Helmut ★★★ Vienna, Austria, 20200420 16:15 (1067 d 03:43 ago) Posting: # 21339 Views: 8,221 
[email protected]: COVID19 ☣️ [Software] 
Dear all, since many of us are working at home now, consider donating your idle computation power to [email protected]* (see also the Wikiarticle). The software is available for Windows, macOS 10.7+, and 64bit Linux. With the end of March users provided 600,000 CPUs and 430,000 GPUs. Their distributed speed reached 1.3 exaFLOPS last week, outperforming the currently leading supercomputer (IBM’s Summit) by one order of magnitude. Note that you have to own the machine. Otherwise, ask your company for permission. I lost 4,500 ranks since midMarch. Great because recently many users (including big players like Oracle, avast) joined the party (see the image). The software allows a lot of adjustments. Since I don’t encode videos or play 3Dgames, my GPU with its 64 CUDA cores is bored. Hence, I fold on the GPU whilst leaving the CPU free for other stuff (like Phoenix, sim’s in ). For a while I used six threads of the CPU but it’s not worth it – on the average outperformed by the GPU by a factor of ~8.5. Don’t worry to toast your machine. The software monitors the CPU’s/GPU’s temperature and goes for at least 15 minutes into idle state if the system gets too hot. The software comes with a large database of CPUs/GPUs and ‘knows’ their critical temperatures. I never faced that in ½ year, neither on my workstation nor my notebook. The former runs 24/7 and is fanless. If the noise of the fans in your machine annoys you, drag the slider in the Advanced Control to the left. You can pause/resume folding at any time. If you want to shut down your machine, I suggest to folding first. The project(s) will automatically resume folding after a reboot.If you’re already running the software, update to v7.6.9 (released 20200418) where you can prioritize COVID19 projects:
— 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 
jag009 ★★★ NJ, 20200423 07:45 (1064 d 12:14 ago) @ Helmut Posting: # 21343 Views: 6,338 
[email protected]: COVID19 ☣️ 
Hi Helmut! ❝ The software allows a lot of adjustments. Since I don’t encode videos or play 3Dgames, my GPU with its 64 CUDA cores is bored. Hence, I fold on the GPU whilst leaving the CPU free for other stuff (like Phoenix, sim’s in R). For a while I used six threads of the CPU but it’s not worth it – on the average outperformed by the GPU by a factor of ~8.5. Would my GPU help? Nvidia 2080ti... 
Helmut ★★★ Vienna, Austria, 20200423 11:34 (1064 d 08:24 ago) @ jag009 Posting: # 21344 Views: 6,320 
[email protected]: COVID19 ☣️ 
Hi John, ❝ Would my GPU help? Nvidia 2080ti... Wow, definitely! Are you a gamer? — 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 
jag009 ★★★ NJ, 20200424 09:51 (1063 d 10:07 ago) @ Helmut Posting: # 21348 Views: 6,227 
[email protected]: COVID19 ☣️ 
Hi Helmut! ❝ ❝ Would my GPU help? Nvidia 2080ti... ❝ Wow, definitely! Are you a gamer? When I have free time. Yes... Will help out :) 
Zoey ☆ NY, 20200723 13:30 (973 d 06:29 ago) @ Helmut Posting: # 21781 Views: 4,197 
[email protected]: COVID19 ☣️ 
I'm new here and this is a good find. I have a nephew who keeps talking about these folding projects which use multiple computers; will definitely share a link with him. He will be happy to be involved. I came here looking to understand a few things about statistics (I have been on other forums too, as conversations really help). I have to write about the subject, some branches and their applications in real life, for a writer friend. I was planning to write a bit about Bioavailability, interpret zscore with examples of its application in these Covid times, and wrap up with geometric sequences in music. I will read and understand more, before I put it all together for him. This has been super helpful. I am hoping this writing assignment will grow to become a regular source of work. Thanks. 
