Category Archives: Statistics

COVID E. Asian death rate is 1/100th the Western rate.

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COVID-19 has a decided racial preference for Western blood, killing Americans and Europeans at more than ten times the rate of people in Japan, China, Hong Kong, Taiwan, Korea, or Vietnam. The chart below shows the COVID-19 death rate per million population in several significant countries countries. The US and Belgium is seen to be more than 100 times worse than China or Hong Kong, etc., based on data from http://www.worldometers.info. IN the figure, the death-rate rank of each country is shown on the left, next to the country name.

For clarity, I didn’t include all the countries of Europe, but note that European countries are the majority of the top ten in terms of deaths per million. Belgium is number one with over 1,400. That is somewhat over 0.14% of the population has died of COVID-19 so far.

Peru has the highest COVID-19 death rate in South America at over 1000 per million, 0.1%. The US rate is similar, 0.082%. These are shockingly high numbers despite our best efforts to stop the disease by mandating masks, closing schools, and generally closing our economies. Meanwhile, in China and Japan, the economies are open and the total death rate is only about 1/100 that of Europe or the Americas. Any health numbers from China are suspect, but here I tend to believe it. Their rates are very similar to those in Hong Kong and Taiwan. At 3 per million, China’s death rate is 1/400 th the rate of the US, and Taiwan’s is lower.

This is not for lack of good healthcare systems in Europe, or lack of preparation. As of December 1-10, Germany, a country of 80 million, is seeing a COVID death rate of 388 per day. Japan, a country of 120 million, sees about 20. These are modern countries with good record keeping; Germany is locked down and Japan is open.

The question is why, and the answer seems to be genetics. A British study of the genetics of people who got the disease particularly severely found a few genes responsible, among these, TYK2. “It is part of the system that makes your immune cells more angry, and more inflammatory,” explained Dr Kenneth Baillie, a consultant in medicine at the Royal Infirmary in Edinburgh, who led the Genomicc project. He’s theory is that versions of this gene can allow the virus to put your immune response “into overdrive, putting patients at risk of damaging lung inflammation.” If his explanation is right, a class of anti-inflammatory drugs could work. (I’d already mentioned data suggesting that a baby aspirin or two seems helpful).

As reported in Nature this week, another gene that causes problems is IFNAR2. IFNAR2 is linked to release of interferon, which helps to kick-start the immune system as soon as an infection is detected.

It could be accidental that Asians are just lucky interns of not having the gene variations that make this disease deadly. Alternately, it could be that the disease is was engineered (in China?) and released either as a bio-attack, or by accident. Or it could be a combination. Whatever the cause of the disease, that east Asians should be spared this way is really weird.

Suggesting that this is not biowarfare is the observation that, in San Francisco, the Asian, per case fatality rate is as high as for white people or higher. One problem with this argument is that there is a difference between death rate per confirmed case and death rate per million population. It is possible that, for one reason or another Chinese people in San Francisco do not seek to be tested until they are at death’s door. Such things were seen in Iran and North Korea, for example. It pushed up the per-case death rate to 100%. Another possibility is that the high death rates in the west reflect disease mutation, or perhaps eastern exposure to a non-deadly variant of COVID that never made it west. If this is the case, it would be just as odd as any other explanation of a100x difference in death rates. Maybe I’m being paranoid here, but as the saying goes, even paranoids have enemies.

I think it’s worth noting this strange statistical pattern, even if I have no clear explanation. My advice: take vitamin D and a baby aspirin; and get a pneumonia shot,. I plan to take the vaccine when it’s offered. If a home test becomes available, I’d use that too. Stay safe folks. Whatever the source, this disease is a killer.

Robert Buxbaum, December 16, 2020.

Aspirin protection from heart attack and COVID-19 death.

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Most people know that aspirin can reduce blood clots and thus the risk heart attack, as shown famously in the 1989 “Physicians’ Health Study” where 22,000 male physicians were randomly assigned to either a regular aspirin (325 mg) every other day or an identical looking placebo. The results are shown in the table below, where “Myocardial Infarction” or “MI” is doctor-speak for heart attack.

TreatmentMyocardial InfarctionsNo InfarctionTotalfraction with MI
Aspirin13910,89811,037139/11,037 = 0.0126
Placebo23910,79511,034239/11,034 = 0.0217

Over the 5 years of the study, the physicians had 378 MI events, but mostly in the group that didn’t take aspirin: 1.28% of the doctors who took aspirin had a heart attack as opposed to 2.17% for those with the placebo. The ratio 1.28/2.17 = 0.58 is called the risk ratio. Apparently, aspirin in this dose reduces your MI risk to 58% of what it was otherwise — at least in white males of a certain age.

A blood clot showing red cells held together by fibrin fibers. Clots can cause heart attack, stroke, and breathing problems. photo: Steve Gschmeissner.

Further study showed aspirin benefits with women and other ethnicities, and benefits beyond hear attack, in any disease that induces disseminated intravascular coagulopathy. That’s doctor speak for excessive blood clots. Aspirin produced a reduction in stroke and in some cancers (Leukemia among them) and now it now seems likely that aspirin reduces the deadliness of COVID-19. Data from Wuhan showed that excessive blood clots were present in 71% of deaths vs. 0.4% of survivors. In the US, some 30% of those with serious COVID symptoms and death show excessive blood clots, particularly in the lungs. Aspirin and Vitamin D seem to help.

.The down-side of aspirin use is a reduction in wound healing and some intestinal bleeding. The intestinal bleeding is known as aspirin burn. Because of these side-effects it is common to give a lower dose today, just one baby aspirin per day, 81 mg. While this does does some good, It is not clear that it is ideal for all people. This recent study in the Lanset (2018) shows a strong relationship between body weight and aspirin response. Based on 117,279 patients, male and female, the Lanset study found that the low dose, baby aspirin provides MI benefits only in thin people, those who weigh less than about 60 kg (130 lb). If you weigh more than that, you need a higher dose, perhaps two baby aspirin per day, or a single adult aspirin every other day, the dose of the original doctors study.

In this study of COVID patients, published in July, those who had been taking aspirin fared far better than those who did not A followup study will examine the benefits of one baby aspirin (81 mg) with and without Vitamin D, read about it here. I should note that other pain medications do not have this blood-thinning effect, and would not be expected to have the same benefit.

While it seems likely that 2 baby aspirins might be better in fat people, or one full aspirin every other day, taking a lot more than this is deadly. During the Spanish flu some patients were given as much as 80 adult aspirins per day. It likely killed them. As Paracelsus noted, the difference between a cure and a poison is the dose.

Robert Buxbaum, November 27, 2020.

