The Massachusetts Hospitalization Puzzle

For everyone dealing with the coronavirus, there is both a societal and personal calculation. The societal calculation revolves around the enormous global and national costs of the pandemic – the staggering number of illnesses, hospitalization, and deaths, as well as the economic toll – massive unemployment, shuttered businesses, and food insecurity.

But there is a personal calculation with which most people wrestle. How likely am I or the people close to me to get sick; and if they get sick, how sick will they be? What are the odds that they will be hospitalized, or obviously even worse, how likely are they to die? This calculation clearly is highly dependent on personal circumstance – age, type of work, underlying health conditions, etc. But a starting point for understanding this is the number of people hospitalized from the coronavirus. (Obviously, this is an incomplete measure of severe illness, as many ill people in long-term care are never hospitalized regardless of how severely ill they become). And here, the available information in Massachusetts is confusing.

The Commonwealth has published a running total of the number of confirmed and suspected Covid-19 cases, total hospitalizations, and total deaths through time. (According to the Dashboard, this information comes from the Bureau of Infectious Disease and Laboratory Sciences). However, when the state changed the definition of probable cases earlier this month, they restated the cumulative number of hospitalizations without providing the details of the historical revisions – unlike what they did for cases and deaths. The number of confirmed and suspected hospitalizations dropped from 13,386 on September 1 to 13,295 the next day.

Fortunately, there is another source of hospitalization data – that provided by hospitals themselves and submitted to the state Department of Public Heath and federal government. Hospitals report both the number of patients currently hospitalized for Covid, and the number of new hospitalizations. Unfortunately, these data on new hospitalizations do not track the data collected by the state – in fact, the number of new probable case hospitalizations reported don’t make much sense if taken at face value.

For the week ending September 3, hospitals in Massachusetts reported an average of 312 patients hospitalized with Covid, an average of 19 new confirmed case admissions, and an average of 126 suspected case admissions, for a total of 145 new admissions. These statistics do not square with what we know about the hospital stays of Covid patients. Since the only way patients leave the hospital is if they are discharged or die, this would imply an average hospital stay of roughly two days, much shorter than what one would expect.

It is unclear exactly what these suspected hospital admissions are tracking, but the definition seems overly broad. According to the dashboard, these suspected cases “are those with symptoms who have not had a test result yet”. Perhaps many of these originally suspected cases turn out to not be Covid patients at all, or there is something else not transparent about this reporting.

However, the number of confirmed hospital admissions does closely track the number of newly hospitalized cases reported by the state up to the point at which the probable case definition was changed, as shown below. Both figures also reinforce the idea that the state has been in rough equilibrium for about the past five or six weeks (this is true for cases, hospitalizations, and deaths), with relatively low case and hospitalization rates.



Massachusetts Reporting Change: Probable Cases

On September 2, Massachusetts once again changed its coronavirus reporting – this time changing the definition of “probable cases”. According to the Massachusetts Dashboard “The previous case definition defined probable cases as individuals: with a positive antigen or serology test AND symptoms or likely exposure; with COVID-19 listed as an underlying or contributing cause of death on a death certificate; and with appropriate symptoms and likely exposure.”

However, “The new case definition updates the clinical criteria associated with COVID-19; defines probable cases as individuals: with a positive antigen test, with COVID-19 listed as an underlying or contributing cause of death on a death certificate, or with appropriate symptoms and likely exposure .” Furthermore, “the criteria indicating likely exposure are now restricted to known contact with a case or association with a specific outbreak. Individuals with positive serology (antibody) tests have been placed in a new suspect category which is not reportable to CDC.”

The Commonwealth indicates that the new reporting standard is more objective, is able to be more consistently applied through time, and brings Massachusetts’ reporting of probable cases more in line with the reporting standards of other jurisdictions. (Note that not all jurisdictions even report probable cases).

Significantly, all of the prior reporting on probable cases, hospitalizations, and deaths has been adjusted and backdated for this change. What are the ramifications of this? First, the Commonwealth reduced the number of probable cases substantially – from 9,755 under the old standard to 1,705 under the new standard (a reduction of 8,050).

The chart below shows the weekly change in probable cases over time. Most of the cases dropped were from May, when the pandemic was raging in Massachusetts. However, a substantial number of cases from June through August were also eliminated.

The number of probable deaths from Covid19 also dropped, but much less substantially – from 233 to 207 (26 deaths). The eliminated probable deaths are spread relatively uniformly over time. Ironically, however, the first death reported in Massachusetts, which occurred on March 10, was a probable case that was eliminated. I have adjusted my reporting statistics where possible to reflect these changes in cases and deaths.

