Climate change mitigation: a solution in search of a problem

The new IPCC report is out this week and the Secretary of the United Nations has issued stern warnings and rebukes. The report’s co-chair James Skea of Imperial College London cautions that “If we continue acting as we are now, we’re not even going to limit warming to 2 degrees, never mind 1.5 degrees.” The authors of the new report argue that we need to halt all fossil fuel developments, and radically change our lifestyles including our diets to save the planet.

I accept the science. More precisely, I embrace the range of possibilities that the IPCC publishes based on the amount of global CO2 emissions and the likely effect on the atmosphere. But embracing atmospheric science is only a small part of the issue. What all the reports and commentary leave out are realistic cost-benefit analyses and the likely economic outcomes even in the upper range of warming forecasts. Of course the media does a poor job of highlighting the likely outcomes or placing them in proper context. Once we think about the outcomes it becomes clear that climate change is a solution in search of a problem.

Global GDP growth: the surest way to smash global poverty.

So, how can I believe the science but not the climate change mitigation story? First we need to be precise in our questions and goals. Clarity matters. Stripping away all the romance, the real question is:

If we want to spend tens of trillions of dollars today to make the world a better place in 2100, what is the most efficient way to proceed?

An answer to this question centers on three lines of reasoning:

1) Lifting worldwide GDP growth.
2) Avoiding a rare but potentially catastrophic possibility.
3) Protecting the planet’s biodiversity.

Implicit in the climate change narrative is the statement that climate change mitigation tops the list for addressing all three points. Let’s address each.

Lifting worldwide GDP

To begin we need a measure and a sense of scale. When comparing economic well-being, economists use GDP – the value created through production of goods and services. Of course GDP is an imperfect measure, but GDP and GDP growth correlate strongly with all the aspects of life that we consider important. We do not see a rush of immigration from countries or regions with high GDP to lower ones; it’s always the other way around. Since 1950, the planet’s GDP has grown by over a factor of 12. As a percentage of the population, fewer people live in abject poverty, lifespans are longer, health care is more readily available, infant and maternal mortality has plummeted. We are better connected, better educated, more fulfilled, more peaceful, and we are more productive than ever before. In short, the world has gotten an awful lot better for so much of the world’s population. Economic growth has been the key feature for shattering poverty. Nothing else comes close. Unfortunately we have a long way to go. There are many parts of the world where GDP growth has been tepid to say the least. On growth considerations, the germane question is:

If we want to spend tens of trillions of dollars today to increase the world’s GDP to the greatest extent possible by 2100, what is the most efficient way to proceed?

Not all countries have seen the same growth prospects and some countries switched paths over time. A great example of a path change occurred with China in the late 1970s. As China opened up and started to move to a more market based economic orientation, GDP per capita exploded. From 1990 to today, China’s GDP per capita has grown by more than 1,000%. When we think about poor countries and the lessons around economic growth, it’s hard to think about anything else! With China, we have a direct example from the last 30 years which shows what is possible by adopting at least some level of a market based economy. Going back to the end of WWII we have examples at least as impressive as modern day China such as South Korea, Japan, Singapore, and Hong Kong. If Africa took a similar trajectory to any of these examples, 1,000+% GDP per capita growth over the next 30 years is not only completely within the realm of possibility but could even be the most likely outcome. Think of a world in which another 2 billion people experience such economic growth.

Now let’s compare 1,000% GDP growth over 30 years to anything that climate change has in store. The best economic estimates suggest that at 6C of warming by the end of the century – the very upper end of the climate models – the world economy will be about 10% smaller than it otherwise would have been without climate change in 2100. Even if the estimate is wrong by a factor of 2, and the actual effect is 20%, the effect size of climate change is about 0.25% of GDP loss per annum! Climate change is peanuts compared to the variation in growth we see between countries which organize around markets and those which do not. So if we want to spend tens of trillions of dollars today with the goal of making the world a better place in 2100, would it not make more sense to use those resources to persuade as much of the world as possible to follow the success path of well known examples? It’s hard to believe that chasing 0.25% per annum growth level effects come out at the top of the list. Such small effects in our own GDP growth sit at the level of the inefficiencies in the Canadian tax code.

Avoiding Catastrophe

It’s pretty clear that if the path to a better world in 2100 is GDP growth, climate change is one of the last places to start – 0.25% per annum growth effects just don’t make the leap for us. But there are other concerns. Suppose that climate change triggers some presently poorly understood tipping point which catastrophically ruins the environment and makes the miracles of economic growth impossible. In that case, spending tens of trillions of dollars today on climate change mitigation might make a lot of sense. But now the question changes:

If we want to spend tens of trillions of dollars today to make the world safer by avoiding a potential yet poorly understood catastrophe by 2100, what is the most efficient way to proceed?

In other words, we seek to spend a lot of money today in a precautionary sense – buying insurance – so we can have a future with economic growth. To answer this question, we need to think about how climate change compares to other potential catastrophes. We are just coming out of a pandemic that in 2020 shrunk the world economy by an effect greater than 10 years worth of expected climate change damage. Now, imagine a pandemic much worse than Covid, or even much worse than the flu of 1919. A severe global pandemic could erase decades of economic growth almost overnight. But it’s not just pandemics. There are only seven principal cereal crops in the world of which just two, wheat and corn, make up over 60% of global production. Suppose that a serious blight or virus destroys much of the world’s grain output, something like the Irish potato famine but on a global scale. Global debt runs could ruin our economies and throw us into a worldwide great depression that lasts decades. And of course nuclear war always hangs over us like the Sword of Damocles, not to mention a comet or asteroid impact, a major volcanic eruption, the collapse of the Earth’s magnetic field…you get the point. There are many, many, low probable highly catastrophic possibilities to worry about all of which could in part be mitigated right now by tens of trillions of dollars worth of spending today. Where do we start? We can’t insure against all possibilities. To make the case that climate change is special, we have to show that somehow, of all the unlikely but horrible possibilities that exist, climate change makes the top of the list on a cost-benefit insurance basis. It’s hard to make that argument, but I have some limited sympathy for it. But to put catastrophic events in perspective, for at least the last decade governments have told banks and corporations to plan carefully around climate change exposure. Now imagine if a decade ago governments instead suggested that financial institutions and businesses put a potential pandemic at the top of their mitigation priorities. Perhaps Covid would have been handled much better. Stuff that really threatens us are events like Covid on steroids; real catastrophes come out of the blue, not something that gives a century of notice with gradual change.

Protecting biodiversity

Climate change mitigation seems like a weird place to start if we want greater economic growth or mitigation against rare but potentially catastrophic outcomes. But climate change might be special when it comes to biodiversity. Perhaps climate change will be so awful for the planet’s plants and animals that, while GDP will hum along, we will irreparably harm the biodiversity of the planet and eventually poison long term growth prospects. Again we need to think in terms of cost-benefit. The question now becomes:

If we want to spend tens of trillions of dollars today to ensure the biodiversity of the planet through 2100, what is the most efficient way to proceed?

