How will we know when we have won?
[Addendum: I have updated the Tableau Pubic presentation with data from Friday April 17. The increase in cases and deaths was not as great as the Governor feared. It looks to me like the rate of increase in both cases and deaths no longer fits an exponential trend curve. Things look like they are slowing down! Overall however, both measures continue to increase. I will address this new data later.]
I have been tracking and commenting on the number of cases and deaths from Kentucky’s coronavirus epidemic. Despite my best effort’s and some requests, the only data I have from Kentucky proper is what has been announced from the governors office during his evening greetings. Given our national slow start in timely testing for the virus, we must assume that the numbers as presented are incomplete– indeed only the tip of the iceberg. We have been warned over the past two evenings, that as data collection is now more systematized, that tonight we should expect a large number of “catch up” cases. For that reason I have not yet updated the numbers in my earlier articles or on my Tableau Public website.
In the meantime, I have been evaluating further the approaches I have been using to visualize the numbers released. Because we are still in the exponential expansion phase of this epidemic and because of some unavoidable scatter in the data, it is very difficult to determine if we are bending our new-case curve, let alone flattening it. It is certain that we have not yet reached the peak incidence of this epidemic.
Are we bending our curve yet?
When a curve on a simple graph plot is going straight up, it is difficult to know when it will stop. For this reason, I have begun using what is called a semi-log plot that allows simultaneous visualization both high and low numbers, and transforms an exponential curve into a straight line. This is a technique used by experienced epidemiologists (of which I am admittedly not one). In doing so, I wanted to feel more confident with the significance of the observation that the data-points of both new cases and deaths from earlier this this week appeared to be falling below the predicted trend-line. That would be nice! There are lots of understandable reasons why that may not be happening including more testing, clusters of deaths in long-term care facilities, more impatient violations of large group gatherings, and the like.
My goal here.
While I am waiting for tonight’s updated numbers, I wanted to try some alternate methods of visualizing the data and get a feel for how reliable they might be in identifying and impact of what we are all trying to do together. I am feeling more confident that using semi-logarithmic plots and applying exponential regression analysis can be useful in identifying trends. Because I find that experts commonly, if not by standard, exclude cases before the 100th when attempting to predict the future. (Early data may be collected in a less formal manner and the randomness inherent in low numbers may offer less predictive value.) I placed a presentation on my Tableau Public website that steps through my thinking. This is what I expect to try in future articles.
Even with all the caveats.
Looking at the various plots and making assumptions about how infectious agent like Covid-19 might be, I was stunned (but should not have been) at the power of exponential (compound) growth. I start from a single case from a hypothetical virus and uses purely hypothetical data. Even if a single infected person passes the disease to only one out of a thousand other people, the number of new cases in Kentucky would be in the tens or hundreds of thousands within 40 days. In addition, I am impressed at how fast things can sneak up on you!
None of this is real epidemiology!
I am not using an accepted epidemiological model. I am learning how to use my tools. For one thing, in the real world, as more people get infected, recovered, or even die, the number of folks eligible to become new cases diminishes.
Here are a two examples from my walk-though exercise.
Below is a regular Cartesian plot from a make-believe epidemic that is still in the exponential expansion phase. Since on the average, an infected person would only pass on the disease to one of 100 other people and so on, the line for the first 22 days is not very impressive. Things take off from there! How can one predict much about the future from inspection of such a curve. Nonetheless, based on available data, this is the current rough shape of our real-life situation in Kentucky!
Here is the same data plotted in a semi-log manner with the first 100 “cases” ignored. The exponential curve has been transformed into a straight line from which it is easier to see changes as they are occurring.
Counting new cases in not enough.
As virus testing ramps up, there is no question that the number of new cases will increase, probably even a lot. So will deaths. Nonetheless I believe this approach provides another dial in the instrument panel of the airplane we are trying to keep in the air on course. We need also to keep track of the impact on our hospitals. What is happening to Covid-19 admissions to hospitals, to ICUs, or the need for mechanical ventilation? What is the observed and actual case mortality? Where are the new cases coming from and how good are we in tracking their contact sources? Is the percent of new tests that are positive falling as we expect them too? What is the background incidence of unknown active or previous infections? What happens to people who appear to have recovered?
In a few hours Governor Andy Beshear will give us the new updated and corrected numbers. He expects them to be worse than the last few because of delays or discontinuities in reporting or collating. All that said, there are positive signs that the hard things we are doing are paying off. We do not have as many cases as some of our neighboring states. Our hospitals are not overwhelmed. We haven’t had to put people out in the Fairground’s overflow ward.
That is not to say that we have landed the plane yet. Residents of long-term care facilities are still particularly vulnerable. The desirable homelike environment they provide facilitates the transmission of the virus. The red-lining of our Black citizens into second-class economic and medical situations is showing up as markedly increased death rates from the virus. Issues like these will not be solved with medical technology or expertise. They are a result of the non-medical determinants of healthcare outcomes. Even so, our healthcare non-system is surely going to have to adapt, as will other of the structural features of our society. I have have often wondered if we would have had our Kentucky Hepatitis-A epidemic two years ago if there had not so many homeless living in our streets. None of us will ever be any healthier than the least of those living amongst us.
As we prepare for the next history-changing pandemic– and in this overstressed and overheated globe it will surely come– we need to do things a lot differently than we do now. We are truly all in this together.
Peter Hasselbacher, MD
April 17, 2020