Statistical Methods for patient chemosensitivity prediction based on in vitro Dose-response Data and A Modified Expectation-maximization (EM) Algorithm for Regression Analysis of Data with Non-ignorable Non-response

The first part of this dissertation concerns statistical analysis of in vitro assay data derived from tumor cells. An in vitro assay, ChemoFxQR , has been developed to predict patient’s clinical chemosensitivity. We explore statistical methods that can more efficiently use the assay data and improve the prediction of clinical outcome. In typical analysis of assay dose-response data, summary statistics such as the area under the dose-response curve, and concentration at half inhibition (IC50) are estimated from the assay data, then these statistics are dichotomized to predict the clinical outcome as sensitive or resistant. Considering the rigidness of the traditional models for dose-response curve fitting and the information loss in use of cell counts in the control wells, here we propose a mixture of exponential functions for fitting the dose-response curve and a branching process-based method to summarize the control well data. Simulation studies and analysis of clinical trial data show that the proposed method improves the prediction performance over some traditional methods. The second part concerns statistical analysis of regression data with nonresponses. Missing data are prevalent in clinical trials and public health studies. The often unknown mechanism for the missing data process may actually be associated with the underlying values. Standard statistical methods, including likelihood-based methods and weighted estimating equations, require a model for the missing-data mechanism and incorporate it in the estimation and inference. Misspecification of the missing-data model often causes biased estimates and wrongful conclusions. The expectation-maximization (EM) algorithm is an iterative algorithm that is often used to find the maximum likelihood estimate for the likelihood-based methods. In the E-steps, given a current estimate and the missing-data mechanism, the conditional expectations of the sufficient statistics are calculated. Under the premise that the current estimate is consistent, we find that those conditional expectations could be approximated from the empirical data without the need for assuming or modeling the missing-data mechanism. Subsequently, we propose a modified EM algorithm regardless of the potential missing-data mechanism. Simulation studies show that the parameter estimates have negligible bias and are more efficient than the initial estimates obtained from external data