Mathematics Ph.D. Dissertations


Simultaneous Inference With Application To Dose-Response Study

Date of Award


Document Type


Degree Name

Doctor of Philosophy (Ph.D.)



First Advisor

John Chen (Committee Chair)

Second Advisor

Hrishikesh Joshi (Other)

Third Advisor

Wei Ning (Committee Member)

Fourth Advisor

Junfeng Shang (Committee Member)


One of the common applications of simultaneous inference problems is in the dose-response study, where different dosage levels need to be tested simultaneously. Although several multiple comparison procedures such as Bonferroni, Holm (1979), Hochberg (1988), Dunnett (1955) can be used to adjust multiplicity and control family-wise error rate, Ma and McDermott (2019) proposed a modification of the MCP-Mod approach to finding the dose-response relationship when the responses are normal. However, there are many cases where the response variable is not symmetry and follows a skew-normal distribution. In my research, we proposed a new multiple contrast test statistic to find the significant dose-response relationship for skew-normal responses. Later, we used the proposed test statistics to find the lower confidence bound in the simultaneous confidence step-wise procedure. Simultaneous confidence sets are used when information regarding follow-up investigation in clinical trials is needed. Further in this dissertation, we discussed the step-wise procedure to find the minimum effective dosage for the survival data. To do this, we combined the Kaplan-Meier estimator to estimate the survival function and Holm’s stepdown procedure to strongly control the family-wise error rate while testing different treatment groups with the control group.