The biggest problems around biodiversity are habitat loss and destruction by direct human intervention. The large mammals of Africa and Asia have nearly been hunted to extinction. Ocean life suffers from over-fishing. Direct human effects on the environment have so far proved far more destructive than the indirect effects caused by climate change. Even if we manage to get all of the Western world on electric cars by 2050, rhinoceroses and elephants will hover near extinction, if not already extinct by then, and another 30 years of over-fishing risks colossal implications for sea life regardless of a slightly cooler climate. I doubt our green infrastructure renewal will save even one giraffe or increase the length of single tuna fish. It’s not clear that climate change is the place to start if we want to protect the environment and biodiversity. Perhaps sectioning off large parts of the Earth as no-go zones for humans might lead to better outcomes. Returning to economic growth, it’s countries with high GDPs per capita that treat their environments the best. Thus a virtuous cycle of higher economic growth with increasingly cleaner environments may end up being the best way to protect the natural world. In that case, the pathway to rapid GDP growth could be the saviour of biodiversity.

Squaring the climate change agenda

Somehow the public has become captivated by an arbitrary, almost magical, threshold of 1.5C of warming with an implicit belief that the world will end at the 2C mark within a hundred years or less. Climate models make no such predictions. Worse, when experts do offer preliminary cost-benefit analyses, they often leave out the effects of human adaptation. Rising sea levels do not mean 187 million people will be displaced over the next century. Urbanization saw billions migrate to cities over the last 100 years. Patterns of human habitation will continue to change over the coming century. Humans live in extreme climates and elevations already, from the Sahara desert to nearly the north pole, from the Tibetan and Andes plateau to The Netherlands and the Mekong Delta. We have lived across this enormous variation for millennia. There is no model of climate change, even with 6C of warming by 2100, that has a level effect larger than the variation that already exists.

The more I think about it, the more I see climate change as a solution in search of a problem. Every time we rephrase the question to precisely address what we hope to achieve in the far off future, climate change does not seem to offer the leading solution. It’s hard to imagine how climate change tops the list for increasing economic growth, protecting us from a potential catastrophe, or sustaining biodiversity. Yes, climate change contributes in some way to all three of these lines, but it’s not leading order. It’s true that climate change is a classic example of an externality in which an unregulated market is unlikely to generate the optimal amount of global warming given the benefits from carbon intensive production that humanity receives. Spending something to mitigate climate change makes sense, but it’s not an all-hands-on-deck-or-it’s-the-end-of-the-world kind of problem and it certainly does not warrant anything close to the attention it receives. And if ultimately the political will is insufficient to address climate change in any substantive way, it’s not a big issue – we’ve learned to live with all kinds of externalities that are just too costly to address. We know how to adapt.

So if climate change represents a rather small or moderate externality, why does it attract so much attention? I am sure there are true believers who claim to “believe the science” and yet focus all their concern on highly improbable catastrophic climate change events as though those outcomes are the most likely to occur. But for others, I think climate change offers a seductive channel for capturing government power. Under the climate change lens, CO2 emissions are a form of pollution, creating an externality for government action to solve. But we have to remember that heavy direct government regulation of pollution is the backdoor to the government marshaling production. After all, pollution is a byproduct of production; you can’t touch one without touching the other. That’s why in industrial settings, economists argue for narrowly targeted pollution mitigation, often emphasizing indirect government involvement that relies on some form of market or price mechanism, tied to carefully delineated property rights and the rule of law. A government that shepherds a sea change of the entire economy through direct action and direct government participation – whether justified or not – ends up in the driver’s seat of the economy, deciding on what gets produced and who produces what. Regardless of intent, as President Eisenhower recognized over 60 years ago, that centralization of power is a danger to democracy and liberty. We face enormous institutional and political risks from the clarion call to centralize power to save the planet from what all reasonable estimates tell us is a rather small problem. But maybe that’s the point…

A pound of flesh nearest the heart

As we enter what are likely the end stages of the Covid-19 pandemic with the virus transitioning to an endemic state, our society has become angry and self-righteous, egged on by our political and chattering class. Pandemics at some point in their trajectory often find someone to blame. During the Black Death, the Jews made for an easy scapegoat, and in more modern times homosexuals served as the perfect minority to hate and blame during the beginning of AIDS pandemic. The pattern is always the same – find a group that nobody likes, claim that they are the party most responsible for the on-going disease, and then pour all of our hate and derision on them. Use political power to punish them and satiate the mob’s need for retribution. Today, with Covid-19, society’s scapegoat is the unvaccinated. Yes, people should get the vaccine; yes, they are safe and effective at preventing serious complications, especially for high risk populations, but a near religious fervor has gripped Canada in blaming the unvaccinated for our current woes with a near insatiable appetite to punish.

American political cartoon by Thomas Nast titled “The Usual Irish Way of Doing Things”, published in Harper’s Weekly, 2 September 1871. Anti-Irish sentiment ran deep in corners of North America during the late 19th century, fed and maintained by the chattering class. The ugliness of the mob.

The story sells itself. Unvaccinated people are much more likely to experience severe illness, hospitalization, or death, especially if they have comorbidities. Currently in Ontario about half of the Covid-19 ICU patients and one quarter of all Covid-19 hospital patients are unvaccinated even though they only represent about 10% of vaccine eligible citizens. Clearly the unvaccinated are highly disproportionate in their need for health care services should they contract Covid-19. Yet the unvaccinated are in fact scapegoats for much larger problems.

The vaccines are not particularly effective in controlling the spread of Covid-19. With the rise of the Omicron variant, Covid-19 is so transmissible that the argument for externalities completely falls apart. The Covid-19 vaccines almost exclusively provide their protection to the person receiving the vaccine, conferring negligible spillover effects in the form of transmission interruption in the wider community. Thus, the refusal to take the vaccine, however misguided, only hurts the unvaccinated person. Most professionals recognize the ineffectiveness of the vaccines to control transmission. Hence, even with 90% of eligible Ontarians vaccinated, we see tens of thousands of new cases per day leading to explosive exponential growth in the vaccinated population. However, politicians and the chattering class argue that the unvaccinated play a special role because they disproportionately place demand on the health care system.

To get a sense of our problems, we can look to our health professionals on the ground. An emergency room physician, Dr. Brett Belchetz, told Global News “We are looking at hospitals that are struggling to keep up and now you add in all of those extra patients…we are in a dangerous situation here. You see patients being treated in the hallway with regularity and often that is just a choice we have to make — provide no care or provide hallway care.” An anonymous nurse added, “the volume of patients is insane. We are so overcapacity.” Dr. Belchetz continued, “It doesn’t take a mathematical genius or an expert in health care to understand that having more people in the province, especially people that are older, that are sicker, with fewer hospital beds, is a recipe for hospitals to operate overcapacity. And not just overcapacity — dangerously overcapacity.” It gets worse, Michael Garron Hospital, formerly Toronto East General Hospital, has postponed seven cancer surgeries as a result of a shortage of beds in the ICU since December. Carmine Stumpo, vice-president of programs at Michael Garron Hospital, says it’s been a juggling act for surgeons, “So we work with our hospitals to ensure that sort of situation hopefully is completely avoided, but if it’s necessary it’s minimized.” Serious issues for sure but these are not stories from this winter or even last winter; they are from the flu season of 2017-18! Ontario hospitals have been in an overcapacity crisis long before Covid-19.

