All numerical examples in this document are, unless otherwise specified, constructed examples. The writer does not ‘know’ what will happen next, not being favored with the gift of prophecy
PROJECTIONS
All statistical projections are based on:
- known numerical patterns such as exponential growth curves, normal distribution curves, and other patterns derived from real events;
- examples of similar events in the past; and
- assessment of the accuracy and variability in the data from the new event.
From this you can work out which past events the new event most resembles, and which mathematical pattern seems most probable.
Other factors to be included when measuring systems involving biology and human behavior are:
- how much behavior will be altered by new factors – the feedback loop between information and behavior; and
- how much the underlying conditions are changing during the process of data capture. Bacteria and viruses are not ball bearings; they alter and mutate in reaction to external conditions, such as antibiotic use, or simple normal genetic ‘shuffling.’
The ‘Black Swan,’ which Nassim Nicholas Taleb has so memorably called the unexpected event that no one prepared for, is an illuminating case.
Until Captain Cook visited Australia, all swans known in the Western world were white. The only black swans were mythical creatures of doom, like the Swan of Tuonela in Finnish myth, and they were black to show demonic associations. If you asked if a real black swan was possible, people might have asked if you hunted unicorns too. In physical terms, a black swan is, and has always been, possible, because that is down to melanin in the feathers. The probability, on the Western evidence, was low, but it could not be zero because the mechanism (melanin) existed to create a black swan. However, in the eighteenth century, no-one knew about melanin.
So just because we cannot imagine something, it does not mean it cannot exist. All projection work has to be aware that this time COULD be different. We will fail if we allow pre-existing prejudices and an over-rigid approach to how we set up models to create a situation where we can only ‘see’ what has happened before and fits comfortably with our world view. However, the stock market saying that ‘This time is different’ – the 4 most expensive words in the language – also need to be in the mix.
Making ‘different’ an excuse for not having examined the underlying evidence is not enough, because the temptation is then to say, ‘It’s so different, we can’t learn from it.’ Or, in other words, “Dear Boss, this was not my fault. Who knew? Better luck next time.”
WHERE ARE WE IN THE CURVE?
We are about 3-4 months into the COVID-19 outbreak. The disease appears to move fast, but have a similar mortality rate to other winter flu epidemics. The problem that has been caused is from the speed of infection, not necessarily its fatality; it has stripped health systems of equipment and beds at the same time as making medical staff fall ill. Fast-moving infections run through a population quickly, but meet the limits of infection earlier. Note that the number of people infected in the end may be no more or less than for a slow-moving infection and there is not necessarily a correlation between speed of infection and fatality.
Most ‘flu seasons’ are 6-7 months long, which suggests that peak infection will be about June. The change in fatalities and infections would then show up about May (see worked example below), but until we have a better fix on the rates of infection, serious infection and fatality, this can only be a suggestion based on previous experience. When the change in cases happens, it will happen fast, for mathematical reasons. Put a large bet now on naming the first politician who will claim that this is because of their ‘drastic action’ or ‘special measures.’
The disease appears to last about 2 weeks if there are no complications. The older and sicker someone is when they get the disease, the more likely they are to have complications such as pneumonia. High death rates in countries like Italy may have several reasons, but the larger proportion of elderly people will be a big one. If you are going to catch it, you are most likely going to get it from the person you share a bed with, not the guy on the other side of the football stadium. Quarantining people into small groups may stop the spread outside groups, but exacerbate infection within the group. The author has her own views on shutting down economies by preventing the movement of healthy people when you do not know the level of infection or the true risk of fatality.
The physical spread should end in mid-year, but the economic damage has been very substantial and may not be reparable within a year. Some industries may be entirely reshaped – such as airlines and long-distance tourism and this dislocation has brought forward an economic downturn which many expected anyway. The main problem after June is not the sickness, but the economic recession we now face.
THE VIRUS: HEALTH PROJECTION
THERE IS NEVER ENOUGH DATA
For a new disease, at the start of an infection, there is no data.
Tracing the start point to what is often called ‘Patient Zero’ does not necessarily give you a disease trajectory. AIDS has now been traced back to the early 1960s and maybe even before, but the take-off point for mass infection was a lot later.
What matters are the rates:
- the rate of infection;
- the rate of serious illness after the infection; and
- the mortality rate.
THE FOLLOWING IS A WORKED EXAMPLE
The population is 1000. Rates below are modelled on the apparent rates for coronavirus or a serious flu:
- The rate of infection is 1 to 3 (every infected person will infect 3 others, while they are infectious).
- The infectious period is 1 week.
- The sickness period is 2 weeks.
- Deaths occur in the second week of sickness.
- Once infected and recovered, the patient has immunity.
- The rate of fatality among the infected is 2%, based on latest WHO data.
- The general rate of fatality from all other causes is 1% per year.
WHAT IS THE DISEASE PROGRESSION?
In a normal year, 10 people would die of other causes.
End of outbreak. The virus ran out of people to infect in week 5. The highest number of people who can die from the disease with 2% fatality across 1000 people is 20.
COMMENT
- This will be an over-estimate, as in a group of 1,000, it is unlikely that an infectious person will carefully select only the uninfected or non-immune to whom to pass their disease. The potential spread rate has to assume some failed infections as well.
- The ‘excess’ deaths in annual figures will be no more than 20. However, it may be that all 10 of the people who would have died are now recorded as dying of the virus. The deaths recorded will then be 10 more than expected. If the pass-on rate is lower, because of ‘unsuccessful’ infections, then the extra deaths will be lower too.
- If the rate of infection is faster, because each person infects e.g., six rather than three, then the progress will be faster, but the virus will run out of uninfected people sooner. The rate of death will be the same (2%).
