• Glenn Wilson
    92
    Updated in comments.
    SMAFAQ now calculates and publishes in each Coronavirus Dashboard a number for estimated active cases of Covid-19 in SMA. This is in addition to publishing the confirmed active cases.

    The method used to calculate Estimated Active Cases provides an estimate based on the number of reported deaths and an Infection Fatality Rate (IFR).

    Why estimate active cases?
    The government has said the real number of infected people is likely significantly higher than the confirmed cases.Reuters

    The government's data captures only a small percent of the actual cases. It is not intended or designed to capture all cases. To get a better picture of what is happening in our community the official data can be extrapolated to provide an estimate of actual infections and active cases. We are providing one method for doing that.

    IFR - Infection Fatality Rate Defined
    This is the percent of all infected people that die from Covid. It is not a known or fixed value but there are various estimates for IFR. There is an exact IFR for SMA every day, we just do not know what it is and will never know exactly what it was.

    It will vary from time to time and from place to place. It is not a constant value, but we use a constant value calculated for Mexico (more on that below) for our estimate.
    See WHO: Estimating mortality from COVID-19.

    Using IFR and reported deaths to estimate actual infections
    Let's say that we believe that we have an IFR of 5% and we have had 10 reported deaths. That would tell us that we would have had about 200 actual infections because 200 infections * 5% IFR = 10 deaths. We can calculate that because 10 / 5% = 200.

    If our official number of cases is 50, then the ratio of actual cases to confirmed cases (Actual to Confirmed Factor) is 200 / 50 = 4.

    Estimated IFR for Mexico
    Using CDC IFR estimates per age ranges and the Mexico age distributions an overall estimated IFR of 0.352% is calculated for Mexico. That is the value we are using. Other estimates are possible. See: covid19-age-stratified-ifr

    A real calculation
    We'll use the estimated IFR for Mexico of 0.352% and the SMA data from Nov 30 of 55 reported deaths and from Nov 16 of 824 cases. We 'look back' two weeks to Nov 16 for the infections number because there is a lag between the time an infection is reported and a potential death results. Also on Nov 30 we have 1037 cases and 792 reported recovered. See Coronavirus Dashboard December 1, 2020.

    Actual to Confirmed Factor = Current Death Count / .352% / Confirmed Cases Two Weeks Ago.
    = 55 / .352% / 824
    = 19

    Estimated active cases = (Current Confirmed Case Count - Current Recovered) * Factor - Current Deaths.
    = (1,037 - 792 ) * 19 - 55
    = 4,600

    Various IFRs
    Wondering how different IFRs affect this estimate? Here are some examples of the same calculation with different IFRs.
    f3v6g0e1g7qexbwn.png
    Edit Dec 4, 2020: I replaced the original image of values with this one that shows the IFRs in descending numerical order for clarity. The values have not changed.

    Calculations in action
    See the google spreadsheet. Look on the SMA Stats tab and the columns Estimated Actual / Confirmed Factor and Estimated Actual Active Cases.

    Issues and Limitations
    The method used is intended to provide an estimate based on the number of reported deaths and an Infection Fatality Rate (IFR). The approach depends on a reasonably accurate death count and a reasonable estimate of IFR over time.

    There are many potential issues and limitations. Some are:
    • The age distribution for Mexico (used to calculate the Mexico IFR) may not match the age distribution for SMA.
    • The IFR data from the CDC may not be accurate for Mexico.
    • The age distribution of those infected may be different than the age distribution used in calculating the overall IFR.
    • The methodology used for gathering the official stats may vary over time.
    • The SMA covid deaths may be significantly different than reported.
    • Two weeks 'look back' for infections to deaths may not be the most appropriate time frame.
    • Maybe I made a calculation error or overlooked something important -- let me know!

    Changes
    Details of the calculation may change over time. For the latest, see the google spreadsheet.

