Bias Reduction and Goodness-of-Fit Tests in Conditional Logistic Regression Models

This dissertation consists of three projects in matched case-control studies. In the firstproject, we employ a general bias preventive approach developed by Firth (1993) to handlethe bias of an estimator of the log-odds ratio parameter in conditional logistic regression bysolving a modified score equation. The resultant estimator not only reduces bias but alsocan prevent producing infinite value. Furthermore, we propose a method to calculate thestandard error of the resultant estimator. A closed form expression for the estimator of thelog-odds ratio parameter is derived in the case of a dichotomous exposure variable. Finitesample properties of the estimator are investigated via a simulation study. Finally, we applythe method to analyze a matched case-control data from a low-birth-weight study.In the second project of this dissertation, we propose a score typed test for checkingadequacy of a functional form of a covariate of interest in matched case-control studies byusing penalized regression splines to approximate an unknown function. The asymptoticdistribution of the test statistics under the null model is a linear combination of several chi-square random variables. We also derive the asymptotic distribution of the test statisticwhen the alternative model holds. Through a simulation study we assess and comparethe finite sample properties of the proposed test with that of Arbogast and Lin (2004). Toillustrate the usefulness of the method, we apply the proposed test to a matched case-controldata constructed from the breast cancer data of the SEER study.Usually a logistic model is needed to associate the risk of the disease with the covariatesof interests. However, this logistic model may not be appropriate in some instances. Inthe last project , we adopt idea to matched case-control studies and derive an informationmatrix based test for testing overall model adequacy and investigate the properties againstthe cumulative residual based test in Arbogast and Lin (2004) via a simulation study. Theproposed method is less time consuming and has comparative power for small parameters.It is suitable to explore the overall model fitting.