If all the unvaccinated had been vaccinated, Covid-19 would still be over-running Ontario’s health care capacity. Data on the comorbidity status of the unvaccinated is not readily available, but at least some of them would have still ended up in the hospital and the ICU vaccinated or not. Eliminating a quarter of the Covid-19 hospital cases in Ontario still leaves us terribly strained. Canada has one of the worst health care capacities in the developed world and vaccinating the last 10% of our population is not nearly enough to hold the ground against the Omicron wave. The unvaccinated are not the cause of hospital overcapacity but they allow our governments to distract us from their failure to build a robust health care system, and their additional failure to build adequate Covid-19 specific health care treatment capacity. Even though we have been trudging along with a broken health care system for decades, which Covid-19 has exposed for all to see, our political class can now just blame the Covid-19 unvaccinated. It’s an easy way out.

Blaming the unvaccinated is bad enough, but the Ontario government’s lockdown policies create a super regressive health care tax. The argument for lockdowns is that, at this point, they are the only way to protect our health care system. I doubt that the lockdown approach is correct, but even if it is, the people who pay for that protection are the working class who can’t find timely daycare for their children and who find themselves locked out of work. They pay the “health care tax” in-kind today, protecting the health care system, to make up for what wasn’t paid earlier. And all the while the laptop class enjoys full salary and the opportunity to work in their pajamas. We’re all in this together….yeah right we are.

How did we get here? Canada has large structural issues that are undermining our democracy and harming our institutions. These problems go well beyond Left vs Right or any political stripe. Our country has not properly addressed its regional composition either in the BNA of 1867 or the Constitution Act, 1982. Instead of a properly constituted federation in which representation by population is tempered by strong regional power, we have quasi-federalism or some kind of hyphenated federalism (executive-federalism, collaborative-federalism, shared-cost-federalism, fiscal-federalism, etc.) and in that regard governments responsible for delivering programs become increasingly divorced from the government that raises the revenue. By constitutional necessity, Canada leans on Ottawa’s spending power to address regional needs which has had the perverse effect of turning health care funding into a circus of side deals between the provinces and the federal government, not to mention the complexities of indigenous health care delivery. The locus of decision-making shifts like sand dunes across the political landscape, making it difficult for the public — and at times even Parliament itself — to hold the appropriate government and decision-making body to account. We have deep structural institutional and democratic problems in Canada which Covid-19 has laid bare through our health care systems. Blaming the unvaccinated for our difficulties in the current Covid-19 Omicron wave distracts us from the important work that lies ahead of us not only for our health care systems but for the health of Confederation itself.

Our experiment in national cruelty

As we approach the nearly two year mark since the start of the Covid-19 pandemic, I am shocked by my fellow citizen’s zeal in pouring cruelty, contempt, and derision on others. Perhaps I shouldn’t be shocked. Cruelty after all is the merging of joy and anger and its expression gives a deep sense of satisfaction to so many, especially when there is political hay to make.

Saturn Devouring His Son by Francisco Goya

The Covid vaccines are amazing. People should get them. The evidence shows overwhelmingly that they prevent serious illness and death, especially among the vulnerable. What the evidence also shows is that the vaccines are not particularly effective at preventing transmission. After a relatively short period of time, measured in months after full vaccination, waning immunity allows for substantial transmission even though the vaccines remain highly effective at preventing serious illness. In short, the vaccines work amazingly well on the most important dimension.

The logic behind vaccine mandates rests on the idea of spillover effects. For vaccines that interrupt transmission, known as sterilizing, your vaccinated neighbours confer protection on you. Vaccines with a sterilizing property create what economists call an externality – the problem that gains based on private decision making alone do not capture the full benefit to society. In such circumstances there is a compelling argument for some level of state coercion to force people to adjust their behaviour. It’s ugly but sometimes necessary. For me to be on board, I have to see that violence or the threat of violence is absolutely necessary to achieve actual consequences which pass a cost benefit test with flying colours. Solzhenitsyn warned us that unlimited power in the hands of limited people always leads to cruelty.

Across Canada people who choose not to get vaccinated stand in front of the pointy end of the state’s monopoly on violence. Some are losing their livelihoods, and all are restricted from full participation in society. Perhaps that level of violence could easily be justified if the vaccines were sufficiently sterilizing, but we know they are not. The vast majority of the benefit from receiving the vaccine accrues to the person who receives it. It’s hard to make the case for coercion in these circumstances.

Whatever one might think of the vaccine hesitant or resistant, these people have the courage of their convictions. I think they are mistaken, but they are clearly not cowards, they are not hypocrites or virtue signallers. Is there any principle in your own life that you believe in so strongly that you would be willing to sacrifice your livelihood, your career, and your social standing? If I’m honest with myself, I don’t know if I’m that brave. Few are.

Even if you come down on the side of vaccine mandates, that despite the small and diminishing spillover effect that the vaccines confer, you still believe that coercion is worth it, we should all show more compassion and understanding with the vaccine hesitant and resistant. We should use our monopoly on violence with great reluctance, with great sadness, and with as much empathy as we can give. I don’t see compassion in my fellow citizen or in the approach used by our politicians and leaders. I see contempt and cruelty applied with alacrity to those who won’t get vaccinated. It makes me sad to see how ugly we are. I guess Solzhenitsyn was right, evil really does pass through every human heart.

Update: January 1, 2022

Contempt and cruelty applied with alacrity.

COVID-19 spring redux: more cowbell

Although we’re more than a year into the COVID-19 pandemic, our ability to protect vulnerable people hasn’t improved much. On a medical front, we’ve advanced with better triage, better treatments, and now a vaccination program – but our public policy looks pretty much the same as it did last spring, expect in Ontario, this time with enhanced police powers.

Ontario is seeing a tidal wave of new infections. While new variants apparently increase risk among younger demographics, the 60+ age group and those with comorbidities experience the majority of the severe illnesses and deaths. Earlier this month, Dr. Micheal Warner pointed out that a person under 50 dies from COVID-19 in Ontario ICUs every 2.8 days. That rate among the young is higher than in the past, but with a current Ontario COVID-19 death rate of about 20 per day, that means about 60 old people are dying for every person under 50, who almost certainly has comorbidities. It’s pretty clear that COVID-19 and its variants are vastly riskier for the elderly and those with comorbidities. Unfortunately, our vaccination program has a long way to go to protect the vulnerable.

Since this pandemic began, our governments at all levels have focused on lockdowns, school closures, travel restrictions, and curfews as the primary mechanism to control COVID-19 community spread. For the last year these policies have shifted most of the suffering onto the poorest people in our society – our essential workers – who are employed in everything from meat-packing plants to supermarkets. Even the homeless haven’t escaped. In January, Ottawa homeless shelters paused intake due to an outbreak among residents and staff. Not only have the poorest faced the brunt of COVID-19, but the vaccination programs have had the greatest penetration with the well-off. For all the rhetoric and all the treasure we’ve spent, we have not protected the vulnerable.

Is this the best we can do?