Pneumonia vaccine in the age of COVID

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A few days ago, I asked for and received the PCV-13 pneumonia vaccine, and a few days earlier, the flu shot. These vaccines are free if you are over 65, but you have to ask for them. PCV-13 is the milder of the pneumonia vaccines, providing moderate resistance to 12 common pneumonia strains, plus a strain of diphtheria. There is a stronger shot, with more side-effects. The main reason I got these vaccines was to cut my risk from COVID-19.

Some 230,00 people have died from COVID-19. Almost all none of them were under 20, and hardly any died from the virus itself. As with the common flu, they died from side infections and pneumonia. Though the vaccine I took is not 100% effective against event these 13 pneumonias, it is fairly effective, especially in the absence of co-morbidities, and has few side effects beyond stiffness in my arm. I felt it was a worthwhile protection, and further reading suggests it was more worthwhile than I’d thought at first.

It is far from clear there will be a working vaccine for SARS-CoV-2, the virus that causes COV-19. We’ve been trying for 40 years to make a vaccine against AIDS, without success. We have also failed to create a working vaccine for SARS, MERS, or the common cold. Why should SARS-CoV-2 be different? We do have a flu vaccine, and I took it, but it isn’t very effective, viruses mutate. Despite claims that we would have a vaccine for COVID-19 by early next year, I came to imagine it would not be a particularly good vaccine, and it might have side effects. On the other hand, there is a fair amount of evidence that the pneumonia vaccine works and does a lot more good than one might expected against COVID-19.

A colleague of mine from Michigan State, Robert Root Bernstein, analyzed the effectiveness of several vaccines in the fight against COVID-19 by comparing the impact of COVID-19 on two dozen countries as a function of all the major inoculations. He found a strong correlation only with pneumonia vaccine: “Nations such as Spain, Italy, Belgium, Brazil, Peru and Chile that have the highest COVID-19 rates per million have the poorest pneumococcal vaccination rates among both infants and adults. Nations with the lowest rates of COVID-19 – Japan, Korea, Denmark, Australia and New Zealand – have the highest rates of pneumococcal vaccination among both infants and adults.” Root-Bernstein also looked at the effectiveness of adult inoculation and child inoculation. Both were effective, at about the same rate. This suggests that the the plots below are not statistical flukes. Here is a link to the scientific article, and here is a link to the more popular version.

An analysis of countries in terms of COVID rates and deaths versus pneumonia vaccination rates in children and adults. The US has a high child vaccination rate, but a low adult vaccination rate. Japan, Korea, etc. are much better. Italy, Belgium, Spain, Brazil, and Peru are worse. Similar correlations were found with child and adult inoculation, suggesting that these correlations are not flukes of statistics.

I decided to check up on Root-Bernstein’s finding by checking the state-by state differences in pneumonia vaccination rates — information available here — and found that the two US states that were hardest hit by COVID, NY and NJ, have among the lowest rates of inoculation. Of course there are other reasons at play. These states are uncommonly densely populated, and the governments of both made the unfortunate choice of sending infected patients to live in old age homes. At least half of the deaths were in these homes.

Pneumonia vaccination may also explain why the virus barely affected those under 20. Pneumonia vaccines was available only in 2000 or so. Many states then began to vaccinate about then and required it to attend school. The time of immunization could explain why those younger than 20 in the US do so well compared to older individuals, and compared to some other countries where inoculation was later. I note that China has near universal inoculation for pneumonia, and was very mildly hit.

I also took the flu shot, and had taken the MMR (measles) vaccine last year. The side effects, though bad, are less bad than the benefits, I thought, but there was another reason, and that’s mimicry. It is not uncommon that exposure to one virus or vaccine will excite the immune system to similar viruses, so-called B cells and T-cell immunity. A recent study from the Mayo Clinic, read it here, shows that other inoculations help you fight COVID-19. By simple logic, I had expected that the flu vaccine would help me this way. The following study (from Root-Bernstein again) shows little COVID benefit from flu vaccine, but evidence that MMR helps (R-squared of 0.118). Let men suggest it’s worth a shot, as it were. Similar to this, I saw just today, published September 24, 2020 in the journal, Vaccines, that the disease most molecularly similar to SARS-CoV-2 is pneumonia. If so, mimicry provides yet another reason for pneumonia vaccination, and yet another explanation for the high correlations shown above.

As a final comparison, I note that Sweden has a very high pneumonia inoculation rate, but seems to have a low mask use rate. Despite this, Sweden has done somewhat better than the US against COVID-19. Chile has a low inoculation rates, and though they strongly enforced masks and social distance, it was harder hit than we were. The correlation isn’t 100%, and masks clearly do some good, but it seems inoculation may be more effective than masks.

Robert Buxbaum, November 7, 2020.

COVID-19 is worse than SARS, especially for China.

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The corona virus, COVID-19 is already a lot worse than SARS, and it’s likely to get even worse. As of today, there are 78,993 known cases and 2,444 deaths. By comparison, from the first appearance of SARS about December 1 2002, there have been a total of 8439 cases and 813 deaths. It seems the first COVID-19 patient was also about December 1, but the COVID-19 infection moved much faster. Both are viral infections, but it seems the COVID virus is infectious for more days, including days when the patient is asymptomatic. Quarantine is being used to stop COVID-19; it was successful with SARS. As shown below, by July 2003 SARS had stopped, essentially. I don’t think COVID-19 will stop so easily.

The process of SARS, worldwide; a dramatic rise and it’s over by July 2003. Source: Int J Health Geogr. 2004; 3: 2. Published online 2004 Jan 28. doi: 10.1186/1476-072X-3-2.

We see that COVID-19 started in November, like SARS, but we already have 10 times more cases than the SARS total, and 150 times more than we had at this time during the SARS epidemic. If the disease stops in July, as with SARS, we should expect to see about a total of 150 times the current number of cases: about 12 million cases by July 2020. Assuming a death rate of 2.5%, that suggests 1/4 million dead. This is a best case scenario, and it’s not good. It’s about as bad as the Hong Kong flu pandemic of 1968-69, a pandemic that killed 60,000 approximately in the US, and which remains with us, somewhat today. By the summer of 69, the spreading rate R° (R-naught) fell below 1 for and the disease began to die out, a process I discussed previously regarding measles and the atom bomb, but the disease re-emerged, less infectious the next winter and the next. A good quarantine is essential to make this best option happen, but I don’t believe the Chinese have a good-enough quarantine.

