Improved Performance and Stability of the Knockoff Filter and an Approach to Mixed Effects Modeling of Sequentially Randomized Trials

The knockoff filter is a variable selection technique for linear regression with finite-sample control of the regression false discovery rate (FDR). The regression FDR is the expected proportion of selected variables which, in fact, have no effect in the regression model. The knockoff filter constructs a set of synthetic variables which are known to be irrelevant to the regression and, by serving as negative controls, help identify relevant variables. The first two thirds of this thesis describe tradeoffs between power and collinearity due to tuning choices in the knockoff filter and provide a stabilization method to reduce variance and improve replicability of the selected variable set using the knockoff filter. The final third of this thesis develops an approach for mixed modeling and estimation for sequential multiple assignment randomized trials (SMARTs). SMARTs are an important data collection tool for informing the construction of dynamic treatment regimens (DTRs), which use cumulative patient information to recommend specific treatments during the course of an intervention. A common primary aim in a SMART is the marginal mean comparison between two or more of the DTRs embedded in the trial, and the mixed modeling approach is developed for these primary aim comparisons based on a continuous, longitudinal outcome. The method is illustrated using data from a SMART in autism research.PHDStatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/163099/1/luers_1.pd