Log in
Register|
martin ★★ Austria, 2012-02-22 14:36 (5226 d 10:56 ago) Posting: # 8151 Views: 5,158 |
|
|
dear all! I recently encountered the following acceptance criteria for showing equivalence to a known fixed value: “the calculated sample mean should not differ more than 1.3 standard deviations (SDs) to the known value for showing equivalence statistically”. I do not know that background but I suppose that this might be related to analytical uncertainty. However, I think that this criterion is counterproductive, because equivalence is “shown” more likely with a high SD rather than with a small SD and that the effect size is not adequately taken into account. I would be grateful for your opinion and/or for published references regarding this approach for showing equivalence “statistically”. best regards martin |
|
Helmut ★★★   Vienna, Austria, 2012-02-22 15:32 (5226 d 10:00 ago) @ martin Posting: # 8153 Views: 4,344 |
|
|
Dear Martin! ❝ […] this criterion is counterproductive, because equivalence is “shown” more likely with a high SD rather than with a small SD and that the effect size is not adequately taken into account. Exactly. ❝ I would be grateful for your opinion and/or for published references regarding this approach for showing equivalence “statistically”. Hhm, no idea. At least in the context of BE this flawed concept was already abandoned with Schuirmann’s TOST in 1983. — Dif-tor heh smusma 🖖🏼 Довге життя Україна! ![[image]](https://static.bebac.at/pics/Blue_and_yellow_ribbon_UA.png) Helmut Schütz ![[image]](https://static.bebac.at/img/CC by.png) The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes |
|
d_labes ★★★ Berlin, Germany, 2012-02-22 18:05 (5226 d 07:27 ago) @ martin Posting: # 8156 Views: 4,425 |
|
|
Dear Martin, dear Helmut! Strange!?  Writing down the sentence "the calculated sample mean should not differ more than 1.3 standard deviations (SDs) to the known value" as formula, with µ0 the known value-1.3*SD < µ - µ0 < 1.3*SDit strongly reminds me of a thing that is called "scaled ABE" in the context of BE studies, but here as a one group test. Isn't it? But in the simple application of the above equation, as the sentence suggests, the method is not described properly I think. There is evidence that one should use 95% confidence intervals for the criterion (µ - µ0)/SD or a linearized version of it. Additionally: Where the constant 1.3 comes from remains questionable. Wellek[1] proposes 0.36 (strict) or 0.74 (liberal) in the context of a two group test. BTW: (µ - µ0)/sd is the effect size in the sense of Cohen. [1] S. Wellek "Testing Statistical Hypotheses of Equivalence" Chapman & Hall / CRC Boca Raton 2000 — Regards, Detlew |
|
martin ★★ Austria, 2012-02-22 19:18 (5226 d 06:13 ago) (edited on 2012-02-22 20:20) @ d_labes Posting: # 8157 Views: 4,416 |
|
|
dear d_labes! thank you very much for pointing this out! Yes it's a one-sample problem where µ0 is a known constant and the data are assumed to be normally distributed. I could imagine that the value of 1.3 is motivated by the normal distribution as approximately 80% of all data fall within -1.3*SD < µ < 1.3*SD.I think Wellek's liberal suggestions of 0.5 for the standardized effect size for the paired t-test is applicable in this setting. From a regulatory point of view, a justification may be needed for using the scaled ABE approach (using a CI for the standardized effect size or for it's linearized version) in this setting when the CV is smaller than 30%. For this reason, I would calculate the 90% CI for the ratio µ/µ0 using the corresponding modified Fieller formula and use the widely known confidence interval inclusion approach with margins for ratios for averages relating to 0.5 for the standardized difference (i.e. 0.8 to 1.25) if the CV is smaller than 30%. what do you think? best regards martin PS.: there were no confidence intervals mentioned in the description of the method |
|
d_labes ★★★ Berlin, Germany, 2012-02-23 09:25 (5225 d 16:06 ago) @ martin Posting: # 8162 Views: 4,305 |
|
|
Dear Martin! ❝ For this reason, I would calculate the 90% CI for the ratio ❝ ❝ what do you think? I think your approach sounds very reasonable, especially for persons working on the field of BE studies  .But maybe others prefer Wellek's direct test methods. ❝ PS.: there were no confidence intervals mentioned in the description of the method Taking the sentence literally is of course 'Kappes' (nonsense). — Regards, Detlew |
Ing. Helmut Schütz