Group sequential designs are widely employed in phase II and phase III clinical trials. We can show that this test is Uniformly Most Powerful (UMP) test for hypotheses (1). Is an integer such that Pr ( S ≤ b + 1 | p = p 0 ) ≤ α.
Consider the test with reject region S ≤ b + 1, where b Pr ( S = s ) = h ( s N, M, n ) = ( M s ) ( N − M n − s ) / ( N n ), (2) Let S denote the number of patients in the sample who respond to the treatment, which is following the hypergeometric distribution, denoted as H (N M n), In order to test the above hypotheses, a sample of n patients selected randomly from the population of N patients is treated. H 1 : P > p 0, or equivalently H 0 : M ≤ M 0 vs. We start our discussion by considering the standard one-stage design for testing Patients response to the drug) is true with p 0 ≤ p 1, then the probability of falsely concluding that the drug is not efficacious is less than a user specified β. We also require if a specified alternative hypothesis H 1 : p ≤ p 1 If the null hypothesis is true, then we require that the probability of falsely concluding that the drug is efficacious is less than a user specified α. That the true response rate is less than some uninteresting level p 0 that is, the new drug shows some activity to fewer than M 0 = N p 0 To conduct clinical trials for such extremely rare disease, the designs developed here are based on testing a null hypothesis H 0 : p ≤ p 0 Von Hippel-Lindau (VHL) disease is another rare autosomal dominant syndrome which affects 1 in 36,000 babies. The disease affects approximately 1 in 140,000 babies and 1 in 60,000 adults a year.
Glycogen storage disease type II (also known as Pompe disease) is an autosomal recessive metabolic disorder which damages muscle and nerve cells throughout the body. For example, the drug is said to show some activity to a cancer patient whose tumor shrinks by at least 50% after the treatment. Care must be taken to explicitly define what is meant by "show some activity". Imagine that if all the patients with the disease were to be treated, the new drug would show some promise of activity to M of them, and therefore the response rate could be defined as p = M/N. Phase II trials of Investigational New Drugs (INDs) are performed in order to assess whether a new drug shows some promise of activity for the disease. Additionally, two types of optimal two-stage designs are examined for a range of design parameters one is optimal in the sense that the expected sample size under the null hypothesis is minimized, and the other is optimal in the sense that the maximum sample size is minimized.Įxact group sequential designs, Hypergeometric distribution, Minimax designs, Optimal designs, Small population, Uniformly most powerful testįor a rare disease, all the patients having the disease constitute a small population of size N. In this manuscript, it is proved that, for hypergeometric proportions, there exist exact group sequential designs that achieve the predesignated significance level and power with maximum total sample size bounded above by the sample size for the corresponding standard exact single-stage test. Although exact group sequential designs are widely employed in phase II clinical trials for binomial proportions, it is unknown whether or not similar tests can be employed for hypergeometric proportions. For a rare disease, all the patients having the disease constitute a small population, and the standard single-stage hypergeometric test is uniformly most powerful to evaluate the response probability of a specific treatment regimen.