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Follow the math!

October 20, 2021

Before there were vaccines, all of those hospitalized for Covid-19 were unvaccinated. Of course. Once people started being vaccinated, some of those nonetheless suffered the disease and were hospitalized. No medicine is perfect. As the fraction of people vaccinated grows, so does the fraction of those hospitalized for disease.

As of last month, 54% of those hospitalized from Covid-19 in Ireland were vaccinated against the disease. That number by itself tells nothing about how well the vaccine is working. Fortunately, the author of that article provides the background rate: 90% of the Irish population now is vaccinated. If the vaccination did no good at all, if it were nothing more than saline water or an amulet, we would expect 90% of those hospitalized to be vaccinated. If that rate were higher, we might suspect the vaccine were somehow making its recipients more susceptible to the disease. The fact that 54% is less than 90% indicates the vaccine is helping. But how much is it helping?

Interestingly, that can be calculated from those two numbers, using some basic probability. The answer that gives is the vaccine is 87% effective, and that hospitalizations would be almost five times higher without so many people vaccinated. I provide two calculations of that below.

VaccineEffectivenessHospitalizationFew people will do that calculation on reading the article. One reason is that few people have studied probability and statistics. Another and better reason is that a calculation derived from a newspaper article, even when correctly done, doesn’t provide a robust model of how a vaccine is doing. Hospitalization counts are noisy. The vaccinated and unvaccinated differ in medically relevant ways. (The probability calculation assumes they are statistically similar.) Different groups received the vaccine at different times. So if one wants a good insight into how the vaccine is doing, one should look at some of the recent studies of that, which apply more careful methodology and more sophisticated statistical techniques. The graph right, showing vaccine effectiveness against hospitalization for different age cohorts, is taken from one such study published this month. The fact that the calculation here gives similar result is an example of where the back of the envelope agrees with more detailed examination. As often happens. Nerds mess up many scraps of paper with such calculations, taking comfort when they agree, and wanting explanation for when they don’t.

Alas, I have seen a few articles and posts that interpret the Irish Times article as somehow indicating that the vaccine is failing. When in fact it shows the opposite.

Understanding data requires following the math. There is no other way. Whenever you read someone who is offering some interpretation of quantitative data, whether epidemiological or otherwise, the first question that should pop into your head is whether the author actually knows the relevant math? Do they read studies on the topic of their article? Do you think they spent a few minutes, calculating on aspects of the data? Well, not many journalists do any of that, because most never studied much math. So the next question is whether they turned to someone who does.

Calculation #1: Using Bayes theorem

The efficacy of a medical treatment is the ratio of how many of those treated suffer the endpoint — in this case, p(H|V), the probability of being hospitalized if vaccinated — to those not so treated — p(H|~V). Subtracted from 1, since that ratio is 0 if the treatment is perfect, and 1 if it is completely ineffective. Bayes’ theorem is one of the core tools for calculating conditional probabilities. So one might try writing both of those according to it:

p(H|V) = p(V|H) * p(H) / p(V)
p(H|~V) = p(~V|H) * p(H) / p(~V)

Well, the article tells what fraction are vaccinated and not, p(V) and p(~V). And what fraction of the hospitalized are vaccinated and not, p(V|H) and p(~V|H). We don’t know the probability that someone in Ireland is hospitalized. But we want the ratio, and that term, p(H), drops out when we divide the first equation by the second.

p(H|V)/p(H|~V) = (p(V|H) * p(~V)) / (p(~V|H) * p(V))
= (0.54 * 0.1) / (0.46 * 0.9)
= 0.13

Subtracting from 1, the vaccine efficacy is 87%.

Calculation #2: From Population Trajectory

Calculating something from a formula sometimes leaves intuition wanting. A more understandable approach to thinking about many statistics problems is to start with a representative sample and calculate its trajectory to the relevant end points. In this case, consider a 100 people who have been exposed to Covid-19, such that they would become hospitalized from it, absent the effects of vaccination. This does not assume that everyone exposed becomes hospitalized. Just that we are looking at the population who would be so. 90 are vaccinated. We can divide those into a number S whom the vaccine saved from hospitalization, and a number F whom the vaccine failed, leading them to a hospital. S+F=90. Per the article, the actual percent of vaccinated among the hospitalized is 54%. Since there are 10 unvaccinated in our sample who were hospitalized, that means 54%=F/(F+10). Solving that gives F = 11.74. That means S=78. Which also is the percent reduction in hospitalization. The vaccine’s efficacy is 78/90. Again, 87%.