    Comments? Feedback?
    Please leave comments below or contact me at .
    Attachment
    calcs4 (17K)
  • Tom Hammer
    21
    I would make an educated guess that because of the expat community and the higher than average income required among Mexicans to live in SMA that the average age in SMA is higher than that of Mexico overall, which has large numbers of children among the poor, and indigenous people for example. So, I'd opt for the next row up on your chart and guess at an IFR of .485% and that gives us a lower figure in SMA of 3375 cases. The answer is obviously very sensitive depending on assumptions we make.
  • Glenn Wilson
    92
    Looking at the current values calculated by UNAM, for Mexico as a whole, they publish a low / high estimate using IFRs of 1% and 0.5% which produce Factors of about 9.5 and 19 for Mexico as a whole.
    cbvfsyl75b0oisti.png
    Source: UNAM.

    To emphasize that this value is an estimate I am going to start publishing the SMAFAQ estimate as a range with the high end of the range as calculated above using an IFR of 0.352% and the low end of the range based on a fixed factor of 10 (which works out to an IFR using recent SMA statistics of about 0.7%).
    Thanks to Daniel D for the link to UNAM data.

    Thanks. Yes, I agree with your point about SMA age ranges. On the other hand, the calculation (of the overall IFR) assumes equal prevalence of Covid among all age ranges, which may not be accurate (the older may take greater care to avoid infection), and deaths may be underreported which would push the calculation in the other direction. But there is a large uncertainty. I hope that publishing this as a range of values makes that clearer.
  • Glenn Wilson
    92
    Every day I publish a Coronavirus Dashboard. Here is todays: Coronavirus Dashboard December 6, 2020. Every day that includes the calculation for the confirmed active cases; today's is 188.

    I do this to try to help keep the community better informed. The problem is that the official stats and the confirmed active cases significantly understate the scope of the pandemic in SMA. Yes, every day the Dashboard includes this warning:
    "The government has said the real number of infected people is likely significantly higher than the confirmed cases." Reuters.

    But, what does significantly higher mean? A reader could take that to mean 20% higher or maybe double. But, the reality is that it is much higher. Since I publish the official stats I feel an obligation to try to clarify what this reality is and what significantly higher means.

    How might you modify your behavior if you thought there were active 188 cases in our community? Or 2,500? Or 5,000?

    Hence, the estimated active cases.

    With today's change in calculating and reporting a range I think this will come closer to my goal of communicating what the real values could be. Part of effective communication is being believed. The alignment with the UNAM values (UNAM has current factors of 9.5-19 for Mexico versus SMAFAQ factors 10-20 for SMA) lends some instant credibility, I think. As does using the calculated IFR based on a CDC study as applied to Mexico age ranges. It is a happy coincidence that the calculation using the IFR works out to about the same factor as the UNAM high factor.

    So, the simple description of the calculated range is that it is calculated about the same for SMA as the range that UNAM calculates for Mexico.

    Further, the high-end of the range is consistent with the CDC estimated IFR by age range applied to Mexico's age range. The low end of the range is consistent with Mexico's Sentinel model (8 for the Sentinel model vs 10 for SMAFAQ).

    All feedback is welcome.
  • Tom Hammer
    21
    Yes, computer told me it hadn't been sent when it had.
  • Glenn Wilson
    92
    This is a repeated comment. I replied to this concern above.

    I have been working on addressing this and related concerns since initially publishing these estimated values. I think I now have an improved approach. Thanks for your input!
  • Tom Hammer
    21
    Do you have access to excess deaths over the same months last year? Even in the US many scientists say that they are a more accurate measure of how many have really died of Covid. Here in Mexico, many locals tell me people are embarrassed and don't want neighbors or friends to know if a relative died of the virus, and many, many are afraid to go to the hospital because "they will die there" so deaths from Covid are not accurately reported at all.
  • Glenn Wilson
    92
    I've seen (and reported) excess deaths for Mexico or parts of Mexico (Mexico City). But nothing specific for SMA. I am using the official / registered deaths for SMA.

