John W. Buchanan, FCAS, MAAA, is Managing Director, Excess & Reinsurance at Verisk
The introduction portion of this article previously appeared in the Physician Insurer magazine Fourth Quarter 2011 as a feature article on the insurance underwriting cycle, and is reprinted herein with permission*. We are providing a link to this original companion article at the end of this article. This article applies the same analogy to COVID-19. We gratefully acknowledge the invaluable assistance of David Sachs, Assistant Professor, Genetics and Genomic Sciences at Mt. Sinai in NYC. Elaine (Yingrui) Lu provided significant statistical and data analysis throughout the process, while Marni Wasserman, Architha Sridharan and Eric Price-Glynn provided additional insights and review of the materials.
Most mornings, I start off the day by thinking about the insurance underwriting cycle. More recently, my similar thoughts go to the reopening issues under COVID-19. Okay, you probably guessed it. I am an actuary. But let me explain.
An analogy between a summer camp prank and the underwriting cycle has been around for decades. I first used this analogy, with accompanying hand-drawn shower scene, some 30 years ago with a large group of insurance and IT professionals in London. The diagram which I hand drew, along with a bathtub/closed claim analogy, held their attention to say the least. I have since used the analogy with many physician and hospital insurer groups in my career.
Now, picture a sly actuary and a hygiene-oriented underwriter attending a summer camp. Every morning, the underwriter takes a long shower. Tiring of waiting for his turn, late one evening the actuary decides to dramatically lengthen the amount of shower tubing. Using his magic formulas, the actuary determines that if he extends the tubing with twists and turns, he can change the amount of time required for the water to work its way through the shower system by 20 seconds.
As is his custom, the next morning the underwriter turns on both the hot and cold water faucet taps equally, and waits ten seconds to test the temperature of the water. As the chilly water from the night before is still working its way through the system, he decides the water is too cold and turns up the hot water and confidently steps in. After another ten seconds, still feeling the chilly water, he turns the cold down and the hot water up even more. Since the water is starting to heat up, he starts to feel good about his decision. Alas, he is deceiving himself.
After another ten seconds he starts to feel the temperature getting hotter and hotter. He quickly turns the hot water down and turns up the cold. After another ten seconds he starts to feel a moderating temperature thinking things are fine. But then after another ten seconds, the water starts to feel frigid again, necessitating another round of turning up the hot water and turning down the cold. The shower cycle starts all over again, until either the underwriter manages to endure excessive hot water and cold water, or gives up and leaves the system.
Then, the actuary with a sly grin steps into the shower, confident in knowing that all he has to do to ride out the hot/cold cycle is to put a moderate amount of hot and cold water into the system—and not overreact to the initial wrong signals.
A. Opening faucet taps vs. Reopening markets under COVID-19
To summarize what’s happening in the shower scene, the length of the tubing significantly delays the information stream between the faucet and the shower head. What’s in the faucet is in fact the controlled actual temperature, while the shower head yields only the uncontrolled perceived temperature.
This scene provides a very strong analogy to the current issues surrounding estimating the impact of reopening markets and society under COVID-19. The length of the tubing is replaced with the length of time between the initial exposure to the virus, through to the long incubation and hospitalization periods. Due to this long period, exacerbated by asymptomatic spread and other issues, we only see the impact of our behavior a couple of weeks later. If we just reopen blindly because things seem OK right now, the problem will repeat itself: invisible community spread followed by the hospital system potentially being overwhelmed again in a few weeks.
For COVID-19, the 20 feet of tubing can be analogous to an average emergence delay of two weeks between the initial exposure to the virus leading to potential infection, hospitalization, and then either recovery or death. The incubation time is considered to be the time between exposure to the infection and the onset of symptoms (often shows up as fever). Typically, the median time can be around 5 days, but could be as long as two weeks. For initial asymptomatic carriers that either eventually become symptomatic or pass the virus to others unwittingly, the length of time from initial exposure to onset of symptoms can be much longer.
When government officials, businesses, and the population feel that the results are favorable (“cold” no issues), testing those with fevers, etc. they ease social distancing or other policies. These additional interactions induce additional exposures. When they feel test results are adverse (“hot”), or hospitals are potentially overwhelmed, they turn down the interconnectivity to allow time for the system to cool off. From a practical standpoint, each additional policy change may be more difficult to implement, as society may not want to go back and forth between shelter stages based on tests, unless they can be convinced of the necessity.
