Bioequivalence and Bioavailability Forum

pharm07 ☆ India, 2022-05-03 11:23 (23 d 07:43 ago) Posting: # 22953 Views: 487	Estimation of sample size for NIT using ISCV By R [Power / Sample Size] Post reply
	Hi, Can anyone guide, how to calculate sample size for NTI category drug using R software? I have primary information as ISCV. Edit: Category changed; see also this post #1. [Helmut] — Regards, pharm07

dshah ★ India/United Kingdom, 2022-05-03 13:04 (23 d 06:01 ago) @ pharm07 Posting: # 22954 Views: 445	Estimation of sample size for NTI using ISCV By R Post reply
	Hello Pharm07! Kindly use PowerTOST and also search for earlier post. Regards, Dshah

Helmut
★★★

Vienna, Austria,
2022-05-03 14:38
(23 d 04:27 ago)

@ pharm07
Posting: # 22955
Views: 432

PowerTOST

Post reply

Hi pharm07,

as suggested by Dshah, assuming a T/R-ratio of 0.975 and a CV of 0.1:

library(PowerTOST) # attach the library theta0 <- 0.975 # assumed T/R-ratio CV <- 0.10 # intra-subject CV (assuming CVwT = CVwR) target <- 0.80 # target power design <- "2x2x4" # mandatory for the FDA # EMA and most others: sampleN.TOST(CV = CV, theta0 = theta0, theta1 = 0.90, design = design, targetpower = target) +++++++++++ Equivalence test - TOST +++++++++++ Sample size estimation ----------------------------------------------- Study design: 2x2x4 (4 period full replicate) log-transformed data (multiplicative model) alpha = 0.05, target power = 0.8 BE margins = 0.9 ... 1.111111 True ratio = 0.975, CV = 0.1 Sample size (total) n power 12 0.856278 # FDA and China CDE: sampleN.NTID(CV = CV, theta0 = theta0, design = design, targetpower = target) +++++++++++ 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 = 0.975 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 # Beware of unequival variances! CV.bad <- signif(CVp2CV(CV, ratio = 1.5), 4) # T worse than R sampleN.NTID(CV = CV.bad, theta0 = theta0, design = design, targetpower = target) +++++++++++ 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) = 0.1096, CVw(R) = 0.0894 True ratio = 0.975 ABE limits = 0.8 ... 1.25 Implied scABEL = 0.9103 ... 1.0986 Regulatory settings: FDA - Regulatory const. = 1.053605 - 'CVcap' = 0.2142 Sample size search n power 20 0.758770 22 0.805070 CV.good <- signif(CVp2CV(CV, ratio = 1 / 1.5), 4) # T better than R sampleN.NTID(CV = CV.good, theta0 = theta0, design = design, targetpower = target) +++++++++++ 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) = 0.0894, CVw(R) = 0.1096 True ratio = 0.975 ABE limits = 0.8 ... 1.25 Implied scABEL = 0.8912 ... 1.1220 Regulatory settings: FDA - Regulatory const. = 1.053605 - 'CVcap' = 0.2142 Sample size search n power 12 0.735990 14 0.814770

More details and examples in this article.

—
Dif-tor heh smusma 🖖
Helmut Schütz

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

pharm07
☆

India,
2022-05-04 08:08
(22 d 10:57 ago)

@ Helmut
Posting: # 22958
Views: 409

PowerTOST

Post reply

HI Helmut,

Thanks for the information.

After installing package from local file, (https://cloud.r-project.org/)

response in R console : > utils:::menuInstallLocal()
package ‘PowerTOST’ successfully unpacked and MD5 sums checked

Even after this step i am not able to attach power tost to the library.

After this step i can able to do further.

[Using R 4.2.0]
Please suggest.

—
Regards,
pharm07

Helmut
★★★

Vienna, Austria,
2022-05-04 10:33
(22 d 08:32 ago)

@ pharm07
Posting: # 22959
Views: 397

PowerTOST

Post reply

Hi pharm07,

» response in R console : > utils:::menuInstallLocal()
»

package ‘PowerTOST’ successfully unpacked and MD5 sums checked

OK, so you ended up as shown there (example for Power2Stage).

» Even after this step i am not able to attach power tost to the library.

Package ≠ library. Not sure what you mean, can you explain?

» After this step i can able to do further.

OK.

» Please suggest.