The other consequence of this change is that it impacts how Massachusetts stands relative to other states in the case horse race (a horse race nobody wants to win). Early on, Massachusetts was third in the country in the number of cases, trailing only New York and New Jersey. As our case rates dropped substantially, and the pandemic spread to the Sun Belt, we had dropped in the rankings to 13th in the total number of cases, and 17th in cases per capita (per the worldometers aggregation site We are now ranked 16th in total cases and 22nd in cases per capita.

Unfortunately, our per capita death ranking remains unchanged – we have the 3rd highest per capita death rate, trailing (once again) only New York and New Jersey.

Data Update

Massachusetts Data Update September 1, 2020

Massachusetts appears to be in Covid equilibrium. Test positivity rates have declined somewhat over the past four weeks, but remain the highest in New England. Testing has ramped up in the past month (perhaps in part because students and some teachers are returning to school at all levels).

An interesting statistic to note is the shift in the composition of those being tested.  Over the past week, almost half of tests performed have been for people who have been tested before.  While this seems to be partly an artifact of more rapid turnaround time for repeat testers, there clearly appears to be increased emphasis on preventative testing. In fact, over the last four weeks the number of repeat tests has increased by almost 300%, compared to an increase of  57% for people being tested for the first time. The shift to  repeat testers are in part the driver of the low overall test positivity rate (currently 1.0%) as they have a much lower positivity rate (currently 0.3%) than people tested for the first time (currently 1.5%). Most of them are being tested asymptomatically.

Massachusetts Testing Statistics
7 Day Trailing Average Results
September 1, 2020
Testing Statistic   Current 7 Days Ago 4 Weeks Ago
Test Positivity Rate (Individuals)   1.6% 1.5% 1.9%
Test Positivity Rate (Include Suspected)   1.7% 1.7% 2.5%
Test Positivity Rate (All Tests)   1.0% 1.1% 1.6%
Test Positivity Rate (New Tests)   1.6% 1.5% 1.9%
Test Positivity Rate (Repeat Testers)   0.3% 0.5% 1.0%
Percentage Repeat Testers   48.5% 39.4% 29.5%
New Tests (Lagged 1 Week)   19,426 17,453 12,354
All Tests (Lagged 1 Week)   32,038 25,356 17,138

Hospitalization figures have remained stubbornly consistent for over a month.  On July 22, there was a large drop in the number of Covid hospitalizations from 532 to 351, and they have remained fairly steady since then.  (The large drop may a result of the federally-mandated  switch in hospital reporting from the CDC to HHS). 

The number of ICU and intubated patients have followed roughly the same pattern – there were 49 patients in the ICU and 29 intubated patients in hospitals on July 23, essentially the same as today.  The number of patients newly admitted to the hospital has remained steady of the past six weeks as well.  While covid-19 is well under control in Massachusetts, it remains nowhere near being extinguished.

Massachusetts Hospitalization Statistics

September 1, 2020


Hospitalization Statistic



7 Days Ago

4 Weeks Ago


Covid Patients Hospitalized





Covid Patients in ICU





Covid Patients Intubed






7-Day Trailing Average New Patients





Not surprisingly, death statistics in Massachusetts roughly track  hospitalization and critcal care statistics. There has been little change in the number of reported deaths (confirmed and suspected) over the past month.  The 7 day trailing number of reported deaths hit 16 on July 16, and has been in a tight range since then.  This reinforces the case that we are in equilibrium.

What remains striking is the high percentage of deaths in long-term care facilities, which has been almost 65% over the course of the pandemic in Massachusetts (and almost 72% of deaths since June 1).  There is no sign that this troubling trend is abating.

The case statistics are a function of both testing and test positivity rates.  The number of cases (confirmed and suspected) of Covid remains high, but this is primarily a function of increased testing, as positivity rates are at or near the all time low.

Massachusetts Reported Case and Death Statistics

7 Day Average Trailing Results

September 1, 2020





7 Days Ago

4 Weeks Ago


Total Deaths





Deaths in Long-Term Facilities





Percent from Long-Term Care






Total Cases Including Suspected






Massachusetts Lags Behind Its Peer States

Massachusetts has done a great job in bringing the coronavirus under control since the early, dark days of Covid-19, when it looked like hospitals in the state would be overrun like those in New York City. And relative to many states in the country, our statistics look pretty good. However, if we compare ourselves to peer states in New England and the Northeast, we’re at the back of the pack, as the following table shows. I’ve defined the peer states as the states with which Massachusetts shares a border, as well as Maine and New Jersey. The data is from Johns Hopkins’ excellent coronavirus tracking site, with population estimates taken from, which also tracks covid statistics.