Several things suggest that the Chinese will not be able to stop this disease, and thus that the spread of COVID-19 will be worse than that of the HK flu and much worse than SARS. For one, both those disease centered in Hong Kong, a free, modern country, with resources to spend, and a willingness to trust its citizens. In fighting SARS, HK passed out germ masks — as many as anyone needed, and posted maps of infection showing places where you can go safely and where you should only go with caution. China is a closed, autocratic country, and it has not treated quarantine this way. Little information is available, and there are not enough masks. The few good masks in China go to the police. Health workers are dying. China has rounded up anyone who talks about the disease, or who they think may have the disease. These infected people are locked up with the uninfected in giant dorms, see below. In rooms like this, most of the uninfected will become infected. And, since the disease is deadly, many people try to hide their exposure to avoid being rounded up. In over 80% of COVID cases the symptoms are mild, and somewhat over 1% are asymptomatic, so a lot of people will be able to hide. The more people do this, the poorer the chance that the quarantine will work. Given this, I believe that over 10% of Hubei province is already infected, some 1.5 million people, not the 79,000 that China reports.

Wuhan quarantine “living room”. It’s guaranteed to spread the disease as much as it protects the neighbors.

Also making me think that quarantine will not work as well here as with SARS, there is a big difference in R°, the transmission rate. SARS infected some 2000 people over the first 120 days, Dec. 1 to April 1. Assuming a typical infection time of 15 days, that’s 8 cycles. We calculate R° for this stage as the 8th root of 2000, 8√2000 = 2.58. This is, more or less the number in the literature, and it is not that far above 1. To be successful, the SARS quarantine had to reduce the person’s contacts by a factor of 3. With COVID-19, it’s clear that the transmission rate is higher. Assuming the first case was December 1, we see that there were 73,437 cases in only 80. R° is calculated as the 5 1/3 root of 73,437. Based on this, R° = 8.17. It will take a far higher level of quarantine to decrease R° below 1. The only good news here is that COVID-19 appears to be less deadly than SARS. Based on Chinese numbers the death rate appears to be about 2000/73,437, or about 3%, varying with age (see table), but these numbers are overly high. I believe there are a lot more cases. Meanwhile the death rate for SARS was over 9%. For most people infected with COVID-19, the symptoms are mild, like a cold; for another 18% it’s like the flu. A better estimate for the death rate of COVID-19 is 0.5-1%, less deadly than the Spanish flu of 1918. The death rate on the Diamond Princess was 3/600 = 0.5%, with 24% infected.

The elderly are particularly vulnerable. It’s not clear why.

Backing up my value of R°, consider the case of the first Briton to contact the disease. As reported by CNN, he got it at conference in Singapore in late January. He left the conference, asymptomatic on January 24, and spent the next 4 days at a French ski resort where he infected one person, a child. On January 28, he flew to England where he infected 8 more before checking himself into a hospital with mild symptoms. That’s nine people infected over 3 weeks. We can expect that schools, factories, and prisons will be even more hospitable to transmission since everyone sits together and eats together. As a worst case extrapolation, assume that 20% of the world population gets this disease. That’s 1.5 billion people including 70 million Americans. A 1% death rate suggests we’ll see 700,000 US deaths, and 15 million world-wide this year. That’s almost as bad as the Spanish flu of 1918. I don’t think things will be that bad, but it might be. The again, it could be worse.

If COVID-19 follows the 1918 flu model, the disease will go into semi-remission in the summer, and will re-emerge in the fall to kill another few hundred thousand Americans in the next fall and winter, and the next after that. Woodrow Wilson got the Spanish Flu in the fall of 1918, after it had passed through much of the US, and it nearly killed him. COVID-19 could continue to rampage every year until a sufficient fraction of the population is immune or a vaccine is developed. In this scenario, quarantine will have no long-term effect. My sense is that quarantine and vaccine will work enough in the US to reduce the effect of COVID-19 to that of the Hong Kong flu (1968), so that the death rate will be only 0.1 – 0.2%. In this scenario, the one I think most likely, the US will experience some 100,000 deaths, that is 0.15% of 20% of the population, mostly among the elderly. Without good quarantine or vaccines, China will lose at least 1% of 20% = about 3 million people. In terms of economics, I expect a slowdown in the US and a major problem in China, North Korea, and related closed societies.

Robert Buxbaum, February 18, 2020. (Updated, Feb. 23, I raised the US death totals, and lowered the totals for China).

A series solution to the fussy suitor/ secretary problem

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One way to look at dating and other life choices is to consider them as decision-time problems. Imagine, for example that have a number of candidates for a job, and all can be expected to say yes. You want a recipe that maximizes your chance to pick the best. This might apply to a fabulously wealthy individual picking a secretary or a husband (Mr Right) in a situation where there are 50 male choices. We’ll assume that you have the ability to recognize who is better than whom, but that your pool has enough ego that you can’t go back to anyone once you’ve rejected the person.

Under the above restrictions, I mentioned in this previous post that you maximize your chance of finding Mr Right by dating without intent to marry 36.8% of the fellows. After that, you marry the first fellow who is better than any of the previous. My previous post had a link to a solution using Riemann integrals, but I will now show how to do it with more prosaic math — a series. One reason for doing this by series is that it allows you to modify your strategy for a situation where you can not be guaranteed a yes, or where you’re OK with number 2, but you don’t like the high odds of the other method, 36.8%, that you’ll marry no one.

I present this, not only for the math interest, but because the above recipe is sometimes presented as good advice for real-life dating, e.g. in a recent Washington Post article. With the series solution, you’re in a position to modify the method for more realistic dating, and for another related situation, options cashing. Let’s assume you have stock options in a volatile stock company, if the options are good for 10 years, how do you pick when to cash in. This problem is similar to the fussy suitor, but the penalty for second best is small.

The solution to all of these problems is to pick a stopping point between the research phase and the decision phase. We will assume you can’t un-cash in an option, or continue dating after marriage. We will optimize for this fractional stopping point between phases, a point we will call x. This is the fraction of guys dated without intent of marriage, or the fraction of years you develop your formula before you look to cash in.

Let’s consider various ways you might find Mr Right given some fractional value X. One way this might work, perhaps the most likely way you’ll find Mr. Right, is if the #2 person is in the first, rejected group, and Mr. Right is in the group after the cut off, x. We’ll call chance of of finding Mr Right through this arrangement C1, where

C1 = x (1-x) = x – x2.

We could used derivatives to solve for the optimum value of x, but there are other ways of finding Mr Right. What if Guy #3 is in the first group and both Guys 1 and 2 are in the second group, and Guy #1 is earlier in the second line-up. You’d still marry Mr Right. We’ll call the chance of finding Mr Right this way C2. The odds of this are

C2 = x (1-x)2/2

= x/2 – x2 + x3/2

There is also a C3 and a C4 etc. Your C3 chance of Mr Right occurs when guy number 4 is in the first group, while #1, 2, and 3 are in the latter group, but guy number one is the first.

C3 = x (1-x)3/4 = x/4 – 3x2/4 + 3x3/4 – x4/4.

I could try to sum the series, but lets say I decide to truncate here. I’ll ignore C4, C5 etc, and I’ll further throw out any term bigger than x^2. Adding all smaller terms together, I get ∑C = C, where

C ~ 1.75 x – 2.75 x2.