    If deaths are higher than reported, then the estimated number of active cases would be higher.
  • Glenn Wilson
    92
    What I should have said is "If deaths are higher than reported, then the high-end estimated number of active cases (using the IFR calculation) would be higher" ... because a higher Factor would be calculated based on the ratio of deaths and reported infections.
  • Tom Hammer
    21
    This is wonderful work and a great and transparent explanation! Thanks.
  • Tom Hammer
    21
    I hope you don't mind another question. Just doing back of the envelope calculations, if there are now ~5,000 active cases, and SMA has roughly 100,000 inhabitants, that's 5% of the population that has active cases! I am not sure how to calculate the next step, but it seems to me if that were true, SMA would fairly quickly reach heard immunity with ~70-80% of the population having been infected.

    By comparison, the US, where the virus is raging out of control, has had in total about 5% who have gotten the virus, ~ 15,000, 000 as of today. So it seems that 5% active cases in SMA is completely out of alignment with a "severe crisis" in the US, while on the surface SMA is not in quite as dire straits. Is there something wrong with my logic?
  • Tom Hammer
    21
    Thinking about it more, I think we can roughly estimate US active cases by the area under the curve of new cases each day. In the last 2 weeks, the US has averaged roughly 170,000 new cases per day. If we estimate that each case lasts 10 days on average, that would be ~1.2 million active cases right now. If cases last 20 days, 2.4 million. That is less than 1% of the population of the US having active cases at any one time, which is more than 5 times less than your estimate (or mine, above), of 5% of the population of SMA.
  • Glenn Wilson
    92
    Thanks for the questions. Some critical analysis is good. :-)

    SMA Population.

    171,857 in 2015 according to: https://www.citypopulation.de/php/mexico-admin.php?adm2id=11003

    The mayor has recently called it "over 200 thousand": https://sanmigueldeallende.gob.mx/presenta-luis-alberto-villarreal-su-segundo-informe-de-resultados/

    Using 200,000 population for SMA and the IFR of 0.352% if everyone became infected that is 704 deaths total. 70% of that is 493. So, to get to 'natural' herd immunity at 70% we would need 429 more deaths in SMA -- we currently have 64. We are 13% (64/493) of the way there.

    5,000 active infections is about 2.5% of the population. 23,800 total infections (1190 times the multiplier of 20) is about 12% of the population of SMA that has or had the virus.

    Mexico and the US are similarly situated with respect to deaths per population from Covid.
    5pbztfd4rse3hgj2.png
    Deaths from COVID-19, normalized by population (Live link to with graph updated to the current data).
    If plotted on that chart SMA would be almost tied with (but just below) Canada.

    Comparing Apples and Apples.
    The CDC IFR applied to the US Population from mbevand/covid19-age-stratified-ifr is 0.738. US deaths as of 2 weeks ago (from Worldometer) was about 265,000. Doing the same calculation for the US as SMA I get a multiplier of 2.34. Which translates to about 11% of the US (15 million * 2.34 / 330 million) has or had, the virus. About the same as SMA, but the US in this analysis has a higher infection fatality rate (IFR) and more deaths per capita.

    "That is less than 1% of the population of the US having active cases at any one time, which is more than 5 times less than your estimate (or mine, above), of 5% of the population of SMA."
    Worldometer shows 6,096,224 active cases for the US. (I have not looked into where Worldometer gets this figure). And, 6 million times 2.34 = 14. 14 / 330 = about 4% of the US population versus 2.5% for SMA.

    I think this shows that these SMAFAQ estimates for SMA are 'reasonable' based on a comparison to the numbers for the US.

    Note: If I am seriously wrong about the population of SMA that changes the population based stats for SMA above. The analysis above could be repeated for SMA at the low end of the estimate range using a multiplier of 10 and an SMA IFR of 0.7% to see how the other end of the range compares.

    It's about 3:50 am and I've just started my first cup of coffee. I may add to or correct this later (as a separate comment, if I do).

