arl_stat
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India,
2020-06-09 09:41
(178 d 19:54 ago)

Posting: # 21515
Views: 2,179
 

 Sample Size for Replicate studies [Power / Sample Size]

Hello Everyone,

Hope all are safe in this Pandemic situation :-)

My query is regarding the estimation of sample size.

For Sample size estimation of replicate study design, the following reference is referred.
J Pharm Pharmaceut Sci (www.cspsCanada.org) 15(1) 73 - 84, 2012.

Please help me to understand the alpha value considered for sample size estimation.

Many thanks in advance. :-)
Helmut
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Vienna, Austria,
2020-06-09 09:49
(178 d 19:46 ago)

@ arl_stat
Posting: # 21516
Views: 1,782
 

 Nominal α

Hi arl_stat,

» Please help me to understand the alpha value considered for sample size estimation.

α is the nominal level of the test. In BE generally 0.05, which gives a two-sided 100 × (1 – 2α) = 90% CI. α is fixed by the authority, i.e., you are not free to choose it in sample size estimation.

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arl_stat
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India,
2020-06-09 10:30
(178 d 19:05 ago)

@ Helmut
Posting: # 21517
Views: 1,784
 

 Nominal α

Thank you sir :-)

there is no alpha value mentioned in the reference. Would like to know, which alpha value is considered in the reference for EMA and FDA.

thank you :-)


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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Vienna, Austria,
2020-06-09 10:42
(178 d 18:53 ago)

@ arl_stat
Posting: # 21518
Views: 1,789
 

 α 0.05

» there is no alpha value mentioned in the reference. Would like to know, which alpha value is considered in the reference for EMA and FDA.

The paper refers to the EMA’s (ABEL) and the FDA’s (RSABE) methods. Hence, 0.05 as usual.
BTW, why don’t you use software like the [image]-package PowerTOST? The methods are supported by the functions sampleN.scABEL() and sampleN.RSABE(). Then you are free to select any GMR and power. With due respect to the two Lászlós I hold that their number of simulations (10,000) is too small (see this post).

At the latest when you have to estimate the sample size for the FDA’s reference-scaling for NTIDs you have to use PowerTOST’s function sampleN.NTIDFDA() anyway. No tables published.

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Helmut Schütz
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arl_stat
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India,
2020-06-11 06:15
(176 d 23:20 ago)

@ Helmut
Posting: # 21526
Views: 1,705
 

 α 0.05

Many thanks Sir. :-)

Page no. 10 of 12 of the article for full replicate study, captures the below table:
Table A2. Sample sizes for the requirements of EMA in 4-period studies
80% POWER
CV  GMR  0.85  0.90  0.95  1.00  1.05  1.10  1.15  1.20
30%       127    35    19    15    18    30    68  >201


I tried calculating the above sample size using the below SAS code but the output did not match.
%let CV=0.30;
proc power;
   TwoSampleMeans Test = Equiv_Mult
      Lower = 0.8
      Upper = 1.25
      Alpha = 0.05
      MeanRatio =  0.85 0.90 0.95
      CV = &CV.
      Power = 0.80  0.90
      NPerGroup = .
   ;
  run;
Output:
Fixed Scenario Elements
Distribution  Lognormal
Method  Exact
Lower Equivalence Bound  0.8
Upper Equivalence Bound  1.25
Alpha  0.05
Coefficient of Variation  0.3


Computed N per Group
Index  Mean Ratio  Nominal Power  Actual Power  N per Group
1         0.85          0.8           0.8           291
2         0.85          0.9           0.9           403
3         0.9           0.8           0.802          78
4         0.9           0.9           0.902         108
5         0.95          0.8           0.803          38
6         0.95          0.9           0.901          51


Please guide.

Thanks in advance.