Last spring, our governments implemented emergency measures in a state of overwhelming panic. This time around, we appear to be recycling the same emergency policy playbook, and in the process, discarding a year’s worth of hard won knowledge about COVID-19. Public Health Ontario has publicly stated that focused measures to protect the vulnerable are not possible:

While age may be the major driver of differential mortality risk, there are important equity-based considerations in understanding risk of dying from COVID-19 in non-elderly populations if public health measures were to focus on the risk to the elderly only….Public health agencies globally have supported the use of physical distancing measures and lockdowns to control community transmission of COVID-19, recognizing that high community transmission renders protection or shielding of higher-risk populations virtually impossible due to the connections within the broader community in which they live. Further, an approach to strict isolation of at-risk populations can also be considered inhumane and unethical.

I am not sure how Public Health Ontario comes to the conclusion that shielding higher-risk populations is virtually impossible, but it certainly points to a lack of creativity and no sense of resolve. The situation reminds me of the Berlin Airlift.

In 1948, as the Cold War was getting started, the Soviet Union prevented all surface traffic from non-Soviet zones from entering West Berlin. Stalin hoped to drive the Western allies out of Berlin, undermine the Marshall Plan for rebuilding the German economy, and place the Soviet Union as the dominant power in Europe. At the time of the blockade, West Berlin had about a month’s worth of food and fuel. The Soviets figured it was impossible to keep West Berlin supplied and the West would quickly capitulate. We didn’t. We organized an airlift that kept West Berlin provisioned for 15 months. In the end it was the Soviet Union that relented. At its peak, the airlift had a plane landing in Berlin every 30 seconds, planes filled with everything the city needed from coal to potatoes. Our response to COVID-19 looks nothing like this.

Constructing an optimal policy should use all available information. We know who the most vulnerable are: the elderly and those with comorbidities such as obesity, hypertension, and diabetes. We must use all we know about COVID-19, pandemics, and public health more generally. Two points stand out:

1) We now know that, for those over age 70, the survival rate from COVID-19 is approximately 95%. That is a terrible problem. For the vast majority of us who are at little risk, the survival rate is at least 99.95% and most likely higher. Comorbidities also increase risk. Healthy people under age 25 have a survival rate of effectively 100%. That is, the high risk group is thousands of times more likely to suffer a severe outcome. Given the extreme differences in survival rates between different population subgroups, it would be surprising if the optimal policy did not include that information.

2) As a biological fact, all pandemics end by herd immunity either by natural infection, vaccination, or some combination of both. The optimal policy that ends the pandemic gets us to herd immunity with the least total harm. Covid-zero is not possible with such a widespread pathogen and the social determinants of health stretch well beyond modern medicine.

Implicitly, our governments are telling us that the first point is irrelevant. They are saying that the optimal policy that offers the best protection to the vulnerable from COVID-19 is to treat the disease as though the risk of severe illness or death is exactly the same for all people in society. Our governments have said that for all the money we’ve spent and for all the economic burden that we have placed on our children and the least financially well-off in our society, there is little that we can do differently. In their view, our polices are close to optimal, and that our knowledge of who is most affected by the virus is of no practical significance for public health policy development. Is it really true that no other policy which uses this information is feasible, politically or otherwise?

The second point has become hopelessly and needlessly politicized. Herd immunity has somehow been equated to a political statement. It is not; it’s biology. As the Harvard epidemiologist Martin Kulldorff says, “it’s weird and stunning to have this discussion about herd immunity—flockimmunitet in Swedish. You wouldn’t have physicists talking about whether we believe in gravity or not. Or two airline pilots saying, ‘Should we use the gravity strategy to get the airplane down on the ground?’ Whatever way they fly that plane—or not fly it—gravity will ensure eventually that the plane is going to hit the ground.” However we get there, herd immunity is the only thing that will end the pandemic.

So what would an optimal policy look like?

First, anyone who is at high risk and who has to work in settings ripe for spread should immediately be put on long term disability that replaces their wage. We should not be sending pre-diabetic, hypertensive, heavy-set 50+ year-olds to essential workplaces. We need legions of young healthy people to step up, train quickly, and fill in. If 20 year-olds with minimal training – often less than a few hours in a Spitfire or a Hurricane – won the Battle of Britain, we can find a way to use our young healthy population to replace high risk workers in everything from meat-packing plants to hospitals. Second, for those in the high risk group who cannot self-isolate, such as poor elderly immigrants in multi-generational homes, re-purpose our hotels. Again, have legions of young and low risk people isolate with them, on rotation, to run operations. Ensure high levels of testing. For those who can self-isolate, our army of young people can still help by delivering groceries, medications, and other necessities. Third, let everyone else go about their normal lives to the greatest extent possible – especially children in schools. As we vaccinate our high risk population with an ever expanding vaccination program, and as the virus spreads among the low risk group, we will reach herd immunity and the pandemic will end. The current policy looks very much like let it rip in slow motion.

Perhaps these ideas are infeasible; perhaps our current policies of lockdowns and curfews are the best we can do. Maybe ideas like mobilizing our young is impossible. Maybe it’s too late. But I challenge anyone to rigorously show that we could not have done better or that we can’t do better now.

With bold leadership and a call to civic duty, our accomplishments during WWII and at the beginning of the Cold War showed how we can do great things under enormous stress, against terrible odds, at extremely high stakes. From the Dunkirk Evacuation to the Berlin Airlift, we never accepted the answer “it’s virtually impossible”.

We’ve been told that our civic duty is to stay home, wear a mask during essential trips, and wait for a vaccine all the while we push Covid-19 onto vulnerable essential workers and their relatives.

I bet we can do better. Let’s focus our protection.

Ontario ICU arrivals and departures as a Skellam process

Figure 1: Net daily change in the Ontario ICU census with Skellam inferred rates. The red lollipop points are days of net inflow and blue lollipop points are days of net outflow. The red ribbon and blue ribbons are the inferred daily ICU arrival and departure rates from the Skellam process. Lockdown imposition and lifting dates indicated.

As Ontario enters a new lockdown, the main concern is a potential overrun of our ICU capacity. A year ago, the Ontario government announced a planned major expansion of provincial ICU capacity, but, given our current limits, it appears that either the plan never came to fruition or that the efforts woefully underestimated possible COVID-19 ICU demand. The Ontario COVID-19 data portal gives the daily ICU COVID-19 census from which we can compute daily changes. As of April 4, Ontario has 451 ICU patients associated with COVID-19. The daily changes give us the net flow but the counting does not tell us how many people actually arrived or departed each day. When we see a daily uptick of 25 people, is that 25 arrivals with no departures or is it 50 arrivals with 25 departures? Both scenarios give the same net change.

