<div dir="auto">Thanks Filippo, <div dir="auto"><br></div><div dir="auto">Your full paper helped me a lot. I think I understand better now. I now think we were thinking of different things. </div><div dir="auto"><br></div><div dir="auto">I was thinking of a function that defines the probability of mortality as a function of time since infection, with the good chance of surviving. This function should look like figure 2 in your paper where higher age individuals have higher chance of dying, yet after a certain point in time those who survived no longer can die, indicating recovery. </div><div dir="auto"><br></div><div dir="auto">It seems that the function you suggested is a little different. If I understand you correctly, you already stratified the group that will die and you are trying to show the probability of an individual dying in a certain day from infection knowing they will die. </div><div dir="auto"><br></div><div dir="auto">Please verify that I am correct. Since I need to know how to use your function. </div><div dir="auto"><br></div><div dir="auto">You have two more interesting elements in the paper that can start interesting discussions: </div><div dir="auto"><br></div><div dir="auto">1. You approach the definition of a comorbidity by a level of damage to tissue. </div><div dir="auto"><br></div><div dir="auto">2. You end the paper by discussing what needs to be done to make models used in medical settings.</div><div dir="auto"><br></div><div dir="auto">Those topics deserve discussion in separate email threads. Yet for now I wish to make sure I understood your model correctly so I can implement it properly. </div><div dir="auto"><br></div><div dir="auto">Happy holidays</div><div dir="auto"><br></div><div dir="auto"><br></div><div dir="auto"> Jacob</div><div dir="auto"><br></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Tue, Dec 22, 2020, 13:38 Filippo Castiglione <<a href="mailto:filippo.castiglione@gmail.com" rel="noreferrer noreferrer" target="_blank">filippo.castiglione@gmail.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">Dear Jacob, the preprint is out. You can have a look at it at<br>
<br>
<a href="https://biorxiv.org/cgi/content/short/2020.12.20.423670v1" rel="noreferrer noreferrer noreferrer noreferrer" target="_blank">https://biorxiv.org/cgi/content/short/2020.12.20.423670v1</a><br>
<br>
However you might not need to read it to figure out your probability function.<br>
In fact, the curve I sent you last time is <br>
<br>
f(t) = 1-P(t) <br>
<br>
where P(t) is the probability of dying at time t. To be precise you have to take<br>
<br>
P(t) = 1- f(t)/100<br>
<br>
because f(t) is expressed in percent. <br>
<br>
it is of course a rough approximation with rough assumptions (e.g., the choice of the cutoff theta I was mentioning in my last mail) but might be a starting point (!?)<br>
<br>
Hope it helps.<br>
All the best<br>
Fil<br>
<br>
<br>
> On 22 Dec 2020, at 10:42, Jacob Barhak <<a href="mailto:jacob.barhak@gmail.com" rel="noreferrer noreferrer noreferrer" target="_blank">jacob.barhak@gmail.com</a>> wrote:<br>
> <br>
> Thanks Filippo,<br>
> <br>
> Your example is nice since you include a functional form that can be reproduced fairly easily by plugging in the coefficients. However, it seems I will have to wait until you upload the paper to biorxiv so I can better understand what you are showing and if I can reuse it. Allow me to explain my thoughts.<br>
> <br>
> Your plot indicates that after 80 days only about 10% of the population have a viral load larger than theta. Also you indicate that your arbitrary death definition is viral load theta above 1000 in day 30. <br>
> <br>
> What I am looking for is a little bit different, What I want is the probability of death as a function on time. For example, I assume the probability at the day of infection will be zero since the virus did not spread in the body and the probability will then gradually rise as days pass until a peak and then drop again and will be close to zero after several weeks when subjects recover and can no longer die from the disease. <br>
> <br>
> The question is if it is possible to derive such a function from your data? - and if yes, exactly how?<br>
> <br>
> When integrating models, many time the issue is that the models presented in the publication need some manipulation, Many times this manipulation is trivial, yet many other times it requires some transformation and deep comprehension of the details and sometimes the model is unusable for some purposes because it calculates something different. This is what I am trying to figure out in this case and I need more information. <br>
> <br>
> Unless you can help extract the function I am looking for before publication, I will have to wait for the preprint and will be happy to continue this public conversation on this thread. <br>
> <br>
> Jacob<br>
> <br>
> On Mon, Dec 21, 2020 at 4:46 AM Filippo Castiglione <<a href="mailto:filippo.castiglione@gmail.com" rel="noreferrer noreferrer noreferrer" target="_blank">filippo.castiglione@gmail.com</a>> wrote:<br>
