Helmut ★★★ Vienna, Austria, 20120321 17:18 (4204 d 10:58 ago) Posting: # 8306 Views: 8,149 

Dear all, Detlew wrote here: ❝ The whole discussion up to here depends on the assumption of lognormality. If this is a reasonable assumption for measures of fluctuation like PTF or swing is left to you. Good question. For C_{max} and AUC there’s a consensus that these metrics are lognormal. See also the empiric distribution of AUCs of methylphenidate in 405 subjects in this presentation which agrees with pharmacokinetic considerations and lead to a multiplicative model (or additive on logtransformed data). Steinijans et al.^{*} state about MR theophylline: The choice of the multiplicative model and hence the ratio analysis for the plateu time T75% C_{max} is motivated by the distribution analysis of the plateau time for the test formulation Euphylong^{®} in n = 102 healthy subjects and n = 85 patients presenting with obstructive pulmonary diseases. The logarithmic normal distribution was superior to the normal distribution (data on file). I looked at my MPH MR data (10–60 mg, SD/MD; linear PK). Data of 303 subjects (HVD, MRT, C_{max}/AUC) and 276 subjects (t_{75%}): Interesting, isn’t it?
— Diftor heh smusma 🖖🏼 Довге життя Україна! _{} Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
ElMaestro ★★★ Denmark, 20120321 18:32 (4204 d 09:44 ago) @ Helmut Posting: # 8307 Views: 7,111 

Dear HS, [nitpick] ❝ For C_{max} and AUC there’s a consensus that these metrics are lognormal. No. There is consensus that you have to analyse the data as though they (the residuals) were normal. It does not mean it is assumed that they are. Regulators, some of them at least, know that normality sometimes really, truly isn't the case but they are willing to ignore this at the evaluation stage. [/nitpick] Anyways, as usual I have no qualified response to any of the core stuff you have raised in this thread. Have a good day. — Pass or fail! ElMaestro 
Helmut ★★★ Vienna, Austria, 20120322 17:06 (4203 d 11:09 ago) @ ElMaestro Posting: # 8317 Views: 7,005 

Dear ElMaestro! ❝ [nitpick] ❝ No. There is consensus that you have to analyse the data as though they (the residuals) were normal. ❝ [/nitpick] Nitpicking is one of my hobbies. Working on the residuals now. ❝ Anyways, as usual I have no qualified response to any of the core stuff you have raised in this thread. I’m interested in underlying distributions. Should give me a clue whether to transform or not. — Diftor heh smusma 🖖🏼 Довге життя Україна! _{} Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
martin ★★ Austria, 20120321 22:16 (4204 d 05:59 ago) @ Helmut Posting: # 8308 Views: 7,139 

dear HS! pretty interesting; thank you very much for sharing this information. If you find some time I would be happy to see the QQ plots and the QQ plots of the logtransformed PK parameters. best regards martin PS.: have you also investigated the distribution of residuals of the applied statistical model? 
Helmut ★★★ Vienna, Austria, 20120322 02:17 (4204 d 01:58 ago) @ martin Posting: # 8309 Views: 7,286 

Dear Martin! ❝ If you find some time I would be happy to see the QQ plots and the QQ plots of the logtransformed PK parameters. Here you are: ❝ PS.: have you also investigated the distribution of residuals of the applied statistical model? I used to analyze HVD, t_{75%}, and MRT untransformed and C_{max}/AUC logtransformed, so I have these residuals on file. Will analyze them the other way ’round time allowing. First impressions (5 studies, 76 subjects): Which one would you prefer? — Diftor heh smusma 🖖🏼 Довге життя Україна! _{} Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
d_labes ★★★ Berlin, Germany, 20120322 10:31 (4203 d 17:45 ago) @ Helmut Posting: # 8310 Views: 7,084 

Dear Helmut! First many thanks for sharing this information. Your pictures are a good example of the inherent difficulties in determining the distribution form empirical. Thus I'm a fan of the arguments for the lognormal distribution via theoretical PK considerations (@EM: even if regulators have written down them in guidances ). ❝ I used to analyze HVD, t_{75%}, and MRT untransformed and C_{max}/AUC logtransformed ... IMHO this is a good choice . Although the residuals (and these count at least I think) don't show a very distinct picture. BTW: Since these metrics (the ones you have shown) are usually not primaries then the question of their (their residuals) distribution is not so much of concern I think. I would handle them only in a descriptive way (mean, sd, median and ... and ...). Or do you analyze those metrics also via ANOVA and (12*alpha) CI's in a standard fashion? My originally question was more in the direction of swing metrics. Do you have similar data for PTF or swing? As for ratios of two terms deemed as lognormally distributed I at least questioning a lognormal distribution. On the other hand one may argue with your results for C_{max}/AUC ... Geary 1947, Biometrika Normality is a myth; there never was, and never will be, a normal distribution. — Regards, Detlew 
Helmut ★★★ Vienna, Austria, 20120322 14:27 (4203 d 13:49 ago) @ d_labes Posting: # 8316 Views: 7,162 