Copy one of the examples of my previous post and paste it to the [image]

console. If you want to go for the FDA’s method, just a one-liner because theta0 = 0.975, design = "2x2x4", and targetpower = 0.8 are defaults of the function. Hence, you have to specify only the CV:

sampleN.NTID(CV = 0.1)

Should give:

+++++++++++ 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 = 0.975 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

Since this is a four-period design, you may want to increase the sample size to compensate for a potential loss in power due to dropouts.

balance <- function(n, n.seq) { # Round up to obtain balanced sequences return(as.integer(n.seq * (n %/% n.seq + as.logical(n %% n.seq)))) } nadj <- function(n, do.rate, n.seq) { # Round up to compensate for anticipated dropout-rate return(as.integer(balance(n / (1 - do.rate), n.seq))) } CV <- 0.1 # Assumed CV do.rate <- 0.15 # Anticipated dropout-rate 15% n <- sampleN.NTID(CV = CV, print = FALSE, details = FALSE)[["Sample size"]] dosed <- nadj(n, do.rate, 2) # Adjust the sample size df <- data.frame(dosed = dosed, eligible = dosed:(n - 2)) for (j in 1:nrow(df)) { df$dropouts[j] <- sprintf("%.1f%%", 100 * (1 - df$eligible[j] / df$dosed[j])) df$power[j] <- suppressMessages( # We know that some are unbalanced power.NTID(CV = CV, n = df$eligible[j])) } print(df, row.names = FALSE) dosed eligible dropouts power 22 22 0.0% 0.91017 22 21 4.5% 0.89602 22 20 9.1% 0.88031 22 19 13.6% 0.86072 22 18 18.2% 0.84179 22 17 22.7% 0.81658 22 16 27.3% 0.78869

If you are confused, see there.

—
Dif-tor heh smusma 🖖
Helmut Schütz

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

pharm07 ☆ India, 2022-05-04 14:54 (22 d 04:12 ago) @ Helmut Posting: # 22961 Views: 366	PowerTOST Post reply
	Hi, » Package ≠ library. Not sure what you mean, can you explain? I meant i was not able to execute library(PowerTOST) command. Now, i am able to estimate sample size..! Your guidance is much more appreciable. Thanks.. — Regards, pharm07

pharm07
☆

India,
2022-05-11 05:30
(15 d 13:35 ago)

@ pharm07
Posting: # 22968
Views: 243

PowerTOST

Post reply

Hi Helmut,

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.
i want to estimate sample size for low to moderate NTID. Also to estimate sample size by assuming 30 & 40 % dropout rate.
I have gone through the examples. Sometimes error comes as its beyond implied limit. Heteroscedasticity can be challenging for me as T>R.

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

—
Regards,
pharm07

Helmut
★★★

Vienna, Austria,
2022-05-11 13:19
(15 d 05:46 ago)

@ pharm07
Posting: # 22970
Views: 212

PowerTOST: sampleN.NTID()

Post reply

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

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

pharm07
☆

India,
2022-05-18 05:18
(8 d 13:47 ago)

@ Helmut
Posting: # 22995
Views: 131

PowerTOST: sampleN.NTID()

Post reply

Hi Helmut,

» 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.

OK. Noted.

» More examples are given there.

OK. I referred these examples.

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

Ok, I have pasted one example which i seems to be work upon.

» That’s possible if you specify a low or high theta0.

OK.

» Yes, you are not alone.
:ponder:

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

Please see below example,
Note : CV is not in scalar form.'

sampleN.NTID(CV = c(0.045,0.07), theta0 = 0.95, targetpower = 0.9)



+++++++++++ 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 = 0.9

CVw(T) = 0.045, CVw(R) = 0.07

True ratio     = 0.95 

ABE limits     = 0.8 ... 1.25 

Implied scABEL = 0.9290 ... 1.0764 

Regulatory settings: FDA 

- Regulatory const. = 1.053605 

- 'CVcap'           = 0.2142 



Sample size search

 n     power

92   0.875810

94   0.882090

96   0.888810

98   0.894060

100   0.898510

102   0.903540

# with 30% DO rate,

# as CV was specified as Vector,
# is following steps right?

balance <- function(n, n.seq) {

  # Round up to obtain balanced sequences

  return(as.integer(n.seq * (n %/% n.seq + as.logical(n %% n.seq))))

}

nadj <- function(n, do.rate, n.seq) {

  # Round up to compensate for anticipated dropout-rate

  return(as.integer(balance(n / (1 - do.rate), n.seq)))

}

CV      <- 0.045               # Assumed CV # how to specify vector CV here?

do.rate <- 0.30                # Anticipated dropout-rate 30%

n       <- sampleN.NTID(CV = CV, print = FALSE, details = FALSE)[["Sample size"]]

dosed   <- nadj(n, do.rate, 2) # Adjust the sample size

df      <- data.frame(dosed = dosed, eligible = dosed:(n - 2))

for (j in 1:nrow(df)) {

  df$dropouts[j] <- sprintf("%.1f%%", 100 * (1 - df$eligible[j] / df$dosed[j]))

  df$power[j]    <- suppressMessages( # We know that some are unbalanced

                      power.NTID(CV = CV, n = df$eligible[j]))

