-parametric analysis yielded suggestive, but substantially weaker, findings. This locus appears to influence the vulnerability to schizophrenia in roughly 15 to 30% of our pedigrees. Evidence for linkage was maximal using an intermediate phenotypic definition and declined when this definition was narrowed or was broadened to include other psychiatric disorders.

The detection of linkage in complex traits, although potentially of the greatest value, has proved very difficult. One reason may be the drastic effect that locus heterogeneity has on statistical power. We propose a new test for linkage in the presence of heterogeneity, based upon the sum of individual pedigree maximum lod scores, combined with a bootstrap method for estimating the null-hypothesis distribution. The technique is designed to exploit modern computer capability and to avoid reliance on asymptotic-distribution theory. Numerical comparisons indicate that for small pedigrees this new test can detect linkage with 30%-50% less data than are required by standard methods. A computer program for simulating the distribution and for performing the test of linkage is available from the authors.

For traits with incomplete penetrance, simultaneous segregation analysis and linkage analysis may offer increased information. Since the numerical properties of the mixed model are a drawback in this more complicated analysis, a second locus is substituted for the polygenic component yielding a simpler and more tractable oligogenic model. While less realistic, the simpler model is not easily discriminated from the mixed model, particularly when used on affection data rather than quantitative traits. Calculations for combined linkage and segregation analysis are described for nuclear families with pointers to account for sampling scheme.

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.

Although multipoint linkage data are becoming quite common, economical and efficient methods for presenting these data are not yet in use. Tables giving the full likelihood function would be very voluminous, whereas reduction to standard lods destroys part of the information. We suggest a special lod table representation which preserves nearly all the information about both gene order and genetic map distance at a great reduction in data presented. Conditional lods, coined "c-lods" to distinguish them clearly from ordinary lods, are calculated for distances between each adjacent pair of loci, with all distances among other loci in the system conditionally optimized. Thus, in an n-locus system, conditional lods are presented for the n - 1 adjacent pairs of loci only. The principal reason for reporting lod scores is the potential for combining data from separate studies to reach conclusive evidence for linkage and gene order. Because estimates of recombination are different in each set of data, the crux of the problem is to present scores that provide a close approximation to the true likelihood away from maximum likelihood (ML). The sum of conditional lods closely approximates the likelihood throughout the domain. Therefore, conditional lods contribute appropriately when mapping from several sources of data, so contradictory estimates can be reconciled efficiently.

A formula is given for the advantage of n-point sampling, which approaches infinity with n. However, 2-point and 3-point analyses extract nearly all the information in such samples and at the same time communicate this information as lods and chi 2, which can be combined with other data by simple addition without reevaluation of the likelihood. When null interference is assumed, map distances and multiple recombination frequencies are inflated, and there is substantial loss of efficiency and of support for the correct order.