Even though the COVID-19 data shows only the net change, we can infer the arrival and departure rates using the Skellam distribution. The Skellam distribution is the difference of two Poisson distributions, k = n_1 - n_2, given by the convolution with a negative sum, namely,

(1)   \begin{equation*} s(k; \mu_1,\mu_2) = \sum_{n=-\infty}^\infty\, p(k+n; \mu_1) p(n; \mu_2),\end{equation*}

where s(k; \mu_1, \mu_2) has support on \{\ldots, -2,-1,0,1,2,\dots\}, and p(k;\mu) = \frac{\mu^k}{k!}e^{-\mu} is the Poisson. The resulting distribution can be expressed in terms of the modified Bessel function,

(2)   \begin{equation*}s(k; \mu_1, \mu_2) = e^{-(\mu_1 + \mu_2)}\left(\frac{\mu_1}{\mu_2}\right)^{k/2} I_{|k|}(2\sqrt{\mu_1\mu_2}) .\end{equation*}

I take the daily difference in the Ontario ICU census data and estimate the Skellam distribution over a 21 day sliding window. The Skellam parameters are the ribbons in figure 1, smoothed with cubic splines with cross validation, and superimposed on the daily net flow. The red ribbon is the arrival process and the blue ribbon is the departure process. Each lollipop point is the net change in the ICU occupation on that day. In figure 2 I show a Q-Q plot of the Pearson residuals from the Skellam model – the model is a reasonably good description of the data generating process. In my analysis I use the R packages Skellam and mgcv (for spline estimation). For clarity, I indicate the lockdown imposition and lockdown lift dates. As of early April 2021, it looks like we are approaching an average of 50 admissions to the ICU every day with an average departure of about 40.

Figure 2: Regression diagnostics

Causation is hard to determine in regressions such as this model, but we see that after the lockdown date on December 26, 2020, the arrival rate quickly plateaued only to begin rising again near the end of the lockdown period. It appears that the lockdown this winter had the effect of tempering arrivals into the ICU. But as always with statistics, we need to be cautious about making causal statements. The arrivals in the ICU are from people who were infected at an earlier date, probably in the neighbourhood of one week earlier. Thus, we see that the arrival rate remains high from the beginning of the lockdown on December 26 through the end of December and early January. We should expect this inertia from infections that occurred near or before the imposition of the lockdown, although there is a distinct possibility that people started to change their behaviour before the lockdown date. But notice that the arrival rate begins to rise sharply almost exactly coincidental with the end of the lockdown on February 16, 2021. This observation suggests that infections were beginning to accelerate at least a week, maybe two, prior to the end of the lockdown. It appears that we would have seen a surge at some level in Ontario’s ICUs even if the lockdown had been maintained through the end of February or longer. Of course it’s quite probable that the resulting surge would have been smaller than the one we are currently witnessing, but to gain insight into such a counterfactual we need to know what caused the acceleration in infections prior to the end of the lockdown. If infections started to rise before the end of the lockdown, is it the result of the new more contagious variants? Is it lockdown fatigue? Is it spread among essential workers? Maybe it’s a combination of effects; I don’t know. Lockdown efficacy rests on that understanding.

Notice that the arrival process turned downward, or at least plateaued, about two weeks after the lockdown date of December 26, 2020, but also notice that the daily number of departures has been steadily increasing throughout the entire winter. Of course we expect that as arrivals increase, departures will eventually increase as well – everyone who enters the ICU eventually leaves. In a steady-state queue, the average departure rate will equal the average arrival rate. With time variation in the arrival process the departure rate will lag as the arrival rate waxes and wanes. It might be instructive to think about the average server load (ICU occupation) of an M/M/c queue (exponentially distributed arrival time, exponentially distributed server times, with c servers) as an approximation to the ICU dynamics. In an M/M/c queue the average number of busy servers (ICU bed occupation) is,

(3)   \begin{equation*} \bar c = \frac{\mu}{\tau}, \end{equation*}

where \mu is the arrival rate and \tau is the average service rate. For example, given an arrival rate of 50 people per day and an average length of stay of 14 days in the ICU, the steady-state average number of people in the ICU would be 700 patients, provided the number of beds (servers) is larger than 700. I don’t know if the length of stay has been varying over time. It would be great to do a full time dependent competing risk survival analysis on that data, but the steady rise in the departure rate that we see over the winter might indicate that the length of stay in the ICU has also been changing with the arrival rate. I don’t know.

There are a number of ways to extend this work. The estimator is crude – instead of a naive 21 day sliding window, it could be built with a Bayesian filter. The Q-Q plot in figure 2 shows that the naive sliding window generates a good fit to the data but if we want to back-out robust estimates of the timing of the infections associated with the arrivals, it might be worth exploring filtering. Second, it is possible to promote the parameters of the Skellam process to functions of other observables such as positive test rates, lagged test rates, time, or any other appropriate regressor and then estimate the model through non-linear minimization. In fact, initially I approached the problem using a polynomial basis over time with regression coefficients, but the sliding window generates a better fit.

Where does this leave us? The precipitous drop in ICU arrivals throughout the summer of 2020 with low social distancing stringency and no lockdowns, along with the steady rise in arrivals beginning in the fall, suggest that Covid-19 will become part of the panoply of seasonal respiratory viruses that appear each year. Hopefully with the vaccines and natural exposure, future seasonal case loads will occur with muted numbers relative to our current experience. Given that the largest mitigating effect, next to vaccines, seems to be the arrival of spring and summer, lockdown or not, the warming weather accompanied by greater opportunities to be outdoors should have a positive effect. Covid-19 cases are plummeting across the southern US states like Texas and Alabama, yet cases are rising in colder northern states like New York and New Jersey. While increased herd immunity in the US from higher levels of vaccination and higher levels of natural exposure must be having an effect on reducing spread, it really does seem like Covid-19 behaves as a seasonal respiratory illness. Hopefully we can expect better days ahead, but, in the end, it is very hard to maintain a large susceptible population in the face of a highly contagious virus that has already become widespread. Perhaps we should have been looking for better public health policies all along.

COVID-19 death count conspiracy theories don’t add up, but won’t someone think of the children?

The Canadian media reminds us daily of the COVID-19 death count. They never fail to mention each time we reach a grim milestone. But I got to thinking, how are COVID-19 deaths really counted? What is the effect size on mortality? In some cases it might be obvious, but I am sure there are many medical cases which are difficult to label, especially since severe illness from COVID-19 strongly tracks the febrile, people with comorbidities, and people of advanced age. Are we under-counting or over-counting COVID-19 deaths? Conspiracy theories abound with wild claims about COVID-19 inflated death counts.

One way we might be able to help calibrate our counting is looking into changes in the Canadian mortality rate. Sure, labelling a COVID-19 death might be difficult, but counting deaths themselves should be much easier. Statistics Canada has several weekly mortality time series for the Canadian population. Using the website https://www.mortality.org/, I download the Statistics Canada mortality data. I have no way of determining the data accuracy, but I will assume that the data are complete enough for my modelling purposes. As always, conclusions are only as good as the data we have.

The first plot shows the raw Statistics Canada mortality rate data. The data are split across cohorts along with the total population. We see some interesting patterns. First, the mortality rate in Canada has been increasing over the last ten years. This increase is not surprising as Canada’s median age is increasing – the effect is probably due to our aging population. Second, the death rate in our oldest cohorts is decreasing. We are probably seeing healthier people reaching these cohorts each year given that smoking rates decreased over the last 30 years and we are probably also seeing the effect of better medicine. That we see declines in the mortality rate of the oldest cohorts but an increasing rate for the entire population is an example of Simpson’s Paradox. The fraction of the Canadian population entering the oldest cohorts is increasing, but we all die at some point!

Annualized Canadian mortality rates by cohort with weekly observations.

