Dissertation > Excellent graduate degree dissertation topics show

The nature of the random allocation rule Drop-the-loser supplement

Author: HuYanQing
Tutor: ZhangLiXin
School: Zhejiang University
Course: Probability Theory and Mathematical Statistics
Keywords: response-adaptive randomization drop-the-loser rule urn ball immigration process response allocation probability generating function
CLC: O213
Type: Master's thesis
Year: 2007
Downloads: 18
Quote: 0
Read: Download Dissertation


In clinical trials, in order to compare the effects of two or more treatments, we ran-domly allocate each patient to one treatment. In view of improving the power of sta-tistical test and also allocating the patients to the better treatment, response-adaptiverandomization is often suggested. The advantage of this kind of randomization is thatwe can make good use of the data obtained thus far, which is useful in deciding whichtreatment should be assigned to the incoming subject. The most popular designs inresponse-adaptive randomization are urn models. However, it is often difficult to makestatistical inferences in response-adaptive randomization due to the dependency of thedata. Usually, advanced mathematical theories, like martingale limit theorems, shouldbe adopted. Another technique is embedding the discrete urn models into a family ofcontinuous Markov processes. In this way, we can deduce the properties of statistics inurn models from the theory of Markov processes.Ivanova (2003) proposed a new kind of urn model which is called the drop-the-loser rule. It has better properties than the play-the-winner rule. For the study of theformer, the main tool is embedding this urn model into a family of linear death pro-cesses with immigration. In this paper, we also want to use this tool, and by utilizingprobability generating functions, we try to get the central limit theorems for the max-imum likelihood estimator of pi. For treatment i, we first obtain the joint probabilitygenerating function for (Xi(t), Yi(t)), from which we can get the characteristic func-tion for t1/2(Xi(t)/t-api/qi, Yi(t)/t-a). When t goes to∞, this characteristic functionhas the form of a normal distribution. Since (?)i(t)=Xi(t)/Xi(t)+Yi(t) is function of(Xi(t)/t, Yi(t)/t), when normalized, (?)i(t) also tends to a normal distribution as t goes to∞. For the central limit theorem of (?)(t)=((?)1(t), ..., (?)K(t)), we can do it in a similarway by first obtaining the joint probability generating function of the correspondingstatistics. And the main task lies in verifying if the characteristic function of a randomvector tends to the one of a multi-normal vector.In order to make connections between the properties of statistics under continuoustime t and the ones of corresponding statistics under discrete urn model, Ivanova (2006)introduced the stopping time Tm, i.e., the moment when type 0 ball is drawn for the m th time. In this paper, we show that under this stopping time, the empirical estimator ofsuccess probability pi, (?)i(Tm)=Xi(Tm)/Xi(Tm)+Yi(Ym), is still the maximum likelihood estimatorof pi.Since the asymptotic variance of the allocation proportion is an important aspectof response-adaptive randomization, we compare these values of two randomizationrules, the drop-the-loser rule and one similar rule. By doing this, we can see why thedrop-the-loser rule is designed in a way that one ball of each type is added at the sametime after an immigration ball is drawn.

Related Dissertations

  1. The Theoretical and Experimental Research on Preload and Supporting Stiffness of a Wire Race Ball Bearing,TH133.331
  2. Design and Research on Stabilization Loop of Gyro Stabilized Pod Control System,V241.5
  3. Research on the Attitude Controller Design and Control Strategy of High Altitude Platform,V249.1
  4. The Research on Paper Currency Classification Method Based on Harr-Like Feature and Minimal Ball Including Samples,TP391.41
  5. Screening Molecular Targets of Phytophthora Sojae RXLR Effectors,S435.651
  6. Studies on Extraction, Isolation, Purification and Antioxidation Activity of Flavonoids from the Fruits of Avicennia Marina,S793.9
  7. Study on Application of Non-phosphate Additive in Frozen Penaeus Vannamei and Mechanism of Water-holding,TS254.4
  8. The Combined Effect of Several Environmental Factor on Fertilization, Hatching and Juvenile Growth of Nile Tilapia,S917.4
  9. Cooperative Education Application talent of local universities and research,G647
  10. A Study of the Contingent Macro-forecast Improvement of Guangdong Ocean and Fishery,D630
  11. The Characteristics of the Nonspecific Immune Responses of Paa Spinosa under Various Environmental Stresses,Q958.1
  12. Lipase-catalyzed Transesterification of Lard to Produce L-ascorbyl Fatty Acid Esters,TS221
  13. Recovery Sulphur from Zinc Concentrate of Pressure Acid Leaching Residue,X751
  14. Modification for PVA-Based Composite Packaging Material with Nano-SiO2 and Its Influence on Fresh Preservation Effect of Salted Duck Eggs,TS253.46
  15. Study on Host Selection of Encarsia Sophia between Bemisia Tabaci B-Biotype and Q-Biotype Nymph,S476.3
  16. Effect on Yield and Quality of Cotton with Soil Waterloged and the Physiological Basis,S562
  17. Effects of Ulinastatin on Inflammatory Response to Cardiopulmonary Bypass in Cardiac Valve Replacement Surgery,R614
  18. Research on the Relationships between Empathic Response and Helping Behaviors to Valuing the Welfare of the Person,B844
  19. Electropolymerization and Electrochromic Properties of Conducting Polymers,O631.3
  20. Study on Selection and Allocation of Agricultural Machinery in Huanghai State Farm,S232.3
  21. Investigations of Bamboo Categories in Shanghai and Their Collocation and Application in Gardens,S795

CLC: > Mathematical sciences and chemical > Mathematics > Probability Theory and Mathematical Statistics > Application of statistical mathematics
© 2012 www.DissertationTopic.Net  Mobile