Secondary Analysis of Case-Control Studies in Genomic Contexts

This dissertation consists of five independent projects. In each project, a novelstatistical method was developed to address a practical problem encountered in genomiccontexts. For example, we considered testing for constant nonparametric effectsin a general semiparametric regression model in genetic epidemiology; analyzed therelationship between covariates in the secondary analysis of case-control data; performedmodel selection in joint modeling of paired functional data; and assessed theprediction ability of genes in gene expression data generated by the CodeLink Systemfrom GE.In the first project in Chapter II we considered the problem of testing for constantnonparametric effects in a general semiparametric regression model when there is thepotential for interaction between the parametrically and nonparametrically modeledvariables. We derived a generalized likelihood ratio test for this hypothesis, showedhow to implement it, and gave evidence that it can improve statistical power whencompared to standard partially linear models.The second project in Chapter III addressed the issue of score testing for theindependence of X and Y in the second analysis of case-control data. The semiparametricefficient approaches can be used to construct semiparametric score tests, butthey suffer from a lack of robustness to the assumed model for Y given X. We showedhow to adjust the semiparametric score test to make its level/Type I error correct even if the assumed model for Y given X is incorrect, and thus the test is robust.The third project in Chapter IV took up the issue of estimation of a regressionfunction when Y given X follows a homoscedastic regression model. We showed howto estimate the regression parameters in a rare disease case even if the assumed modelfor Y given X is incorrect, and thus the estimates are model-robust.In the fourth project in Chapter V we developed novel AIC and BIC-type methodsfor estimating the smoothing parameters in a joint model of paired, hierarchicalsparse functional data, and showed in our numerical work that they are many timesfaster than 10-fold crossvalidation while at the same time giving results that areremarkably close to the crossvalidated estimates.In the fifth project in Chapter VI we introduced a practical permutation testthat uses cross-validated genetic predictors to determine if the list of genes in questionhas “good” prediction ability. It avoids overfitting by using cross-validation toderive the genetic predictor and determines if the count of genes that give “good”prediction could have been obtained by chance. This test was then used to exploregene expression of colonic tissue and exfoliated colonocytes in the fecal stream todiscover similarities between the two.