Dear Detlew! ❝ Your pictures are a good example of the inherent difficulties in determining the distribution form empirical. I would rather say: Impossibility in any given study due to limited sample size, but good chances if a wealth of historical data is available. ❝ Thus I'm a fan of the arguments for the lognormal distribution via theoretical PK considerations. Absolutely. I have no problems with AUC (and C_{max} as well) but fail to derive a reasonable justification for others. Walnut brain. At the first BioInternational there was this poll amongst participants about transformations. Result was ⅓ always, ⅓ never, ⅓ casebycase. My idea was to study the empirical distributions of less common metrics to derive a suggestion (of course applicable only to a specific drug/formulation). ❝ ❝ I used to analyze HVD, t_{75%}, and MRT untransformed and C_{max}/AUC logtransformed ... ❝ ❝ IMHO this is a good choice . OK, but how did you conclude that? ❝ Although the residuals (and these count at least I think) don't show a very distinct picture. Yes, the sample size I assessed is yet inconclusive. See here for the final outcome. ❝ BTW: Since these metrics (the ones you have shown) are usually not primaries then the question of their (their residuals) distribution is not so much of concern I think. I would handle them only in a descriptive way (mean, sd, median and ... and ...). Or do you analyze those metrics also via ANOVA and (12*alpha) CI's in a standard fashion? These data come from MR products. I calculated the CIs – but only descriptively. ❝ My originally question was more in the direction of swing metrics. Do you have similar data for PTF or swing? As for ratios of two terms deemed as lognormally distributed I at least questioning a lognormal distribution. On the other hand one may argue with your results for C_{max}/AUC ... Well, that’s the reason I started a new thread. I never calculated Swing. Though I have a lot of MD studies the pooled sample size / drug is too small to assess the empiric distributions. I would expect PTF to have a similar distribution as C_{max}/AUC (at least if C_{min} ⇒ LLOQ). ❝ Normality is a myth; there never was, and never will be, a normal distribution. Nice quote. — Diftor heh smusma 🖖🏼 Довге життя Україна! _{} Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
ElMaestro ★★★ Denmark, 20120322 19:16 (4203 d 09:00 ago) @ Helmut Posting: # 8318 Views: 7,013 

Hi HS, this thread gave me an idea (sorry for going a bit off topic now): The whole general use of log transformation is quite unjustified from a biological perspective, but has a lot of appeal from a mathematical perspective in that it rectifies an assumption that must hold for normal dists and which can strictly be said to be violated with untransformed values. But other empirical transformations might have appeal as well. Someone should therefore make an Al Gore Rhythm which could find the 'best' transformation among a set of possible transformations (this would by nature have to be a limited number of known transformations) on a limited number of datasets and see if there's anything useful, like consensus, coming out for whichever parameters are of interest. Of course, there's trouble ahead: It might not be easy to define an objective function that gives a clearcut winner. I am myself in uncharted territory here but I would perhaps naïvely start with something like the ShapiroWilks statistic or a regression goodnessoffit statistic from the QQ plot, and then make sure not to compare it between datasets but only within. Just another useless idea from ElMaestro... I should perhaps just stick to poetry?!? — Pass or fail! ElMaestro 
Helmut ★★★ Vienna, Austria, 20120323 02:50 (4203 d 01:25 ago) @ ElMaestro Posting: # 8319 Views: 7,170 

Dear ElMaestro! ❝ this thread gave me an idea (sorry for going a bit off topic now): That’s perfect on topic! ❝ The whole general use of log transformation is quite unjustified from a biological perspective, but has a lot of appeal from a mathematical perspective in that it rectifies an assumption that must hold for normal dists and which can strictly be said to be violated with untransformed values. But other empirical transformations might have appeal as well. Yep. ❝ Someone should therefore make an Al Gore Rhythm which could find the 'best' transformation among a set of possible transformations (this would by nature have to be a limited number of known transformations) on a limited number of datasets and see if there's anything useful, like consensus, coming out for whichever parameters are of interest. Right. \(1/\sqrt{x}\) is a nice one. I think there are different parties out there:
❝ Of course, there's trouble ahead: It might not be easy to define an objective function that gives a clearcut winner. Yep. Generally the sample size is much too small. Whilst logtransform is a clear winner in the 405 subjects (slide 43) I would not bet on the SW’s in the next slide (12 subjects; p 0.29668 vs. 0.85764). Normality tests are no decision tools between two transformations. ❝ I am myself in uncharted territory here but I would perhaps naïvely start with something like the ShapiroWilks statistic or a regression goodnessoffit statistic from the QQ plot, and then make sure not to compare it between datasets but only within. What do you mean by “only within”? If we run them on the single studies, power will be too low (see the example above) and inconclusive. That’s why Volker Steinijans looked at the distribution of historical data and defined the method of a particular study a priori. I think that’s the way to go. But: Requires data, data, data. So here we are – 10 studies on MR methylphenidate formulations (designs 2×2, 6×3, 4×4; 10–60 mg, 12–24 subjects/study, 174 subjects total; t_{75%}, HVD, MRT_{t}, C_{max}/AUC_{t}): Tails are amazing. We use a pretty sensitive method; LLOQ <1% of C_{max}, residual AUC <5%, residual AUMC <15%… ❝ Just another useless idea from ElMaestro... I should perhaps just stick to poetry?!? Have you tried that before? Far more complicated. — Diftor heh smusma 🖖🏼 Довге життя Україна! _{} Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 