    If you spot any errors (math, or logic, or ...) or if I left off anything important let me know. More feedback in general is always welcome.
  • Glenn Wilson
    92
    The CDC IFR applied to the US Population from mbevand/covid19-age-stratified-ifr is 0.738% (I left off the '%' sign above).
  • Glenn Wilson
    92
    I said "So, to get to 'natural' herd immunity at 70% we would need 429 more deaths in SMA ... "
    That assumes, of course, that people get and retain immunity after being infected ... and that 70% is a level where herd immunity would kick in.
  • Glenn Wilson
    92
    To correct / clarify / explain, where I said: "The CDC IFR applied to the US Population from mbevand/covid19-age-stratified-ifr is 0.738(%). US deaths as of 2 weeks ago (from Worldometer) was about 265,000. Doing the same calculation for the US as SMA I get a multiplier of 2.34."
    (I messed this up. The formula uses cases from two weeks ago and current deaths.)

    The calculation referred to above is (should have been):
    Actual to Confirmed Factor = Current Death Count / IFR / Confirmed Cases Two Weeks Ago.
    = 291495 / .738% / 12780051
    = 3.09 which I'll round to 3.

    ... and then with the corrected factor ...

    Which translates to about 14% of the US (15 million * 3 / 330 million) has or had, the virus. More than SMA, and the US in this analysis has a higher infection fatality rate (IFR) and more deaths per capita.

    "That is less than 1% of the population of the US having active cases at any one time, which is more than 5 times less than your estimate (or mine, above), of 5% of the population of SMA."
    Worldometer shows 6,096,224 active cases for the US. (I have not looked into where Worldometer gets this figure). And, 6 million times 3 = 18. 18 / 330 = about 5% of the US population versus 2.5% for SMA.
  • Glenn Wilson
    92
    I'm not sure what to make of this and how it might impact the IFR we're using for SMA.

    Mexico’s coronavirus spokesman said Thursday the country’s median age of death from COVID-19 was a shockingly young 55, as compared to an average of 75 in many European countries. ...

    López-Gatell said the country’s high rates of obesity, diabetes and hypertension explained Mexico’s lower average age of death. He said Mexico has among the highest rate of obesity in the world.
    AP: Mexico's COVID-19 deaths average 55 years vs. 75 in Europe
  • Glenn Wilson
    92
    Some more info to ponder:
    The National Institute of Public Health (INSP) released the preliminary results of the National Health and Nutrition Survey (ENSANUT), according to which 31 million Mexicans (25%) of the total population have been exposed to the SARS-CoV-2 virus since the beginning of the pandemic in the country.Cambio de Michoacán: According to a survey, at least 31 million Mexicans have been exposed to Covid

    255. Ministry of Health presents preliminary results of the National Survey of Health and Nutrition COVID-19 (sp) | English.
  • Glenn Wilson
    92
    Feb 20, 2021:
    Official count is 2 million coronavirus cases but university says it’s at least 17 million.
    vaccination-1.jpg
    The real case tally is at least nine times higher than the official total and could be up to 26 times higher, according to UNAM estimates.
    Mexico News Daily
    SMAFAQ uses the same basic approach as UNAM to calculate estimated actual cases, as described above, with a few different assumptions.
  • Glenn Wilson
    92
    Some additional data:
    Mexico says COVID-19 deaths likely 60% higher than confirmed toll.
    ?m=02&d=20210328&t=2&i=1556503099&r=LYNXMPEH2R0BA&w=800
    Mexico's death toll from the coronavirus pandemic is likely at least 60% higher than the confirmed number, putting it in excess of 300,000, according to government data.
    Reuters
    See also: Excess Mortality in Mexico (sp).
    SMAFAQ: What do the CDMX death certificates tell us? Updated October 27.
  • Glenn Wilson
    92
    COVID: They estimate that almost half of Guanajuato could have been infected.
    contagios-covid-guanajuato-universidad-de-washington.jpg_673822677.jpg
    A report from the University of Washington estimates that by April, between 41 and 49% of Guanajuato could have been infected with COVID at some point.
    Periódico AM (sp) | English.
    GW: This is consistent with the high estimate calculated by SMAFAQ for GTO. 131,382 confirmed cases * 23 = 3,021,786.
    For SMA this same calculation is 2,751 confirmed cases * 22 = 60,522 estimated total infections from a population of about 174 thousand.
    Why does GTO have a multiplier of 23 and SMA have a multiplier of 22? Because they are calculated for each separately as described above.
    See: Google Spreadsheet.
  • Tom Hammer
    21
    Hi Glenn,

