The pharmaceutical industry is currently facing an industry wide problem of high attrition rates for new compounds and rising development costs. As a result of this, there is an emphasis on making the development process more ecient. By learning more about new compounds in the early stages of development, the aim is to stop ineective compounds earlier and improve dose selection for compounds that progress to phase III. One approach to this is to use adaptive designs. The focus of this thesis is on response adaptive designs within phase IIb dose-finding studies. We explore adapting the subject allocations based on accrued data, with the intention of focusing the allocation on the interesting parts of the curve and/or the best dose for phase III. In this thesis we have used simulation studies to assess the operational characteristics of a number of response adaptive designs. We found that there were consistent gains to be made by adapting when we were relatively cautious in our method of adaptation. That is, the adaptive method has the opportunity to alter the subject allocation when there is a clear signal in the data, but maintains roughly equal allocation when there is a lot of variability in the data. When we used adaptive designs that were geared to randomising subjects to a few doses, the results were more varied. In some cases the adaptation led to gains in efficacy whilst in others it was detrimental. One of the key aims of a phase IIb dose-finding study is to identify a dose to take forward into phase III. In the final chapter, we show that the way in which we choose the dose for phase III affects the expected gain, and so begin to consider how we can optimise the decision making process.

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This thesis is motivated by an adaptive design which was developed to inoculate healthy volunteers with nontypeable Haemophilus influenzae. The goal was to estimate the doses at which 50% (HCD50) and 90% (HCD90) of subjects became colonized. A fifteen-subject study was designed in two stages, with the first six subjects allocated sequentially. The design was chosen based on scientific and statistical arguments, however, due to limited time, heuristic decisions were made for expedience. This design and a number of alternative designs are evaluated in depth by simulation, under both Bayesian and frequentist criteria. In this thesis, Bayesian myopic strategies with one-step- , two-step- and three-step-look-ahead procedures are investigated. The optimal design is defined as the one with minimum expected loss where the loss is the sum of the posterior variance of the HCD50 and HCD90. The higher the expected loss, the worse the design. Designs using different prior distribution are examined. In addition, the toxicity-response relationship can also be incorporated in selecting the optimal design. A new model considering both colonization (efficacy) and adverse event (toxicity) is proposed, and design procedures developed. Furthermore, restrictions on the probability of toxicity are implemented. The results from simulations show that it is beneficial to look more steps ahead in determining the optimal dose although the benefit may not be large. The is true for both univariate (colonization) and bivariate (colonization and toxicity) models. For the bivariate model, as the restriction becomes more conservative (the probability of toxicity is constrained to be smaller), the expected loss becomes larger and early stopping may occur. Non-sequential designs are also found and examined using D and A criteria for optimal design. The expected loss is computed to evaluate the designs and to compare with sequential strategies. From the simulation results, it shows that using sequential design strategies does improve the performance of the design compared to using non-sequential strategies, and the improvement may be large.

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Indiana University-Purdue University Indianapolis (IUPUI) / The late-onset outcome issue is common in early phase dose- nding clinical trials. This problem becomes more intractable in phase I/II clinical trials because both toxicity and e cacy responses are subject to the late-onset outcome issue. The existing methods applying for the phase I trials cannot be used directly for the phase I/II trial due to a lack of capability to model the joint toxicity{e cacy distribution. We propose a conditional weighted likelihood (CWL) method to circumvent this issue. The key idea of the CWL method is to decompose the joint probability into the product of marginal and conditional probabilities and then weight each probability based on each patient's actual follow-up time. We further extend the proposed method to handle more complex situations where the late-onset outcomes are competing risks or semicompeting risks outcomes. We treat the late-onset competing risks/semi-competing risks outcomes as missing data and develop a series of Bayesian data-augmentation methods to e ciently impute the missing data and draw the posterior samples of the parameters of interest. We also propose adaptive dose- nding algorithms to allocate patients and identify the optimal biological dose during the trial. Simulation studies show that the proposed methods yield desirable operating characteristics and outperform the existing methods.

