Plastic instability due to collective dislocation effect in Portevin-Le Chatelier effect and dislocation nucleation
Two manifestations of plastic instability, the Portevin-Le Chatelier (PLC) effect and the coopera... more Two manifestations of plastic instability, the Portevin-Le Chatelier (PLC) effect and the cooperative nucleation of dislocation loops, have been studied. In the experimental part of the work, two creep-type mechanical tests have been conducted on a Cu-10at.%Al single crystal and a Mg single crystal to study the plastic instability in the PLC effect and dislocation nucleation respectively. The deformation modes of Cu-10at.%Al single crystal at different temperatures or loading conditions have been further studied by optical microscope and transmission electron microscope observations. The distribution of solute atoms around a moving dislocation has been obtained for a finite system. The dynamic interaction between the diffusing solute atoms and a moving dislocation has been studied using the Kinetic Monte Carlo (KMC) simulation of tensile and creep tests. The importance of dislocation interaction in the plastic instability of the PLC effect has also been studied by using a multi-dislocation system. In the study of the cooperative dislocation nucleation, a new method has been developed to calculate the image stress in a finite sample, which has been subsequently used to calculate the mean field stress responsible for the constructive dislocation interaction between nucleating dislocation loops.
Outcome-based adaptive randomization for binary data in clinical trials---Compare and contrast
ABSTRACT Monte Carlo simulation has been conducted to investigate parameter estimation and hypoth... more ABSTRACT Monte Carlo simulation has been conducted to investigate parameter estimation and hypothesis testing in some well known adaptive randomization procedures. The four urn models studied are Randomized Play-the-Winner (RPW), Randomized Pôlya Urn (RPU), Birth and Death Urn with Immigration (BDUI), and Drop-the-Loses Urn (DL). Two sequential estimation methods, the sequential maximum likelihood estimation (SMLE) and the doubly adaptive biased coin design (DABC), are simulated at three optimal allocation targets that minimize the expected number of failures under the assumption of constant variance of simple difference (RSIHR), relative risk (ORR), and odds ratio (OOR) respectively. Log likelihood ratio test and three Wald-type tests (simple difference, log of relative risk, log of odds ratio) are compared in different adaptive procedures. Simulation results indicates that although RPW is slightly better in assigning more patients to the superior treatment, the DL method is considerably less variable and the test statistics have better normality. When compared with SMLE, DABC has slightly higher overall response rate with lower variance, but has larger bias and variance in parameter estimation. Additionally, the test statistics in SMLE have better normality and lower type I error rate, and the power of hypothesis testing is more comparable with the equal randomization. Usually, RSIHR has the highest power among the 3 optimal allocation ratios. However, the ORR allocation has better power and lower type I error rate when the log of relative risk is the test statistics. The number of expected failures in ORR is smaller than RSIHR. It is also shown that the simple difference of response rates has the worst normality among all 4 test statistics. The power of hypothesis test is always inflated when simple difference is used. On the other hand, the normality of the log likelihood ratio test statistics is robust against the change of adaptive randomization procedures.
Bayesian adaptive randomization designs for targeted agent development
Clinical Trials, 2010
With better understanding of the disease&... more With better understanding of the disease's etiology and mechanism, many targeted agents are being developed to tackle the root cause of problems, hoping to offer more effective and less toxic therapies. Targeted agents, however, do not work for everyone. Hence, the development of target agents requires the evaluation of prognostic and predictive markers. In addition, upon the identification of each patient's marker profile, it is desirable to treat patients with best available treatments in the clinical trial accordingly. Many designs have recently been proposed for the development of targeted agents. These include the simple randomization design, marker stratified design, marker strategy design, efficient targeted design, etc. In contrast to the frequentist designs with equal randomization, we propose novel Bayesian adaptive randomization designs that allow evaluating treatments and markers simultaneously, while providing more patients with effective treatments according to the patients' marker profiles. Early stopping rules can be implemented to increase the efficiency of the designs. Through simulations, the operating characteristics of different designs are compared and contrasted. By carefully choosing the design parameters, types I and II errors can be controlled for Bayesian designs. By incorporating adaptive randomization and early stopping rules, the proposed designs incorporate rational learning from the interim data to make informed decisions. Bayesian design also provides a formal way to incorporate relevant prior information. Compared with previously published designs, the proposed design can be more efficient, more ethical, and is also more flexible in the study conduct. Response adaptive randomization requires the response to be assessed in a relatively short time period. The infrastructure must be set up to allow timely and more frequent monitoring of interim results. Bayesian adaptive randomization designs are distinctively suitable for the development of multiple targeted agents with multiple biomarkers.