    I continue to appreciate your wonderful reporting and your valiant attempts to enlighten me earlier in the year about the logic and the math of your calculations. I return with a question from months ago--the average estimated cases is still quite high, let's estimate 3,000 reported every day. If cases were actually that high + the number of people in the municipality now vaccinated, wouldn't we have reached something close to the much ballyhooed (and perhaps near-impossible but still worth talking about) herd immunity by now?
  • Glenn Wilson
    92


    Thanks for your critical eye and the question: "the average estimated cases is still quite high, let's estimate 3,000 reported every day. If cases were actually that high + the number of people in the municipality now vaccinated, wouldn't we have reached something close to the much ballyhooed (and perhaps near-impossible but still worth talking about) herd immunity by now?"

    Short answer: no.

    Longer answer: The calculated multiplier for SMA cases (the high end estimate) is 22. That can change based on the ratio of deaths to cases but 22 is the highest it has been. On today's Dashboard we have a total of 2785 confirmed cases. 2785 x 22 = 61,270 total estimated cases in SMA.

    The municipality of SMA has a population of 174,615 in the latest census. And, 61,270 / 174,615 = 35%.

    About 13% of that 174 thousand are 'older adults' (60 and over). If we make the most optimistic possible estimation that 100% of them got vaccinated (I'm guessing it was closer to 75%) and that none of them previously had Covid-19 and just add in all 13% then that is 35% +13% = 48%. Still a long way from anything close to an amount needed for herd immunity.

    (I skipped the teachers and medical professionals in that quick estimate but I think the overestimate for the 60+ crowd more than covers those numbers.)

    So, not herd immunity, but still there is great value in getting these most vulnerable vaccinated. See: "Vaccinate the 20% of the country that represent 95% of the deaths"

    A possible point of confusion with my daily estimates is those are estimated active cases. Not estimated new cases. Cases stay active until resolved through either recovery or death. If we had 3000 or so new cases every day in SMA we would all have had Covid-19 some time ago.
  • Glenn Wilson
    92
    SMAFAQ published estimated active cases using this model for some time. It has done a good job of estimating a factor to use to get a feel for the actual number of total Covid-19 infections in SMA, in my opinion and was useful as Covid-19 peaked in SMA. However, as the number of new cases and deaths from Covid-19 in SMA decline this model overestimates the current number of active infections. In any case it has outlived its usefulness and I will no longer be publishing the estimated active cases. Thanks to William Conklin for helping to clarify my thoughts on this.
  • Glenn Wilson
    92
    I think the model did a good job at estimating total infections using the factors of 10 and 22 for the low and high estimates, respectively. Applying those factors directly to recovered cases and using a factor of 1 for deaths apparently leads to a discrepancy in the estimated active cases over time.

    For example, using today's (June 2) values of 2808 total cases, 2588 confirmed cases and 217 deaths and the low estimate factor of 10 we get estimated active cases = (2808-2588)*10 - 217 = 2200 -217 = 1983.

    Which seems reasonable. Except that the 2200 active cases, before adjusting for deaths, implies 220 official confirmed cases with the factor of 10. To get 220 new confirmed cases in SMA you would have to include all new cases from March 16 to today. It does not seem reasonable, to me, that cases from March and April would still be 'active'. So, this simple formula is not fully accounting for actual recoveries (and deaths) in calculating estimated active cases. I could try to adjust the calculation to account for only more recent cases but that complicates things so, for now, it seems reasonable to just stop publishing those values.

    I do think the estimated active cases served a useful purpose in pointing out that the actual number was "much higher" than the official confirmed numbers even though we never knew (and will never know) exactly how much higher.
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