A casual glance at the plot doesn’t seem to scream a large COVID-19 effect in 2020, but we have to be careful – looks can be deceiving. We have a long term trend superimposed on a noisy periodic time series and we are trying to detect changes at the tail end of the process. A nice way to proceed is to use generalized additive models (GAM). I will be using Simon Wood’s mgcv R package.

The model I have in mind is a GAM with a cyclic cubic spline with a 52 week period, s_1, and a trend spline, s_2,

(1)   \begin{equation*}\text{rate}_i = s_1(\text{week.number}_i) + s_2(\text{time}_i) + \epsilon_i.\end{equation*}

It’s a simple model, but it should be able to pull out a signal or trend, if one exists.

Given that COVID-19 has proven more dangerous to the 75-84 year old cohort, I will start there. The second plot shows the results of the model normalized to the downward linear drift in the data. My model does well fitting the data – well enough to understand the broad features – but an examination of the residuals, while normal in their distribution, exhibit some autocorrelation. There is subtle time series structure that my model misses but for the purposes of detecting the long term trend, this model does reasonably well. We see that the cyclic part peaks during the fall/winter, and the spline trend term sharply moves up through 2020, the effect from COVID-19. The trend component also shows the years with a particularly strong flu season.

GAM: Cyclic and trend components with normalized mortality data for 75-84 year old cohort.

In the next figure I show the long term trend in the mortality rate for the 75-84 year old cohort relative to the background. We see that COVID-19 has lifted the mortality rate for this group by about 4.5%, about 4 times the effect of a bad flu year. The final figure shows the long term trend with the original data. Repeating this analysis for the entire population, we see that the over all effect of COVID-19 on the Canadian population is to lift the mortality rate by about 5% above background. We can see the effect in the next two figures.

GAM trend component relative to the background mortality rate in the 75-84 year old cohort.

This helps us answer the question about over counting. If the effect is about 5% and if it sustains for all of 2020, given that about 280,000 Canadians died in 2019, the results suggest that the annual total COVID-19 effect is 15,000 excess in Canada. While it looks like the current official number of 21,000 COVID-19 deaths might be a little bit high, we need to caution that conclusion based on substitution effects. People travelled less in 2020, so some types of accidents are probably down with deaths from COVID-19 making up part of the difference. Those types of substitution effects would mask the severity of COVID-19 in the mortality rate data. On the other hand, there are other substitution effects, such as self-harm, that have probably increased over 2020, which push up the overall mortality rate from non-COVID-19 (or at least indirect) causes. A much more detailed analysis of all the substitution effects would be required to really know just how much over or under counting is present in the COVID-19 death totals. The official count broadly concords with my simple GAM analysis on the mortality rate. My guess is that if there is bias in the official tally, it would probably lean a touch in the over counting direction, but nothing like the crazy conspiracy theories.

GAM: inferred trend in the mortality rate for the 75-84 year old cohort.
GAM: inferred trend in the mortality rate for all Canadians.

The shocking part of what the data teach us is in the 0-14 year old cohort. I repeat the same analysis and show the long term trend in the figures below. We see that in 2020, the mortality rate for children under 15 years old is up over 20%! That equates to approximately an extra 10 childhood deaths each week across Canada. We know that COVID-19 has a very low mortality rate with children, lower in fact than the seasonal flu, and yet we see a dramatic rise in childhood mortality in the data. This analysis is not causal, but if COVID-19 is an unlikely culprit, it must be some other environmental factor. We know that child abuse and domestic violence has increased as the result of stay-at-home orders. Teachers and school staff have a difficult time detecting abuse and neglect in online classes. When this pandemic ends, it will be very much worth while combing through the 0-14 year old cohort data and unpacking the effects of COVID-19 mitigation efforts on childhood well-being.

GAM trend component relative to the background mortality rate in the 0-14 year old cohort.
GAM: inferred trend in the mortality rate for children under 15 years old.

The CBC and the chattering class

A few months ago I wrote a blog post about the limits of science in forming public policy. Since then the chattering class has only gotten worse and the CBC cheerleads it all the way.

On Thursday November 26, the CBC ran an article Secret recordings reveal political directives over Alberta’s pandemic response in what can only be described as form of gutter-level journalism that will serve to damage the working relationships between Alberta’s scientific advisors, specifically Dr. Deena Hinshaw, and government decision makers in the response to COVID-19. The CBC provides a platform to University of Alberta associate law professor Ubaka Ogbogu who, quoted in the article, said “If the government is not following scientific advice, if it is not interested in measures that will effectively control a pandemic that is killing Albertans, then Hinshaw owes us the responsibility of coming out and saying, ‘They are not letting me do my job’…The focus needs to be on the disease, on how you stop it, not the economy. Nothing is more important.” On Friday the CBC followed up with a response from Dr. Hinshaw, who feels personally betrayed, and added, “I was not elected by Albertans. The final decisions are up to elected officials who were chosen by Alberta. This is how democracy works.” Dr. Hinshaw is the only professional in this sordid mess.

With their article, the CBC is appealing to the I-believe-the-science crowd, an intolerant wokeist slogan that reflects a distrust in democracy, incrementalism, consensus building, and an attitude with little recognition for the difficulties in real decision making. Increasingly, the new chattering class feels that the job of our elected officials is to hand the keys of the state over to the “experts” obediently accept “solutions” (I believe the science, after all) and leave the room. Our democracy doesn’t work that way for a reason – experts are not accountable like our elected officials. Liberal democracy may not be perfect, but it has given us a quality of life unprecedented in human history with stability and peace that is the envy of the world. Accountable legislatures are among our institutions that make it all possible. You’d think that this ground would have been covered in middle school. I hope the forthcoming investigation finds those responsible for the leak, and if they are civil servants, fire them.

As a scientist, I really detest this trend of looking to science to provide the answer to our social and moral questions. From COVID-19 to climate change, the chattering class appeals to “settled science” as a mechanism to prescribe policy solutions. Science can do no such thing. Scientific discoveries by themselves do not have moral implications. This wokester attitude of believing-the-science for public policy is not unlike the 15th century Catholic Church’s persecution of Galileo in reverse. What we discover about the world does not tell us what we should do or how we should treat our fellow human beings. When it comes to public policy, science cannot make the decision for us. In the public sphere everything is a trade-off. Those trade-off decisions create suffering and make losers out of some people regardless of which choice we make. How we balance that suffering – how we gain the acceptance of those who lose – is part of the grand bargain built into our liberal democracy. It’s how we create legitimacy. That’s not a scientific question! Believe-the-science is nothing but vacuous wokeist sloganeering.

With COVID-19, our elected officials have a monstrously difficult task. Science is an input, but it cannot offer the solution. COVID-19 mitigation strategies will cost lives no matter what we do. Our polices risk a debt crisis, falling productivity, business destruction, and a potential for the gutting of human capital formation with long term consequences. Balancing those choices and risks against protecting society from the immediate harm of COVID-19 is not obvious; it’s not as easy as professor Ogbogu would have us believe. A policy that saves as many near-term lives as possible, damn the consequences, is a moral choice, a political choice, not a scientific one. In a liberal democracy our elected representatives make decisions that best reflect our collective values. The CBC did us all a disservice by reporting these secret recordings. The CBC undermined Alberta’s efforts to build legitimacy and made Dr. Hinshaw’s job even more difficult than it already is.