To find the optimal x, take the derivative and set it to zero:

dC/dx = 0 ~ 1.75 -5.5 x

x ~ 1.75/5.5 = 31.8%.

That’s not an optimal answer, but it’s close. Based on this, C1 = 21.4%, C2 = 14.8%, C3 =10.2%, and C4= 7.0% C5= 4.8%Your chance of finding Mr Right using this stopping point is at least 33.4%. This may not be ideal, but you’re clearly going to very close to it.

The nice thing about this solution is that it makes it easy to modify your model. Let’s say you decide to add a negative value to not ever getting married. That’s easily done using the series method. Let’s say you choose to optimize your chance for either Mr 1 or 2 on the chance that both will be pretty similar and one of them may say no. You can modify your model for that too. You can also use series methods for the possibility that the house you seek is not at the last exit in Brooklyn. For the dating cases, you will find that it makes sense to stop your test-dating earlier, for the parking problem, you’l find that it’s Ok to wait til you’re less than 1 mile away before you settle on a spot. I’ll talk more about this latter, but wanted to note that the popular press seems overly impressed by math that they don’t understand, and that they have a willingness to accept assumptions that bear only the flimsiest relationship to relaity.

Robert Buxbaum, January 20, 2020

A mathematical approach to finding Mr (or Ms) Right.

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A lot of folks want to marry their special soulmate, and there are many books to help get you there, but I thought I might discuss a mathematical approach that optimizes your chance of marrying the very best under some quite-odd assumptions. The set of assumptions is sometimes called “the fussy suitor problem” or the secretary problem. It’s sometimes presented as a practical dating guide, e.g. in a recent Washington Post article. My take, is that it’s not a great strategy for dealing with the real world, but neither is it total nonsense.

The basic problem was presented by Martin Gardner in Scientific American in 1960 or so. Assume you’re certain you can get whoever you like (who’s single); assume further that you have a good idea of the number of potential mates you will meet, and that you can quickly identify who is better than whom; you have a desire to marry none but the very best, but you don’t know who’s out there until you date, and you’ve an the inability to go back to someone you’ve rejected. This might be he case if you are a female engineering student studying in a program with 50 male engineers, all of whom have easily bruised egos. Assuming the above, it is possible to show, using Riemann Integrals (see solution here), that you maximize your chance of finding Mr/Ms Right by dating without intent to marry 36.8 % of the fellows (1/e), and then marrying the first fellow who’s better than any of the previous you’ve dated. I have a simpler, more flexible approach to getting the right answer, that involves infinite serieses; I’ll hope to show off some version of this at a later date.

Bluto, Popeye, or wait for someone better? In the cartoon as I recall, she rejects the first few people she meets, then meets Bluto and Popeye. What to do?

With this strategy, one can show that there is a 63.2% chance you will marry someone, and a 36.8% you’ll wed the best of the bunch. There is a decent chance you’ll end up with number 2. You end up with no-one if the best guy appears among the early rejects. That’s a 36.8% chance. If you are fussy enough, this is an OK outcome: it’s either the best or no-one. I don’t consider this a totally likely assumption, but it’s not that bad, and I find you can recalculate fairly easily for someone OK with number 2 or 3. The optimal strategy then, I think, is to date without intent at the start, as before, but to take a 2nd or 3rd choice if you find you’re unmarried after some secondary cut off. It’s solvable by series methods, or dynamic computing.

It’s unlikely that you have a fixed passel of passive suitors, of course, or that you know nothing of guys at the start. It also seems unlikely that you’re able to get anyone to say yes or that you are so fast evaluating fellows that there is no errors involved and no time-cost to the dating process. The Washington Post does not seem bothered by any of this, perhaps because the result is “mathematical” and reasonable looking. I’m bothered, though, in part because I don’t like the idea of dating under false pretense, it’s cruel. I also think it’s not a winning strategy in the real world, as I’ll explain below.

One true/useful lesson from the mathematical solution is that it’s important to learn from each date. Even a bad date, one with an unsuitable fellow, is not a waste of time so long as you leave with a better sense of what’s out there, and of what you like. A corollary of this, not in the mathematical analysis but from life, is that it’s important to choose your circle of daters. If your circle of friends are all geeky engineers, don’t expect to find Prince Charming among them. If you want Prince Charming, you’ll have to go to balls at the palace, and you’ll have to pass on the departmental wine and cheese.

If you want Prince Charming, you may have to associate with a different crowd from the one you grew up with. Whether that’s a good idea for a happy marriage is another matter.

The assumptions here that you know how many fellows there are is not a bad one, to my mind. Thus, if you start dating at 16 and hope to be married by 32, that’s 16 years of dating. You can use this time-frame as a stand in for total numbers. Thus if you decide to date-for-real after 37%, that’s about age 22, not an unreasonable age. It’s younger than most people marry, but you’re not likely to marry the fort person you meet after age 22. Besides, it’s not great dating into your thirties — trust me, I’ve done it.

The biggest problem with the original version of this model, to my mind, comes from the cost of non-marriage just because the mate isn’t the very best, or might not be. This cost gets worse when you realize that, even if you meet prince charming, he might say no; perhaps he’s gay, or would like someone royal, or richer. Then again, perhaps the Kennedy boy is just a cad who will drop you at some time (preferably not while crossing a bridge). I would therefor suggest, though I can’t show it’s optimal that you start out by collecting information on guys (or girls) by observing the people around you who you know: watch your parents, your brothers and sisters, your friends, uncles, aunts, and cousins. Listen to their conversation and you can get a pretty good idea of what’s available even before your first date. If you don’t like any of them, and find you’d like a completely different circle, it’s good to know early. Try to get a service job within ‘the better circle’. Working with people you think you might like to be with, long term, is a good idea even if you don’t decide to marry into the group in the end.

Once you’ve observed and interacted with the folks you think you might like, you can start dating for real from the start. If you’re super-organized, you can create a chart of the characteristics and ‘tells’ of characteristics you really want. Also, what is nice but not a deal-breaker. For these first dates, you can figure out the average and standard deviation, and aim for someone in the top 5%. A 5% target is someone whose two standard deviations above the average. This is simple Analysis of variation math (ANOVA), math that I discussed elsewhere. In general you’ll get to someone in the top 5% by dating ten people chosen with help from friends. Starting this way, you’ll avoid being unreasonably cruel to date #1, nor will you loose out on a great mate early on.

Some effort should be taken to look at the fellow’s family and his/her relationship with them. If their relationship is poor, or their behavior is, your kids may turn out similar.