Helmut ★★★ Vienna, Austria, 20200723 18:02 (973 d 01:57 ago) @ Zoey Posting: # 21782 Views: 4,510 

Hi Zoey, ❝ I'm new here and this is a good find. Welcome to the club. ❝ I was planning to write a bit about Bioavailability,… Bioavailability (BA), bioequivalence (BE) and an excursion into pharmacokinetics (PK)… Absolute BA is^{ a}$$f=\frac{{\color{Blue}{AUC_{\textrm{EV}}}}\: {\color{Black}\times}\: {\color{Red}{D_{\textrm{IV}}}}}{\color{Red}{{AUC_{\textrm{IV}}}}\:{\color{Black}\times}\: {\color{Blue}{D_{\textrm{EV}}}}}\tag{1}$$where$$AUC=\int_{0}^{\infty}C(t)\tag{2}$$is the Area Under the Curve (\(\small{AUC}\)) as the integral of the concentrationtime curve from the time of administration \(\small{(t=0)}\) to infinite time.^{ b} \(\small{\textrm{EV}}\) denotes an extravascular^{ c} and \(\small{\textrm{IV}}\) an intravenous dose \(\small{D}\). Sometimes you’ll find \(\small{F}\) instead, which is simply \(\small{f}\) in percent. In the example above \(\small{F=100\%}\) because the same doses were administered and \(\small{AUCs}\) are identical. BTW, \(\small{f_{\textrm{abs}}}\) is an oxymoron. If \(\small{\textrm{EV}}\) is an orally administered solution and \(\small{f<1}\), it means that the drug is not completely absorbed and/or partly degrades in the GItract and/or is metabolized (already in the gut wall and/or the liver). From a clinical perspective a high \(\small{f}\) is desirable because we can expect low variability. On the other hand, drugs with low \(\small{f}\) can be effective as well. One example are bisphosphonates with \(\small{F\sim 24\%}\). The first part of the \(\small{\textrm{EV}}\)curve shows absorption, i.e., how the drug permeates through the gastric membranes. That’s a continuous process which decreases with time because less drug remains in the GItract. For some highly soluble and highly permeable drugs (e.g., salbutamol) after an inhalation maximum concentrations are reached extremely fast and the onset of action occurs in less than 15 minutes. Good news for asthmatics. Relative BA compares two extravascular doses, or$$f_{\textrm{rel}}=\frac{{\color{Green}{AUC_{\textrm{EV}_1}}}\times {\color{Blue}{D_{\textrm{EV}_2}}}}{{\color{Blue}{AUC_{\textrm{EV}_2}}}\times {\color{Green}{D_{\textrm{EV}_1}}}}.\tag{3}$$If \(\small{\textrm{EV}_1}\) is a pharmaceutical product and \(\small{\textrm{EV}_2}\) an orally administered solution, it shows the influence of the formulation on BA. Here the \(\small{AUC\textrm{s}}\) are identical but the maximum concentration (\(\small{C_{\textrm{max}}}\)) of \(\small{\textrm{EV}_1}\) is lower and observed at a later time. That’s common since the formulation has to disintegrate first and then the drug dissolve. If \(\small{\textrm{EV}_1}\) is an immediaterelease product it is desirable to match the solution as close as possible. If you have a toothache and take a painkiller, you don’t want to get the effect after a couple of hours… On the other hand, if \(\small{\textrm{EV}_2}\) is an immediaterelease product and \(\small{\textrm{EV}_1}\) a modifiedrelease product intended for chronic use, such a delayed and reduced \(\small{C_{\textrm{max}}}\) is desirable. It might increase compliance (say, if the patient has to take the MRproduct only once a day instead of the IRproduct twice a day) and reduce adverse events due to extreme concentrations (after multiple doses the fluctuations of concentrations will be lower). In the late 1980s this was summarized in the catchphrase “The flatter is better”. In BE \(\small{\textrm{EV}_1}\) is the new (Test, \(\small{\textrm{T}}\)) treatment and \(\small{\textrm{EV}_2}\) the standard (Reference, \(\small{\textrm{R}}\)) treatment compared at the same dose. Hence, the dose cancels out from \(\small{(3)}\) and we obtain$$f_{\textrm{rel}}=\frac{AUC_{\textrm{T}}}{AUC_{\textrm{R}}}.