Evidence of Jones' Guilt

@kflo although I was able to reproduce Cowan’s model for the examples he gave I was unable to get anywhere with the decay portion using my approach.

However I did find a possible alternative. This alternate formulation is easy enough to “read backwards” and program for the decay segment.

Instead of adding “all the shifted curves together” for a certain t value we add all but one (the top one) after the last bottom spike.

It seems plausible to me, hopefully to you as well.

If it works I think smoothness and symmetry will be maintained.

I’m kind of bummed that this looks so easy. Here I thought I was in new territory but it seems kind of trivial…….

Graphs within the next 2 hours.

Edit: the concept is simple the implementation is a little bit more tricky. It's going to take longer than 2 hours.
 
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@kflo I derped and forgot to include a picture to show what I was talking about in the last post.

BuZA3AW.jpg


So I'll just repeat the last post

although I was able to reproduce Cowan’s model for the examples he gave I was unable to get anywhere with the decay portion using my approach.

However I did find a possible alternative. This alternate formulation is easy enough to “read backwards” and program for the decay segment.

Instead of adding “all the shifted curves together” for a certain t value we add all but one (the top one) after the last bottom spike.

It seems plausible to me, hopefully to you as well.

If it works I think smoothness and symmetry will be maintained.

I’m kind of bummed that this looks so easy. Here I thought I was in new territory but it seems kind of trivial…….

Graphs within the next 2 hours.

Edit: the concept is simple the implementation is a little bit more tricky. It's going to take longer than 2 hours.
 
@kflo I derped and forgot to include a picture to show what I was talking about in the last post.

BuZA3AW.jpg


So I'll just repeat the last post

although I was able to reproduce Cowan’s model for the examples he gave I was unable to get anywhere with the decay portion using my approach.

However I did find a possible alternative. This alternate formulation is easy enough to “read backwards” and program for the decay segment.

Instead of adding “all the shifted curves together” for a certain t value we add all but one (the top one) after the last bottom spike.

It seems plausible to me, hopefully to you as well.

If it works I think smoothness and symmetry will be maintained.

I’m kind of bummed that this looks so easy. Here I thought I was in new territory but it seems kind of trivial…….

Graphs within the next 2 hours.

Edit: the concept is simple the implementation is a little bit more tricky. It's going to take longer than 2 hours.
Isn’t a difference that m3 would still be accumulating when subsequent doses of the parent are taken? The Cowan example the drug measured is quickly being diluted by the time the next dose is taken. It peaks immediately and then quickly drops.
 
Isn’t a difference that m3 would still be accumulating when subsequent doses of the parent are taken? The Cowan example the drug measured is quickly being diluted by the time the next dose is taken. It peaks immediately and then quickly drops.

Without a doubt the m3 graph when subjected to the same algorithm will not produce a jigsaw saturation pattern. It will accumulate a lot faster than it decays resulting in a high peak with little to no decay in between. Recall the post where I showed a peak of ~3000 pg/ml for 30 daily doses compared to a peak of ~150 pg/ml for a single dose. That should happen again.

The previous picture is just an illustration of a specific case. The general algorithm can be applied to many cases resulting in different behavior.
 
@kflo I think this is progress. Don't know if it is right but it is "comfortable".
Cowan's Accumulation Scheme for 1 day half life and dosing daily
7ZfF2Yb.jpg

My recreation of Cowan's accumulation scheme with proposed decay scheme
f5QB8VH.jpg

Cowan's Accumulation Scheme for 5 day half life and daily dosing
gAdr6pg.jpg

My recreation of Cowan's accumulation scheme with proposed decay scheme
9Yt50YD.jpg


Honestly I was banging my head against a wall trying to figure it out. Turned out to be WAY easier than I thought.

I don't know if the decay scheme is correct BUT at the very least it is consistent with the accumulation scheme.

I'll try to apply the same scheme to turinabol m3 today.

Confession: I hard code a lot of parameters instead of defining variables and functions which makes for more tedious book keeping. It's a bad habit that I need to break.

Also without an explicit formula for Cowan's single dose excretion curve I assumed exponential. My graphs therefore may not look as smooth but the saturation points are nearly identical.
 
