## PowerTOST: sampleN.NTID() [Power / Sample Size]

Hi pharm07,

» Let me understand again by looking following framework,
» Following data is available with me,
» Target power : eg, 0.8, .85, 0.9, CwT,CwR,sigWT,SigWR,theta0,theta1,theta2.

Although you could give values of theta1 and theta2, for the FDA keep the defaults of 0.8 and 1.25 (i.e., don’t specify anything): Additionally to passing RSABE and the variance-comparison you must pass conventional ABE.

» i want to estimate sample size for low to moderate NTID.

More examples are given there.

» Also to estimate sample size by assuming 30 & 40 % dropout rate.

See the two supportive functions in the section about dropouts in the named article.

» I have gone through the examples. Sometimes error comes as its beyond implied limit.

That’s possible if you specify a low or high theta0. Background: \eqalign{s_0&=0.1\tag{1}\\ \theta_\text{s}&=\frac{\log_e(1/0.9)}{s_0}\approx1.053605\ldots\\ \left\{\theta_{\text{s}_1},\theta_{\text{s}_2}\right\}&=\exp(\mp\theta_\text{s}\cdot s_\text{wR}), } where $$\small{s_0}$$ is the regulatory switching condition, $$\small{\theta_\text{s}}$$ the regulatory constant, and finally $$\small{\left\{\theta_{\text{s}_1},\theta_{\text{s}_2}\right\}}$$ are the implied limits. Say, you assume $$\small{CV_\text{wR}=0.1}$$. Since $$s_\text{wR}=\sqrt{\log_e(CV_\text{wR}^2+1)}\tag{2}$$ and by using $$\small{(1)}$$ you end up with $$\left\{\theta_{\text{s}_1},\theta_{\text{s}_2}\right\}=\left\{0.9002,1.1108\right\}.\tag{3}$$ In other words, for this $$\small{CV_\text{wR}}$$ any theta0 outside these limits cannot work. That’s by design:

library(PowerTOST) sampleN.NTID(CV = 0.1, theta0 = 0.90) +++++++++++ FDA method for NTIDs ++++++++++++            Sample size estimation --------------------------------------------- Study design:  2x2x4 (TRTR|RTRT) log-transformed data (multiplicative model) 1e+05 studies for each step simulated. alpha  = 0.05, target power = 0.8 CVw(T) = 0.1, CVw(R) = 0.1 True ratio     = 0.9 ABE limits     = 0.8 ... 1.25 Implied scABEL = 0.9002 ... 1.1108 Regulatory settings: FDA - Regulatory const. = 1.053605 - 'CVcap'           = 0.2142 Error: theta0 outside implied scABE limits! No sample size estimable.

Would you want to estimate a sample size for conventional ABE with a T/R-ratio outside 80–125%? Try:

sampleN.TOST(CV = 0.1, theta0 = 0.7999) # any (!) CV, targetpower, design

For NTIDs the FDA requires stricter batch-release spec’s (±5% instead of the common ±10%). There­fore, theta0 = 0.975 is the default of this function. I would not go below 0.95 unless the CV is relatively high (no scaling if $$\small{CV_\text{wR}\geq0.2142}$$).

» Heteroscedasticity can be challenging for me as T>R.

Yes, you are not alone.

» Can you check and verify if i am using correct programming.

I can’t till you post an example which you consider problematic.

Dif-tor heh smusma 🖖
Helmut Schütz

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