> Dear Jacob, please see attachment as a reply to your mail.<br>
> <br>
> I could parametrise the “model” further with respect to patient’s age but I though the reply in attachment might be already ok for your purpose. You tell me. <br>
> <br>
> As for the permission to use it for commercial purposes I can declare no restrictions (so far ;).<br>
> <br>
> Best wishes<br>
> Fil <br>
> <br>
> <br>
> <br>
> > On 20 Dec 2020, at 23:53, Jacob Barhak <<a href="mailto:jacob.barhak@gmail.com" rel="noreferrer noreferrer noreferrer" target="_blank">jacob.barhak@gmail.com</a>> wrote:<br>
> > <br>
> > Well Filippo, <br>
> > <br>
> > Since the discussion is relevant to the comorbidities subgroup and to the integration subgroup, you will find both mailing lists CCd. I suggest we try to keep this discussion public and merge it with the working group activities. I believe others will find interest in this discussion as it may be relevant to their activities. I am copying the entire email conversation below. <br>
> > <br>
> > To your question about if I am suggesting to use your whole model to simulate mortality?<br>
> > <br>
> > The answer is: almost. <br>
> > <br>
> > Your model has important utility towards calculating mortality. However, I only need your output at this point. What I am asking for is the output of your model as a function. Something like:<br>
> > <br>
> > probability_death = f (days since infection)<br>
> > <br>
> > And at this initial point f does not have to be in functional form. It is enough for simulation purposes to have an x,y table where x is from 0 to 60 in days for each day and the associated mortality probability. <br>
> > <br>
> > And it is ok if you give me several assumptions with different cutoff values in your model. <br>
> > <br>
> > The ensemble model will balance those assumptions with other models and assumptions. If the assumptions do not merge well with other assumptions/models, the ensemble model should assign them less influence. <br>
> > <br>
> > So if you can use the model you showed at the webinar to derive different mortality functions and send those to me as a table - it will be great.<br>
> > <br>
> > However, please also make sure you give me permission to use those for commercial purposes - I do intend to monetize my technology and therefore avoid using information that has restrictions. I did declare a conflict of interest and I am making it public. However, I hope we can still collaborate. <br>
> > <br>
> > Jacob<br>
> > <br>
> > --<br>
> > Jacob Barhak Ph.D. <br>
> > Sole Proprietor, Software Developer, and Computational Disease Modeler<br>
> > <a href="https://sites.google.com/view/jacob-barhak/home" rel="noreferrer noreferrer noreferrer noreferrer" target="_blank">https://sites.google.com/view/jacob-barhak/home</a><br>
> > <br>
> > <br>
> > <br>
> > <br>
> > On Sun, Dec 20, 2020 at 2:40 AM Filippo Castiglione <<a href="mailto:filippo.castiglione@gmail.com" rel="noreferrer noreferrer noreferrer" target="_blank">filippo.castiglione@gmail.com</a>> wrote:<br>
> > Dear Jacob, sure this conversation is open. <br>
> > <br>
> > Coming back to the mortality model question are you suggesting to use my whole model to simulate mortality? If yes, then It is possible at the condition that we define when the simulation should stop for “death”. <br>
> > <br>
> > <br>
> > Best<br>
> > <br>
> > --- Filippo (@iPhone)<br>
> > <br>
> >> On 19 Dec 2020, at 21:48, Jacob Barhak <<a href="mailto:jacob.barhak@gmail.com" rel="noreferrer noreferrer noreferrer" target="_blank">jacob.barhak@gmail.com</a>> wrote:<br>
> >> <br>
> >> <br>
> >> Thanks Filippo,<br>
> >> <br>
> >> Yes, you are correct, the mortality models are not accurate. All models are assumptions - none of them are really accurate. The Reference Model was built to figure out how well they perform and provide a reference modelers can compare their models to.<br>
> >> <br>
> >> Your suggestions make sense and in fact I already have several mortality models plugged into my model. Yet those are simplified and not multi scale models.<br>
> >> <br>
> >> The value in your approach is that it makes this multi scale - if you would plug your model in the ensemble and the ensemble will prefer it to other models - this will give the multi scale model validation of sorts. <br>
> >> <br>
> >> And with your permission, I would like to add this conversation to the co-morbidities mailing list that I plan to create or to the integration mailing list in the integration working group portal:<br>
> >> <a href="https://lists.simtk.org/pipermail/vp-integration-subgroup/" rel="noreferrer noreferrer noreferrer noreferrer" target="_blank">https://lists.simtk.org/pipermail/vp-integration-subgroup/</a><br>
> >> <br>
> >> Hopefully you are ok with making this conversation public and part of the working group discussions.<br>
> >> <br>
> >> Jacob<br>
> >> <br>
> >> <br>
> >> <br>
> >> On Sat, Dec 19, 2020 at 2:48 AM Filippo Castiglione <<a href="mailto:f.castiglione@iac.cnr.it" rel="noreferrer noreferrer noreferrer" target="_blank">f.castiglione@iac.cnr.it</a>> wrote:<br>
> >> Hi Jacob. <br>