Johns Hopkins Testing and Death Statistics

Massachusetts and Peer States

As of August 29, 2020

  Deaths Per 100,000 Residents   7 Day  Positivity Rate   Testing Rate (per 100)
State Last Week Last Month   Last Week Last Month   Last Week Last Month
Massachusetts 1.7 6.6   1.7 2.0   2.2 7.8
Rhode Island 1.5 3.7   1.3 1.9   3.8 13.7
New York 0.3 1.3   0.8 0.8   2.8 11.7
New Jersey 0.3 2.1   1.3 1.4   1.8 8.4
New Hampshire 0.2 1.3   1.2 1.5   0.9 3.7
Maine 0.1 0.8   0.6 0.7   2.1 6.7
Connecticut 0.1 1.0   0.9 0.8   2.9 9.8
Vermont 0.0 0.2   0.5 0.5   1.9 5.9

I’ve pulled together three statistics: death rates, testing positivity rates, and overall testing rates; and show each for the past week and past month, as per Hopkins. The states are sorted from worst to best death rates over the past week. Massachusetts continues to have a stubbornly high death rate, with only Rhode Island coming close. The other peer states have significantly lower rates – including New York and New Jersey, which were much more heavily ravaged at the beginning of the outbreak.

Why is this? It is difficult to know precisely, but about 70% of our deaths are coming from people in long-term care settings. I don’t know the percentages in other states, but it is surprising that the high death rate in those facilities continues months after the peak.

We’re also at the back of the pack when it comes to test positivity rate, although the gap between Massachusetts and our peer states is much lower. It may be harder to control the virus in a more urban state, which would explain why the positivity rates in Rhode Island and New Jersey are also relatively high, and Vermont and Maine have the best recent record here. But New York and Connecticut are also urban, and have much better statistics than we do. (New Jersey, Rhode Island, Massachusetts and Connecticut are the mostly densely populated states in the country in that order, and New York is the 7th most densely populated).

In terms of testing, we’re squarely in the middle of the group. Rhode Island leads the testing Olympics, perhaps because CVS is headquartered there (over the entire pandemic it is the top state in the country for testing per capita), followed by New York, and Connecticut. We’re doing relatively well, but not terrifically so. We started out as one of the better testing states, then fell back for some time. We’re now ranked 13th overall in the country per capita, but for a period of time we were testing less than the national average. Testing has picked up again, a positive sign.

Data Update

Massachusetts Data Update August 29, 2020

Case positivity rates remain at or near pandemic lows. The trailing 7 day average positivity rate for individuals is 1.5%. This is just up a tick from the pandemic low of 1.4%. The 7 day average positivity rate based on tests is at 1.0% – 0.4% for retested individuals, and 1.5% for newly tested individuals. The 1.0% figure is a pandemic level low. The positivity rate including suspected cases is 1.7%, also a pandemic level low.

The trailing 7-day reported death total of confirmed and suspected cases is 17. This has moved up somewhat during the past several days, but has hovered between 13 and 17 since mid-July. The great majority of deaths continue to come from long-term care facilities – over the past week, about 70% of deaths have been in long-term care facilities.

The 7-day trailing average of reported cases (confirmed and suspected) is 352 (adjusted for the absence of reporting on August 23). While this is higher than during most of July, this is due to increased testing, as positivity rates now are lower than they were throughout July. Testing has ramped up considerably, with about 17,000 new individuals tested on average each day in August so far, compared to about 12,000 each day during July.


Calculating Covid-19 Positivity Rates

On August 12, 2020, the Commonwealth of Massachusetts changed the way that it calculated the positivity rate from covid-19 testing. This reduced the headline positivity rate from covid-19 testing in Massachusetts. It is also misleading, and counter to the way in which most aggregators calculate positivity rates. This post serves to explain the differences between this calculation and the two other more widely used methods.

In all cases, the positivity rate is a simple ratio between two numbers. The numerator uses some definition of cases or positive tests results. The denominator uses some definition of tests or tested people. The positivity rate is just (Cases or Test Results) / (Tests or Tested People) (multiplied by 100 to convert to percent, if desired). In Massachusetts, and generally elsewhere, the results are restricted to tests obtained through molecular (PCR) tests, not antibody or antigen tests.

Focus on Tests (Massachusetts Method)

The Massachusetts method changes the focus of positivity rates from individuals to tests. It simply uses the ratio of the number of positive tests to the ratio of tests performed. The upshot of this is that repeat testers can have a significant impact on the positivity rate. For example, if a professional athlete gets tested every day, all of those tests increase the denominator in the calculation (regardless of whether the athlete tests positive or negative on any given test).