Anyone reading that article, who understands statistics, will take away from those numbers that the vaccine seems to be working very well in Ireland, and that it has saved the hospitals from a wave of Covid-19 patients that otherwise would be much larger.

First, exercise

October 18, 2021

Unsurprisingly, a metastudy comparing exercise to weight loss for those who are overweight finds that the former carries the clear benefit, in lowering mortality. (Cite.

And researchers at Edith Cowan University studying prostate cancer find a mechanism by which exercise might slow its advance. 

By themselves, neither of those studies are terribly convincing. The first is a metastudy, and the second purely a lab result. I could write a post each on why to be wary of those. In this case, they don’t stand alone. They are the latest in thousands of studies. Go. Exercise. 

Thoughts while reading a book

October 14, 2021

Somehow I never quite realized when most every book I read was done on my phone. Now, I’m reading a history that isn’t available digitally. And find it an awkward thing. I’m back to using a highlighter for passages I might want to revisit. That won’t provide me an easy way to scan or search them. The dog-eared pages might help with that. That physical piece of bound paper always finds itself to some place where I don’t expect it to be, when I want to read it. It is never with me if I’m out and about. And once I finish, I will have to find a permanent place for it on my shelves. All things we once took for granted, as part and parcel of reading, now revealed as encumbrances.

Edgar_Degas_Portrait_of_DurantyIf I admit to some nostalgia for musty stacks, the truth is that card catalogs and inter-library loans and qualifications to visit restricted stacks always were both barrier and tool. There was joy in finding a referenced work that contained what you had hoped, mostly because the route to discovery was tricky. The literate world has changed. If some curmudgeons complain, they will no more wrangle the genie back in the bottle than has any curmudgeon past. The truth is I like having my library with me, on a tool I carry with me anyway for many other purposes. And yes, that library includes the marine charts for the waters that interest me. As the marketing quip goes, there’s an app for that. 

Infectious disease

October 13, 2021

Not long past, even in the richer parts of the world, most people died from infectious disease. The Smithsonian has a good article on the battle against diptheria.

Malaria still kills a half million people every year. So it is great news that GlaxoSmithKline has made the first vaccine that may make some headway against it. Some reading that article may worry that the vaccine is only 50% effective. If it remains that effective, it will save millions of lives. We in the developed world have become so accustomed to vaccines with very high efficacy that we forget what progress was made in other times and places with more basic tools. 

The coup’s aftermath, part 1

October 11, 2021

Trump’s attempt to overturn the 2020 election was stymied at his every turn by Republican office holders who resisted his ploys. Georgia Secretary of State Raffensperger would not conjure the desired 11,000 votes. Several high officials in the Department of Justice resigned or threatened to resign rather than act on Trump’s false election claims. Pence refused to play his assigned role.

While the lawyers who were the public side of the coup are facing legal sanctions and defamation lawsuits, Trump largely has avoided any consequence. So far. He is holding rallies as if planning for a comeback. More significantly, he is targeting those Republicans who put their duty over their partisan loyalty. I suspect he will be successful in that. Raffensperger can write a book on integrity. That will not change the nature of the cult. If he thinks he can survive in today’s GOP standing on integrity, he has seriously misread the direction of the party.

Trump’s coup failed only because he did not have loyal lieutenants already installed in the positions needed, or the ready leverage to subvert those who weren’t with the program. That was a scarily thin line. While he may hope that his efforts now pave the way for his political return, it is more likely they will serve a future strongman who is better at politics.