After a while, you can say, I’ll marry the best I see, or the best that seems like he/she will say yes (a smaller sub-set). You should learn from each date, though, and don’t assume you can instantly size someone up. It’s also a good idea to meet the family since many things you would not expect seem to be inheritable. Meeting some friends too is a good idea. Even professionals can be fooled by a phony, and a phony will try to hide his/her family and friends. In the real world, dating should take time, and even if you discover that he/ she is not for you, you’ll learn something about what is out there: what the true average and standard deviation is. It’s not even clear that people fall on a normal distribution, by the way.

Don’t be too upset if you reject someone, and find you wish you had not. In the real world you can go back to one of the earlier fellows, to one of the rejects, if one does not wait too long. If you date with honesty from the start you can call up and say, ‘when I dated you I didn’t realize what a catch you were’ or words to that effect. That’s a lot better than saying ‘I rejected you based on a mathematical strategy that involved lying to all the first 36.8%.’

Robert Buxbaum, December 9, 2019. This started out as an essay on the mathematics of the fussy suitor problem. I see it morphed into a father’s dating advice to his marriage-age daughters. Here’s the advice I’d given to one of them at 16. I hope to do more with the math in a later post.

The electoral college favors small, big, and swing states, punishes Alabama and Massachusetts.

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As of this month, the District of Columbia has joined 15 states in a pact to would end the electoral college choice of president. These 15 include New York, California, and a growing list of solid-blue (Democratic party) states. They claim the electoral must go as it robed them of the presidency perhaps five times: 2016, 2000, 1888, 1876, and perhaps 1824. They would like to replace the electoral college by plurality of popular vote, as in Mexico and much of South America.

All the big blue states and some small blue states have joined a compact to end the electoral college. As of 2019, they are 70% of the way to achieving this.

As it happens, I had to speak on this topic in High School in New York. I for the merits of the old system beyond the obvious: that it’s historical and works. One merit I found, somewhat historical, is that It was part of a great compromise that allowed the US to form. Smaller states would not have joined the union without it, fearing that the federal government would ignore or plunder them without it. Remove the vote advantage that the electoral college provides them, and the small states might have the right to leave. Federal abuse of the rural provinces is seen, in my opinion in Canada, where the large liberal provinces of Ontario and Quebec plunder and ignore the prairie provinces of oil and mineral wealth.

Several of the founding federalists (Jay, Hamilton, Washington, Madison) noted that this sort of federal republic election might bind “the people” to the president more tightly than a plurality election. The voter, it was noted, might never meet the president nor visit Washington, nor even know all the issues, but he could was represented by an elector who he trusted, he would have more faith in the result. Locals would certainly know who the elector favored, but they would accept a change if he could justify it because of some new information or circumstance, if a candidate died, for example, or if the country was otherwise deadlocked, as in 1800 or 1824.

Historically speaking, most electors vote their states and with their previously stated (or sworn) declaration, but sometimes they switch. In, 2016 ten electors switched from their state’s choice. Sven were Democrats who voted against Hillary Clinton, and three were Republicans. Electors who do this are called either “faithless electors” or “Hamilton electors,” depending on whether they voted for you or against you. Hamilton had argued for electors who would “vote their conscience” in Federalist Paper No. 68.  One might say these electors threw away their shot, as Hamilton did not. Still, they showed that elector voting is not just symbolic.

Federalist theory aside, it seems to me that the current system empowers both large and small states inordinately, and swing states, while disempowering Alabama and Massachussetts. Change the system and might change the outcome in unexpected ways.

That the current system favors Rhode Island is obvious. RI has barely enough population for 1 congressman, and gets three electors. Alabama, with 7 congressmen, gets 9 electors. Rhode Islanders thus get 2.4 times the vote power of Alabamans.

It’s less obvious that Alabama and Massachussetts are disfavored compared to New Yorkers and Californians. But Alabama is solid red, while New York and California are only sort of blue. They are majority Democrat, with enough Republicans to have had Republican governors occasionally in recent history. Because the electoral college awards all of New York’s votes to the winner, a small number Democrat advantage controls many electors.

In 2016, of those who voted for major party candidates in New York, 53% voted for the Democrat, and 47% Republican. This slight difference, 6%, swung all of NY’s 27 electors to Ms Clinton. If a popular vote are to replace the electoral college, New York would only have the net effect of the 6% difference; that’s about 1 million net votes. By contrast, Alabama is about 1/3 the population of New York, but 75% Republican. Currently its impact is only 1/3 of New York’s despite having a net of 2.5 million more R voters. Without the college, Alabama would have 2.5 times the impact of NY. This impact might be balanced by Massachusetts, but at the very least candidates would campaign in these states– states that are currently ignored. Given how red and blue these states are, it is quite possible that the Republican will be more conservative than current, and the Democrat more liberal, and third party candidates would have a field day as is common in Mexico and South America.

Proposed division of California into three states, all Democrat-leaning. Supposedly this will increase the voting power of the state by providing 4 more electors and 4 more senators.

California has petitioned for a different change to the electoral system — one that should empower the Democrats and Californians, or so the theory goes. On the ballot in 2016 was bill that would divide California into three sub-states. Between them, California would have six senators and four more electors. The proposer of the bill claims that he engineered the division, shown at right, so skillful that all three parts would stay Democrat controlled. Some people are worried, though. California is not totally blue. Once you split the state, there is more than three times the chance that one sub-state will go red. If so, the state’s effect would be reduced by 2/3 in a close election. At the last moment of 2016 the resolution was removed from the ballot.

Turning now to voter turnout, it seems to me that a change in the electoral college would change this as well. Currently, about half of all voters stay home, perhaps because their state’s effect on the presidential choice is fore-ordained. Also, a lot of fringe candidates don’t try as they don’t see themselves winning 50+% of the electoral college. If you change how we elect the president we are sure find a new assortment of voters and a much wider assortment of candidates at the final gate, as in Mexico. Democrats seem to believe that more Democrats will show up, and that they’ll vote mainstream D, but I suspect otherwise. I can not even claim the alternatives will be more fair.

In terms of fairness, Marie de Condorcet showed that the plurality system will not be fair if there are more than two candidates. It will be more interesting though. If changes to the electoral college system comes up in your state, be sure to tell your congressperson what you think.

Robert Buxbaum, July 22, 2019.

Vitamin A and E, killer supplements; B, C, and D are meh.

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It’s often assumed that vitamins and minerals are good for you, so good for you that people buy all sorts of supplements providing more than the normal does in hopes of curing disease. Extra doses are a mistake unless you really have a mis-balanced diet. I know of no material that is good in small does that is not toxic in large doses. This has been shown to be so for water, exercise, weight loss, and it’s true for vitamins, too. That’s why there is an RDA (a Recommended Daily Allowance). 