\tag{4}$$In fig. 2 above \(\small{f_{\textrm{rel}}=100\%}\) but the maximum concentration of \(\small{\textrm{T}}\) is lower than the one of \(\small{\textrm{R}}\). Hence, regulatory agencies require not only a comparison of the “extent of absorption” \(\small{AUC}\) but also of the “rate of absorption” (assessed by \(\small{C_{\textrm{max}}}\) and – sometimes – its time \(\small{t_{\textrm{max}}}\)). The definition as given in the Code of Federal Regulations, Title 21, Volume 5, Chapter I, Part 314, Suppart A, $314.3: Bioequivalence is the absence of a significant difference in the rate and extent to which the active ingredient or active moiety in pharmaceutical equivalents or pharmaceutical alternatives becomes available at the site of drug action when administered at the same molar dose under similar conditions in an appropriately designed study. Since this a legal text, “significant” is used here in the common meaning (MerriamWebster 2 a) and not in the statistical sense (MW 2 b). The statistical methods are recommended in regulatory guidances. Since they are only a kind of “soft law”, one can deviate from them with a proper justification.Also note the “site of action”. In general this relates to receptors which may be located at a limited area (e.g., ones regulating blood pressure in the carotid sinus), more widely spread (in the central nervous system), or almost ubiquitous (pain receptors throughout the body except the brain). Biopsies are definitely not an option and generally we measure concentrations in plasma. Main assumptions and conditions in BE:
Although applied in the early days of BE, we abandoned testing for a significant difference decades ago. Instead a “clinically not relevant difference” \(\small{\Delta}\) is used, which is generally 0.20 (or 20%). For Narrow Therapeutic Index Drugs (NTIDs) or Highly Variable Drugs (HVDs) \(\small{\Delta}\) might be smaller or larger.^{ d} Concentrations cannot be negative and therefore, assuming that they are normally distributed$$C\in \mathbb{R}\:\vee \{\infty,+\infty\}\tag{5}$$would be stupid. Instead we assume a lognormal distribution$$C\in \mathbb{R}^+\:\vee \{>0,+\infty\}\tag{6}$$where concentrations are positive. For convenience (our statistical models require additive effects) we [log_{ℯ}transform our data. This affects also the limits of our acceptance range (AR) \(\small{\{\theta_1,\theta_2\}}\), i.e., for the common \(\small{\Delta}\) of 0.20 we obtain \(\small{\theta_1=1\Delta=80\%}\) and \(\small{\theta_2=1/(1\Delta)=125\%}\). Note that in the log_{ℯ}domain (where the analysis is performed) perfectly matching products with a \(\small{\textrm{T}/\textrm{R}}\)ratio of 100% have \(\small{\log_{e} 1=0}\) and limits are symmetric with \(\small{\log_{e} \theta_1\sim 0.2231}\) and \(\small{\log_{e} \theta_2\sim +0.2231}\). Then we state two hypotheses:$$H_0:\; \mu_{\textrm{T}}/\mu_{\textrm{R}}\notin \{\theta_1,\theta_2\}\tag{7.1}$$$$H_{\textrm{a}}:\; \mu_{\textrm{T}}/\mu_{\textrm{R}}\in \{\theta_1,\theta_2\}\tag{7.2}$$where \(\small{H_0}\) is the “Null Hypothesis” of bioinequivalence and \(\small{H_{\textrm{a}}}\) the “Alternative Hypothesis” of bioequivalence. Note that we cannot “proove” anything in science; here we hope to reject the Null Hypothesis (and implicitly accepting the alternative of BE). By means of Harry Potter’s magic wand we obtain from our study a “point estimate” (the most likely result) and its \(\small{100(12\alpha)=90\%}\)^{ e} confidence interval (CI). Since sample sizes might be small (occasionally only twelve volunteers), we cannot use a test based on the normal distribution^{ f} but have to employ the tdistribution. There are three^{ g} possible outcomes (see also this presentation, slides 29–30):
Ask ten physicians how bioequivalence works and eleven of them will get it wrong. Many believe [sic] that with an acceptance range of 80–125% two products might differ by 45% ignoring the fact that each of them had to pass BE with the confidence interval inclusion approach.^{ i}The FDA retrospectively assessed 2,070 ANDAs from 1996 to 2007.^{ j} It turned out that the average deviation from the RLD (referencelisted drug, i.e., the originator’s approved via an NDA) was 3.56% for \(\small{AUC}\) and 4.35% for \(\small{C_{\textrm{max}}}\). Furthermore, in nearly 98% of the BE studies […], the generic product’s \(\small{AUC}\) differed from that of the innovator product by less than 10%… Regrettably there is still a negative attitude against generic drugs amongst stakeholders (patients, pharmacists, physicians).