Laura R ☆ Israel, 20210201 10:19 (1227 d 21:31 ago) Posting: # 22197 Views: 2,403 

Dear Forum, I was interesting to hear thoughts about the need to power a DP study for a 505b2: BE between T and R will be demonstrated at one dose level. The PK of the drug is linear over the entire range however because of nonproportionality composition between T strengths we will run also a DP trial (for T only). Power model at alpha = 0.05 will be used, so the 90% CI of the slope will be compared to the [0.80, 1.25] bounds. Couldn't find any reference/guidance on the need to base sample size to achieve 80% or 90% power (in our case this will result in a very large study), and from review of precedents this sort of trials are many times nonpowered and only descriptive. Any comment is appreciated. Best, 
Helmut ★★★ Vienna, Austria, 20210201 12:34 (1227 d 19:16 ago) @ Laura R Posting: # 22198 Views: 1,923 

Hi Laura, ❝ […] power a DP study for a 505b2: ❝ […] The PK of the drug is linear over the entire range however because of nonproportionality composition between T strengths we will run also a DP trial (for T only). ❝ Power model at alpha = 0.05 will be used, so the 90% CI of the slope will be compared to the [0.80, 1.25] bounds. Let’s consider the power model:$$\small{\mu_j=\alpha\cdot D_{j}^{\;\beta}}\tag{1},$$where \(\small{\mu}\) is the respective PK metric and \(\small{D}\) the administered dose; both at level \(\small{j}\). For convenience generally the linearized model is used:$$\small{\log_{e}(\mu_j)=\alpha+\beta\cdot\log_{e}(D_j)},\tag{2}$$Whether only the extent of absorption (AUC) or additionally the rate (C_{max}) should be assessed is the topic of heated debates in the PK community… Whilst you start with \(\small{\left\{\theta_1,\theta_2\right\}}\) (e.g., \(\small{\left\{0.80,1.25\right\}}\)), you have to modify the acceptance range.^{1,2} When \(\small{r}\) is the ratio of highest and lowest dose levels, the parameter of interest is \(\small{r^{\,\beta1}}\) or the ratio of dosenormalized means \(\small{r_\textrm{dnm}}\). Dose proportionality is defined if \(\small{r^{\,\beta1}}\) is within a predefined acceptance range \(\small{\left\{\theta_\textrm{L},\theta_\textrm{U}\right\}}\). Since \(\small{r_\textrm{dnm}}\) is a function of \(\small{\beta}\), evaluation of dose proportionality can be performed through a \(\small{100(12\alpha)}\) confidence interval of \(\small{\beta}\) with the following modified acceptance range:$$\small{\left\{\theta_\textrm{L},\theta_\textrm{U}\right\}=\left\{1+\frac{\log_{e}(\theta_1)}{\log_{e}(r)}, 1+\frac{\log_{e}(\theta_2)}{\log_{e}(r)}\right\}}\tag{3}$$Example for \(\small{\left\{\theta_1,\theta_2\right\}=\left\{0.80,1.25\right\}}\): \(\small{\begin{matrix} In my European hybrids acc. to 2001/83/EC, Article 10(3) I used a mixedeffects model^{3} (fixed effect \(\small{D}\) and random effect \(\small{subject}\)) with restricted maximum likelihood estimation and Satterthwaite’s degrees of freedom. This allows to use incomplete data (subjects with missing periods). I guess that’s fine for the FDA as well. ❝ Couldn't find any reference/guidance on the need to base sample size to achieve 80% or 90% power (in our case this will result in a very large study),… Don’t know any reference but in my hybrids I used 80%. ❝ … and from review of precedents this sort of trials are many times nonpowered… If that’s accepted by the agency, fine. ❝ … and only descriptive. Mine were confirmatory (luckily never beyond \(\small{r=8}\)). In a purely exploratory setting you might consider more liberal \(\small{\left\{\theta_1,\theta_2\right\}}\). Hummel et al.^{4} proposed even \(\small{\left\{0.50,2.0\right\}}\)… See also the vignette of the package PowerTOST .
— Diftor heh smusma 🖖🏼 Довге життя Україна! _{} Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
Laura R ☆ Israel, 20210202 19:03 (1226 d 12:47 ago) @ Helmut Posting: # 22203 Views: 1,786 

Thanks for the insights, will post any update. 