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jdfr ☆ Portugal, 2024-12-05 17:34 (46 d 12:15 ago) Posting: # 24312 Views: 4,169 |
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Dear all, I am writing here for the first as I came across PBE. I need to use it to compare and prove equivalence between R and T in vitro measurements. An example: https://www.accessdata.fda.gov/drugsatfda_docs/psg/budesonide_inhalation_sus_20929_rc_09-12.pdf Was wondering if anyone could explain me the math notation, so that I can build an R script. Does anyone have experience with it? Best, |
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ElMaestro ★★★ Denmark, 2024-12-17 23:50 (34 d 05:59 ago) @ jdfr Posting: # 24321 Views: 2,746 |
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Hi jfdr, ❝ Was wondering if anyone could explain me the math notation, so that I can build an R script. Does anyone have experience with it? This is not too difficult but it does take a bit of time. Which part are you struggling with? — Pass or fail! ElMaestro |
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jdfr ☆ Portugal, 2025-01-06 12:14 (14 d 17:36 ago) @ ElMaestro Posting: # 24323 Views: 689 |
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Hi ElMaestro, Only now had the chance to come back at this topic. I believe that I can extract MSB and MSW from an ANOVA. Is that correct? What I am struggling the most is with calculating the components for point and confidence interval estimation (table after step 4). Should I compute them one by one, or is there any package / analysis technique from which I can extract these components. I am not really familiarized with those notations. Best regards and a wonderful 2025, jdfr |
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ElMaestro ★★★ Denmark, 2025-01-06 13:52 (14 d 15:57 ago) @ jdfr Posting: # 24324 Views: 673 |
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Hi jdfr, ❝ I believe that I can extract MSB and MSW from an ANOVA. Is that correct? That would in principle be correct, I think. however if you ask me there is no reason to do so since the guidance (stop 2) directly gives the equations on how to calculate these quantities. ❝ What I am struggling the most is with calculating the components for point and confidence interval estimation (table after step 4). Should I compute them one by one, or is there any package / analysis technique from which I can extract these components. I am not really familiarized with those notations. I do not know of a package that does it for you. There may be smarter ways of doing it, but in my implementation I build / calculate the rows on the tables one by one and at the end all there's left is just a bit of summation to do. I follow strictly the calculation suggested in the guidance. To do so I need to understand the meaning of the notation. — Pass or fail! ElMaestro |
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jdfr ☆ Portugal, 2025-01-07 13:08 (13 d 16:42 ago) @ ElMaestro Posting: # 24325 Views: 609 |
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Hi ElMaestro, Thank you very much for clarifying! Should one use log transformed data? In step 1 it says so, but when calculating ED from table in step 3, the final value comes from calculating using mean values from the untransformed variable. ❝ That would in principle be correct, I think. If I were to do an ANOVA to extract MSB and MSW, should I use a single effect of the containers or add any other effect to it? Doing so didn't lead me to achieve the same results as the ones found in the example. ❝ however if you ask me there is no reason to do so since the guidance (stop 2) directly gives the equations on how to calculate these quantities. It might be easier that way, but I am having trouble in computing the numerator of both MSB and MSW. Any tip? Also, could you clarify "Xbar ijk is the average m life stages for ith bottle in batch # j", please? ❝ I do not know of a package that does it for you. There may be smarter ways of doing it, but in my implementation I build / calculate the rows on the tables one by one and at the end all there's left is just a bit of summation to do. I follow strictly the calculation suggested in the guidance. To do so I need to understand the meaning of the notation. Thank you for the clarification. I will compute them one by one, it shouldn't be that hard. Many thanks in advance. |
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ElMaestro ★★★ Denmark, 2025-01-07 14:50 (13 d 14:59 ago) @ jdfr Posting: # 24326 Views: 591 |
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Hi jdfr, ❝ Should one use log transformed data? In step 1 it says so, but when calculating ED from table in step 3, the final value comes from calculating using mean values from the untransformed variable. From the top of my head I think the only thing they do not tell you in the guidance is that the sample data is already ln-tranformed. ❝ If I were to do an ANOVA to extract MSB and MSW, should I use a single effect of the containers or add any other effect to it? Doing so didn't lead me to achieve the same results as the ones found in the example. You would need to combine some mean squares for MSB as variability between comes from different units and different batches. I do not readily have a recipe. I am sure it can be worked out pretty easily, but again why do it when the guidance has a perfect example with equations for it? ❝ It might be easier that way, but I am having trouble in computing the numerator of both MSB and MSW. Any tip? ❝ Also, could you clarify "Xbar ijk is the average m life stages for ith bottle in batch # j", please? Xbarijk. is to be understood as: The value of X for the i'th unit of the j'th batch for the k'th product averaged over the m stages of your data. — Pass or fail! ElMaestro |
