The number of new cases of corona virus announced by the Governor last evening was not as high as was feared. There was concern that changes in data collection techniques would cause an artifactual “catch-up” spike. The aggregate numbers of both cases and deaths is still rising but not as strongly exponential as before. The daily count of new cases may be leveling off, but the number of viral tests performed daily is also declining. Current case mortality is hovering at 5% of identified cases. The percent of viral tests that are positive has been slowly rising– currently 8.2%. Both of these latter two statistics reflect the fact that sicker and high-risk individuals are still being preferentially tested. As long as we are hamstrung by lack of testing capacity and timely reporting, Kentucky is in no position to open up its economy by relaxing the fundamental epidemiological principles necessary to control this extraordinarily infectious agent.
This morning I simplified and updated the data visualizations currently on the Tableau Public pages of KHPI. I include some of the semi-log plots that I discussed yesterday, but as it happens, the aggregate numbers of cases and deaths are falling off even this trend line. Visual inspection confirms that the plots are rising less steeply especially for the number of aggregate cases. (Aggregate deaths might be expected to lag new case discovery.) Muddying the water however, is the fact that rather than increasing, the number of tests performed (and reported publicly) is actually declining! What is not looked for is rarely found. We are still largely flying in twilight– if not the dark.
[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!
I do not believe we are in any position in Kentucky to let go of the alligator we are wrestling. I am still waiting for better clarity of what we are actually facing.
Both new cases and deaths from Covid-19 infection continue to rise sharply in Kentucky. Observed mortality of confirmed cases remains above 5%. Simple daily plots of the numbers of cases by themselves cannot indicate whether we are turning a corner or flattening a curve. Comparison with other states and the nation as a whole does suggest our efforts to mitigate the disease are having an effect. Plotting the data on a logarithmic scale makes visualizing small and large numbers together on the same scale more accessible to analysis. More to the point here, such semi-log plots of the numbers enable us to observe whether the rate of increase in cases or deaths is actually slowing down. Over the past few days, there have been tantalizing suggestions that in fact that both cases and deaths are in fact doing so. Additional reported numbers over the next few days will clarify this hoped-for shift. Nonetheless, we have not achieved plateaus of either daily reported cases or deaths. In fact, semi-log plots of the number of new cases over the 30 days since the 100th new case show continued exponential growth with doubling times of every 5 days. Unless the very recent possible dip in new cases is real, at the current rate of increase, Kentucky will reach 10,000 total cases as early as May 4th. It seems to me that now is not the time to throw in the towel. It is appropriate to begin planning for an eventual data-driven, gradual, and stepwise reversal of our current non-medicinal efforts to deal with this stunningly infectious new disease, but otherwise it’s not very smart to do so precipitously. We have much more to learn about what is happening behind the scenes and our testing capability is still on its baby legs.
A higher than expected observed mortality rate does not accurately reflect overall case mortality. There are other things to worry about at this point- like some folks selfishly ignoring the prohibition of large group meetings!
[Addendum April 10, 2020: Governor Beshear announced this evening 90 new deaths, the largest in a single day by far.]
Since my article of April 3, the number of tallies of daily cases and deaths has increased. The figure below reflects the numbers released last evening on April 6 by Governor Andy Beshear. Click on the graphic to enlarge it. [An interactive graphic with updated data and alternate visualizations can be accessed here.]
The data underlying this figure can be viewed on my Tableau Public Website using the interactive link above. The data I present are the unchanged numbers as announced at the end of each day at the Governor’s public briefings. It should be noted that these announced counts have been continuously subject to adjustment by the Commonwealth to correct for duplications, late entries due to weekends, or other minor edits, but remain reasonably accurate as we go day to day.
It would be nice to believe that the slight downturn in the green “Positive Tests/Cases” line reflects the “flattening of the curve” that we are all working for. Things should become more apparent over the next few days. Recognize however, that Kentucky is testing many more people for viral infection. Yesterdays announcement noted that some 18,000 people had tests, compared to 2,556 just one week ago! The lesson here is “Seek and ye shall find.” There has always been– and still are– many more infected people in the community than we knew of. Many if not most of these have no or minimal symptoms. We should expect to see the number of new cases go up, especially if the new testing contract with Gravity Diagnostics works as hoped. A continuing increase in new cases should not be used to justify backing off from our efforts to protect each other from ourselves!
The Observed Mortality Rate depicted in the red line above represents the known number of deaths up to that day as a percent of the total number of known positive tests for virus at that time. The fact that this calculated mortality rate is still rising– indeed higher than the mortality rate in places whose epidemics have been running longer– is actually expected and should not cause disproportionate alarm at this point. Because of the lack of earlier testing, the true number of community infections was much underestimated. Only the most severe cases were identified and we expect a higher mortality in this subset of patients.
Recall too that the symptom-free incubation period between exposure and symptoms can range from 2 to 14 days. Similarly, infected people who eventually die do not generally do so on the first day of their symptoms. In a sense then, the Observed Mortality Rate curve is catching up with the number of unrecognized infections that occurred at a time of low testing. This observed mortality rate is surely higher than the actual case mortality rate which is a measure of how many infected people eventually die of their Coronavirus infection. What I expect to occur is that the Observed Mortality Rate will in near weeks begin to decline and level off at a considerably lower level. Epidemiologists all over the world are waiting to see what that level will be and who is most vulnerable.
I would like to have seen a more dramatic decline in numbers nationally, but we were as a country late to the game and it shows. My hometown of New York City, where I learned to be a physician and know its hospitals, is taking a terrible beating. In Kentucky we learned from the experiences of other nations, cities, and institutions and made the hard decisions early. I give our Public Health Department and the Governor’s offices much credit. I am following their advice and you should too.
Peter Hasselbacher, MD Emeritus Professor of Medicine, UofL April 7, 2020
If I have made an error in math or terminology or understanding, please help me correct it.