}

print(df, row.names = FALSE)

dosed eligible dropouts   power

   58       58     0.0% 0.92040

   58       57     1.7% 0.91575

   58       56     3.4% 0.91254

   58       55     5.2% 0.90722

   58       54     6.9% 0.90364

   58       53     8.6% 0.89761

   58       52    10.3% 0.89257

   58       51    12.1% 0.88767

   58       50    13.8% 0.88215

   58       49    15.5% 0.87672

   58       48    17.2% 0.86952

   58       47    19.0% 0.86376

   58       46    20.7% 0.85690

   58       45    22.4% 0.84922

   58       44    24.1% 0.84310

   58       43    25.9% 0.83486

   58       42    27.6% 0.82810

   58       41    29.3% 0.81915

   58       40    31.0% 0.81109

   58       39    32.8% 0.80105

   58       38    34.5% 0.79410

Kindly guide me with this example, i want to check whether i am making a mistake or not. :confused:

—
Regards,
pharm07

Helmut
★★★

Vienna, Austria,
2022-05-18 14:30
(8 d 04:36 ago)

@ pharm07
Posting: # 23002
Views: 111

sampleN.NTID(): Example

Post reply

Hi pharm07,

» Kindly guide me with this example, i want to check whether i am making a mistake or not. :confused:

In your second script you forgot to state theta0 = 0.95. Hence, the default theta = 0.975 was employed.

library(PowerTOST)

balance <- function(n, n.seq) {

  # Round up to obtain balanced sequences

  return(as.integer(n.seq * (n %/% n.seq + as.logical(n %% n.seq))))

}

nadj <- function(n, do.rate, n.seq) {

  # Round up to compensate for anticipated dropout-rate

  return(as.integer(balance(n / (1 - do.rate), n.seq)))

}

CV      <- c(0.045, 0.07)      # First element CVwT, second CVwR

do.rate <- 0.30                # Anticipated dropout-rate 30%

n       <- sampleN.NTID(CV = CV, theta0 = 0.95, targetpower = 0.90,

                        print = FALSE, details = FALSE)[["Sample size"]]

dosed   <- nadj(n, do.rate, 2) # Adjust the sample size

df      <- data.frame(dosed = dosed, eligible = dosed:(n - 2))

for (j in 1:nrow(df)) {

  df$dropouts[j] <- sprintf("%.1f%%", 100 * (1 - df$eligible[j] / df$dosed[j]))

  df$power[j]    <- suppressMessages(

                      power.NTID(CV = CV, theta0 = 0.95, n = df$eligible[j]))

}

print(df, row.names = FALSE)



 dosed eligible dropouts   power

   146      146     0.0% 0.97046

   146      145     0.7% 0.96815

   146      144     1.4% 0.96887

   146      143     2.1% 0.96730

   146      142     2.7% 0.96592

   146      141     3.4% 0.96512

   146      140     4.1% 0.96470

   146      139     4.8% 0.96316

   146      138     5.5% 0.96322

   146      137     6.2% 0.96172

   146      136     6.8% 0.96048

   146      135     7.5% 0.95969

   146      134     8.2% 0.95892

   146      133     8.9% 0.95649

   146      132     9.6% 0.95497

   146      131    10.3% 0.95505

   146      130    11.0% 0.95347

   146      129    11.6% 0.95245

   146      128    12.3% 0.95101

   146      127    13.0% 0.94969

   146      126    13.7% 0.94851

   146      125    14.4% 0.94723

   146      124    15.1% 0.94594

   146      123    15.8% 0.94386

   146      122    16.4% 0.94258

   146      121    17.1% 0.94121

   146      120    17.8% 0.94039

   146      119    18.5% 0.93931

   146      118    19.2% 0.93649

   146      117    19.9% 0.93461

   146      116    20.5% 0.93393

   146      115    21.2% 0.93164

   146      114    21.9% 0.92946

   146      113    22.6% 0.92741

   146      112    23.3% 0.92519

   146      111    24.0% 0.92361

   146      110    24.7% 0.92132

   146      109    25.3% 0.91851

   146      108    26.0% 0.91725

   146      107    26.7% 0.91563

   146      106    27.4% 0.91393

   146      105    28.1% 0.91186

   146      104    28.8% 0.90848

   146      103    29.5% 0.90711

   146      102    30.1% 0.90354

   146      101    30.8% 0.90250

   146      100    31.5% 0.89851

—
Dif-tor heh smusma 🖖
Helmut Schütz

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

pharm07 ☆ India, 2022-05-19 05:36 (7 d 13:30 ago) @ Helmut Posting: # 23003 Views: 92	sampleN.NTID(): Example Post reply
	Hi Helmut, I got it..! Thanks for the interaction and time — Regards, pharm07

Estimation of sample size for NIT using ISCV By R [Power / Sample Size]

Estimation of sample size for NTI using ISCV By R

PowerTOST

PowerTOST

PowerTOST

PowerTOST

PowerTOST

PowerTOST: sampleN.NTID()

PowerTOST: sampleN.NTID()

sampleN.NTID(): Example

sampleN.NTID(): Example