^{ k} Possibly the perception of “cheaper = of poor quality” triggers a nocebo effect in patients and physicians are mislead by various case reports about “failing drugs”. In the early days of BE innovator companies tried hard to falsify the concept of BE. They performed therapeutic equivalence (TE) studies in a large number of patients together with BE studies in healthy volunteers. The idea behind was: If the BE study passes and the TE study fails it would show that the concept is wrong. Lot of money spent, no avail; BE “works”. Soon the innovators realized that if they would succeed in falsifying the concept, they would shoot themselves in the foot.^{ l} They have also to demonstrate BE when scalingup manufacturing from the small batches (likely less than 10,000 units) used in their Phase III studies to the final production batch size (sometimes millions of units). Furthermore, BE is also required if the formulation is substantially changed. People would be surprised how far the originator’s product might have ‘drifted’ from the original BA (see this post). Hope that helps. [list=a][*]On the premise of linear pharmacokinetics, i.e., both absorption and elimination are independent from dose. THX to John for pointing that out! We cannot administer drugs with low \(\small{f}\) at the same dose because the \(\small{\textrm{IV}}\) dose may lead to adverse effects. In a later stage of development doseproportionality has to be assessed anyhow. Given recent advances in bioanalytics – which allows measuring extremely low concentrations – an alternative is microdosing. [*]Of course, we cannot measure the concentration until \(\small{t=\infty}\). With a few exceptions (e.g., alcohol) – for \(\small{\textrm{EV}}\)^{ c} once absorption is essentially complete – concentrations follow an exponential decrease, i.e.,$$C(t)=C_0 \exp (k_{\textrm{el}}\times t)\tag{8}$$where \(\small{k_{\textrm{el}}}\) is the elimination rate constant. In practice we measure as long as we can (in the example for 24 hours), estimate \(\small{k_{\textrm{el}}}\) by loglinear regression and perform an extrapolation by$$AUC_{0\infty}=\int_{0}^{t}C(t)+\frac{\widehat{C_{{\textrm{t}}}}}{k_{\textrm{el}}}\tag{9}$$BTW, have you ever heard the term “half life”? It’s obtained by \(\small{t_{1/2}=\log_{e} 2 / \small{k_{\textrm{el}}}}\). In my examples I had \(\small{k_{\textrm{el}}}\;0.1733\) and therefore, \(\small{t_{1/2}=0.6931/0.1733\sim 4\;\textrm{hours}.}\) To the right a plot like fig. 1 but with concentrations in a logarithmic scale. After the \(\small{\textrm{IV}}\) dose every \(\small{t_{1/2}}\) the concentration drops by 50%: \(\small{100 \xrightarrow[4\,\textrm{h}:\,^1/_2]{t_{1/2}}50 \xrightarrow[8\,\textrm{h}:\,^1/_4]{t_{1/2}}25 \xrightarrow[12\,\textrm{h}:\,^1/_8]{t_{1/2}}12.5 \xrightarrow[16\,\textrm{h}:\,^1/_{16}]{t_{1/2}}6.25 \xrightarrow[20\,\textrm{h}:\,^1/_{32}]{t_{1/2}}3.125 \xrightarrow[24\,\textrm{h}:\,^1/_{64}]{t_{1/2}}1.5625.}\) After five half lives (here 20 hours) already 96.875% of the drug left the systemic circulation. We see also that after \(\small{2\times t_{{\textrm{max}}}}\) (8 hours) of the \(\small{\textrm{EV}}\) dose its elimination runs in parallel to the one of the \(\small{\textrm{IV}}\) dose, meaning that absorption is essentially complete. That’s good because we can estimate its \(\small{k_{\textrm{el}}}\) which we need in extrapolating the \(\small{AUC}\) acc. to \(\small{(9)}\). [*]Extravascular means any route of administration which is not intravenous (a fast injection or an infusion), e.g., oral, sublingual, rectal, vaginal, topical (transdermal systems, creams, ointments, …), inhalation, intranasal, ophthalmic, intramuscular and subcutaneous injections, … Hence, it can be more complicated than in the simple examples before. In fig. 4 \(\small{\textrm{EV}_1}\) is a socalled “pulsatile” oral formulation, which releases 60% of the dose fast (for a rapid onset of effect) and 40% with a slower absorption \(\small{t_{1/2}}\) after four hours (for maintenance of effect). \(\small{\textrm{EV}_2}\) is a transdermal system, where the patch is removed after eight hours. [*]For NTIDs in some jurisdictions \(\small{\Delta}\) is fixed at 0.10, which gives an acceptance range (AR) of 