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Response adaptive randomization represents a major advance in clinical trial methodology that helps balance the benefits of the collective and the benefits of the individual and improves efficiency without undermining the validity and integrity of the clinical research. Response adaptive designs use information so far accumulated from the trial to modify the randomization procedure and deliberately bias treatment allocation in order to assign more patients to the potentially better treatment. No attention has been paid to incorporating the problem of errors-in-variables in adaptive clinical trials. In this work, some important issues and methods of response adaptive design of clinical trials in the presence of mismeasurement are examined. We formulate response adaptive designs when the dichotomous response may be misclassified. We consider the optimal allocations under various objectives, investigate the asymptotically best response adaptive randomization procedure, and discuss effects of misclassification on the optimal allocation. We derive explicit expressions for the variance-penalized criterion with misclassified binary responses and propose a new target proportion of treatment allocation under the criterion. A real-life clinical trial and some related simulation results are also presented.

Response adaptive randomization represents a major advance in clinical trial methodology that helps balance the benefits of the collective and the benefits of the individual and improves efficiency without undermining the validity and integrity of the clinical research. Response adaptive designs use information so far accumulated from the trial to modify the randomization procedure and deliberately bias treatment allocation in order to assign more patients to the potentially better treatment. No attention has been paid to incorporating the problem of errors-in-variables in adaptive clinical trials. In this work, some important issues and methods of response adaptive design of clinical trials in the presence of mismeasurement are examined. We formulate response adaptive designs when the dichotomous response may be misclassified. We consider the optimal allocations under various objectives, investigate the asymptotically best response adaptive randomization procedure, and discuss effects of misclassification on the optimal allocation. We derive explicit expressions for the variance-penalized criterion with misclassified binary responses and propose a new target proportion of treatment allocation under the criterion. A real-life clinical trial and some related simulation results are also presented.

The most common type of confirmatory trial is a randomised trial comparing the experimental treatment of interest to a control treatment. Confirmatory trials are expensive and take a lot of time in the planning, set up and recruitment of patients. Efficient methodology in clinical trial design is critical to save both time and money and allow treatments to become available to patients quickly. Often there are data available on the control treatment from a previous trial. These historical data are often used to design new trials, forming the basis of sample size calculations, but are not used in the analysis of the new trial. Incorporating historical control data into the design and analysis could potentially lead to more efficient trials. When the historical and current control data agree, incorporating historical control data could reduce the number of control patients required in the current trial and therefore the duration of the trial, or increase the precision of parameter estimates. However, when the historical and current data are inconsistent, there is a potential for biased treatment effect estimates, inflated type I error and reduced power. We propose two novel weights to assess agreement between the current and historical control data: a probability weight based on tail area probabilities; and a weight based on the equivalence of the historical and current control data parameters. For binary outcome data, agreement is assessed using the posterior distributions of the response probability in the historical and current control data. For normally distributed outcome data, agreement is assessed using the marginal posterior distributions of the difference in means and the ratio of the variances of the current and historical control data. We consider an adaptive design with an interim analysis. At the interim, the agreement between the historical and current control data is assessed using the probability or equivalence probability weight approach. The allocation ratio is adapted to randomise fewer patients to control when there is agreement and revert back to a standard trial design when there is disagreement. The final analysis is Bayesian utilising the analysis approach of the power prior with a fixed weight. The operating characteristics of the proposed design are explored and we show how the equivalence bounds can be chosen at the design stage of the current study to control the maximum inflation in type I error. We then consider a design where a treatment arm is added to an ongoing clinical trial. For many disease areas, there are often treatments in different stages of the development process. We consider the design of a two-arm parallel group trial where it is planned to add a new treatment arm during the trial. This could potentially save money, patients, time and resources. The addition of a treatment arm creates a multiple comparison problem. Dunnett (1955) proposed a design that controls the family-wise error rate when comparing multiple experimental treatments to control and determined the optimal allocation ratio. We have calculated the correlation between test statistics for the method proposed by Dunnett when a treatment arm is added during the trial and only concurrent controls are used for each treatment comparison. We propose an adaptive design where the sample size of all treatment arms are increased to control the family-wise error rate. We explore adapting the allocation ratio once the new treatment arm is added to maximise the overall power of the trial.