B. Standard Testing Issues and Prevalence in the Population
A standard disease testing problem is inaccuracy in the tests and testing procedure used to determine policy. All designed tests, strive to reduce the occurrence of what are called False Positives or False Negatives. This issue is not just related to COVID-19, but to assessing most other diseases (problem addressed by Bayes theorem).
Diseases will rarely have what are called “signature” characteristics to determine with certainty the root cause (asbestos/mesothelioma is one of those exceptions). It is still not clear whether COVID-19 is a “signature” disease. For severe cases with clinical symptoms, doctors can usually tell without a test that its COVID-19, especially if they have just been presented with dozens of similar cases from a population. Much more common is the need to design tests to not only accurately test positive cases, but also accurately test negative cases. These tests are designed to balance what are called sensitivity factors (i.e., the probability of a positive test result if diseased) and specificity factors (the probability of a negative test result if not diseased). Accurate outcomes are called Positive predictive value (PPV) and Negative predictive value (NPV). These tests are improved over time, but the necessary development and testing period adds to the overall delay in knowing whether particular patients have the disease or are carriers. At the peak of an outbreak, they might not even test everyone. The overall test accuracy then becomes highly dependent on both the test accuracy, which is a moving target, as well as the prevalence of the disease in the population at any moment.
There are currently three basic test types: diagnostic (PCR-polymerase chain reaction to match SARS-CoV-2 RNA sequence) to diagnose people who are currently sick, antibody to identify those who were previously infected, and antigen which is a quick test to detect active infections to screen those who need a more definitive test. It is worth noting at the time of this writing, that the diagnostic test for RNA, given the difficulty of swabbing in exactly the right place (vs. antibodies which are dispersed throughout our blood), can have a lower sensitivity factor, and can therefore generate many more false negatives for current infection.
To illustrate this testing issue, see Figure 1, using an antibody test as an example. The goal in this case is to determine if a test comes back positive, what is the chance that the patient had been sick with the disease? Or vice-versa. For a disease that is relatively prevalent in the population (top illustrative scenario if NYC at 20% with antibody sensitivity 94% and specificity 99% factors), a standard test will be relatively accurate at 96% PPV. On the other hand, if the population prevalence factor is much rarer (say 1%, or 5%), the PPV drops to only 49% and 83% respectively. Given those low results, resources would be expended to try to improve the accuracy of the tests for varying populations.
With COVID-19, the disease will typically go from rare to highly prevalent and move back to rare. Potentially, herd immunity levels may eventually be reached, when a significant part of the population either develops antibodies, have suffered significant fatalities, or a protective vaccine is developed and widely administered. The overall accuracy of the tests, and predictive value, are then highly affected not only by the type of test, but by what part of the progression the disease is in.
Figure 1 – Standard Testing Issues (using Bayes Theorem)
Figure 1 – Standard Testing Issues (using Bayes Theorem)
C. Various Lag Issues under COVID-19
In addition to standard testing inaccuracies, the long COVID-19 incubation period of two weeks creates a problem as to when and how often to do the testing. This long incubation period is just part of the lag involved that makes this virus especially difficult to assess. Many people have symptoms that start out mild, including many people who might not bother to tell anyone. This is especially if they have financial difficulties and don't want to miss work. But those cases have the potential to go downhill fast after about five or six days, with an extreme variability of less than 24 hours or it may take several weeks. For severe cases there can be a delay of over two weeks between getting exposed and landing in the hospital. The severity of the cases vary person to person, ranging from no symptoms to severe, with all potentially still spreading it. These uncertainties create extra policy decision difficulties in whether to shelter or reopen.
As an example of the reopening issue, let's say a particular state or region opens completely without any restrictions. New outbreaks could be seeded into the community, but testing results or hospitalizations may not pick up for a number of weeks. In that time, the amount of spread could be significant, depending upon general changes in human behavior and results of potentially inaccurate testing. If we observe and control potential outbreaks with testing and contact tracing, we can attempt to reduce its impact without overloading the healthcare system. If we don’t observe and adjust for it, in a few weeks many people could start showing up to the hospital, so we might need to shelter again or invoke other remedies. That may be too late for a large number of people with mild symptoms, or who may still be incubating and end up being hospitalized over the subsequent weeks. Hospitalization surges could continue for weeks after shutdowns are implemented. Many hospitalized people end up staying for weeks before recovering or dying, leading to additional delays before the number of fatalities catches up.