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jdfr ☆ Portugal, 2025-01-07 18:10 (13 d 11:39 ago) @ ElMaestro Posting: # 24327 Views: 578 |
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Hi ElMaestro, ❝ From the top of my head I think the only thing they do not tell you in the guidance is that the sample data is already ln-tranformed. Everything is clear now  ❝ You would need to combine some mean squares for MSB as variability between comes from different units and different batches. I do not readily have a recipe. I am sure it can be worked out pretty easily, but again why do it when the guidance has a perfect example with equations for it? I am having trouble translating the numerators into code, that's why I was trying to find an ANOVA that could give me both MSB and MSW but I fully understand that it is easier to code directly the formulas given. Should I calculate (mean(stage1)+mean(stage2)+mean(stage3))/number of stages? Best regards, |
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ElMaestro ★★★ Denmark, 2025-01-07 19:55 (13 d 09:54 ago) @ jdfr Posting: # 24328 Views: 584 |
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Hi jdfr, ❝ I am having trouble translating the numerators into code, that's why I was trying to find an ANOVA that could give me both MSB and MSW but I fully understand that it is easier to code directly the formulas given. Should I calculate (mean(stage1)+mean(stage2)+mean(stage3))/number of stages? Actually, I do not think such a quantity is used to derive the HEta value, is it? Here's how I would approach it: 1. You know you need Xbarijk. and Xbar..k. to calculate the two MSB values. First create those functions. 2. Now you can easily derive the MSBs. 3. Since you have Xbarijk. you also get the two MSWs now. 4. Now you easily derive the sigmas. 5. Then fetch the critical values of chi square and t at the necessary df's. 6. At this point you can easily derive Hd, H1-H4 and determine if you are scaling or not. 7. Derive the HEta corresponding to your scaling decision and Bob's your uncle. Good luck. — Pass or fail! ElMaestro |
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jdfr ☆ Portugal, 2025-01-08 11:13 (12 d 18:37 ago) @ ElMaestro Posting: # 24329 Views: 534 |
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Hi ElMaestro, I am really thankful for your whole explanation on the topic. Your checklist is very clear and I am building my R script based on the same topics. Nevertheless, I am blocked for days in Xbarijk., that's where I am stuck. I cannot understand how to calculate it nor integrate it in the sum function. In ❝ ❝ (mean(stage1)+mean(stage2)+mean(stage3))/number of stages? I was wondering if that would be the way to calculate it, but it seems it isn't. Do you have any clarification on this topic? |
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ElMaestro ★★★ Denmark, 2025-01-08 12:02 (12 d 17:47 ago) @ jdfr Posting: # 24330 Views: 525 |
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Hi jdfr, ❝ I was wondering if that would be the way to calculate it, but it seems it isn't. Do you have any clarification on this topic? Xbarijk. is very simple: Let us say you look at the 8th unit from batch 2 of the ref product. Let us say that you are coding ref as k=1 (which would most likely imply that you code Test as k=2). So we are looking at samples with i=8, j=2 k=1. Assume on the ln-scale you have three measurements: Beginning: 1.6 Middle: 1.8 End: 1.7 Let us further say you code Beginning as s=1, middle as s=2, end as s=3. So, in fact you have X8211=1.6 X8212=1.8 X8213=1.7 Averaging across stages you get Xbarijk.=1.7. This is the average observation across stages for that specific unit in question. Of course in FDA's sample set they did not code units nicely as i=1,2,3... It is up to you to handle that part. Same for batches, stages. — Pass or fail! ElMaestro |
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jdfr ☆ Portugal, 2025-01-08 18:45 (12 d 11:04 ago) @ ElMaestro Posting: # 24331 Views: 487 |
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Hi ElMaestro, Thank you very much for your patience. I have it all working now! Actually I did understand Xbarijk as you explained before and had tried it but the problem with my script was that I was wrongfully using N (sample size) and not n (number of cannisters per batch) on the denominator. (Nothing would work doing this)  Sorry for bothering, and thank you for your help! I hope this thread helps someone in the future. Best, |
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jdfr ☆ Portugal, 2025-01-09 10:16 (11 d 19:33 ago) @ ElMaestro Posting: # 24333 Views: 407 |
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Hi ElMaestro, A question arose, when thinking about examples. Imagining that no canister replication (life stage) was tested (m = 1), what considerations should be taken into account? Should MSW be set to zero ad follow the same approach? On the example it is mentioned that when m = 1, E2 and E4s should not be used, so I believe that it would be the case, but would you do it in another way? Should one test MSW as the variation within batch and not within canister? |
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ElMaestro ★★★ Denmark, 2025-01-09 15:46 (11 d 14:04 ago) @ jdfr Posting: # 24335 Views: 387 |
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Hi jdfr, ❝ Should MSW be set to zero ad follow the same approach? On the example it is mentioned that when m = 1, E2 and E4s should not be used, so I believe that it would be the case, but would you do it in another way? ❝ Should one test MSW as the variation within batch and not within canister? No, MSW is variability within units. This quantity is relevant when you test across stages. If there is just one stage then you have no way to estimate a within-unit-variability, hence E2, E4 are left out. — Pass or fail! ElMaestro |
Ing. Helmut Schütz