Edit: Tabulators changed to spaces and BBcoded. Code and results BBCoded; see also this post #6. [Helmut]
Helmut
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Vienna, Austria,
2020-06-11 10:26
(176 d 19:09 ago)

@ arl_stat
Posting: # 21527
Views: 1,675
 

 RSABE ≠ ABE: Simulations mandatory

Hi arl_stat,

we cannot estimate the sample size of any reference-scaling method directly. These methods are frameworks: The decision whether conventional ABE or reference-scaling is used depends on the observed CVwR, for the EMA there is an upper cap at 50%, and all agencies impose a point estimate restriction of 80.00–125.00%. Contrary to ABE with fixed limits, the Null hypothesis is generated in face of the data. Power (and hence, the sample size) given these conditions cannot be derived analytically. We need simulations (as in the paper).
Your SAS-code is for ABE with fixed limits of 80–125%. Though it is possible to set up simulations for reference-scaling in SAS (105 studies at least), expect runtimes of many hours.* Please read now this post as I already suggested previously.

Below a comparison of Table A2 of the two Lászlós for CVwR 30% and results obtained by PowerTOST. Runtime for the 16 scenarios on my machine three seconds. Good luck with SAS.

library(PowerTOST)
GMR   <- seq(0.85, 1.2, 0.05)
power <- c(0.8, 0.9)
A2    <- c(127, 35, 19, 15, 18, 30, 68, ">201",
           180, 49, 25, 19, 24, 42, 95, ">201")
res   <- data.frame(power = power, GMR = rep(GMR, length(power)), A2 = A2)
j     <- 0
for (k in seq_along(power)) {
  for (l in seq_along(GMR)) {
    j               <- j + 1
    tmp             <- sampleN.scABEL(CV = 0.3, theta0 = GMR[l],
                                      design = "2x2x4", targetpower = power[k],
                                      details = FALSE, print = FALSE)
    res$n.ABEL[j]   <- tmp[["Sample size"]]
    res$pwr.ABEL[j] <- round(tmp[["Achieved power"]], 4)
    tmp             <- sampleN.TOST(CV = 0.3, theta0 = GMR[l],
                                    design = "2x2x4", targetpower = power[k],
                                    details = FALSE, print = FALSE)
    res$n.ABE[j]    <- tmp[["Sample size"]]
    res$pwr.ABE[j]  <- round(tmp[["Achieved power"]], 4)
  }
}
print(res, row.names = FALSE)

Gives

power  GMR   A2 n.ABEL pwr.ABEL n.ABE pwr.ABE
  0.8 0.85  127    128   0.8044   146  0.8014
  0.9 0.90   35     34   0.8028    40  0.8100
  0.8 0.95   19     18   0.8276    20  0.8202
  0.9 1.00   15     14   0.8130    16  0.8225
  0.8 1.05   18     18   0.8352    20  0.8290
  0.9 1.10   30     30   0.8132    34  0.8097
  0.8 1.15   68     68   0.8042    78  0.8041
  0.9 1.20 >201    280   0.8019   322  0.8020
  0.8 0.85  180    180   0.9002   202  0.9009
  0.9 0.90   49     48   0.9002    54  0.9016
  0.8 0.95   25     24   0.9124    26  0.9043
  0.9 1.00   19     18   0.9101    20  0.9133
  0.8 1.05   24     24   0.9182    26  0.9112
  0.9 1.10   42     42   0.9067    46  0.9021
  0.8 1.15   95     96   0.9009   108  0.9033
  0.9 1.20 >201    398   0.9004   444  0.9004




  • Wonnemann M, Frömke C, Koch A. Inflation of the Type I Error: Investigations on Regulatory Recommendations for Bioequivalence of Highly Variable Drugs. Pharm Res. 2015;32(1):135–43. doi:10.1007/s11095-014-1450-z.
    Meinolf Wonnemann reported in a personal message to Detlew Labes that 10,000 simulations in SAS “ran over night”…

Dif-tor heh smusma 🖖
Helmut Schütz
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The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes
arl_stat
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India,
2020-06-29 05:05
(159 d 00:30 ago)

@ Helmut
Posting: # 21589
Views: 1,265
 

 RSABE ≠ ABE: Simulations mandatory

Thank you sir. :-)
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