There's going to be some additional testing lags depending on the state of the outbreak as related to the medical system. For example, at the peak of the outbreak, people were only getting tested if they were struggling to breathe, meaning that testing and hospitalization were pretty close to each other. When the situation loosened up, people initiated testing earlier, if they have a fever or a positive contact. Then they may be told to wait it out at home until they are struggling to breath. It's basically the difference between testing for clinical reasons vs. testing for public health reasons. Doctors may not be concerned about testing people unless the test would alter the treatment. Doctors may test people mostly to know if they should be treated in the COVID-19 ward or not. But public health people may want to do additional testing to control the outbreaks.
Defining "asymptomatic", but disease carriers, can also be very difficult. Some people remember mild symptoms even if they're not diagnosed with anything. If you don’t have symptoms, it’s perhaps gone in a few weeks. But we don’t have verification on this. Some may just carry the virus for a protracted amount of time, potentially infecting many others they contact. We also don’t have verification that people who are infected by COVID-19 develop immunities for months, years, or for their lifetime. People may develop the disease again.
At the time of this writing, based on Covid Tracking Project (CTP) data, Figure 2 illustrates conversion percentages and lags between some of the various stages. Shown are four stages and conversions from # of people tested, those who test positive, those that are hospitalized, and those that either recover or suffer a fatality. In this illustration, approximately 5.6% of the US cases that test positive (median state average 4.3% with states ranging from 1.1% to 9.5%), ultimately result in a fatality. Also, according to this data, 31.9% of those who enter the hospital and are diagnosed with COVID-19, do not survive. A full rendering of the lags and stage conversions in the system would involve capturing quality data throughout the virus lifecycle. And then statistical analysis of all the different stages: initial exposures, testing, hospitalization, ICU admittance, intubations, recoveries and fatalities. All of these statistics and indications are complicated by inaccuracies in the actual tests and variations between states and even over time in data reporting protocol. Test statistics, with different definitions used, are particularly problematic. Some data accumulations grade the quality of the data given by each of the states. Even after significant data scrubbing, anomalies still exist.
Figure 2 – Lags between Testing, Positive Indications, Hospitalizations, Fatalities
Figure 2 – Lags between Testing, Positive Indications, Hospitalizations, Fatalities
It is likely cases and deaths are both underestimated, with cases being more underestimated than deaths. Therefore, the generally reported case-fatality rates are likely overestimated. However, consistent snapshot analyses of places will typically indicate lower fatality rates early in the outbreak, which then creep up over time as the deaths catch up.
D. Extra difficulties presented by COVID-19
The impact of various corona or other viruses can range from making us moderately to extremely ill. And in extreme cases can affect many vital organs at the same time. Other issues, such as blood clotting throughout the body in severe cases, are just starting to be known. Viruses are deeply intertwined within us, in ways that we are just starting to understand. Since its first discovery, COVID-19 has presented additional hurdles in understanding its path and trajectory. There are difficulties in not only understanding how the COVID-19 virus was first created and evolved. But also the difficulties in understanding how the virus spreads within our bodies, as well as how it spreads communally. Discoveries are constantly being made as to new symptoms discovered or the impact of age, pre-dispositions, and other demographic characteristics. Adding to total lag, an extraordinary amount of time is often spent in the ICU or on ventilators, just keeping patients alive, so the patient’s immune system can get strong enough to allow them to recover.
Confounding the issue, is that COVID-19 continually surprises us, acting in ways that we don’t understand. Case count and other projections sometimes don’t work out the way we would expect. It is uncertain why certain states or regions, contrary to common perceptions about degree of shutdown or reopen and adjusting for population density, may not exhibit diagnosed case loads or fatalities consistent with common expected causations.
Figure 3 shows an example of how states are being separated into those large states (NY/NJ) that as of this writing are potentially “on the other side of the curve” vs. the rest of the country separated into those that were sheltered, reopened a few weeks prior to this analysis, and never sheltered. Considerable effort in the coming months and seasons will be expended to try to understand various hypotheses and corresponding results. Subsequent projections and “skill testing” will be done to see if valid projections are able to be made, either on a macro basis, or on a state by state or shelter status.