Background: Response-adaptive randomizations are able to assign more patients in a comparative cl... more Background: Response-adaptive randomizations are able to assign more patients in a comparative clinical trial to the tentatively better treatment. However, due to the adaptation in patient allocation, the samples to be compared are no longer independent. At large sample sizes, many asymptotic properties of test statistics derived for independent sample comparison are still applicable in adaptive randomization provided that the patient allocation ratio converges to an appropriate target asymptotically. However, the small sample properties of commonly used test statistics in response-adaptive randomization are not fully studied. Methods: Simulations are systematically conducted to characterize the statistical properties of eight test statistics in six response-adaptive randomization methods at six allocation targets with sample sizes ranging from 20 to 200. Since adaptive randomization is usually not recommended for sample size less than 30, the present paper focuses on the case with a sample of 30 to give general recommendations with regard to test statistics for contingency tables in response-adaptive randomization at small sample sizes. Results: Among all asymptotic test statistics, the Cook's correction to chi-square test (T MC ) is the best in attaining the nominal size of hypothesis test. The William's correction to log-likelihood ratio test (T ML ) gives slightly inflated type I error and higher power as compared with T MC , but it is more robust against the unbalance in patient allocation. T MC and T ML are usually the two test statistics with the highest power in different simulation scenarios. When focusing on T MC and T ML , the generalized drop-the-loser urn (GDL) and sequential estimation-adjusted urn (SEU) have the best ability to attain the correct size of hypothesis test respectively. Among all sequential methods that can target different allocation ratios, GDL has the lowest variation and the highest overall power at all allocation ratios. The performance of different adaptive randomization methods and test statistics also depends on allocation targets. At the limiting allocation ratio of drop-the-loser (DL) and randomized play-the-winner (RPW) urn, DL outperforms all other methods including GDL. When comparing the power of test statistics in the same randomization method but at different allocation targets, the powers of log-likelihood-ratio, log-relative-risk, logodds-ratio, Wald-type Z, and chi-square test statistics are maximized at their corresponding optimal allocation ratios for power. Except for the optimal allocation target for log-relative-risk, the other four optimal targets could assign more patients to the worse arm in some simulation scenarios. Another optimal allocation target, R RSIHR , proposed by Rosenberger and Sriram (Journal of Statistical Planning and Inference, 1997) is aimed at minimizing the number of failures at fixed power using Wald-type Z test statistics. Among allocation ratios that always assign more patients to the better treatment, R RSIHR usually has less variation in patient allocation, and the values of variation are consistent across all simulation scenarios. Additionally, the patient allocation at R RSIHR is not too extreme. Therefore, R RSIHR provides a good balance between assigning more patients to the better treatment and maintaining the overall power.
Plastic instability due to collective dislocation effect in Portevin-Le Chatelier effect and dislocation nucleation
Two manifestations of plastic instability, the Portevin-Le Chatelier (PLC) effect and the coopera... more Two manifestations of plastic instability, the Portevin-Le Chatelier (PLC) effect and the cooperative nucleation of dislocation loops, have been studied. In the experimental part of the work, two creep-type mechanical tests have been conducted on a Cu-10at.%Al single crystal and a Mg single crystal to study the plastic instability in the PLC effect and dislocation nucleation respectively. The deformation modes of Cu-10at.%Al single crystal at different temperatures or loading conditions have been further studied by optical microscope and transmission electron microscope observations. The distribution of solute atoms around a moving dislocation has been obtained for a finite system. The dynamic interaction between the diffusing solute atoms and a moving dislocation has been studied using the Kinetic Monte Carlo (KMC) simulation of tensile and creep tests. The importance of dislocation interaction in the plastic instability of the PLC effect has also been studied by using a multi-dislocation system. In the study of the cooperative dislocation nucleation, a new method has been developed to calculate the image stress in a finite sample, which has been subsequently used to calculate the mean field stress responsible for the constructive dislocation interaction between nucleating dislocation loops.
Outcome-based adaptive randomization for binary data in clinical trials---Compare and contrast
ABSTRACT Monte Carlo simulation has been conducted to investigate parameter estimation and hypoth... more ABSTRACT Monte Carlo simulation has been conducted to investigate parameter estimation and hypothesis testing in some well known adaptive randomization procedures. The four urn models studied are Randomized Play-the-Winner (RPW), Randomized Pôlya Urn (RPU), Birth and Death Urn with Immigration (BDUI), and Drop-the-Loses Urn (DL). Two sequential estimation methods, the sequential maximum likelihood estimation (SMLE) and the doubly adaptive biased coin design (DABC), are simulated at three optimal allocation targets that minimize the expected number of failures under the assumption of constant variance of simple difference (RSIHR), relative risk (ORR), and odds ratio (OOR) respectively. Log likelihood ratio test and three Wald-type tests (simple difference, log of relative risk, log of odds ratio) are compared in different adaptive procedures. Simulation results indicates that although RPW is slightly better in assigning more patients to the superior treatment, the DL method is considerably less variable and the test statistics have better normality. When compared with SMLE, DABC has slightly higher overall response rate with lower variance, but has larger bias and variance in parameter estimation. Additionally, the test statistics in SMLE have better normality and lower type I error rate, and the power of hypothesis testing is more comparable with the equal randomization. Usually, RSIHR has the highest power among the 3 optimal allocation ratios. However, the ORR allocation has better power and lower type I error rate when the log of relative risk is the test statistics. The number of expected failures in ORR is smaller than RSIHR. It is also shown that the simple difference of response rates has the worst normality among all 4 test statistics. The power of hypothesis test is always inflated when simple difference is used. On the other hand, the normality of the log likelihood ratio test statistics is robust against the change of adaptive randomization procedures.
