TitleMaximally selected test statistics
NameMa, Yuhui (author), Strickland, Pamela A. Ohman (chair), Lu, Shou-En (internal member), Shih, Weichung Joe (internal member), Fiedler, Nancy (internal member), Xie, Min-ge (outside member), Rutgers University, Edward J. Bloustein School of Planning and Pub. Policy,
DescriptionIn clinical or public health research studies, an investigator often assumes that some continuous predictive variable X allows classifying study population into a risk and a normal group with respect to a response variable Y. The aim of these research efforts is to transform a continuous variable into a binary variable by identifying a threshold or cutpoint in the predictor to distinguish different groups with high or low probabilities of favorable outcomes. Several methods including maximally selected chi-square statistics, maximally selected rank statistics and Koziol’s exact finite sample distribution approach to search for the optimal cut point have been reviewed and compared in Chapter 1. Since utilizing the maximally selected rank statistic to analyze semi-continuous predictors has not been discussed in the literatures, this dissertation provides the comparison of the null distribution, power curve, precision of cut point estimation between semi-continuous and continuous predictive variables via simulation. In Chapter 2, we confirmed the critical values to reject the null hypotheses are lower in semi-continuous predictors compare to continuous predictors. In Chapter 3, we show the power of maximally selected rank statistic from the semi-continuous predictor is stochastically larger than that from the continuous predictor. In Chapter 4, we found besides the sample size and effect size, the location of the true cut-point also affects the precision of the cut-point estimates. Compared to the continuous predictor, the semi-continuous predictor has higher percentage of correct cut-point estimates. The null distributions for semi-continuous predictor simulated in Chapter 1 are then applied to the study of “lead exposure, HPA dysfunction, blood pressure and hypertension risk” (Fiedler 2010) in Chapter 6 to determine the cut point in blood lead level that triggers increased stress. This application focused on the multivariate relationship between predictor variables and response variable, which were not discussed in the literature. After adjusted by other confounder variables through the regression residuals, a significant cut-point of 2 μg/dL in blood lead level is identified. Since the use of the regression residual of the response variable violates the independence assumption of this maximally selected rank statistics, this dissertation also demonstrated the robustness of this assumption in chapter 5.
NoteIncludes bibliographical references
Noteby Yuhui Ma
CollectionBloustein Grad. School of Planning and Pub. Policy ETD Collection
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.