Figure 3 – Tracking COVID-19 by state / shelter order (shelter status @5/4/2020)
Figure 3 – Tracking COVID-19 by state / shelter order
Complicating our understanding and causative analysis is COVID-19’s long and variable incubation period, and often asymptotic or mild symptoms of unknown connection. Over time and in the coming seasons, the virus may also potentially exhibit various single base mutations or more complicated recombinations in the longer term. When two different coronaviruses infect the same cell, the virus copying mechanism will often blend them by splicing large pieces of one virus genome into another. To help illustrate the mechanism, mutating the genome one base at a time is like starting with a functioning car, and randomly changing the shape of some component. It will take a long time to improve the car that way. Usually this will either have no effect, or break the car. Coronaviruses, which have some of the longest known RNA genomes, reduce this process by "proofreading" with a protein called nsp14, which detects mistakes during copying and fixes them.
Recombination on the other hand is like starting with two cars that both work, but are different, and swapping out components. E.g. combining the engine of one car with the wheels of another. The process won't necessarily “improve” the virus, but it's more likely to result in something that at least works, creating additional analytical complexities. This recombination process is similar to how human parent DNA is combined to produce new DNA in the children. Coronaviruses appear to be quite adept at this recombination.
So, where are we?
As of this writing, we don't really know what's going to happen. It seems clear that we are dealing with an evolving pandemic, one that continuously confounds medical experts. A virus that can chart many courses, twisting and turning, over the immediate headline cycles, months and seasons. It also seems clear that we would prefer to measure the various risk factors and adjust continuously. Rather than guessing and then waiting a couple of weeks to see if we were right. A goal of minimizing deaths and maximize rebuilding of the economy will require coordination between the government, private institutions, and medical institutions. And capturing and analyzing volumes of data to stay steps ahead of the curves thrown at us by the virus.
How can we reduce the risk? Very importantly, we need to do all that we can to reduce the knowledge delay built into the system. We need to measure all the inputs, knobs, and outputs of the system. And assess the prediction skill of each of the factors. In other words, look to see what early indications of trouble are in the system and act aggressively accordingly.
Mobility data gathered from e.g. cell phones is starting to prove an extraordinarily accurate predictive tool for the epidemiological community. Much like centralized water leak or fire detection system for related property losses. The mobility signal provides a direct measure of the degree of “opening” zeroing in on rates of person-person interactions in a way previously impossible, at least at scale. Subject to initial Effective Reproduction number (R(t)) and possible shift factors such as (non)compliance with mask-wearing and physical distancing guidelines, local infection growth rates are a function of mobility. Intuitively presumed true, and now argued rigorously in the case of state differences in the US.
“Testing and tracing everyone” could be rather practically difficult, not to mention socially/culturally impossible. As an alternative, the potential early warning provided by wastewater RNA monitoring could significantly reduce the cost in time, and ultimately lives lost, as part of a robust testing mechanism. “Smart testing” using RNA monitoring or other measures could help tell the public health community when and where to deploy scarce test/trace resources.
We can utilize actuarial techniques to supplement existing procedures, to help estimate lags and conversion factors, which can be seen in the COVID-19 progression from exposures and testing to fatalities. Many actuaries spend their careers investigating the intricacies of the insurance process from policies written and accidents occurring to ultimate loss settlement. When individual data is presented with two or more dates, that information can be set up in what are called “triangles”. Analogously, if COVID-19 data can be produced with multiple dates, such as date of initial exposure, hospital admittance, and then recovery or fatality dates, a very similar triangle procedure can be incorporated to give earlier warnings of troubles, or lack thereof. Cohorts, such as all people exposed at a particular event, can be traced and analyzed through the various emergence steps. Hot/cold indications and signaling decisions can be enhanced by using multi-disciplinary problem solving methods (applying epistemological concepts).
Whatever new types of “bypass tubes” can be created to reduce the emergence lag, and get a more accurate early signal, will help decision makers improve the delicate balance of social responsibilities and the economy. We should use smart testing techniques, contact tracing, and isolation when hot spots are identified. We should improve data collection methods and validation, including utilizing enhanced methods of analyzing any newly available data sources. Shortening the tube length will allow us to much more quickly observe the otherwise "invisible" incubation and asymptomatic virus spread. And see results, with a much smaller delay, to decide whether the policies are working or not. Minimizing delay in the feedback signal is critical.
Now: What will you be thinking of when you take your next shower?
*Prior article, “The Medical Professional Liability Cycle: Entering Hot Water?”, was published in the fourth quarter 2011 edition of Physician Insurer. For a copy of the original article, contact Communications@MPLassociation.org.