Bioequivalence and Bioavailability Forum

Better 0.95 or 0.90 [Power / Sample Size]

posted by Helmut  – Vienna, Austria, 2017-12-29 17:18 (2449 d 12:07 ago) – Posting: # 18127
Views: 34,254

Hi kms,

❝ ❝ In this case, why they assume GMR=1.10 instead of the "normal" 0.95/1.05.

❝

❝ This was […] a very rare case, but in General GMR would be taken as 0.95/1.05 as you said, but the power remains same as 95% to 99%

Similar ≠ same.

CV 0.20, GMR 1.10, target 80%, n 32 (power 81.01%), no dropouts expected

1e+05 simulated studies with “post hoc” power of
  ≥ target    : 54.04%
  ≥ achieved  : 51.57%
  ≥ 0.90      : 26.98%
  [0.95, 0.99]: 10.41%
  ≥ 0.95      : 12.50%

CV 0.20, GMR 1.05, target 80%, n 18 (power 80.02%), no dropouts expected

1e+05 simulated studies with “post hoc” power of
  ≥ target    : 48.45%
  ≥ achieved  : 48.41%
  ≥ 0.90      : 25.26%
  [0.95, 0.99]:  9.72%
  ≥ 0.95      : 12.92%

I still don’t understand what you wrote above:

❝ […] always it is coming in the interval 95 to 99 and some times 100

BTW, power curves are not symmetric in raw scale but in log-scale (see this post). If you are not – very – confident about the sign of ∆, I recommend to use GMR=1–∆ in order to be on the safe side. By this, power is preserved for GMR=1/(1–∆) as well. If you use GMR=1+∆, power for GMR=1–∆ will be insufficient:

cat(paste0("\u2206 with unknown sign: ", 100*delta, "%",
    "\n  based on GMR = 1 \u2013 \u2206 = ",
    sprintf("%5.4f", 1-delta), "      : n ",
    plan.1[["Sample size"]],
    "\n  based on GMR = 1 + \u2206 = ",
    sprintf("%5.4f", 1+delta), "      : n ",
    plan.2[["Sample size"]],
    "\n  based on GMR = 1 / (1 + \u2206) = ",
    sprintf("%5.4f", 1/(1+delta)), ": n ",
    plan.3[["Sample size"]],
    "\n  based on GMR = 1 / (1 \u2013 \u2206) = ",
    sprintf("%5.4f", 1/(1-delta)), ": n ",
    plan.4[["Sample size"]],
    "\n\nTrue GMR = ", sprintf("%5.4f", 1-delta),
    "\n  n ", plan.2[["Sample size"]], ", power ",
    sprintf("%4.2f%%", 100*power.TOST(CV=CV, theta0=1-delta,
    n=plan.2[["Sample size"]])),
    "\n  n ", plan.1[["Sample size"]], ", power ",
    sprintf("%4.2f%%", 100*plan.1[["Achieved power"]]),
    "\nTrue GMR = ", sprintf("%5.4f", 1/(1+delta)),
    "\n  n ", plan.3[["Sample size"]], ", power ",
    sprintf("%4.2f%%", 100*plan.3[["Achieved power"]]),
    "\n  n ", plan.1[["Sample size"]], ", power ",
    sprintf("%4.2f%%", 100*power.TOST(CV=CV, theta0=1/(1+delta),
    n=plan.1[["Sample size"]])),
    "\nTrue GMR = ", sprintf("%5.4f", 1+delta),
    "\n  n ", plan.2[["Sample size"]], ", power ",
    sprintf("%4.2f%%", 100*plan.2[["Achieved power"]]),
    "\n  n ", plan.1[["Sample size"]], ", power ",
    sprintf("%4.2f%%", 100*power.TOST(CV=CV, theta0=1+delta,
    n=plan.1[["Sample size"]])),
    "\nTrue GMR = ", sprintf("%5.4f", 1/(1-delta)),
    "\n  n ", plan.4[["Sample size"]], ", power ",
    sprintf("%4.2f%%", 100*plan.4[["Achieved power"]]),
    "\n  n ", plan.2[["Sample size"]], ", power ",
    sprintf("%4.2f%%", 100*power.TOST(CV=CV, theta0=1/(1-delta),
    n=plan.2[["Sample size"]])), "\n"))