Shame on the CBC.

I met Ezekiel Bulver last month

Richard Feynman once said, “I’ve concluded that it’s not a scientific world.” He observed that people often believe so many wonderful things that the real message behind the scientific method has failed to percolate through societya method of systematic doubt in which nothing is ever certain and concepts only ever reside on a graduated scale somewhere between, but never at the ends of, absolute falsity or absolute truth. He saved his worst scorn for the many scientists who, by their training, are supposed to know better. In my experience, little has changed in the nearly half century since his remarks.

I have the opportunity to share my work on COVID-19 and interact with epidemiologists from around the country and around the world, yet the most shocking part of my experience is running into Ezekiel Bulver. C.S. Lewis met him first:

...Ezekiel Bulver, whose destiny was determined at the age of five when he heard his mother say to his father—who had been maintaining that two sides of a triangle were together greater than a third— “Oh you say that because you are a man.” “At that moment”, E. Bulver assures us, “there flashed across my opening mind the great truth that refutation is no necessary part of argument. Assume that your opponent is wrong, and explain his error, and the world will be at your feet. Attempt to prove that he is wrong or (worse still) try to find out whether he is wrong or right, and the national dynamism of our age will thrust you to the wall.” That is how Bulver became one of the makers of the Twentieth Century.

Of course Bulver never existed, he is a rhetorical device created by C.S. Lewis himself, but this behaviour, bulverismthe logical fallacy of assuming someone’s argument is invalid or false at the outset, and then attempting to explain how the person became so mistaken by hypothesizing about her beliefs, psychology or motives, with no regards to the actual argument itselfhas no place in scientific discourse. Bulversim gets us nowhere. The other side could just as easily use the argument against you. Not only is bulverism disrespectful but it’s pure foolishness. C.S. Lewis again,

If you try to find out which [ideas] are tainted by speculating about the wishes of the thinkers, you are merely making a fool of yourself. You must first find out on purely logical grounds which of them do, in fact, break down as arguments. Afterwards, if you like, go on and discover the psychological causes of the error...You must show that a man is wrong before you start explaining why he is wrong.

Bulverism is antithetical to the scientific method and scientists who use it have stopped being scientists. You would’ve embarrassed yourself in front of Feynman practicing it. Arguing that papers or ideas on COVID-19 from highly respectable epidemiologists and other researchers, who argue in good faith, should be ignored at face value because of perceived ideology or inferred political beliefs is not science. There is plenty of uncertainty around COVID-19 and plenty of room for legitimate scientific disagreement. If we want to serve the public good, let’s stop inviting Mr. Bulver to the conversation.

Are lockdowns effective at stopping Covid-19?

My data science team continues to research COVID-19 propagation and measures that we can take in work environments to limit spread. We keep a sharp eye on the literature for interesting and novel statistical techniques applied to COVID-19 data and we recently came across a wonderful paper by Simon N. Wood. Readers of this blog might recognize Professor Wood’s name from a previous blog post where I promoted his book on Generalized Additive Models.

In his new paper Did COVID-19 infections decline before the UK lockdown?, Professor Wood examines the arrival dates of fatal infections across the England and Wales and determines when fatal infections peaked. He finds that fatal infections were in substantial decline at least five or six days before the lockdowns started. Furthermore, he finds that the fatal infection profile does not exhibit a regime change around the lockdown date and that the profile for England and Wales follows a similar trajectory as Sweden. The result here is important because Professor Wood focuses on the most reliably collected data – deaths due to COVID-19. Studies that focus on case counts to infer epidemiological parameters are always compromised by data that is highly truncated and censored, often in ways that are largely unknown to the researcher. While we can gain some insight from such data, results are often as informed by prior beliefs as much as by the data itself leaving us in an unfortunate position for constructing scientifically based policy.

Death data are different. In this case, the clinical data directly measure the epidemiological quantities of interest. Death data from COVID-19, while not perfect, are much better understood and recorded than other COVID-19 quantities. To understand the effect of interventions from lockdowns, what can we learn from the arrival of fatal infections without recourse to strong modelling or data assumptions? This is where Professor Wood’s paper really shines.

Before discussing Professor Wood’s paper and results, let’s take a trip down epidemiological history lane. In September 1854, London experienced an outbreak of cholera. The outbreak was confined to Broad Street, Golden Square, and adjoining streets. Dr. John Snow painstakingly collected data on infections and deaths, and carefully curated the data into geospatial representations. By examining the statistical patterns in the data, questioning outliers, and following up with contacts, Dr. Snow traced the origin of the outbreak to the Broad Street public water pump. He made the remarkable discovery that cholera propagated through a waterborne pathogen. The handle to the pump was removed on September 8, 1854, and the outbreak subsided.

But did removing the pump handle halt the cholera outbreak? As a cause and effect statement, Dr. Snow got it right, cholera transmission occurs through contaminated water, but evaluation of the time series data show that the removal of the handle of the Broad Street water pump is not conclusively linked to the cause of the outbreak subsiding. Edward Tufte has a wonderful discussion of the history of Dr Snow’s statistical work in Visual Explanations. 5th edition. Cheshire, Connecticut: Graphics Press, 1997, Chapter 2, Visual and Statistical Thinking: Displays of Evidence for Making Decisions. Let’s look at the time series of deaths in the area of London afflicted by the cholera outbreak in the plots below.

From Tufte: Visual Explanations

We clearly see that deaths were on the decline prior to the pump handle’s removal. People left the area, and people modified their behaviour. While the removal of the pump handle probably prevented future outbreaks and Dr. Snow’s analysis certainly contributed heavily to public health, it’s far from clear that the pump handle’s removal was a leading cause in bringing the Broad Street outbreak under control. Now, if we aggregate the data we can make it look like removing the pump handle was the most important effect. See the lower plot in the above figure. Tufte shows what happens if we aggregate on a weekly basis, and the confounding becomes even greater if we move the date ahead by two days to allow for the lag between infection and death. With aggregation we arrive at a very misleading picture, all an artifact of data manipulation. Satirically, Tufte imagines what our modern press would have done with Dr. Snow’s discovery and the public health intervention of removing the handle with the following graphic:

From Tufte: Visual Explanations

Fast forward to 2020 – Professor Wood is our modern day Dr. Snow. The ultimate question that Professor Wood seeks to answer is: When did the arrival of fatal infections peak? He is looking to reconstruct the time course of infections from the most reliable data sources available. We know from the COVID-19 death data that deaths in the UK eventually declined after the lockdowns came into effect (March 24, 2020) which seems to point to the effectiveness of the intervention. But an infection that leads to a fatality takes time. Professor Wood builds a model, without complex assumptions, to account for this lag and infer the infection date time series. He works with COVID-19 death data from the Office of National Statistics for England and Wales, the National Health System hospital data, and the Folkhälsomyndigheten daily death data for Sweden. In the figure below we see his main result: In the UK, COVID-19 fatal infections were in decline prior to the lockdowns, peaking 5 to 6 days earlier. The UK profile follows Sweden which did not implement a lockdown.

