Bioequivalence and Bioavailability Forum • Primary and secondary parameters for SS study for EU

ratnakar1811
★

India,
2012-03-19 13:49
(4410 d 18:01 ago)

Posting: # 8295
Views: 7,216

Primary and secondary parameters for SS study for EU [Regulatives / Guidelines]

Dear All,

This is to confirm what all primary and secondary PK parameters and criteria for BE should be considered for steady state study for a modified released tablet for EU submission?

As per current EU guideline it only mentions about AUC0-tau to be considered as the additional parameter for bioequivalence. Whereas for Steady State study for immediate release formulations it mentions parameters like AUC0-tau, Cmax,ss and Tmax,ss also.

But as per FDA we do consider Cmin, Cav, degree of fluctuation [(Cmax-Cmin)/Cav], and swing [(Cmax-Cmin)/Cmin].

Thanking you for your guidance in advance.

Ratnakar

Helmut
★★★

Vienna, Austria,
2012-03-19 15:18
(4410 d 16:33 ago)

@ ratnakar1811
Posting: # 8296
Views: 6,512

MR MD studies (EMA)

Post reply

Dear Ratnakar!

❝ […] what all primary and secondary PK parameters and criteria for BE should be considered for steady state study for a modified released tablet for EU submission? As per current EU guideline it only mentions about AUC0-tau to be considered as the additional parameter for bioequivalence.

Unfortunately the MR NfG is quite old (1999) and somewhat ambiguous:

4.1 Bioavailability studies
The purpose of these studies is to characterise the modified drug formulation in vivo by investigating

the rate and extent of absorption
fluctuations in drug concentrations

4.1.1. Rate and extent of absorption, fluctuation
Rate and extent of absorption from a modified release formulation should be evaluated by comparison with an immediate release formulation following single and repeated dosing. Fluctuations in drug concentrations should be studied following repeated dosing. It should be demonstrated that the modified release formulation has the claimed release characteristics, produces similar or less fluctuations as the immediate release product and comparable total systemic exposure that is acceptable in comparison to that of the immediate release product. The pharmacokinetic parameters of interest are AUC, C_max and C_min or other means reflecting fluctuation.

5.1 Prolonged release formulations
Assessment of bioequivalence will be based on AUC_τ, C_max and C_min applying similar statistical procedures as for the immediate release formulations.

5.2 Delayed release formulations
Bioequivalence is assessed using the same main characteristics and statistical procedures as for immediate release formulations with emphasis on the delayed release characteristics.

Interesting points:

Neither %PTF nor Swing are mentioned explicitly; only ‘or other means reflecting fluctuation’ (as an alternative to C_max and C_min). But don’t take this literally. C_max is required anyhow (4.1, 5.1/5.2). C_max & %PTF worked in almost all of my studies (got some deficiency letters asking for C_min). Never submitted Swing and was also never asked.
Fluctuation: No equivalence to IR, but non-superiority!
No testing of C_min / fluctuation for DR (no or only minor accumulation expected). Could refer to the current IR guideline and the Overview of comments:
“By C_min,ss we mean the concentration at the end of the dosage interval, i.e. C_trough. However, in bioequivalence studies for immediate release formulations there is no need to report C_trough and fluctuation. The guideline has been revised. We see no need to include swing […]”
The MR GL is under revision (draft expected by the end of QII/2012). What I would expect / hope for:
■ No MD studies if no accumulation (SD AUC_t/AUC_∞ >80%).
■ For others C_min,ss mandatory (if clinically relevant?), %PTF supportive.
■ Partial AUCs for pulsatile/biphasic products (see this thread).
■ Scaling for C_max,ss and C_min,ss.

❝ Whereas for Steady State study for immediate release formulations it mentions parameters like AUC0-tau, Cmax,ss and Tmax,ss also.

T_max – where?

❝ But as per FDA we do consider Cmin, Cav, degree of fluctuation [(Cmax-Cmin)/Cav], and swing [(Cmax-Cmin)/Cmin].

Not relevant here. BTW, I can’t imagine that FDA rejects a study based on failing Swing if all other metrics pass. Swing is a lousy metric, since you divide by the one concentration with the largest variability of the entire profile.