∆ with unknown sign: 10%
  based on GMR = 1 – ∆ = 0.9000      : n 38
  based on GMR = 1 + ∆ = 1.1000      : n 32
  based on GMR = 1 / (1 + ∆) = 0.9091: n 32
  based on GMR = 1 / (1 – ∆) = 1.1111: n 38

True GMR = 0.9000
  n 32, power 75.17%
  n 38, power 81.55%
True GMR = 0.9091
  n 32, power 81.01%
  n 38, power 86.76%
True GMR = 1.1000
  n 32, power 81.01%
  n 38, power 86.76%
True GMR = 1.1111
  n 38, power 81.55%
  n 32, power 75.17%

In simple words, for ∆ 10% assume a GMR of 0.90 (which will preserve power for GMR up to 1.1111) and for ∆ 5% a GMR of 0.95 (covers up to 1.0526·).
If you assume a GMR of 1.10 power will be preserved only down to 0.9090 and with 1.05 down to 0.9524 – not to 0.90 or 0.95 as many probably expect.

—
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:

• Power is getting high kms.srinivas 2017-12-26 07:39 [Power / Sample Size] 
  • Power is getting high? d_labes 2017-12-26 12:08
  • Stop estimating post hoc power! Helmut 2017-12-26 12:22
    • Stop estimating post hoc power! kms.srinivas 2017-12-26 13:00
      • Stop estimating post hoc power! ElMaestro 2017-12-26 14:11
      • Simulations Helmut 2017-12-26 15:51
        • Simulations BE-proff 2017-12-27 06:53
          • Simulations ElMaestro 2017-12-27 07:25
          • Simulations Yura 2017-12-27 08:23
            • Simulations kms.srinivas 2017-12-27 09:11
              • Simulations Yura 2017-12-27 10:07
                • α and 1–β Helmut 2017-12-27 12:57
                  • α and 1–β Yura 2017-12-27 13:33
                    • α and 1–β Helmut 2017-12-27 14:31
                      • α and 1–β Yura 2017-12-28 06:50
                        • Educate the IEC and regulators Helmut 2017-12-28 11:30
              • “Forced BE” 101 Helmut 2017-12-27 12:23
                • “Forced BE” 101 kms.srinivas 2017-12-27 12:41
                  • Would you be so kind answering our questions? Helmut 2017-12-27 13:02
                    • Would you be so kind answering our questions? kms.srinivas 2017-12-28 05:53
                      • Yes, but why? Helmut 2017-12-28 11:47
                        • Yes, but why? DavidManteigas 2017-12-28 16:59
                          • Optimists and pessimists Helmut 2017-12-28 17:33
                            • "normal" GMR setting d_labes 2017-12-28 18:57
                              • Example for discussion mittyri 2017-12-28 22:06
                                • Example for discussion Helmut 2017-12-28 22:33
                              • I prefer to play it safe Helmut 2017-12-28 22:10
                          • Full ACK d_labes 2017-12-28 17:41
                          • About GMR 1.10 kms.srinivas 2017-12-29 13:20
                            • Better 0.95 or 0.90Helmut 2017-12-29 16:18
                        • Yes, but why? Yura 2017-12-29 13:46
                        • Buffon's needle Astea 2018-01-20 23:55
                          • Buffon's needle Oleg777 2018-10-09 22:48
                            • 0.95 or 1.05 Helmut 2018-10-10 13:41
                          • Buffon's needle Helmut 2018-10-10 12:46
                            • Buffon's needle Astea 2018-10-11 23:14
                              • School maths Helmut 2018-10-12 01:10
                                • School russian Astea 2018-10-12 12:41
                                • Offtop: Umschrift der westlichen Eigennamen auf Russisch mittyri 2018-10-12 23:25
                    • EEU? mittyri 2017-12-28 21:52
                      • EEU? Yura 2017-12-29 13:41
                        • EEU - pharmacokinetic equation??? mittyri 2017-12-29 14:11
                      • EEU? Beholder 2018-01-16 15:10
          • Simulations xtianbadillo 2018-01-18 22:22
  • Numbers don't lie ElMaestro 2017-12-28 20:13