The development of pharmaceutical products is risky, challenging, slow, costly and time-consuming endeavor. An analysis which takes into account that projects which were neither success nor fair suggests that it usually takes about 10-15 years to develop one new medicine from the time it is discovered to when it is available for commercial marketing and treating patients. The average cost to research and develop each successful drug is estimated to be $800 million to $1 billion and 70% of the cost of pharmaceutical development is wasted on drugs that do not even make it to market.
By the time a drug company applies to the Food and Drug Administration (FDA) for marketing approval of a new product, on average it has performed more than 70 clinical studies on at least 4,000 patients. Despite a better understanding of disease etiology and advance in medical technology, there is only 1 out of 10,000 candidates screened in the laboratory that will survive to market launch, and more than 60% of the potential candidates that enter clinical trials fail. Furthermore, the success rate of the phase III stage of the clinical development has fallen by 30% [1]. On the other hand, the development of biomedical science has been raised to cure many diseases nowadays and been full of potential. Nevertheless, the number of the biomedical products and new drugs submitted to the FDA and approved by the FDA does not increase. One of the probable reasons may be that the drug screening process should become more efficient and effective to let the biomedical science fill with full potential. As a result, there is an urgent need of new strategies and methodologies for overall success improving, efficient, and cost-effective designs to screen potential candidates based on the idea of the proof of the concept for efficacy in a rapid and reliable manner to minimize the total sample size and hence to shorten the duration of the trials.
Trials of pharmaceutical agents have been divided into phase Ⅰ─ Ⅳ. The drug
first was developed and tested in the laboratory. Once it is done and ready for testing in the human subjects, a phase Ⅰ trial is conducted. The purpose of the phase Ⅰ trial is to examine the drug tolerance, metabolism and study the drug toxicity in human and also identify the best dose to be used. Then, the phase II trial may employ the best dose identified in the phase Ⅰ study to assess the efficacy of the drug and determine whether it should be tested in further phase Ⅲ trial. The phase Ⅲ trial consists of therapeutic confirmatory studies and establishment of the safety profile by comparing the drug with other compound being used to treat the condition. The phase Ⅳ trial two-stage designs, the approaches commonly used are Gehan design, Simon optimal design, and the minimax design. These designs are based on the frequentist statistical approach. For Simon’s two-stage design, it requires some specific input, including uninteresting level, target level, type Ⅰ error and type II error. The sample sizes are evaluated subjected to the constraint upon the type Ⅰ error and type II error. The idea of the two-stage approach is presented as follows. When the first stage is completed, the trial would be terminated if the response rate does not exceed some critical value indicating that the drug has low efficacy and is not recommended to the next step of the trial. Otherwise, more patients are enrolled and treated in the second stage. After the second stage is completed, the final analysis is performed with the outcomes of the first and the second stage. The drug would be rejected if the overall response rate is less than some critical level and not be recommended to the phase Ⅲ trial.
Otherwise, the drug would be recommended to the phase Ⅲ trial. Simon [4] proposed
the “Optimal two-stage designs for phase II clinical trials” with binary response endpoints. Tsou et al. [5] proposed a two-stage screening design based on continuous efficacy endpoints under the framework of Simon two-stage design.
The main concept of Bayesian approach is the incorporation of the prior distribution which brings in the prior experience or information. So, the Bayesian design in Simon [4] allows for the formal incorporation of relevant information from the other resources of the evidence in the monitoring and analysis of the trial. With a Bayesian approach, we can obtain the posterior distribution of the true response rate.
This allows us to compute the probability that the response rate falls within the region of interest. For example, we can derive the interval with a 95 per cent probability of containing the true response rate. On the other hand, the frequentist approach cannot answer this kind of questions.
Several Bayesian designs have been proposed for phase II trials, for example methods proposed by Thall [6], Heitjan [7], and Sylverster [8], while most of these are not the real two-stage design but the continuous monitoring design of the trial. In particular, Thall and Simon proposed a design which involves the continual accrual of patients until the new drug is shown with high posterior probability to be either promising or not promising, or until a predetermined maximum sample size is reached.
Their design requires the specifications of an informative clinical prior for the response rate of the standard drug which has been found to be the best so far, and a non-informative clinical prior for the response rate of the new drug [6]. In contrast, instead of the prior for the new drug, Heitjan’s design requires the specification of hypothetical skeptical and enthusiastic priors. Both Thall and Simon’s as well as Heitjan’s designs make use of probability distributions for both the response proportions of the standard drug as well as the new drug. This is unlike the framework of the frequentist designs in which only take account of the response rate of the
standard drug.
Tan and Machin [3] proposed two Bayesian designs for phase II trials which are like the frameworks of designs of Thall [6], Heitjan [7] and Sylverster [8]. The design does not require the specification of a loss or utility function and only need to specify a prior distribution for the response rate of the new drug and not the standard drug as well. It would make the design to be similar to the frequentist approach of two stage phase II clinical trials.
In this thesis, two Bayesian designs for phase II trials with continuous endpoints will be developed. One is the single threshold Bayesian design and another is the dual threshold Bayesian design. These two designs are presented in Section 2 and 3, respectively. The methods to determine the sample size and to determine whether to recommend the drug to the phase Ⅲ trial or not are also proposed. In Section 4, the numerical results of sample sizes and simulation studies are shown. Comparison with Simon design will be given in Section 5. Discussion and conclusion are made in Section 6.