> >> <br>
> >> The only thing I feel to suggest is to use survival curves of covid patients. I don’t know if you can recall them somewhere from clinical available data (e.g., <a href="https://bmcpublichealth.biomedcentral.com/articles/10.1186/s12889-020-09721-2" rel="noreferrer noreferrer noreferrer noreferrer" target="_blank">https://bmcpublichealth.biomedcentral.com/articles/10.1186/s12889-020-09721-2</a>). <br>
> >> You might be interested in age-related of such curves (Kaplan-Meier curves plot 1-P(death)).<br>
> >> <br>
> >> I might calculated them starting from my simulations but they would be inaccurate because based on an artificial definition of “death” that, of course, I don’t have. Let me know if you want to try it anyway but I suggest to look for them around.<br>
> >> <br>
> >> Another very simple stylised model of mortality would be to use a reverse sigmoid function to represent the upside-down sigmoid shape (long right tail) of a generic Kaplan-Meier plot centred around the "typical value” time of death. For instance such t could be in the range 7-15 days, for instance, 1-0.2/(1+exp(7-x)) where 1-0.2 is the asymptotic value and 7 is the typical death t.<br>
> >> <br>
> >> Let me know if I expressed my thoughts clearly.<br>
> >> <br>
> >> All the best<br>
> >> Fil<br>
> >> <br>
> >> > On 18 Dec 2020, at 18:38, Jacob Barhak <<a href="mailto:jacob.barhak@gmail.com" rel="noreferrer noreferrer noreferrer" target="_blank">jacob.barhak@gmail.com</a>> wrote:<br>
> >> > <br>
> >> > Hi Filippo,<br>
> >> > <br>
> >> > Following your talk at the webinar yesterday, you may recall that I was interested in a mortality model based on time.<br>
> >> > <br>
> >> > I wanted to communicate with you about it to see what is possible.<br>
> >> > <br>
> >> > I am looking for models to plug into my ensemble model. You can see quickly how it looks in this video - I am pointing at the point where I show some ensemble results: <br>
> >> > <a href="https://youtu.be/aTB8-XEZheU?t=1000" rel="noreferrer noreferrer noreferrer noreferrer" target="_blank">https://youtu.be/aTB8-XEZheU?t=1000</a> <br>
> >> > <br>
> >> > I am actively looking for several types of models to integrate into my model. One of the models can be mortality models. Currently I use two different models for mortality - one of overall risk and one for death. I do not have a probability of death per day from infection and looking at your plots I figured you may have something - even at a level of an assumption.<br>
> >> > <br>
> >> > Do you think it is possible to get such models from you and if so, under what terms?<br>
> >> > <br>
> >> > Hopefully you can help.<br>
> >> > <br>
> >> > Jacob<br>
> >> > <br>
> >> > <br>
> >> > <br>
> >> > On Mon, Dec 7, 2020 at 7:57 AM Jacob Barhak <<a href="mailto:jacob.barhak@gmail.com" rel="noreferrer noreferrer noreferrer" target="_blank">jacob.barhak@gmail.com</a>> wrote:<br>
> >> > Ok Filippo, <br>
> >> > <br>
> >> > You are in a similar situation to many others. <br>
> >> > <br>
> >> > Your situation is very common and well understood. <br>
> >> > <br>
> >> > Jacob<br>
> >> > <br>
> >> > On Mon, Dec 7, 2020, 02:37 Filippo Castiglione <<a href="mailto:f.castiglione@iac.cnr.it" rel="noreferrer noreferrer noreferrer" target="_blank">f.castiglione@iac.cnr.it</a>> wrote:<br>
> >> > Dear Jacob, sorry for the late response.<br>
> >> > <br>
> >> > I recently realised I had subscribed to too many groups to be practically able to follow, so opted out from many of them included the comorbidity. I asked Bruce to update the groups’ lists.<br>
> >> > <br>
> >> > All the best<br>
> >> > Fil<br>
> >> > <br>
> >> > > On 6 Dec 2020, at 06:23, Jacob Barhak <<a href="mailto:jacob.barhak@gmail.com" rel="noreferrer noreferrer noreferrer" target="_blank">jacob.barhak@gmail.com</a>> wrote:<br>
> >> > > <br>
> >> > > Hi Filippo,<br>
> >> > > <br>
> >> > > You were listed as interested in comorbidities within the viral pandemic working group. I am going over each member personally to see why they signed up.<br>
> >> > > <br>
> >> > > I looked at your web site:<br>
> >> > > <br>
> >> > > <a href="https://www.iac.cnr.it/~filippo/about-me.html" rel="noreferrer noreferrer noreferrer noreferrer" target="_blank">https://www.iac.cnr.it/~filippo/about-me.html</a><br>
> >> > > <br>
> >> > > Your interest in co-morbidities is visible directly from what you state in your web site:<br>
> >> > > "particular interest in the immune system and related pathologies"<br>
> >> > > <br>
> >> > > I wonder why you did not respond to my email to step up and co-lead this sub-working group. After all you have many publications and experience in leadership.<br>
> >> > > <br>
> >> > > Hopefully my personal email will get a response.<br>
> >> > > <br>
> >> > > Jacob<br>
> >> > > <br>
> >> > > --<br>
> >> > > Jacob Barhak Ph.D.<br>
> >> > > <a href="https://sites.google.com/view/jacob-barhak/home" rel="noreferrer noreferrer noreferrer noreferrer" target="_blank">https://sites.google.com/view/jacob-barhak/home</a><br>
> >> > > <br>
> >> > <br>
> >> <br>
> <br>
<br>
</blockquote></div>