Lets begin with Vitamin A. That’s beta carotene and its relatives, a vitamin found in green and orange fruits and vegetables. In small doses it’s good. It prevents night blindness, and is an anti-oxidant. It was hoped that Vitamin A would turn out to cure cancer too. It didn’t. In fact, it seems to make cancer worse. A study was preformed with 1029 men and women chosen random from a pool that was considered high risk for cancer: smokers, former smokers, and people exposed to asbestos. They were given either15 mg of beta carotene and 25,000 IU of vitamin A (5 times the RDA) or a placebo. Those taking the placebo did better than those taking the vitamin A. The results were presented in the New England Journal of Medicine, read it here, with some key findings summarized in the graph below.

Comparison of cumulative mortality and cardiovascular disease between those receiving Vitamin A (5 times RDA) and those receiving a placebo. From Omenn et. al, Clearly, this much vitamin A does more harm than good.

The main causes of death were, as typical, cardiovascular disease and cancer. As the graph shows, the rates of death were higher among people getting the Vitamin A than among those getting nothing, the placebo. Why that is so is not totally clear, but I have a theory that I presented in a paper at Michigan state. The theory is that your body uses oxidation to fight cancer. The theory might be right, or wrong, but what is always noticed is that too much of a good thing is never a good thing. The excess deaths from vitamin A were so significant that the study had to be cancelled after 5 1/2 years. There was no responsible way to continue. 

Vitamin E is another popular vitamin, an anti-oxidant, proposed to cure cancer. As with the vitamin A study, a large number of people who were at high risk  were selected and given either a large dose  of vitamin or a placebo. In this case, 35,000 men over 50 years old were given either vitamin E (400 to 660 IU, about 20 times the RDA) and/or selenium or a placebo. Selenium was added to the test because, while it isn’t an antioxidant, it is associated with elevated levels of an anti-oxidant enzyme. The hope was that these supplements would prevent cancer and perhaps ward off Alzheimer’s too. The full results are presented here, and the key data is summarized in the figure below. As with vitamin A, it turns out that high doses of vitamin E did more harm than good. It dramatically increased the rate of cancer and promoted some other problems too, including diabetes.  This study had to be cut short, to only 7 years, because  of the health damage observed. The long term effects were tracked for another two years; the negative effects are seen to level out, but there is still significant excess mortality among the vitamin takers. 

Cumulative incidence of prostate cancer with supplements of selenium and/or vitamin E compared to placebo.

Cumulative incidence of prostate cancer with supplements of selenium and/or vitamin E compared to placebo.

Selenium did not show any harmful or particularly beneficial effects in these tests, by the way, and it may have reduced the deadliness of the Vitamin A.. 

My theory, that the body fights cancer and other disease by oxidation, by rusting it away, would explain why too much antioxidant will kill you. It laves you defenseless against disease As for why selenium didn’t cause excess deaths, perhaps there are other mechanisms in play when the body sees excess selenium when already pumped with other anti oxidant. We studied antioxidant health foods (on rats) at Michigan State and found the same negative effects. The above studies are among the few done with humans. Meanwhile, as I’ve noted, small doses of radiation seem to do some good, as do small doses of chocolate, alcohol, and caffeine. The key words here are “small doses.” Alcoholics do die young. Exercise helps too, but only in moderation, and since bicycle helmets discourage bicycling, the net result of bicycle helmet laws may be to decrease life-span. 

What about vitamins B, C, and D? In normal doses, they’re OK, but as with vitamin A and E you start to see medical problems as soon as you start taking more– about  12 times the RDA. Large does of vitamin B are sometimes recommended by ‘health experts’ for headaches and sleeplessness. Instead they are known to produce skin problems, headaches and memory problems; fatigue, numbness, bowel problems, sensitivity to light, and in yet-larger doses, twitching nerves. That’s not as bad as cancer, but it’s enough that you might want to take something else for headaches and sleeplessness. Large does of Vitamin C and D are not known to provide any health benefits, but result in depression, stomach problems, bowel problems, frequent urination, and kidney stones. Vitamin C degrades to uric acid and oxalic acid, key components of kidney stones. Vitamin D produces kidney stones too, in this case by increasing calcium uptake and excretion. A recent report on vitamin D from the Mayo clinic is titled: Vitamin D, not as toxic as first thought. (see it here). The danger level is 12 times of the RDA, but many pills contain that much, or more. And some put the mega does in a form, like gummy vitamins” that is just asking to be abused by a child. The pills positively scream, “Take too many of me and be super healthy.”

It strikes me that the stomach, bowel, and skin problems that result from excess vitamins are just the problems that supplement sellers claim to cure: headaches, tiredness, problems of the nerves, stomach, and skin.  I’d suggest not taking vitamins in excess of the RDA — especially if you have skin, stomach or nerve problems. For stomach problems; try some peniiiain cheese. If you have a headache, try an aspirin or an advil. 

In case you should want to know what I do for myself, every other day or so, I take 1/2 of a multivitamin, a “One-A-Day Men’s Health Formula.” This 1/2 pill provides 35% of the RDA of Vitamin A, 37% of the RDA of Vitamin E, and 78% of the RDA of selenium, etc. I figure these are good amounts and that I’ll get the rest of my vitamins and minerals from food. I don’t take any other herbs, oils, or spices, either, but do take a baby aspirin daily for my heart. 

Robert Buxbaum, May 23, 2019. I was responsible for the statistics on several health studies while at MichiganState University (the test subjects were rats), and I did work on nerves, and on hydrogen in metals, and nuclear stuff.  I’ve written about statistics too, like here, talking about abnormal distributions. They’re common in health studies. If you don’t do this analysis, it will mess up the validity of your ANOVA tests. That said,  here’s how you do an anova test. 

Statistics for psychologists, sociologists, and political scientists

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In terms of mathematical structure, psychologists, sociologists, and poly-sci folks all do the same experiment, over and over, and all use the same simple statistical calculation, the ANOVA, to determine its significance. I thought I’d explain that experiment and the calculation below, walking you through an actual paper (one I find interesting) in psychology / poly-sci. The results are true at the 95% level (that’s the same as saying p >0.05) — a significant achievement in poly-sci, but that doesn’t mean the experiment means what the researchers think. I’ll then suggest another statistic measure, r-squared, that deserves to be used along with ANOVA.

The standard psychological or poly-sci research experiments involves taking a group of people (often students) and giving them a questionnaire or test to measure their feelings about something — the war in Iraq, their fear of flying, their degree of racism, etc. This is scored on some scale to get an average. Another, near-identical group of subjects is now brought in and given a prompt: shown a movie, or a picture, or asked to visualize something, and then given the same questionnaire or test as the first group. The prompt is shown to have changed to average score, up or down, an ANOVA (analysis of variation) is used to show if this change is one the researcher can have confidence in. If the confidence exceeds 95% the researcher goes on to discuss the significance, and submits the study for publication. I’ll now walk you through the analysis the old fashioned way: the way it would have been done in the days of hand calculators and slide-rules so you understand it. Even when done this way, it only takes 20 minutes or so: far less time than the experiment.