—
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Helmut Schütz

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Jaime_R ★★ Barcelona, 2012-03-19 17:26 (4410 d 14:24 ago) @ Helmut Posting: # 8298 Views: 6,248	Non-superiority Post reply
	Dear Helmut! ❝ ● Fluctuation: No equivalence to IR, but non-superiority! Oh, I missed that! Being less than a statistical amateur, does that require the upper one-sided 95% CL included in 125% – or, if the statistical software (e.g. WinNonlin) does not give this result directly – assessing the upper limit of the 90% CI only? How can we calculate the sample size? — Regards, Jaime

Helmut
★★★

Vienna, Austria,
2012-03-19 17:59
(4410 d 13:51 ago)

@ Jaime_R
Posting: # 8299
Views: 6,250

Non-superiority

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Dear Jaime!

❝ […] does that require the upper one-sided 95% CL included in 125% – or […] – assessing the upper limit of the 90% CI only?

Both will work.

❝ How can we calculate the sample size?

Ouch; good question! Steven Julious (Sample Sizes for Clinical Trials, 2010) gives a method for cross-over studies (actually the other way ’round: non-inferiority) but only for normal distributed data. Have to sleep over it.

—
Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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d_labes
★★★

Berlin, Germany,
2012-03-20 16:48
(4409 d 15:03 ago)

(edited by d_labes on 2012-03-21 11:35)
@ Helmut
Posting: # 8305
Views: 6,846

'Non-superiority' - sample size

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Dear Helmut, dear Jaime!

❝ ❝ […] does that require the upper one-sided 95% CL included in 125% – or […] – assessing the upper limit of the 90% CI only?

❝

❝ Both will work.

With the exception that the ICH E9 guidance suggests for one sided CIs an alpha=0.025 I think. Or am I wrong :confused:

. That would require 95% CI's and assessing their upper limit only.

❝ ❝ How can we calculate the sample size?

❝

❝ Ouch; good question! Steven Julious (Sample Sizes for Clinical Trials, 2010) gives a method for cross-over studies (actually the other way ’round: non-inferiority) but only for normal distributed data. Have to sleep over it.

Non-superiority is a rather unusual term :cool:

. The other way round - non-inferiority - would mean that we formulate our problem as non-inferiority.
It's easy. Instead of the hypotheses

H0: µT/µR > 1.25 ('superiority')

HA: µT/µR < 1.25 ('non-superiority')

we formulate

H0: µR/µT < 0.8  ('inferiority')

HA: µR/µT > 0.8  ('non-inferiority')

In case of log-normal distributed data the hypotheses change as usual to hypotheses of differences

H0: log(µR) - log(µT) < -0.2231436 ('inferiority')

HA: log(µR) - log(µT) > -0.2231436 ('non-inferiority')

The corresponding test is a one-sided t-test which has power for a 2x2 crossover (Julious "Sample Sizes for Clinical Trials", 2010, equation 6.22)
1-beta = pt(t_1-alpha,n-2,df=n-2,tau)

Edit: I can only reproduce PASS values for power and sample size if I use power=1-pt(...) although Julious termed (1-beta) power :confused:

where pt() is the cumulative distribution function of the non-central t-distribution with non-centrality parameter
tau= abs((log(µT)-log(µR) - d)*sqrt(n)/sqrt(2*MSE))
and d=log(R0) with R0 the null or 'true' ratio.

BTW: PASS 2008 has a module "Noninferiority & superiority -> Two means in a 2x2 crossover -> specify using ratios" that will do the calculations for you. It contains also an option in that module which allows the calculations for the 'non-superiority' case named "Higher is bad".

If you don't own PASS here a quick shot in R:
(design is in the moment only a place holder, nothing other then 2x2 crossover is implemented)

# power function

# set margin to 1.25 to get 'higher is bad'

power.noninf <- function(alpha=0.025, margin=0.8, ratio0, CV, n, design="2x2")

{

  df   <- n-2    

  tval <- qt(1-alpha,df)

  se2  <- log(CV^2+1)

  tau  <- abs( (log(ratio0)-log(margin))*sqrt(n)/sqrt(2*se2) )

  return(1-pt(tval,df,tau))

}



# start value for sample size search from large sample formula

.sampleN0.noninf <- function(alpha=0.025, targetpower=0.8, margin, ratio0, CV)