From Simon N. Wood: https://arxiv.org/abs/2005.02090

The technique he uses is rather ingenious. He uses penalized smoothing splines with a negative binomial counting process, while allowing for weekly periodicity. The smooth that picks up the trend in deaths is mapped back to the arrival of the fatal infections using the distribution of infection to death. Based on hospitalization data and other sources, the distribution is well described by a lognormal with a mean of 26.8 days and standard deviation of 12.4 days. The mapping matrix that uses the distribution is near singular but the smoothing penalty handles this problem.

One might be tempted to think that the time series reconstruction might be biased in the sense that an intervention will always see the peak behind the intervention date and that the distribution of time until death from a fatal infection smears the the peak backward. Thus, we might be fooled into believing that a peak with a decline through the intervention date might not be caused by the intervention when in fact the effect was generated by the intervention with a sharp discontinuity. Professor Wood model checks with simulated data in which fatal infections arrive at high rate and then plummet at a lockdown intervention. He then tests how well the method captures the extreme discontinuity. We can see that method does very well in picking up the discontinuity in the figure below.

From Simon N. Wood: https://arxiv.org/abs/2005.02090

There are issues that could undermine the conclusions and Wood expounds on them in his paper. The problem of hospital acquired infections is important. People already in the hospital are often weak and frail and thus the duration of COVID-19 until death will be shortened should they become fatally infected. Professor Wood is focusing on community transmission since it is this effect that lockdowns and social distancing targets. Hospital acquired transmissions will bias the inference, but the proportion of hospital acquired infections in the death data would have to be quite high for it to radically alter the conclusions of Wood’s results. He discusses a mixture model to help understand this effect. There are also problems concerning bias in the community acquired fatal disease duration including the possibility of age dependent effects. Again, to substantially change the conclusions, the effects would have to be large.

Professor Wood is careful to point out that his paper does not prove that peak fatal infections occurred in England and Wales prior to the lockdowns. But the results do show that in the absence of strong assumptions, the most reliable data suggest that fatal infections in England and Wales were in decline before the lockdowns came into effect with a profile similar to that of Sweden. Like Dr. Snow’s pump handle, the leading effects that caused the decline in deaths in the UK may not have been the lockdowns, but the change in behaviour that had already started by early March, well before the lockdowns.

Professor Wood’s results may have policy implications and our decision makers would be wise to include his work in their thinking. We should look to collect better data and use similar analysis to understand what the data tell us about the effectiveness of any public health initiative. At the very least, this paper weakens our belief that the blunt instrument of lockdowns is the primary mechanism by which we can control COVID-19. And given the large public health issues that lockdowns also cause – everything from increased child abuse to future cancer patients who missed routine screening to increasing economic inequality – we must understand the tradeoffs and the benefits of all potential actions to the best of our ability.

Covid-19 and decisions under uncertainty

Three excellent essays recently appeared in the Boston Review by Jonathan Fuller, John Ioannidis, and Marc Lipsitch on the nature of epidemiology, and the use of data in making public health decisions. Each essay makes great points, especially Professor Ioannidis’ emphasis that Covid-19 public health decisions constitute trade-offs – other people will die based on our decisions to mitigate Covid-19. But I think all of all three essays miss the essential question, which transcends Covid-19 or even public health:

What is the optimal way to make irreversible decisions under uncertainty?

The answer to this question is subtle because it involves three competing elements: time, uncertainty, and irreversibility. In a decision making process, time gives us the opportunity to learn more about the problem and remove some of the uncertainty, but it’s irreversibility that makes the problem truly difficult. Most important problems tend to have a component of irreversibility. Once we make the decision, there is no going back or it is prohibitively expensive to do so, and our opportunity to learn more about the problem is over.

Irreversibility coupled with uncertainty and time means there is value in waiting. By acting too soon, we lose the opportunity to make a better decision, and by waiting too long, we miss the opportunity altogether. Waiting and learning incurs a cost, but that cost is often more than offset by the chance to make a better and more informed decision later. The value of waiting in finance is part of option pricing and that value radically changes optimal decision making. There is an enormous amount of research on option valuation with irreversible decisions. The book Investment Under Uncertainty by Avinash Dixit and Robert Pindyck provides a wonderful introduction to the literature. When faced with an irreversible decision, the option value can be huge, even dwarfing the payoff from immediate action. At times, learning is the most valuable thing we can do. But for the option to have value, we must have time to wait. In now-or-never situations, the option loses its value completely simply because we have no opportunity to learn. The take-a-way message is this: the more irreversible the decision, the more time you have, and the more uncertainty you face, the larger the option value. The option value increases along each of these dimensions, thereby increasing the value of waiting and learning.

Covid-19 has all of these ingredients – time, uncertainty, and irreversibility. Irreversibility appears through too many deaths if we wait too long, and economic destruction requiring decades of recovery if we are too aggressive in mitigation (while opening up global financial risks). There is a ton of uncertainty surrounding Covid-19 with varying degrees of limited time windows in which to act.

Those who call for immediate and strong Covid-19 mitigation strategies recognize irreversibility – we need to save lives while accepting large economic costs – and that even though we face enormous uncertainty, the costs incurred from waiting are so high compared to immediate action that the situation is ultimately now-or-never. There is no option value. Those who call for a more cautious and nuanced approach also see the irreversibility but feel that while the costs from learning are high and time is short, the option value is rescued by the enormous uncertainty. With high uncertainty, it can be worth a lot to learn even a little. Using the lens of option valuation, read these two articles by Professor Ioannidis and Professor Lipsitch from this March and you can see that the authors are actually arguing over the competing contributions of limited time and high uncertainty to an option’s value in an irreversible environment. They disagree on the value of information given the amount of time to act.

So who’s right? In a sense, both. We are not facing one uncertain irreversible decision; we face a sequence of them. When confronted by a new serious set of problems, like a pandemic, it can be sensible to down-weight the time you have and down-weight the uncertainty (by assuming the worst) at the first stage. Both effects drive the option value to zero – you put yourself in the now-or-never condition and you act. But for the next decision, and the next one after that, with decreasing uncertainty over time, you change course, and you use information differently by recognizing the chain of decisions to come. Johan Giesecke makes a compelling argument about the need for a course change with Covid-19 by thinking along these lines.

While option valuation can help us understand the ingredients that contribute to waiting, the uncertainty must be evaluated over some probability measure, and that measure determines how we weigh consequences. There is no objectively correct answer here. How do we evaluate the expected trade-off between excess Covid-19 deaths among the elderly vs a lifetime of lost opportunities for young people? How much extra child abuse is worth the benefit of lockdowns? That weighing of the complete set of consequences is part of the totality of evidence that Professor Ioannidis emphasizes in his essay.

Not only does time, uncertainty, and irreversibility drive the option value, but so does the probability measure. How we measure consequences is a value judgment, and in a democracy that mesaure must rest with our elected officials. It’s here that I fundamentally disagree with Professor Lipsitch. In his essay, he increasingly frames the philosophy of public health action in terms of purely scientific questions. But public action, the decision to make one kind of costly trade-offs against another – and it’s always about trade-offs – is a deeply political issue. In WWII, President Truman made the decision to drop the bomb, not his generals. Science can offer the likely consequences of alternative courses of public health actions, but it is largely silent on how society should weigh them. No expert, public health official, or famous epidemiologist has special insight into our collective value judgment.