90.00–111.11%. The FDA recommends that the AR is “scaled” based of the variability of the referencedrug and – in rare cases – it might be even narrower. For HVDs \(\small{\Delta}\) some jurisdictions recommend a fixed \(\small{\Delta}\) of 0.25, which gives an AR of 75.00–133.33%. Others recommend “referencescaling”, where \(\small{\Delta\leqslant 0.3016}\) might lead to an AR of up to 69.84–143.19%. HVDs are safe drugs because they have a flat doseresponse curve (large differences in concentrations lead to small differences in effects). If they would have a step doseresponse curve they would not get approved first because in the Phase III studies – due to the high variability – there would be an unacceptable high number of patients experiencing AEs (toxicity) and lacking effects. Furthermore, if there would problems become evident in Phase IV studies (post marketing) or pharmacovigilance they would have been taken off the market. In short, HVDs “work” despite their high variability which justifies a wider AR for them. [*]Why not the 95% CI which is employed in Phase III clinical studies of a new treatment? In those studies a onesided test is performed (hoping that the treatment is superior to placebo or an established standard treatment). Hence, the patient’s risk (the Type I Error) is 5%. Yes, there is a 5% chance that even a “blockbusterdrug” does not perform better than snake oil… In BE we want limit the patient’s risk to 5% as well. However, in a particular patient concentrations can be either too low or too high but obviously not at the same time. Hence, the 90% CI covers both scenarios in the population of patients. [*]Like in your example about \(\small{Z}\)scores. With 50 students it’s fine because the tdistribution approaches the normal distribution reasonably fast. Most people happily apply \(\small{\mathcal{N}}\) if \(\small{n\geqslant 30}\). However, in BE we are a cautious bunch and always use tests based on the tdistribution. [*]From a regulatory point of view the outcome is dichotomous; either the study passed (#1) or it failed (#2 or #3). From the producer’s perspective only #3 is a disaster. In the gray zone (#2) there is still hope. [*]All applicable regulatory guidances mandate that the study is designed for a certain – high – power (i.e., 80–90%). Quoting the guideline “Statistical Principles for Clinical Trials” of the International Council for Harmonisation:
[*]If the true \(\small{\textrm{T}/\textrm{R}}\)ratio would be 80% or 125%, even a study with the entire population of our lovely planet will fail to show BE since the lower (or upper) confidence limit would be outside the AR. [*]Davit BM, Nwakama PE, Buehler GJ, Conner DP, Haidar SH, Patel DT, Yang Y, Yu LX, Woodcock J. Comparing Generic and Innovator Drugs: A Review of 12 Years of Bioequivalence Data from the United States Food and Drug Administration. Ann Pharmacother. 2009; 43(10): 1583–97. doi:10.1345/aph.1M141. PMID 19776300. [*]Dunne SS, Dunne CP. What do people really think of generic medicines? A systematic review and critical appraisal of literature on stakeholder perceptions of generic drugs. BMC Medicine. 2015; 13:173. doi:10.1186/s1291601504153. PMID 26224091. Open access. [*]The Phase III study of the first statin (simvastatin) was performed in thousands (‼) of patients. Such a high number was required to demonstrate superiority to a lowcholesterol diet; the study took 5½ years. Can you imagine how many patients would be required to show a difference between two products of ≤20%? Maybe 12,000 and the study would take ages to complete. BTW, Phase III studies of two COVID19 vaccine candidates started in 30,000 volunteers each…[/list] — 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 
Zoey ☆ NY, 20200724 14:10 (972 d 05:49 ago) @ Helmut Posting: # 21784 Views: 4,129 

❝ Hope that helps. Yes, some of it makes sense Helmut. I am not trained to understand it all. Many thanks. 
Helmut ★★★ Vienna, Austria, 20200724 16:33 (972 d 03:26 ago) @ Zoey Posting: # 21786 Views: 4,067 

Hi Zoey, ❝ I am not trained to understand it all. No worries. If you have questions, feel free to ask. ❝ Many thanks. Welcome. — 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 