I’ll call the “off the street score” for the ith subject, Xi°. It would be nice if papers would publish these, but usually they do not. Instead, researchers publish the survey and the average score, something I’ll call X°-bar, or X°. they also publish a standard deviation, calculated from the above, something I’ll call, SD°. In older papers, it’s called sigma, σ. Sigma and SD are the same thing. Now, moving to the group that’s been given the prompt, I’ll call the score for the ith subject, Xi*. Similar to the above, the average for this prompted group is X*, or X°-bar, and the standard deviation SD*.

I have assumed that there is only one prompt, identified by an asterix, *, one particular movie, picture, or challenge. For some studies there will be different concentrations of the prompt (show half the movie, for example), and some researchers throw in completely different prompts. The more prompts, the more likely you get false positives with an ANOVA, and the more likely you are to need to go to r-squared. Warning: very few researchers do this, intentionally (and crookedly) or by complete obliviousness to the math. Either way, if you have a study with ten prompt variations, and you are testing to 95% confidence your result is meaningless. Random variation will give you this result 50% of the time. A crooked researcher used ANOVA and 20 prompt variations “to prove to 95% confidence” that genetic modified food caused cancer; I’ll assume (trust) you won’t fall into that mistake, and that you won’t use the ANOVA knowledge I provide to get notoriety and easy publication of total, un-reproducible nonsense. If you have more than one or two prompts, you’ve got to add r-squared (and it’s probably a good idea with one or two). I’d discuss r-squared at the end.

I’ll now show how you calculate X°-bar the old-fashioned way, as would be done with a hand calculator. I do this, not because I think social-scientists can’t calculate an average, nor because I don’t trust the ANOVA function on your laptop or calculator, but because this is a good way to familiarize yourself with the notation:

X°-bar = X° = 1/n° ∑ Xi°.

Here, n° is the total number of subjects who take the test but who have not seen the prompt. Typically, for professional studies, there are 30 to 50 of these. ∑ means sum, and Xi° is the score of the ith subject, as I’d mentioned. Thus, ∑ Xi° indicates the sum of all the scores in this group, and 1/n° is the average, X°-bar. Convince yourself that this is, indeed the formula. The same formula is used for X*-bar. For a hand calculation, you’d write numbers 1 to n° on the left column of some paper, and each Xi° value next to its number, leaving room for more work to follow. This used to be done in a note-book, nowadays a spreadsheet will make that easier. Write the value of X°-bar on a separate line on the bottom.

T-table

T-table

In virtually all cases you’ll find that X°-bar is different from X*-bar, but there will be a lot of variation among the scores in both groups. The ANOVA (analysis of variation) is a simple way to determine whether the difference is significant enough to mean anything. Statistics books make this calculation seem far too complicated — they go into too much math-theory, or consider too many types of ANOVA tests, most of which make no sense in psychology or poly-sci but were developed for ball-bearings and cement. The only ANOVA approach used involves the T-table shown and the 95% confidence (column this is the same as two-tailed p<0.05 column). Though 99% is nice, it isn’t necessary. Other significances are on the chart, but they’re not really useful for publication. If you do this on a calculator, the table is buried in there someplace. The confidence level is written across the bottom line of the cart. 95% here is seen to be the same as a two-tailed P value of 0.05 = 5% seen on the third from the top line of the chart. For about 60 subjects (two groups of 30, say) and 95% certainty, T= 2.000. This is a very useful number to carry about in your head. It allows you to eyeball your results.

In order to use this T value, you will have to calculate the standard deviation, SD for both groups and the standard variation between them, SV. Typically, the SDs will be similar, but large, and the SV will be much smaller. First lets calculate SD° by hand. To do this, you first calculate its square, SD°2; once you have that, you’ll take the square-root. Take each of the X°i scores, each of the scores of the first group, and calculate the difference between each score and the average, X°-bar. Square each number and divide by (n°-1). These numbers go into their own column, each in line with its own Xi. The sum of this column will be SD°2. Put in mathematical terms, for the original group (the ones that didn’t see the movie),

SD°2 = 1/(n°-1) ∑ (Xi°- X°)2

SD° = √SD°2.

Similarly for the group that saw the movie, SD*2 = 1/(n*-1) ∑ (Xi*- X*)2

SD* = √SD*2.

As before, n° and n* are the number of subjects in each of the two groups. Usually you’ll aim for these to be the same, but often they’ll be different. Some students will end up only seeing half the move, some will see it twice, even if you don’t plan it that way; these students’ scares can not be used with the above, but be sure to write them down; save them. They might have tremendous value later on.

Write down the standard deviations, SD for each group calculated above, and check that the SDs are similar, differing by less than a factor of 2. If so, you can take a weighted average and call it SD-bar, and move on with your work. There are formulas for this average, and in some cases you’ll need an F-table to help choose the formula, but for my purposes, I’ll assume that the SDs are similar enough that any weighted average will do. If they are not, it’s likely a sign that something very significant is going on, and you may want to re-think your study.

Once you calculate SD-bar, the weighted average of the SD’s above, you can move on to calculate the standard variation, the SV between the two groups. This is the average difference that you’d expect to see if there were no real differences. That is, if there were no movie, no prompt, no nothing, just random chance of who showed up for the test. SV is calculated as:

SV = SD-bar √(1/n° + 1/n*).

Now, go to your T-table and look up the T value for two tailed tests at 95% certainty and N = n° + n*. You probably learned that you should be using degrees of freedom where, in this case, df = N-2, but for normal group sizes used, the T value will be nearly the same. As an example, I’ll assume that N is 80, two groups of 40 subjects the degrees of freedom is N-2, or 78. I you look at the T-table for 95% confidence, you’ll notice that the T value for 80 df is 1.99. You can use this. The value for  62 subjects would be 2.000, and the true value for 80 is 1.991; the least of your problems is the difference between 1.991 and 1.990; it’s unlikely your test is ideal, or your data is normally distributed. Such things cause far more problems for your results. If you want to see how to deal with these, go here.

Assuming random variation, and 80 subjects tested, we can say that, so long as X°-bar differs from X*-bar by at least 1.99 times the SV calculated above, you’ve demonstrated a difference with enough confidence that you can go for a publication. In math terms, you can publish if and only if: |X°-X*| ≥ 1.99 SV where the vertical lines represent absolute value. This is all the statistics you need. Do the above, and you’re good to publish. The reviewers will look at your average score values, and your value for SV. If the difference between the two averages is more than 2 times the SV, most people will accept that you’ve found something.

If you want any of this to sink in, you should now do a worked problem with actual numbers, in this case two groups, 11 and 10 students. It’s not difficult, but you should try at least with these real numbers. When you are done, go here. I will grind through to the answer. I’ll also introduce r-squared.

