Massachusetts Numbers – Fewer Deaths on Sundays

A quick glance at the Massachusetts daily coronavirus deaths might lead you to think that church services are somehow protective against coronavirus. For the last three Sundays in Massachusetts the daily death count has been substantially lower than the surrounding days.

Data collection is a tricky thing, and to stick with the religious theme, often the devil is in the details. The Massachusetts daily death count does not count the deaths that happened that day, but rather that came in via various reporting processes, and where definitely linked as a coronavirus related death. For the example the deaths 70 deaths reported on 4/12/2020 by the State of Massachusetts actually occurred on 04/02/2020 through 4/12/2020. So at least one of the deaths reported on 4/12 had occurred 10 days early.

So given that death information needs to be collected from various sources and then in some instances linked to coronavirus infection status, it is no surprise that less of that process happens on Sundays when the staff who must do this kind of tallying and linking are more likely to be off of work. Massachusetts is not unique in having these data anomalies. It is just that I live in Massachusetts so I have been looking at my state’s data with greater interest.

The coronavirus data poses many data analysis challenges. Each day Massachusetts, and many other states, report a total count of tests administered and a total count of new positive tests. An important indicator of how the outbreak is progressing is the percent of tests that are positive. One would be tempted to simply divide the number of positive tests by the total tests performed each day to get a percent positive.

Figure 1: Three ways of estimating Coronavirus Percent Positive Rate

But like the daily deaths, the daily positive test results are not generally resulting from the tests performed on that date. Daily positive results are the positive results that have been received on that day. Testing lag times have been a problem during this epidemic. Some rapid test system are expected very soon, but for most of the tests performed to date have been taking one to many days to be returned. If the rate at which we perform tests was relatively constant this might not be a problem, but over the past few weeks Massachusetts has massively increased testing from a few hundred tests per day in early March to over 6000 per day.

Figure 1 shows three different ways of estimating the percent positive rate in Massachusetts testing. The black line is the crude estimate of simply dividing the daily positive by the daily count of tests administered. The light green line assumes a one day lag, so today’s positives are divided by yesterdays total tests administered. The red line tries to smooth out some of the daily ups and downs in testing. The average number of positives over the last three days, are divided by the average testing from a three day period, where those three days reflect a 1 day lag.

Divining meaning out of the various zigs and zags of figure 1 may be impossible. It is clear that over time, not only are we seeing a greater number of cases (see figure 2), but the percent of tests that yield a positive result are increasing. The red line does show an interesting peak around March 25th, followed by a decline and then almost a week of a relatively constant test positive rate (around 17%). Massachusetts implemented two major steps toward social distancing on March 15th (school closings) and March 23rd (Closing on non-essential businesses). People with the infection, can infect others over a period of many days (7-10). If social distancing were to be effective, you might expect to see a decline and or leveling off in percent of people testing positive starting a few days after implementation of new social distancing rules. Though if that is what we see in the red line of figure 1, the data after April 2nd shows a resumption of increase positivity.

Figure 2: Daily count of new positive coronavirus test results.

But Who Is Being Tested?

One big problem in interpreting this data is that it is a little unclear who the people being testing represent. They certainly are not a “representative” sample of the entire Massachusetts population. If they were that would mean somewhere in the vicinity of 30 to 40% of the Massachusetts population were infected, which might actually be a good thing in terms of herd immunity (but that is the subject for another post). Though the guidelines for who should be tested have changed somewhat since mid March, we can assume that for the most part the tests are being performed on people who are at a high risk for infection. That includes medical personnel, first responders, people admitted to the hospital with severe respiratory symptoms and the elderly who are considered high risk. Its also likely to include some of the worried well, in particular the rich and famous worried well.

Perhaps the state is doing some tests on a surveillance basis to better estimate the underlying infection rate in the general population. But with this aggregate data of tests which are heavily biased toward those at increased risk, its hard figure how this data might relate to the general infection rate in the general population. And its data about the general population that is needed to make estimates about future impact on the state and the hospital system. It is important not to treat the number of new positive cases each day as if they represented anything like the total number of new cases in the state. Given the continued shortage of testing, the resulting “rationing” of tests, the high rate of asymptomatic cases, and the limited utility of testing for the average person already staying at home, it is really impossible to infer much from our current testing, about the state as a whole.

However, the fact that an increasing percentage of those being testing are turning out positive, combined with the fact that we are testing more people than ever, suggests that Massachusetts is not near its peak yet. If we were consistently testing “high risk” citizens, and the outbreak were leveling off, one would expect that as the state expanded the scope of those high risk individuals, we would be expanding into groups of people who were at slightly lower in risk than those tested at the start. That is, as you cast a larger net around high risk people, you would expect to include more people whose risk was not quite as high as those you first caught. With a larger net, you would expect a small decline in the percent positive. We are seeing just the opposite. As we test more people, we are seeing a higher infection rate.

What happens next – only time will tell.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

Create your website with
Get started
%d bloggers like this: