Abstract:
In recent years, with the advancement observation in human genetic studies, the clinical trial community increasingly recognizes that the homogeneous patients may be heterogeneous at the genomic level. Such genomic technologies manage to bring along some possible avenues for developing genomic biomarkers to predict a genomically responsive patient subset that may have higher likelihood of benefiting from treatments. Additional genomic information can generate an appealing conceptual framework from the patient’s perspective in addressing the needs stemmed from personalized medicine during well-controlled clinical trials. There are many perceived benefits of personalized medicine that are based on the notion of being genomically proactive in disease identification, prevention and even better-stopping the recurrence all together.

The utility of personalized medicine in clinical trial can be well characterized through adaptive patient enrichment design. The adaptive enrichment approaches permit assessment of treatment effect that may be applicable to specific patient sets due to heterogeneous patient characteristics and/or different responses to the treatment. In this thesis, we adopt a weighted z-test to generate a test procedure, and the conditional power as our enrichment criterion and provide the type I error rate, power performance and sample size which are needed in respect to different weight t.

Keywords: adaptive design, conditional power, enrichment design, genomic biomarker, weighted z-test

Contents
1. Introduction 1
2. The Problem Under Study 2
3. Statistical Method in a Simple Scenario 4
3.1 Decision Rule Issue 4
3.2 Test Statistic Issue 5
3.3 Interim Assessment 6
3.4 Type I Error Issue 8
3.5 Power Calculation 10
4. Statistical method in Scenario II 11
4.1 Decision Rule Issue 11
4.2 Sample Size & Critical Value Adjustment: 13
5. Estimation of Treatment Effect Size 18
6. Simulation and Some Observed Properties 20
6.1 For Scenario I 21
6.2 For Scenario II 29
6.3 Estimation of Treatment Effect 35
7. Conclusion and Discussion 38
References 39

References
[1] Jack Bowden and Ekkehard Glimm. Unbiased estimation of selected
treatment means in two-stage trials. Biometrical Journal, 50:515–527,2008.
[2] Shein-Chung Chow and Mark Chang. Adaptive Design Methods in Clin-
ical Trials. Chapman and Hall/CRC, 2007.
[3] Lu Cui, H. M. James Hung, and Sue-Jane Wang. Modification of sample
size in group sequential clinical trials. Biometrics, Vol. 55, No. 3:853–857,1999.
[4] FDA. Guide for Industry. 2010.
[5] K. K. Gordon Lan, Yuhwen Soo, Cynthia Siu, and Mey Wang. The use of weighted z-tests in medical research. Journal of Biopharmaceutical Statistics, 15:625–639, 2005.
[6] Gang Li, Weichung J. Shih, Tailiang Xie, and Jiang Lu. A sample size adjustment procedure for clinical trials based on conditional power. Biostatistics, 3,2:277–287, 2002.
[7] Sue-Jane Wang, H. M. James Hung, and Robert T. ONeill. Adaptive patient enrichment designs in therapeutic trials. Biometrical Journal, 51:358–374, 2009.
[8] Sue-Jane Wang, Robert T. ONeill, and H.M.James Hung. Approaches to evaluation of treatment effect in randomized clinical trials with genomic
subset. Pharmaceutical Statistics, 6:227–244, 2007.
[9] Peter Bauer and Franz Koenig. The reassessment of trial perspectives
from interim data - critical view. Statistics in Medicine, 25:23–36, 2006.