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@kflo @fzoid4454
I'm getting 283 days for a single dose of 20mg and 331 days for 30 daily doses of 20mg. As it pertains to the Jones case

1) I have to concede that if Cowan's model is applicable then Jones' test results are indeed "trace".

2) However he's been testing positive for trace amounts much longer than 331 days.

3) However as a counterpoint to 2) that could be due to inter-individual variability

4) I'm inclined to believe that if he was intentionally doping then at some point he would have tested in the ng/ml range.



There's still work to be done but as of right now I am willing to give him the benefit of doubt. This is all contingent on Cowan's model being applicable. That may be a disappointment to some in this thread but whatever. I'm going to keep going.

I want to assess inter-individual variability when it comes to the clomiphene test results and apply it to turinabol m3. I believe the clomiphene paper said something about the applicability of the study to chlorinated steroids (which turinabol is). That would at least give me some framework.

I think the key to reconstructing single dose data from truncated multiple dose data ( and then extrapolating for complete multiple dose data to find final day) has something to do with "delayed differential equations". But right now that idea isn't solidified it's just something I'm pondering.

xqfVQFU.jpg


Naturally blue is single dose, and orange/red is multiple dose.

Edit: I'd really like to see specific gravity data.
 
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@kflo @fzoid4454
I'm getting 283 days for a single dose of 20mg and 331 days for 30 daily doses of 20mg. As it pertains to the Jones case

1) I have to concede that if Cowan's model is applicable then Jones' test results are indeed "trace".

2) However he's been testing positive for trace amounts much longer than 331 days.

3) However as a counterpoint to 2) that could be due to inter-individual variability

4) I'm inclined to believe that if he was intentionally doping then at some point he would have tested in the ng/ml range.



There's still work to be done but as of right now I am willing to give him the benefit of doubt. This is all contingent on Cowan's model being applicable. That may be a disappointment to some in this thread but whatever. I'm going to keep going.

I want to assess inter-individual variability when it comes to the clomiphene test results and apply it to turinabol m3. I believe the clomiphene paper said something about the applicability of the study to chlorinated steroids (which turinabol is). That would at least give me some framework.

I think the key to reconstructing single dose data from truncated multiple dose data ( and then extrapolating for complete multiple dose data to find final day) has something to do with "delayed differential equations". But right now that idea isn't solidified it's just something I'm pondering.

xqfVQFU.jpg


Naturally blue is single dose, and orange/red is multiple dose.

Edit: I'd really like to see specific gravity data.
Thanks. You’re at least getting some results that seem to hold together. I won’t say that I have high confidence in the result because its likely at least some of the underlying assumptions are off but you at least seem to be producing results that could be consistent with your inputs and assumptions.

Curious what you get if you increase from 20mg to say 40 or 60? There’s some conflicting information on tbol protocols but 20mg is on the low side from most sources. So curious how the dose changes the window in your model.

Not sure I buy that the accumulation for 30 days only adds 18 days (331 days is 301 days after the last dose, compared to 283 for a single dose) but I suppose it is plausible. And yes, you are coming around on the idea that inter-individual variability can play a big role in the window. As well as behavior impacts (dehydration for example)….we don’t really have enough information on how long the individual in the study was actually tested after he initially showed no detection.

But good job. :)

You seem to be getting a better intuition on what you’re seeing as well as what else needs to be studied to increase the overall understanding and accuracy. Keep learning. This isn’t just for a jon jones thread for you…..:)
 
Thanks. You’re at least getting some results that seem to hold together. I won’t say that I have high confidence in the result because its likely at least some of the underlying assumptions are off but you at least seem to be producing results that could be consistent with your inputs and assumptions.

Curious what you get if you increase from 20mg to say 40 or 60? There’s some conflicting information on tbol protocols but 20mg is on the low side from most sources. So curious how the dose changes the window in your model.

Not sure I buy that the accumulation for 30 days only adds 18 days (331 days is 301 days after the last dose, compared to 283 for a single dose) but I suppose it is plausible. And yes, you are coming around on the idea that inter-individual variability can play a big role in the window. As well as behavior impacts (dehydration for example)….we don’t really have enough information on how long the individual in the study was actually tested after he initially showed no detection.

