Advances in random forest tuning and improvements in false discovery rate controlling procedures via test-specific covariate adjustments

Each chapter of this dissertation is devoted to one of three topics. The first two are novel false discovery rate (FDR) controlling methods in different situations, and the third deals with a new tuning parameter selection approach for the random forest method in regression problems. The primary research of this dissertation is to develop methods for controlling FDR while conducting multiple hypothesis tests with gene expression data. The first topic of this dissertation is a gene-specific covariate-based FDR-controlling method. We propose gene length as a potential gene-specific covariate. We develop a method based on covariate-specific conditional null probability for promising hypotheses with low p-values. We prove that the method controls positive FDR (pFDR) and provide an equivalent statement producing the method's rejection rule. Simulations demonstrate our method controls over pFDR, and the suggested method is better than existing methods in terms of true positive rate and summary statistics for the receiver operating characteristic (ROC) curve. Using data provided by Dr. Lim, we observe that our method rejects more null hypotheses at most target levels than existing methods. Another topic of this dissertation is developing an FDR-controlling method for circumstances where data are obtained from the pilot and main studies. We assume each study has unique properties such as sample size and error variance. Our method's rejection rule permits a higher p-value rejection threshold for the main study when the p-value for the pilot study is relatively low. This relationship enables us to evaluate fewer rejection rules than a competing method, resulting in more inference power. Our simulation study demonstrates our approach for combining results from two studies is superior to existing methods and controls FDR to a predetermined level. The number of rejected null hypotheses in the data analysis was greater than that of competing methods. The last topic of the dissertation is a unique tuning approach for random forest (RF) regression. We propose a case-specific tuning strategy for selecting the RF tuning parameter values of mtry and nodesize. We provide an example showing case-specific tuning parameters can be useful by demonstrating that the best choice for tuning parameter values varies across the predictor space. The tuning algorithm is then outlined mathematically. In a simulation study, our approach outperforms the conventional algorithms implemented in various R packages to minimize mean squared prediction error. Moreover, this method outperforms competing methods for the majority of the datasets we examined.

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