{

  n0 <- 2*log(CV^2+1)*(qnorm(targetpower)+ qnorm(1-alpha))^2 / (log(ratio0)-log(margin))^2

  return(ceiling(n0))

}



# sample size estimation for non-inferiority test

sampleN.noninf <- function(alpha=0.025, targetpower=0.8, margin=0.8, 

                           ratio0=1.05, CV, design="2x2", details=FALSE)

{ 

  step <- 2

  n    <- .sampleN0.noninf(alpha=alpha, targetpower=targetpower, 

                           margin=margin, ratio0=ratio0, CV=CV)

  if (n<=4) n <- 4

  if (details){

    cat("Sample size search\n")

    cat(" n  power\n")

  }

  n    <- step*(n%/%step) 

  pow  <- power.noninf(alpha=alpha, margin=margin, ratio0=ratio0, CV=CV, n=n)

  

  if (details) cat(n,pow,"\n")

  while (pow>targetpower){

    if (n<=4) break

    n <- n - step

    pow  <- power.noninf(alpha=alpha, margin=margin, ratio0=ratio0, CV=CV, n=n)

    if (details) cat(n,pow,"\n")

  }

  while(pow<targetpower){

    n <- n+step

    pow  <- power.noninf(alpha=alpha, margin=margin, ratio0=ratio0, CV=CV, n=n)

    if (details) cat(n,pow,"\n")

  }

  if (details) return(invisible(n)) else return(n)                       

}

For a targetpower=0.8, CV=0.3, margin=0.8 the last function will give the sample sizes

       alpha=

ratio0 0.025  0.05 

  0.9   100    80

  0.95   48    38

  1.0    30    24

  1.05   22    16

  1.1    16    14

The whole discussion up to here depends on the assumption of log-normality. If this is a reasonable assumption for measures of fluctuation like PTF or swing is left to you.

—
Regards,

Detlew

d_labes
★★★

Berlin, Germany,
2012-03-22 11:20
(4407 d 20:31 ago)

@ Helmut
Posting: # 8312
Views: 6,163

To err is Julious

Post reply

Dear All!

In my previous post I have noticed that I could reproduce the power and sample size for non-inferiority trials only if I used
1-beta = 1 - pt(t_1-alpha,n-2,df=n-2,tau)

Seems even the pope can err :-D

.
The formulas given in the book

S.A. Julious
"Sample Sizes for Clinical Trials"
Chapman & Hall/CRC, 2010

are in error here, not only for the non-inferiority case (chapter 6) but also for the superiority tests (chapter 3/4).

Compare them to those in the paper

S.A. Julious
"TUTORIAL IN BIOSTATISTICS
Sample sizes for clinical trials with Normal data"
Statist. Med. 2004; 23: 1921-1986

where the formulas are yet given with power=1-probt(...).
Compare further the results of the normal approximation formulas
(f.i. formula 6.21 1-beta = pnorm(tau-t_1-alpha,n-2)
to see that 1-probt(...) is correct.
With tau=2.5, df=7, alpha=0.05 (in R syntax):


(6.21) pnorm(2.5 - qt(1-0.05, df=7))       =0.72755

(6.22) pt(qt(1-0.05,df=7), df=7, 2.5)      =0.27283

       1 - pt(qt(1-0.05,df=7), df=7, 2.5)  =0.72717 q.e.d.

BTW: Would it desirable to have non-inferiority power / sample size in PowerTOST (although it is not based on TOST but on OOST :cool:

- one one-sided t-test)? I could ask the author if he had some spare time :lol2:

—
Regards,

Detlew

Helmut
★★★

Vienna, Austria,
2012-03-30 16:13
(4399 d 16:37 ago)

@ d_labes
Posting: # 8353
Views: 6,028

PowerTOST 0.9-6 on CRAN

Post reply

Dear Detlew!

❝ I could ask the author if he had some spare time.

Obviously he had. :-D

Released 2012-03-26:

functions added for power and sample size calculations based on non-inferiority t-test. This is not a TOST procedure but eventually useful if the question of 'non-superiority' within a BE study must be evaluated.
Hint: Evaluation of Fluctuation in the EMA MR NfG (1999) between modified release formulation and immediate release product.

New functions power.noninf(), sampleN.noninf().

THX for PowerOOST!

—
Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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