narra1813
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India,
2019-08-10 11:21
(1667 d 15:28 ago)

Posting: # 20491
Views: 4,726
 

 Sample size calculation for NTI molecules [Power / Sample Size]

Dear All,

By using the only power and sample size how we can calculate the N for NTI molecules. what about the other parameters.

Calculating the probability of passing (power) and the sample size (to meet a desired power target) are just two sides of the same coin. One determines the power at a fixed value of n (number of subjects) and the other determines n for a fixed value of power.

FDA published a paper that gives the results of the correct simulations; Jiang W, et al, A Bioequivalence Approach for Generic Narrow Therapeutic Index Drugs: Evaluation of the Reference-Scaled Approach and Variability Comparison Criterion, The AAPS Journal, 17(4), 2015.

Please provide your valuable suggestion on the same, for my understanding the same.


Edit: I deleted another post with identical text. Please follow the Forum’s Policy. I activated the PM-function and edited your profile[Helmut]

Regards

Narra Narendra Babu
Helmut
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Vienna, Austria,
2019-08-10 13:23
(1667 d 13:26 ago)

@ narra1813
Posting: # 20492
Views: 4,216
 

 PowerTOST: sampleN.NTIDFDA()

Hi Narra,

❝ By using the only power and sample size how we can calculate the N for NTI molecules. what about the other parameters.


As with any other reference-scaling method we have to use simulations. The conditions for BE of NTIDs are summarized in this post and the statistical method is given in the FDA’s warfarin-guidance.

Sample size estimations are implemented in function sampleN.NTIDFDA() of the [image]-package PowerTOST since 2013. :thumb up:
Example: CVwT = CVwR = 10%, expected T/R-ratio 97.5%, desired (target) power 80%.

library(PowerTOST)
sampleN.NTIDFDA(CV = 0.1)

Gives:

+++++++++++ FDA method for NTIDs ++++++++++++
           Sample size estimation
---------------------------------------------
Study design:  2x2x4
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     = 0.975
ABE limits     = 0.8 ... 1.25
Implied scABEL = 0.9002 ... 1.1108
Regulatory settings: FDA
- Regulatory const. = 1.053605
- 'CVcap'           = 0.2142

Sample size search
 n     power
14   0.717480
16   0.788690
18   0.841790

Note that in this simple call defaults of the function are applied, namely a full replicate 2-sequence 4-period design (TRTR|RTRT), identical within-subject CVs of T and R, desired (target) power 80%, and T/R 97.5% (the FDA requires for NTIDs tighter content specifications).
Let’s explore what happens if T has a higher variability (15%) than R (10%). Abbreviated output.

print(sampleN.NTIDFDA(CV = c(0.15, 0.1), details = FALSE,
                      print = FALSE)[8:9], row.names = FALSE)
Sample size Achieved power
         32        0.81756

Much higher sample size because it will be more difficult to meet the sWT/sWR criterion.

Note that the FDA wants a 4-period full replicate. If you are concerned about blood loss and/or dropouts you may consider a 3-period full replicate (TRT|RTR). Since that deviates from the guidance, I recommend to initiate a controlled correspondence with the OGD first. Like the first example but for 90% power:

sampleN.NTIDFDA(CV = 0.1, design = "2x2x3", targetpower = 0.9)

+++++++++++ FDA method for NTIDs ++++++++++++
           Sample size estimation
---------------------------------------------
Study design:  2x2x3
log-transformed data (multiplicative model)
1e+05 studies for each step simulated.

alpha  = 0.05, target power = 0.9
CVw(T) = 0.1, CVw(R) = 0.1
True ratio     = 0.975
ABE limits     = 0.8 ... 1.25
Implied scABEL = 0.9002 ... 1.1108
Regulatory settings: FDA
- Regulatory const. = 1.053605
- 'CVcap'           = 0.2142

Sample size search
 n     power
34   0.894880
36   0.910210


We can also explore deviations from our assumptions (only equal CVs implemented). For the first example, minimum acceptable power 70% (default of the function):

pa.NTIDFDA(CV = 0.1)

Sample size plan RSABE NTID
 Design alpha CVwT CVwR theta0 theta1 theta2 Sample size Achieved power Target power
  2x2x4  0.05  0.1  0.1  0.975    0.8   1.25          18        0.84179          0.8

Power analysis
CV, theta0 and number of subjects which lead to min. acceptable power of at least 0.7:
 CV = (0.0622, 0.3344), theta0= 0.9602
 N = 14 (power= 0.7175)


[image]


Note the interesting behavior of power with various CVs. If the CV gets smaller, limits get tighter and power drops. On the other hand, if the CV increases, we have wider limits and gain power. If the CVwR >21.42% the additional criterion “must pass 80–125%” becomes increasingly important and power drops.

