Many health conditions, including cancer and mental illnesses, are rated on ordinal scales. Most of these conditions are affected by interacted genetic and environmental factors. Existing methods in genetic segregation or linkage analyses are helpful in identifying complex genetic bases for qualitative and quantitative traits. But few methods or software are available to accommodate ordinal traits. The focus of my studies is to develop methodologies to analyze pedigrees with ordinal traits.; First, we proposed a latent variable model for segregation analysis to assess the familial aggregation and inheritability of ordinal-scaled diseases. We expanded the proportional-odds model by including the latent variables that represent common environmental factors and genetic contributions. The estimation procedure employed the EM algorithm for maximization and a peeling algorithm for computational efficiency. Asymptotic theories of test statistics were developed and simulation studies were conducted to confirm the theories. When applied to the Yale alcoholism data, our model suggested a major gene component, which had not been revealed previously in the same dataset.; We also developed the latent variable model for linkage analysis of ordinal traits in order to identify the location of an underlying disease gene relative to a marker. The likelihood ratio test was used for detecting evidence of linkage. Through simulation studies, we found that the power of our proposed model is substantially higher than that of the binary-trait-based linkage analysis methods and that our test statistic is robust with regard to certain parameter misspecifications.; Using the linkage model, we performed a genome scan of the hoarding phenotype in 53 nuclear families. Standard linkage scans were also performed using programs Gene-Hunter and Allegro and failed to reveal any marker significantly linked to the binary hoarding phenotypes. However, our method identified three markers at 4q34-35, 5q35.2-35.3 and 17q25 that manifest significant allele sharing.; Finally, we considered various ascertainment effects upon parameter estimates and explored ways of bias adjustment. We performed simulation studies for various ascertainment schemes including the one used in the family study of alcoholism.
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