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

❝ 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*🖖🏼 Довге життя Україна!

_{}

Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮

Science Quotes

### Complete thread:

- Estimation of sample size for NIT using ISCV By R pharm07 2022-05-03 11:23 [Power / Sample Size]
- Estimation of sample size for NTI using ISCV By R dshah 2022-05-03 13:04
- PowerTOST Helmut 2022-05-03 14:38
- PowerTOST pharm07 2022-05-04 08:08
- PowerTOST Helmut 2022-05-04 10:33
- PowerTOST pharm07 2022-05-04 14:54
- PowerTOST pharm07 2022-05-11 05:30
- PowerTOST: sampleN.NTID()Helmut 2022-05-11 13:19
- PowerTOST: sampleN.NTID() pharm07 2022-05-18 05:18
- sampleN.NTID(): Example Helmut 2022-05-18 14:30
- sampleN.NTID(): Example pharm07 2022-05-19 05:36

- sampleN.NTID(): Example Helmut 2022-05-18 14:30

- PowerTOST: sampleN.NTID() pharm07 2022-05-18 05:18

- PowerTOST: sampleN.NTID()Helmut 2022-05-11 13:19

- PowerTOST pharm07 2022-05-11 05:30

- PowerTOST pharm07 2022-05-04 14:54

- PowerTOST Helmut 2022-05-04 10:33

- PowerTOST pharm07 2022-05-04 08:08