But good job. :)

You seem to be getting a better intuition on what you’re seeing as well as what else needs to be studied to increase the overall understanding and accuracy. Keep learning. This isn’t just for a jon jones thread for you…..:)

Yeah I don't have high confidence in my results either. I think the underlying assumption of how the metabolite eliminates in urine being similar to how parent drugs accumulate in plasma may be seriously flawed.

https://www.boomer.org/c/p4/c05/c0502.php

I haven't made sense of all the above but there seems to be an interplay of coupled differential equations.

I don't know how to change dosages in my model: I based my model of 20mg data and iterated with Cowan's model found in the 2017 Macolin Anti-Doping documents which may be different than the model talked about in Dylan Scott's Arbitration. If I could get my hands on 5mg data from the new paper maybe I could make some atheoretic inferences about how dosages change things.

One thing I'm not wavering on is that a single dose 20mg Oral Turinabol m3 excretion curve can be described by a solution to a linear non-homogenous 3rd order differential equation. The fit is too good and I don't think anyone has done it. That's a feather in my cap and I hold to that.

Maybe I can use that knowledge and work backwards from the link. That's a vague description of how I plan to proceed but that's because I don't know what I'm talking about (yet):cool:.

And you're right this is bigger than Jon Jones for me. I've put in a good amount of work and I plan to put in more. And if in the end when my knowledge is solidified I reach a conclusion that exonerates Jones then so be it. I'm not going to learn about delayed differential equations, vector spaces, regression methods, and pharmacokinetics so I can throw it all away and stick to my guns.

Hopefully I can slap a document together with enough good work that someone in the anti-doping scientific community will be like "okay this guy is serious, he's not some jerk-off haphazardly playing with python and matlab, he's committed to learning the intricacies of the issue, underlying theory, and advanced data analysis". That's my hope.
 
Yeah I don't have high confidence in my results either. I think the underlying assumption of how the metabolite eliminates in urine being similar to how parent drugs accumulate in plasma may be seriously flawed.

https://www.boomer.org/c/p4/c05/c0502.php

I haven't made sense of all the above but there seems to be an interplay of coupled differential equations.

I don't know how to change dosages in my model: I based my model of 20mg data and iterated with Cowan's model found in the 2017 Macolin Anti-Doping documents which may be different than the model talked about in Dylan Scott's Arbitration. If I could get my hands on 5mg data from the new paper maybe I could make some atheoretic inferences about how dosages change things.

One thing I'm not wavering on is that a single dose 20mg Oral Turinabol m3 excretion curve can be described by a solution to a linear non-homogenous 3rd order differential equation. The fit is too good and I don't think anyone has done it. That's a feather in my cap and I hold to that.

Maybe I can use that knowledge and work backwards from the link. That's a vague description of how I plan to proceed but that's because I don't know what I'm talking about (yet):cool:.

And you're right this is bigger than Jon Jones for me. I've put in a good amount of work and I plan to put in more. And if in the end when my knowledge is solidified I reach a conclusion that exonerates Jones then so be it. I'm not going to learn about delayed differential equations, vector spaces, regression methods, and pharmacokinetics so I can throw it all away and stick to my guns.

Hopefully I can slap a document together with enough good work that someone in the anti-doping scientific community will be like "okay this guy is serious, he's not some jerk-off haphazardly playing with python and matlab, he's committed to learning the intricacies of the issue, underlying theory, and advanced data analysis". That's my hope.
I don’t think you can exonerate jones. You can make it more plausible that he’s not guilty of reingestion.

And don’t worry about the anti-doping scientific community yet. First try get buy-in from the scientific / data science community that your models are sound. Then you can try the anti-doping community. :)

Again, in the end, more studies are needed before any real conclusions can be made. That much is certain.
 
I don’t think you can exonerate jones. You can make it more plausible that he’s not guilty of reingestion.

And don’t worry about the anti-doping scientific community yet. First try get buy-in from the scientific / data science community that your models are sound. Then you can try the anti-doping community. :)

Again, in the end, more studies are needed before any real conclusions can be made. That much is certain.

Agreed on all points. and Lmao at how many things I've forgotten about Differential Equations. Need a serious refresher before I can begin to expand my knowledge.
 
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