The papers in this section address the use of linkage disequilibrium (LD) and combined LD and linkage methods to map disease genes, using one or more of the asthma data sets provided for Genetic Analysis Workshop 12. Because these methods have been applied to real data sets in which the underlying asthma susceptibility loci are not yet known, success cannot be measured against the "correct" answers as with simulated data. The authors are, however, able to compare results across data sets, introduce or compare methods using appropriate data sets, and explore their methods in the face of real-life limitations such as missing data, small samples, and diverse family structures. Two papers explore the analysis of transmission disequilibrium for a quantitative variable, serum IgE levels. Grier et al. compare six quantitative transmission/ disequilibrium. tests (QTDT) across a number of data sets, finding moderate agreement for five of the six tests but modest replication across data sets. Jedrey et al. apply one of these tests to two data sets that used the same markers (Hutterite and CSGA), and fluid considerable overlap in the regions producing significant results (but not for each study's most positive region). Both papers also explore the use of covariates such as age, sex, and race, which had a substantial effect in the analysis of Jedrey et al. Grier et al. comment on the importance of log transformation when the variable of interest is not normally distributed. The remaining papers consider the categorical asthma phenotype. Three papers address the study of LD in multiplex pedigree samples. One issue is how to control for the correlation of affected siblings' genotypes in tests of LD. Bertram et al. compare the TDT(PAIRS) option of TDTEX, which uses the first two sibs of a sibship, to a modification of the family-based association test (FBAT) using empirical variance estimation (EV-FBAT), so that more complex pedigrees can be studied. They report no increased statistical significance in two asthma data sets (German and CSGA), but there were no strongly significant findings-one of the hazards of using real data sets. Two papers introduce tests that combine linkage and LD analysis into a single statistic. Jiang et al. propose an LD-lod statistic. Z-scores from nonparametric linkage (NPL) and multiallele TDTs are combined depending on the sign of the NPL score. Zhang et al. propose a tree-based analysis of linkage and association and apply it to selected markers from the German and CSGA asthma data sets. Finally, Levinson et al. focus on LD mapping in isolated populations, applying haplotype sharing analysis to the Hutterite genome scan data. The test statistic is determined by both by the number of chromosomes sharing a haplotype surrounding a particular marker and the length of the shared haplotypes. Several of the positive markers are in regions supported by other asthma studies. These papers reflect an increasing diversity and complexity of LD analysis methods relevant to studies of common disorders. The TDT [Spielman et al., 1993] was published 8 years ago. The simulated LD problem for GAW9 2 years later was approached with new methods permitting analysis of multiple alleles at a single marker in trios with categorical traits. Now, 6 years later, we see comparison of multiple methods for quantitative traits, tests for LD in multiply-affected pedigrees including joint consideration of linkage and LD, and a variety of approaches to single-marker and haplotype-based analysis of LD in isolated or admixed populations. Other papers in this volume on the simulated data sets consider a variety of multivariate approaches to narrowing candidate regions based on patterns of LD in very fine marker or SNP maps. A number of questions emerge. The basis for the observed differences among QTDT and TDT tests requires fin-ther study to guide the choice of tests for particular studies. The integration of linkage and LD statistics will certainly receive more attention. As both Jiang et al. and Zhang et al. point out, tests of within-family allele sharing (linkage) and of across-family allele or haplotype sharing (association or LD) are independent under the null hypothesis, so that combined tests should have more power. Studies of small isolated populations are a case in point: marker-marker LD was observed in the Hutterite data sets. While this background "noise" may reduce power of LD mapping for the first stages of gene mapping (as in the asthma data set) combined linkage and LD tests should improve power. Certainly investigators should be made aware of the wider range of analytic options now available, and attention should be paid to further innovations and comparisons of methods in real and simulated data sets.