We can also explore which of the three criteria are most important. Again the first example and the estimated sample size 18:

power.NTIDFDA(CV = 0.1, n = 18, details = TRUE)

  p(BE)  p(BE-sABEc)    p(BE-ABE) p(BE-sratio)
0.84179      0.85628      1.00000      0.97210

The scaled criterion drives the sample size.

The second example where CVwT > CVwR:

power.NTIDFDA(CV = c(0.15, 0.1), n = 32, details = TRUE)

  p(BE)  p(BE-sABEc)    p(BE-ABE) p(BE-sratio)
0.81756      0.92270      1.00000      0.87137

Here the sWT/sWR criterion drives the sample size.

❝ FDA published a paper* …

❝ Please provide your valuable suggestion on the same, for my understanding the same.


Hope the above helps.


  • Jiang W, Makhlouf F, Schuirmann DJ, Zhang X, Zheng N, Conner D, Yu LX, Lionberger R. A Bioequivalence Approach for Generic Narrow Therapeutic Index Drugs: Evaluation of the Reference-Scaled Approach and Variability Comparison Criterion. AAPS J. 2015;17(4):891–901. doi:10.1208/s12248-015-9753-5. [image] PMC Free Full text.

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Mahmoud
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Jordan,
2024-02-06 12:45
(26 d 13:04 ago)

@ Helmut
Posting: # 23858
Views: 410
 

 PowerTOST: sampleN.NTIDFDA()

Dear Helmut

Study design:  2x2x4

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     = 0.975

ABE limits     = 0.8 ... 1.25

Implied scABEL = 0.9002 ... 1.1108

Regulatory settings: FDA

- Regulatory const. = 1.053605

- 'CVcap'           = 0.2142


what do mean about 'CVcap' = 0.2142
Thank you
Mahmoud


Edit: Full quote removed. Please delete everything from the text of the original poster which is not necessary in understanding your answer; see also this post #5[Helmut]
Helmut
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2024-02-06 14:51
(26 d 10:57 ago)

@ Mahmoud
Posting: # 23859
Views: 405
 

 'CVcap'

Hi Mahmoud,

❝ what do mean about 'CVcap' = 0.2142

Quoting my previous post:

If the CVwR >21.42% the additional criterion “must pass 80–125%” becomes increasingly important and power drops.


It’s not explicitly stated in the FDA’s guidances (therefore, we give it in quotes) but can be easily derived with a little algebra. In a nutshell: Limits are scaled based on \(\small{CV_\text{wR}}\) with the FDA’s regulatory constant \(\small{\theta_0}\) in the first place. But for any \(\small{CV_\text{wR}>21.42\%}\) that would result in implied limits \(\small{\left\{L,U\right\}}\), which are wider than 80.00 – 125.00%. That’s not we want for an NTID.$$\eqalign{
\Delta&=1/0.9\approx 1.11111\\
\sigma_\text{w0}&=0.10\\
\theta_0&=\frac{\log_e\Delta}{\sigma_\text{w0}}\approx1.053595\\
s_\text{wR}&=\sqrt{\log_e(CV_\text{wR}^2+1)}⁠\\
\left\{L,U\right\}&=100\exp(\mp\theta_0\cdot s_\text{wR})
}$$Practically the limits are scaled indeed, but if the study would have passed, additionally inclusion within the conventional 80.00 – 125.00% limits is assessed as well.
That’s numerically the same as if scaling would be ‘capped’ at \(\small{CV_\text{wR}=21.42\%}\).

If algebra is not your thing, try this:

fun <- function(x) {
  Delta   <- 1.11111 # aproximate; only the FDA knows why
  sigma.0 <- 0.10
  theta.0 <- log(Delta) / sigma.0
  swR     <- sqrt(log(x^2 + 1))
  # the implied upper limit which is ≈1.25
  U       <- exp(theta.0 * swR)
  return(U - 1.25)
}
CVcap  <- uniroot(fun, interval = c(0.01, 0.3),
                  extendInt = "upX")$root # numerically find the CV where U ≈1.25
cat(sprintf("\'CVcap\' = %.4g\n", CVcap))

'CVcap' = 0.2142


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d_labes
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Berlin, Germany,
2024-02-26 11:54
(6 d 13:55 ago)

@ Helmut
Posting: # 23882
Views: 143
 

 sampleN.NTIDFDA(), power.NTIDFDA, pa.NTIDFDA are deprecated

Hi Helmut, Hi Mahmoud,

please take into consideration that funtions dealing with the FDA method for NTID's have now aliases without FDA in their names. That was implemented since the evaluation methods requested by the FDA are also required by China CDE.

The aliases are power.NTID(), sampleN.NTID(), and pa.NTID().

The functions power.NTIDFDA(), sampleN.NTIDFDA(), and pa.NTIDFDA() are deprecated and will be removed in the next release.

Regards,

Detlew
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