Trump is more symptom than cause. Alas, looking at the broader picture isn’t necessarily cheerful. The cult Trump rode to power existed before he jumped into politics, seeing that he could ride it. It shows every sign of dominating the GOP for years to come. The difference between state senator Ed McBroom, who exposed Trump’s election lies in Michigan, and Staci Burk, who was eager to spread them in Arizona, doesn’t have an obvious tie to political ideology. Both are Republican. Both likely see eye to eye on a variety of issues from taxes to the role of religion in the US. The difference between them is integrity in contrast to susceptibility to weaponized bullshit. That leaves McBroom with no place in today’s GOP. That party seems destined to travel a dark route for the foreseeable future.

The structural weaknesses of American democracy are even longer standing. The right wing doesn’t have to rely on persuading most Americans. The corruption that feeds the cult also makes it suited to taking advantage of every hole in our legal system.

Perhaps the generations that have been raised with the internet will become savvier. Perhaps, despite Covid-19 being the favorite subject of those who weaponize bullshit — or because? — that will generate broader concern for facts and science. Perhaps criminal prosecutions will further expose those who supported the Trump administration. The future is hard to scry.

Update: Republicans who are unwilling to travel the current direction of that party make a plea.

Boat stories

October 7, 2021

RarebitMatthew Rhys and Keri Russell bought an old Wheeler Playmate a few years back, restored her, and now puts her up for charter. Anyone thinking of trying similar, other than my Maine friend who makes it look easy, should read that article carefully, regarding the time and effort it took, far beyond early expectations. A new version of Wheeler Boats sells a new version of Hemingway’s Pilar. It is cold-molded. You will spend less for something stronger and requiring much less maintenance. “Less,” of course, is relative. And perhaps not the point, when trying to replicate a token of the past.

On sad note, a cruising couple is discovered dead, their sailboat stranded high on Rockaway Beach in Oregon.

Borders and disease

October 6, 2021

New Zealand was one of the select few nations that had managed to avoid Covid-19 through border controls. Many don’t realize how difficult that is to do. The discipline has to apply to everyone. Quarantine must be mandatory. And rigorous contact tracing must back up any infections detected.

Portugal_CovidWhere that had been succeeding for New Zealand, it now has failed. The more infectious delta variant has made an outbreak. So they had better see if they can follow Portugal, where most everyone qualifying to receive a vaccine has done so. The diagram attached (click for full size) shows new cases there, per capita.

Once an infectious disease is endemic in a nation, it’s far from clear how much border control can help with it. That’s like try to control a forest fire that is actively burning sections of land by making sure there are no more careless campers. It’s too late for that. Nations that rely on a large amount of international travel never had much opportunity to do that. Covid-19 was seeded in the NYC area, from international travel with Europe, before we first restricted travel to China. At the present, a million and a half people arrive in the US. Every day. Tens of thousands no doubt are carrying some infectious disease. Closing the border, or even just enforcing a rigorous quarantine for those arriving, always was a step too far. Because of the economic fallout, from the cultural impediments to doing so, and too late when first discussed.

Mandating vaccination for those entering would be more plausible. Though I see little reason to think it would much change the course of the disease here. One reason nations do that is to avoid the trouble that comes from visitors arriving and then getting sick. That is why some nations with yellow fever require visitors to be vaccinated for that. They don’t worry that more bodies feeding the mosquitoes will increase the disease. They just don’t want visitors to get sick soon after arriving.

Neuron complexity

October 5, 2021

McCulloch-Pitts-computational-model-of-a-neuronI doubt anyone ever viewed the McCulloch-Pitts model of a neuron as anything more than a simplistic stab at the underlying biology. On the other hand, the degree of complexity of the individual neuron shown by some recent work is pretty amazing. (Cite.) There is a certain beauty in using neural networks to study actual neurons.

There rightly has been quite a bit of press about the discovery that capillary damage is part of the etiology of Alzeheimer’s. That buttresses what I have noted about some of the observational studies of exercise and nutrition, that the things that support arterial health also are the things that provide some protection against that form of dementia.

Global connectivity

October 4, 2021

The fundamental and most important kind of digital communication is what the telegraph first introduced and what we still use to remind our partners to pick up milk: short text messages, delivered quickly, even if some latency means that conversations might be stretched out rather than having two-way immediacy. Lynk has demonstrated the capability of providing that world-wide by satellite, to ordinary cellphones.