If someone is retested frequently, and never get a positive test result, this reduces the positivity rate compared to a calculation in which each person is counted only once. The flip-side of this is that if an individual tests positive, and comes back to be tested again a week later, and tests positive a second time, this will again count as a positive test. Hence, there is no guarantee that this method will result in a lower positivity rate, but it generally does. Most of the people being retested are presumably doing so for health and safety reasons, and not because they suspect they have Covid or have tested positive in the past.

In Massachusetts, the number of people being retested is quite significant. For example, as of this writing, about 30-35% of the tests being conducted in Massachusetts over the past several weeks are for people being retested. These people have a much lower positivity rate than people being tested for the first time – the trailing 7-day positivity rate for the re-testers is 0.4% (as of August 27) compared to 1.5% for those who have only been tested once.

Focus on Individuals Tested (Standard Method)

A more common approach to calculating positivity is to focus on individuals, not tests. Until August 12th, this is the way that Massachusetts calculated positivity rates. Each person is only counted once both for determining the numerator (with this method the number of cases) and denominator (with this method the number of individuals tested) in the positivity rate calculation.

To focus on the professional athlete or safety professional again, this means that each retest does not change the denominator of the calculation, regardless of the test results. Each person is only counted once, regardless of how many times they are tested. If an individual does test positive, this will count as a positive case, even if they are tested two weeks later and then get a negative test result. This retest with a negative result does not increase either the numerator or denominator in the calculation.

However, if a person has a negative test result, but comes back later and tests positive, the numerator will increase by one person, but the denominator doesn’t change. (This all presupposes nobody is reinfected with Covid. Although there have been recent validated reports of reinfection, this remains exceedingly rare as of now).

Include Suspected Cases (Enhanced Method)

The final method to calculate positivity rates is to include suspected cases in the calculation. Essentially, this method (used by Johns Hopkins, among others, in its calculations) assumes that all individuals suspected of having Covid, if tested, would test positive. By definition, this increases the positivity rate compared to the standard method. Specifically, the calculation is:

(Individuals with Positive Covid Tests + Probable Cases) / (Individuals Tested for Covid + Probable Cases).

In other words, the number of probable or suspected cases is added to both the numerator and denominator in the calculation. In Massachusetts, the number of probable cases is not insignificant. Over the life of the pandemic, almost 8% of all confirmed and probable cases have been probable, and over the past several weeks, this figure has ranged between 15% and 20% of probable and suspected cases. Hence, the positivity rate calculated this way has been noticeably higher than calculated the standard way.


(1) Testing Based Calculation (Massachusetts)

All Positive Molecular Tests / All Molecular Tests Performed.

(2) Individual Based Calculation (Standard)

All Individuals with Positive Molecular Test / All Individuals with Molecular Test.

(3) Enhanced Calculation (Include Probable)

(All Individuals with Positive Molecular Test + Individuals Probably Infected) / All Individuals with Molecular Test + Individuals Probably Infected).



This is the inaugural post for this site dedicated to reviewing the state of coronavirus in the Commonwealth of Massachusetts. I had been thinking about a blog for quite some time, but had been satisfied with occasional comments on Boston Globe articles about the coronavirus – in particular, the Globe’s daily article which focuses on the latest statistics published at roughly 4 pm each day by the Commonwealth in its Covid-19 Dashboard. That daily article seemed generally to just parrot the headline numbers released by the Commonwealth, without any deeper analysis.

I have felt increasingly constrained by the Globe’s comment section. First, although I’m interested in a daily recap of the statistics, I thought that would become quite repetitive and boring for most Globe readers. However, I realize that there is a subset of readers who are interested in that, as well as other analysis of what is happening with testing, cases, hospitalizations, and (unfortunately) deaths. So this format gives me freedom to write about what is interesting to me (and hopefully others), and to go somewhat beyond the headline numbers. Second, the Globe comment section has been increasingly taken over by individuals with a particular axe to grind (I hesitate to call them trolls), with whom I’m tired of dealing. No need to name names, but anyone who finds their way here from there will know to whom I’m referring.

The purpose of this blog is to provide relatively untainted commentary about the coronavirus in Massachusetts (I use the word relatively because I understand that I, like everyone else, have particular biases that influence what I write about and how I write about it). I have been relatively impressed with the response to the coronavirus in Massachusetts after some initial missteps (and those might not have been avoidable), but a bit dismayed with recent changes in the Dashboard, which have reduced the amount and variety of information published. The Commonwealth had done an excellent job of providing information sliced and diced in various ways. It has backed off of that, for reasons I’m unaware of.

In any case, off we go.