The contemplated average success probability for normally distributed models with an application to optimal sample sizes selection

• Published in: Statistics in medicine Vol. 39; no. 23; pp. 3173 - 3183
• Main Authors: Zhang, Ying‐Ying, Rong, Teng‐Zhong, Li, Man‐Man
• Format: Journal Article
• Language: English
• Published: England Wiley Subscription Services, Inc 15.10.2020
• Subjects: average success probability; contemplated average success probability; normal model; optimal plan of sample sizes; Phase II and Phase III trials; Success; normal model; average success probability; contemplated average success probability; Phase II and Phase III trials; optimal plan of sample sizes
• ISSN: 0277-6715; 1097-0258
• DOI: 10.1002/sim.8658

We analytically obtain the average success probability (ASP) and the contemplated average success probability (CASP) for normally distributed observed differences in the treatment group and the placebo group means of the early trial and the confirmatory trial, assuming a uniform noninformative prior for the population treatment effect and a common known variance of the observations from both groups. For the CASP optimization problem with a fixed subtotal sample size of the early trial and the confirmatory trial of one arm larger than a threshold, we obtain the optimal plan of the sample sizes in a theorem. Moreover, in the theorem, we obtain the analytical formula of the optimal CASP as an increasing function of the subtotal sample size. After that, we calculate and compare the numerical values of the ASP with those in Table 1 of Chuang‐Stein (2006). Finally, we investigate the numerical features of the CASP and find the optimal plan of the sample sizes for a given subtotal sample size.