This dissertation consists of three projects in matched case-control studies. In the first project, we employ a general bias preventive approach developed by Firth (1993) to handle the bias of an estimator of the log-odds ratio parameter in conditional logistic regression by solving a modified score equation. The resultant estimator not only reduces bias but also can prevent producing infinite value. Furthermore, we propose a method to calculate the standard error of the resultant estimator. A closed form expression for the estimator of the log-odds ratio parameter is derived in the case of a dichotomous exposure variable. Finite sample properties of the estimator are investigated via a simulation study. Finally, we apply the 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 checking adequacy of a functional form of a covariate of interest in matched case-control studies by using penalized regression splines to approximate an unknown function. The asymptotic distribution 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 statistic when the alternative model holds. Through a simulation study we assess and compare the finite sample properties of the proposed test with that of Arbogast and Lin (2004). To illustrate the usefulness of the method, we apply the proposed test to a matched case-control data 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 covariates of interests. However, this logistic model may not be appropriate in some instances. In the last project , we adopt idea to matched case-control studies and derive an information matrix based test for testing overall model adequacy and investigate the properties against the cumulative residual based test in Arbogast and Lin (2004) via a simulation study. The proposed method is less time consuming and has comparative power for small parameters. It is suitable to explore the overall model fitting.
This dissertation consists of three projects in matched case-control studies. In the first project, we employ a general bias preventive approach developed by Firth (1993) to handle the bias of an estimator of the log-odds ratio parameter in conditional logistic regression by solving a modified score equation. The resultant estimator not only reduces bias but also can prevent producing infinite value. Furthermore, we propose a method to calculate the standard error of the resultant estimator. A closed form expression for the estimator of the log-odds ratio parameter is derived in the case of a dichotomous exposure variable. Finite sample properties of the estimator are investigated via a simulation study. Finally, we apply the 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 checking adequacy of a functional form of a covariate of interest in matched case-control studies by using penalized regression splines to approximate an unknown function. The asymptotic distribution 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 statistic when the alternative model holds. Through a simulation study we assess and compare the finite sample properties of the proposed test with that of Arbogast and Lin (2004). To illustrate the usefulness of the method, we apply the proposed test to a matched case-control data 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 covariates of interests. However, this logistic model may not be appropriate in some instances. In the last project , we adopt idea to matched case-control studies and derive an information matrix based test for testing overall model adequacy and investigate the properties against the cumulative residual based test in Arbogast and Lin (2004) via a simulation study. The proposed method is less time consuming and has comparative power for small parameters. It is suitable to explore the overall model fitting.