The worked problem: Assume you have two groups of people tested for racism, or political views, or some allergic reaction. One group was given nothing more than the test, the other group is given some prompt: an advertisement, a drug, a lecture… We want to know if we had a significant effect at 95% confidence. Here are the test scores for both groups assuming a scale from 0 to 3.

Control group: 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3.  These are the Xi° s; there are 11 of them

Prompted group: 0, 1, 1, 1, 2, 2, 2, 2, 3, 3.  These are the Xi* s; there are 10 of them.

On a semi-humorous side: Here is the relationship between marriage and a PhD.

Robert Buxbaum, March 18, 2019. I also have an explanation of loaded dice and flipped coins; statistics for high school students.

Measles, anti-vaxers, and the pious lies of the CDC.

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Measles is a horrible disease that contributed to the downfall that had been declared dead in the US, wiped out by immunization, but it has reappeared. A lot of the blame goes to folks who refuse to vaccinate: anti-vaxers in the popular press. The Center for Disease Control is doing its best to promote to stop the anti-vaxers, and promote vaccination for all, but in doing so, I find they present the risks of measles worse than they are. While I’m sympathetic to the goal, I’m not a fan of bending the truth. Lies hurt the people who speak them and the ones who believe them, and they can hurt the health of immune-compromized children who are pushed to vaccinate. You will see my arguments below.

The CDC’s most-used value for the mortality rate for measles is 0.3%. It appears, for example, in line two of the following table from Orenstein et al., 2004. This table also includes measles-caused complications, broken down by type and patient age; read the full article here.

Measles complications, death rates, US, 1987-2000, CDC.

Measles complications, death rates, US, 1987-2000, CDC, Orenstein et. al. 2004.

The 0.3% average mortality rate seems more in tune with the 1800s than today. Similarly, note that the risk of measles-associated encephalitis is given as 10.1%, higher than the risk of measles-diarrhea, 8.2%. Do 10.1% of measles cases today produce encephalitis, a horrible, brain-swelling disease that often causes death. Basically everyone in the 1950s and early 60s got measles (I got it twice), but there were only 1000 cases of encephalitis per year. None of my classmates got encephalitis, and none died. How is this possible; it was the era before antibiotics. Even Orenstein et. al comment that their measles mortality rates appear to be far higher today than in the 1940s and 50s. The article explains that the increase to 3 per thousand, “is most likely due to more complete reporting of measles as a cause of death, HIV infections, and a higher proportion of cases among preschool-aged children and adults.”

A far more likely explanation is that the CDC value is wrong. That the measles cases that were reported and certified as such are the ones that are the most severe. There were about 450 measles deaths per year in the 1940s and 1950s, and 408 in 1962, the last year before the MMR vaccine was developed and by Dr. Hilleman of Merck (a great man of science, forgotten). In the last two decades there were some 2000 measles cases reported US cases but only one measles death. A significant decline in cases, but the ratio does not support the CDC’s death rate. For a better estimate, I propose to divide the total number of measles deaths in 1962 by the average birth rate in the late 1950s. That is to say, I propose to divide 408 by the 4.3 million births per year. From this, I calculate a mortality rate just under 0.01% in 1962, That’s 1/30th the CDC number, and medicine has improved since 1962.

I suspect that the CDC inflates the mortality numbers, in part by cherry-picking its years. It inflates them further by treating “reported measles cases.” as if they were all measles cases. I suspect that the reported cases in these years were mainly the very severe ones. Mild case measles clears up before being reported or certified as measles. This seems the only normal explanation for why 10.1% of cases include encephalitis, and only 8.2% diarrhea. It’s why the CDC’s mortality numbers suggest that, despite antibiotics, our death rate has gone up by a factor of 30 since 1962.

Consider the experience of people who lived in the early 60s. Most children of my era went to public elementary schools with some 1000 other students, all of whom got measles. By the CDC’s mortality number, we should have seen three measles deaths per school, and 101 cases of encephalitis. In reality, if there had been one death in my school it would have been big news, and it’s impossible that 10% of my classmates got encephalitis. Instead, in those years, only 48,000 people were hospitalized per year for measles, and 1,000 of these suffered encephalitis (CDC numbers, reported here).

To see if vaccination is a good idea, lets now consider the risk of vaccination. The CDC reports their vaccine “is virtually risk free”, but what does risk-free mean? A British study finds vaccination-caused neurological damage in 1/365,000 MMR vaccinations, a rate of 0.00027%, with a small fraction leading to death. These problems are mostly found in immunocompromised patients. I will now estimate the neurological risk for actual measles based on the ratio of encephalitis to births, as before using the average birth rate as my estimate for measles cases; 1000/4,300,000 = 0.023%. This is far lower than the risk the CDC reports, and more in line with experience.

The risk for neurological damage from measles that I calculate is 86 times higher risk than the neurological risk from vaccination, suggesting vaccination is a very good thing, on average: The vast majority of people should get vaccinated. But for people with a weakened immune system, my calculations suggest it is worthwhile to not immunize at 12 months as doctors recommend. The main cause of vaccination death is encephalitis, but this only happens in patients with weakened immune systems. If your child’s immune system is weakened, even by a cold, I’d suggest you wait 1-3 months, and would hope that your doctor would concur. If your child has AIDS, ALS, Lupus, or any other, long-term immune problem, you should not vaccinate at all. Not vaccinating your immune-weakened child will weaken the herd immunity, but will protect your child.

We live in a country with significant herd immunity: Even if there were a measles outbreak, it is unlikely there would be 500 cases at one time, and your child’s chance of running into one of them in the next month is very small assuming that you don’t take your child to Disneyland, or to visit relatives from abroad. Also, don’t hang out with anti-vaxers if you are not vaccinated. Associating with anti-vaxers will dramatically increase your child’s risk of infection.

As for autism: there appears to be no autism advantage to pushing off vaccination. Signs of autism typically appear around 12 months, the same age that most children receive their first-stage MMR shot, so some people came to associate the two. Parents who push-off vaccination do not push-off the child’s chance of developing autism, they just increase the chance their child will get measles, and that their child will infect others. Schools are right to bar such children, IMHO.

I’ve noticed that, with health care in, particular, there is a tendency for researchers to mangle statistics so that good things seem better than they are. Health food: is not necessarily so healthy as they say; nor is weight loss. Bicycle helmets: ditto. Sometimes this bleeds over to outright lies. Generic modified grains were branded as cancer-causing based on outright lies and  missionary zeal. I feel that I help a bit, in part by countering individual white lies; in part by teaching folks how to better read statistic arguments. If you are a researcher, I strongly suggest you do not set up your research with a hypothesis so that only one outcome will be publishable or acceptable. Here’s how.

Robert E. Buxbaum, December 9, 2018.