- Only if the rate of mortality gets higher, will more people die. The rate change in infection may cause a peak to happen sooner, but it does not kill more people.
- If a brake is put on the rate of infection, by ‘distancing’ or other measures, the fatality rate does NOT alter, but the length of time of the outbreak is extended. This means fewer seriously ill people turning up in hospital at one time.
- Re-infection rates need to be added, but in a largely immune population (or a vaccinated one) these will be low. The seriousness of a re-infection is not necessarily higher than for a first infection.
- The mortality rate in this example is not a function of the rate of spread: mild illnesses can spread as fast as serious ones. If the mortality rate dropped to 1%, 10 fewer people would die, but the same number would have the illness. And the annual statistics might show no trace of the outbreak in deaths at all.
- (Please feel free to change the assumptions for your own calculations, but keep in line with reported data).
- If people die in week 1 rather than week 2, the capacity of the outbreak to spread is reduced. If people are infectious for longer, it can spread faster, but the mortality rate remains the same.
- ‘Herd immunity’ kicks in over a long outbreak. It does not show up in the initial weeks. By the end of the example outbreak, all survivors have immunity, but by week 5, it was 39%, and there was still a large pool of uninfected and non-immune people as of week 4. ‘Herd immunity’ has different rates for different diseases, but is normally designated at 70% immunity and higher
PROJECTING THE CURVE FOR CORONAVIRUS
The number of illnesses or deaths does not tell you what the curve is, unless you also know the number of infections, the proportion of these which are serious, and the rate at which immunity is developing.
If there are lots of people dying, you may have:
- a more widespread infection than you thought, which may be ‘invisible’ in some subjects;
- an infection which has a different method of transmission than you thought;
- a fatality rate which is higher than you thought.
In case 1, the scale has been underestimated, not necessarily the fatality.
In case 2, you may not be looking at the right things to control spread. Never assume. It is not hot weather that brings plague, but rats and their infected fleas, and fleas like hot summers.
In case 3, fatalities are always a shock, but they happen for a reason. Reactions to deaths still need to be about identifying the true cause.
If case 1 is also highly infectious, it will run through the available subjects fast, and death rates will drop suddenly (see week 7 above).
If case 1 is a slow infection, death rates will NOT drop very fast.
In case 2, whatever you do may seem not to work and this will cause panic. Identification of the error is vital.
In case 3, there needs to be a reset on the expectations for the disease, but check the rate of spread, because this may not have changed. Fatalities will not fall more than the model suggests unless catching a case early makes a difference to mortality rates, because you have a good treatment.
TESTING
Sometimes, early testing makes a difference to medical intervention. Sometimes, however, it does not.
Testing is a vital part of mapping the spread of diseases, and estimating factors such as immunity, or the impacts on general health, or re-infection rates, but unless you select what you are testing for very carefully, it may not tell you anything you did not know, or add any useful information.
Testing is not always of immediate medical use.
If you have a patient who has difficulty breathing, you give them a respirator before you give them a test. You can see what the problem is, and you know delay is dangerous.
If you have no good treatment for a disease, testing does not help you. You now have a patient where you know what the disease is, but you still have no treatment (a lot of neurological conditions are like this).
In tracing the curve for an epidemic, testing – which needs only be on a sample, not an entire population – gives a truer reading for rates of infection, spread and mortality, which can be used to plan and place resources. It does not change the medical treatment of those who fall ill.
Once you have done the sample survey, you do not need to test again for base information, unless you wish to track numbers. Rates of mortality for a given disease are not likely to alter much in the short term, as this is not a Hollywood movie. Spread may change, if the methods being used to contain it are ineffective.
Yet testing healthy individuals to get a nil result is a doubtful use of resource:
- If it is nil because they are uninfected, unless you have a vaccine, all you can do is tell them to take care.
- If they are immune, this is useful information and they can go back to work.
- However, if the rate of immunity is low, you may spend a lot of effort testing people who turn up nil.
Focusing testing on areas where it will make a difference, where immunity is useful (e.g., in medical staff and other key workers) must be a priority over people who are already ill (because you know they are ill), or people who are not ill.
Vaccines are rarely 100% effective, and most are not a treatment if you are already infected. If you are immune, you do not need one. If vaccines can be developed within the timescale of an outbreak, they are most useful for key workers and the highly vulnerable. Most vaccines have taken a year or more to create and test for safety.
MEASURING DEATH
Lots of people get ill or die every day; the question is whether the rate at which they are dying or getting ill is higher because of an outbreak.
Now for some unpleasant calculations. This is not how most people choose to think of their lives, but actuaries and insurance companies do this all the time and have been doing it for three centuries.
Every breath you take could be your last. Most of the time, it isn’t. One day, it will be.
Living forever has a zero-probability attached, as of 2020.
When you die, it is either down to being in the wrong place at the wrong time – standing in front of a large bus travelling at high speed, for example – but more often, for most of us, we die from a combination of health conditions and diseases.
By the time you are 80, you will probably have several conditions which might, in the end, kill you.
If you have diabetes, heart problems are a common complication, and your general state
of health will be affected – you will be more susceptible to other infections like flu.
With diabetes and a serious heart condition at age 85, your chances of dying within a year are 20%.
Without an infection, you die in October. With an infection, you die in February.
What have you died of? And did the infection outbreak make a difference?
Clue: your death will not show up as ‘extra’ in annual statistics, and it is up to the doctor to assign a cause of death. They may decide that the nearest ‘cause’ is your heart attack. (Cause of death is a study in itself and follows protocols set down by national medical associations, but there is an element of judgement).
If unexpected people die – young people who are not previously known to be ill or vulnerable – this makes a difference to measured statistics.
But working out whether vulnerable people die OF or WITH a disease on top of other conditions is far harder to estimate. However, that is a vital part of public health monitoring.