MessageinabottleThat may not sound earth shattering. SpaceX, OneWeb, and Amazon are planning to deliver broadband worldwide. The difference is that those all require special transceivers designed to work with each company’s satellite cluster. For the consumer, that significantly raises the price of entry, requires setting up equipment, entails commitment to a service, and creates a barrier to  mobile use. Their business model is to replace your cable company. Which indeed would be a good thing. But it’s a large thing, both to deliver, and in switching consumers’ current practice. Lynk’s business model is to work with existing carriers to provide messaging where cell towers don’t reach:

According to Lynk’s research, the average mobile phone in use today on Earth is only connected to a terrestrial network about 85 percent of the time. So as many as 750 million people are experiencing disconnectivity at a given time. That’s the market Lynk intends to serve. So far the company has reached carrier agreements with Aliv in the Bahamas and Telecel Centrafrique in the Central African Republic.

To the customers whose carriers interconnect with Lynk, it merely means they get charged some small fee per SMS, when they text where cell towers aren’t visible. Would I pay a quarter per SMS, to send and receive text messages while on a boat delivery to the Caribbean? Or in some remote spot of south Texas outside cell range? Oh, hell yeah. I suspect that goes for most who have been disappointed on multiple occasions that they weren’t yet in range of a cell tower. And Lynk will provide that, with just a small fraction of their planned cluster launched. The growth in their cluster reduces latency. Until, eventually, they can provide full broadband. There’s something deliciously organic about that business model. 

AST, a Texas company with ticker ASTS, is planning direct satellite to cell device broadband, launching large satellites with phased array antennas. Their plan is running into some resistance from regulators. I suspect they will overcome that. Fewer, larger satellites seem to me no more a space pollution problem than more, smaller ones. Unlike Lynk, they are going to try the big leap to full 4G/5G connectivity. Which requires getting most of their cluster launched and working before delivering service to customers, some years down the road.

My investment vision usually proves wrong. With that caveat made, I suspect the companies that are going direct to cellphone will prevail over those requiring a specialized transceiver.  The way to eliminate the cable companies isn’t by replacing what they deliver to your home, and the current equipment in your home to handle that. Rather, it is to make your existing cellphone have all the connectivity you want wherever you happen to be. Your laptop then gets connected the same way it does now, by wifi. Just through your cellphone, rather than through your home router. Or, your laptop disappears, in favor of a screen and keyboard as extensions to your phone, when you want those. All those modems, wifi routers, satellite dishes, wifi extenders, and related cables in your house? They become obsolete. Like acoustic modems before them. And the sooner, the better. No one ever wanted any of that. They were just the burdens people accepted, to get connected.

A step toward public integrity

October 1, 2021

I agree with Binyamin Appelbaum that it is inherently corrupting when a government official holds an interest in a specific company. No matter how much that official tries to act with integrity and impartiality, such investment will earn an undue fraction of their mindshare, creating biases that cannot be overcome simply by trying to act with impartiality. Appelbaum proposes:

Public officials should be restricted to passive investments like index mutual funds, which invest in broad categories of companies or assets. Anything else, like a family business, should have to go in a blind trust.

Is a blind trust enough? Even if someone puts their meat packing plant, as example, into a blind trust, they still are aware of the nature of that business. Their financial interest in it will sway what they read about related industry and how they think about it. That in turn biases all sorts of decisions, even in someone trying hard to act responsibly and fairly. Why not require liquidation, rather than a mere curtain, with everyone knowing what is behind it? Public service is a full-time commitment. When someone accepts appointment as a judge, or wins public office, or otherwise works in government, they should divest their interest in specific private business. That does not require divesting wealth. As Appelbaum points out, the modern financial world provides plenty of diversified, passive investments to grow it. Nor does it mean they cannot reenter the business world when they are done with public service. It merely requires they not pursue both simultaneously, linking those interests in ways they shouldn’t be.

The problem, of course, is that reform of this sort is not politically exciting. Few will push for it. Too many voters seem not to care. Including many who are quick voice complaints about political corruption.