Bayesian adaptive randomization designs for targeted agent development
Clinical Trials, 2010
With better understanding of the disease&... more With better understanding of the disease's etiology and mechanism, many targeted agents are being developed to tackle the root cause of problems, hoping to offer more effective and less toxic therapies. Targeted agents, however, do not work for everyone. Hence, the development of target agents requires the evaluation of prognostic and predictive markers. In addition, upon the identification of each patient's marker profile, it is desirable to treat patients with best available treatments in the clinical trial accordingly. Many designs have recently been proposed for the development of targeted agents. These include the simple randomization design, marker stratified design, marker strategy design, efficient targeted design, etc. In contrast to the frequentist designs with equal randomization, we propose novel Bayesian adaptive randomization designs that allow evaluating treatments and markers simultaneously, while providing more patients with effective treatments according to the patients' marker profiles. Early stopping rules can be implemented to increase the efficiency of the designs. Through simulations, the operating characteristics of different designs are compared and contrasted. By carefully choosing the design parameters, types I and II errors can be controlled for Bayesian designs. By incorporating adaptive randomization and early stopping rules, the proposed designs incorporate rational learning from the interim data to make informed decisions. Bayesian design also provides a formal way to incorporate relevant prior information. Compared with previously published designs, the proposed design can be more efficient, more ethical, and is also more flexible in the study conduct. Response adaptive randomization requires the response to be assessed in a relatively short time period. The infrastructure must be set up to allow timely and more frequent monitoring of interim results. Bayesian adaptive randomization designs are distinctively suitable for the development of multiple targeted agents with multiple biomarkers.
Background: Response-adaptive randomizations are able to assign more patients in a comparative cl... more Background: Response-adaptive randomizations are able to assign more patients in a comparative clinical trial to the tentatively better treatment. However, due to the adaptation in patient allocation, the samples to be compared are no longer independent. At large sample sizes, many asymptotic properties of test statistics derived for independent sample comparison are still applicable in adaptive randomization provided that the patient allocation ratio converges to an appropriate target asymptotically. However, the small sample properties of commonly used test statistics in response-adaptive randomization are not fully studied. Methods: Simulations are systematically conducted to characterize the statistical properties of eight test statistics in six response-adaptive randomization methods at six allocation targets with sample sizes ranging from 20 to 200. Since adaptive randomization is usually not recommended for sample size less than 30, the present paper focuses on the case with a sample of 30 to give general recommendations with regard to test statistics for contingency tables in response-adaptive randomization at small sample sizes. Results: Among all asymptotic test statistics, the Cook's correction to chi-square test (T MC ) is the best in attaining the nominal size of hypothesis test. The William's correction to log-likelihood ratio test (T ML ) gives slightly inflated type I error and higher power as compared with T MC , but it is more robust against the unbalance in patient allocation. T MC and T ML are usually the two test statistics with the highest power in different simulation scenarios. When focusing on T MC and T ML , the generalized drop-the-loser urn (GDL) and sequential estimation-adjusted urn (SEU) have the best ability to attain the correct size of hypothesis test respectively. Among all sequential methods that can target different allocation ratios, GDL has the lowest variation and the highest overall power at all allocation ratios. The performance of different adaptive randomization methods and test statistics also depends on allocation targets. At the limiting allocation ratio of drop-the-loser (DL) and randomized play-the-winner (RPW) urn, DL outperforms all other methods including GDL. When comparing the power of test statistics in the same randomization method but at different allocation targets, the powers of log-likelihood-ratio, log-relative-risk, logodds-ratio, Wald-type Z, and chi-square test statistics are maximized at their corresponding optimal allocation ratios for power. Except for the optimal allocation target for log-relative-risk, the other four optimal targets could assign more patients to the worse arm in some simulation scenarios. Another optimal allocation target, R RSIHR , proposed by Rosenberger and Sriram (Journal of Statistical Planning and Inference, 1997) is aimed at minimizing the number of failures at fixed power using Wald-type Z test statistics. Among allocation ratios that always assign more patients to the better treatment, R RSIHR usually has less variation in patient allocation, and the values of variation are consistent across all simulation scenarios. Additionally, the patient allocation at R RSIHR is not too extreme. Therefore, R RSIHR provides a good balance between assigning more patients to the better treatment and maintaining the overall power.
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