<div dir="ltr">Thanks Fil,<div><br></div><div>You helped a lot. However, to make sure we are on the same page, I decided to implement the function using python and show you the plot - just to make sure I implemented your instructions correctly - I rather show you my understanding so you can tell me if this looks reasonable to you.</div><div><br></div><div>Attached is the link to an archive that contains the code and the output. </div><div><a href="https://drive.google.com/file/d/12AU3xsjUk8xVBbb7UmO4hE-ldGj_QJ08/view?usp=sharing">https://drive.google.com/file/d/12AU3xsjUk8xVBbb7UmO4hE-ldGj_QJ08/view?usp=sharing</a><br></div><div><br></div><div>Once you open the archive you should see the interactive plot inside as an html file - you should be able to open it with a modern browser like chrome, edge, or firefox <br></div><div><br></div><div>As for the code I assigned copyright to you and added some documentation. If you have someone in your team familiar with python , you just need to install holoviews and panel to create the plots. I did not put the code in Github - I leave this to you - I am just interested in using the function in my ensemble and need verification that this is correct. Yet if you want, I will be happy to upload it to my github account if we decide on a proper license like MIT / BSD or even preferred CC0 to release this to the public without copyright restrictions. </div><div><br></div><div>For now, please just verify this is correct - I noticed peak mortality increases by age from 50 days to 61 days - is this correct or did I misunderstand something? </div><div><br></div><div>Hopefully this is correct and I can continue to plug in the model into the ensemble.</div><div><br></div><div> Jacob</div><div><br></div><div><br></div><div><br></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Sun, Dec 27, 2020 at 11:13 PM Filippo Castiglione <<a href="mailto:filippo.castiglione@gmail.com">filippo.castiglione@gmail.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">Jacob, <br>
<br>
I forgot to say that after you have calculated the function F’, which is the probability-density-function of the event “death”, you have to multiply to an age-dependent coefficient which can be found in fig.3 panel A of my paper divided by 100 (because there it is expressed in percent).<br>
<br>
In other words for instance the probability to die at day x with respect to the age-class 40-49 is <br>
<br>
1.25/100 * F’(x,a,b,c) with <br>
<br>
a=95.351153808322 <br>
b=0.173066025988826 <br>
c=51.92498287875<br>
<br>
Sorry for the lack of precision. <br>
I hope it is clearer now.<br>
Fil<br>
<br>
<br>
<br>
> On 27 Dec 2020, at 15:51, Filippo Castiglione <<a href="mailto:filippo.castiglione@gmail.com" target="_blank">filippo.castiglione@gmail.com</a>> wrote:<br>
> <br>
> Hi Jacob, let me reply below<br>
> <br>
>> 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. <br>
>> <br>
>> 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. <br>
> <br>
> Ok (in my last reply I was incorrect), then the function you are looking for is the derivative of the one I sent you (normalised dividing by 100), namely,<br>
> <br>
> F(x,a,b,c) = S(x,a,b,c) / 100<br>
> <br>
> and its derivative is <br>
> <br>
> F’(x,a,b,c) = (a * b exp(-b * (-c + x))) / (100 (1 + exp(-b * (-c + x)))^2)<br>
> <br>
> Now the values of the parameters a,b,c are those I sent you last time IF<br>
> we consider the age-UNstratified population.<br>
> <br>
> Otherwise, if we go by age (age ranges as in the paper), then the parameters are:<br>
> <br>
> age range 0-39<br>
> a=96.56299632152<br>
> b=0.185777403544838<br>
> c=49.8164210315686<br>
> <br>
> age range 40-49<br>
> a=95.351153808322 <br>
> b=0.173066025988826 <br>
> c=51.92498287875<br>
> <br>
> age range 50-59<br>
> a=94.2976479245251 <br>
> b=0.165018635066338 <br>
> c=54.1494851021362<br>
> <br>
> age range 60-69<br>
> a=91.3990353489634 <br>
> b=0.158299883031816 <br>
> c=55.5935133562513<br>
> <br>
> age range 70-79<br>
> a=88.9048923236574 <br>
> b=0.152924609509616 <br>
> c=57.7447222979953<br>
> <br>
> age range 80+<br>
> a=85.6674967019556 <br>
> b=0.14040123117131 <br>
> c=61.383806850923<br>
> <br>
>> Please verify that I am correct. Since I need to know how to use your function. <br>
> <br>
> Let me know if F’ (F-prime) is the function you were looking for. It should be it.<br>
> <br>
>> You have two more interesting elements in the paper that can start interesting discussions: <br>
>> <br>
>> 1. You approach the definition of a comorbidity by a level of damage to tissue. <br>
> <br>
> Yes, given the elements in my simulation, that is a possible choice for the definition (not really of the comorbidity) of the “severity” of the disease. It is a tricky point to link some computer output to a “clinical endpoint”, that is, something used by clinician to assess the disease status. But a very important point.<br>
> <br>
> All the best<br>
> Fil<br>
> <br>
>> 2. You end the paper by discussing what needs to be done to make models used in medical settings.<br>
>> 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. <br>
>> <br>
>> Happy holidays<br>
>> <br>
>> <br>
>> Jacob<br>
>> <br>
>> <br>
>> On Tue, Dec 22, 2020, 13:38 Filippo Castiglione <<a href="mailto:filippo.castiglione@gmail.com" target="_blank">filippo.castiglione@gmail.com</a>> wrote:<br>
>> 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" 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" 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" 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" 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" 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" 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" 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" 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" 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" 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" 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" 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" 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" 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" 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" 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" target="_blank">https://sites.google.com/view/jacob-barhak/home</a><br>
>>>>>>> <br>
>>>>>> <br>
>>>>> <br>
>>> <br>
>> <br>
> <br>
<br>
</blockquote></div>