Age Analysis

Massachusetts Covid Breakdown by Age Part IV: Death Analysis

This is the fourth in the series of posts analyzing Covid by age group in Massachusetts – and particularly grim, as it focuses on deaths and death rates. As expected, death statistics provide the sharpest delineation of how Covid is affecting different age groups, with a far higher death rate among seniors, particularly those 80 and over. The data for this post have been updated to October 10 to incorporate the latest weekly report released by the state.

Figure 1 shows the sharp decline in death rates for those 80 and over from the end of May through the beginning of August, with weekly death rates leveling off at about 20 per 100,000. (At its peak at the end of
April, the death rate for people 80 and up was more than 10 times this level). There is a similar but less pronounced decline for seniors between 60 and 79. Death rates for the 40 to 59 age group fell also, but are sufficiently small that the decline doesn’t show in the figure. Death rates for those under 40 are very small.

Figure 2 shows that the overwhelming majority of deaths are for people 60 and older – over the course of the pandemic, almost 95% of deaths in Massachusetts have been in this age group. Slightly under 5% of deaths have been for people aged 40 to 59, and about one-half of one percent of deaths have been for those under 40. The see-saw pattern of deaths in the figure, especially noticeable in the over 80 and the 40 to 59 cohorts since August, is likely an artifact of my methodology for processing the inadequate information provided weekly by the state.

Figure 3, which shows the death to population ratio for the age cohorts, most starkly points how those 80 plus have been disproportionately impacted by the pandemic. Slightly more than 4% of the state population is in this group, but it accounts for over 60% of deaths. Seniors from 60 to 79 are also dying at a disproportionately high rate, but much less so than those 80 and over.

Age Analysis

Massachusetts Covid Breakdown by Age Part III: Hospitalization Analysis

This is the third in a series of posts about how Covid has affected different age groups in Massachusetts. As I noted in the post describing my calculation methodology (, the hospitalization information provided by the state appears unreliable. First, it does not align with  hospitalization admissions provided to the state by hospitals directly ( Second, the weekly breakdown of hospitalizations by age under counts new hospitalizations compared to the daily data provided by the state in its race / ethnicity report. So this analysis should be viewed with some skepticism – although it probably is roughly correct in a broad sense.

Figure 1 shows the rate of new hospitalizations for each age cohort, with a later start to the figure because of the higher rate of hospitalizations for the 80 plus cohort earlier in the pandemic. (At its peak, the weekly new hospitalization rate for that group was roughly 180 per 100,000). As expected given what we know about Covid, these rates sort in descending order from oldest to youngest cohort.

The number of new hospitalizations for the 80 plus group sharply declined during May (not shown) and June, falling almost 95% from the end-of-April peak by early July. The decline also occurred for the other age cohorts in May and June, but not quite as sharply. Since June, the new hospitalization rate has been relatively stable regardless of age – the recent uptick in hospitalizations from the data provided by hospitals is not yet evident in these state-provided data by the beginning of October.

One other point. Since June 1 approximately 70% of reported deaths in Massachusetts have been residents of long-term care facilities. Many of these ill long-term care residents are never admitted to the hospital, and the bulk of them are 80 and over (and the overwhelming majority are 60 and over). Thus, any measure of illness that looks at hospitalizations to cases will likely underestimate the severity of Covid, particularly in the senior population.

Figure 2 shows the percentages of new hospitalizations by age cohort. It is difficult to discern meaningful patterns here (perhaps a result of the unreliability of the data). Younger seniors (60 to 79) have tended to be hospitalized the most. However, there are about 4 1/2 times more people in Massachusetts between 60 and 79 than there are 80 and over. While about 15% of hospitalizations have been for people 40 and under since the end of June, they are over half the population of Massachusetts. Still, this is perhaps a higher percentage than one might expect (and flies in the face of some of the folk wisdom about Covid).

Figure 3 shows the ratio of new hospitalizations to population for each age cohort. This clearly shows the relative extent to which seniors have become hospitalized from Covid, particularly those 80 and up. (The dip in the percentages for those 80 and older for about a month from mid-August to mid-September is probably an artifact of the unreliability of the data and my calculation approach). Most surprising to me is the 40 to 59 year old age group, for which new hospitalizations almost track their population share, particularly in the last month. I would have expected this percentage to be lower.

Data Update

Massachusetts Data Update October 12, 2020

Very little has changed on the testing front since the last update five days ago.  7 day positivity rates for newly tested individuals are still 3.6% (they have been between 3.5% and 3.7% every day since September 29) and  the overall test positivity rate is 1.1% (it has remained there every day since September 28, with one exception).  A minor change is that the positivity rate for repeat testers is now 0.3%, after holding at 0.2% for a month. Three-quarters of the tests done are for repeat testers, and the number of tests is increasing slowly – now at 60,000 per day on average.


Table 1: Massachusetts Testing Statistics
7 Day  Trailing Average
October 12, 2020
Testing Statistic Current 7 Days Ago 4 Weeks Ago
Test Positivity Rate (Individuals) 3.6% 3.7% 2.3%
Test Positivity Rate (Include Suspected) 3.8% 4.0% 2.5%
Test Positivity Rate (All Tests) 1.1% 1.2% 0.8%
Test Positivity Rate (Newly Tested) 3.6% 3.7% 2.3%
Test Positivity Rate (Repeat Testers) 0.3% 0.2% 0.2%
Percentage Repeat Testers 75.5% 73.6% 70.5%
Newly Tested (Lagged 1 Week) 15,927 15,449 18,368
All Tests (Lagged 1 Week) 60,215 57,687 49,180


If there is a flashing yellow sign, it is for hospitalizations.  The 7 day average of hospitalized patients is over 500, a level not seen since mid-July.  We’re closing in on almost 40 new patients per day, the highest figures since the end of June.  ICU patients and intubated patients remain elevated compared to a month ago.


Table 2: Massachusetts Hospitalization Statistics
7 Day Trailing Average
October 12, 2020
Hospitalization Statistic Current 7 Days Ago 4 Weeks Ago
Covid Patients Hospitalized 505 438 328
Covid Patients in ICU 85 86 58
Covid Patients Intubed 29 30 22
New Confirmed Patients 37 33 18
Percent ICU / Hospitalized 17% 20% 18%
Percent Intubated / ICU 35% 35% 37%


Cases also remain elevated, and deaths continue unabated  The 7 day average of deaths has been between 12 and 17 since late August.  The anomalous one-day report for long-term care facility deaths (43 deaths in long-term care facilities, but only 20 overall deaths on October 5) has rolled off the current statistics and is now embedded in the figure for one week ago.


Table 3: Massachusetts Reported Case and Death Statistics
7 Day Trailing Average
October 12, 2020
Statistic Current 7 Days Ago 4 Weeks Ago
Total Deaths Including Suspected 12 16 12
Total  Deaths Confirmed Only 12 16 12
Deaths in Long-Term Facilities (All Cases) 8 15 7
Percent from Long-Term Care 67% 89% 59%
Total Cases Including Suspected 602 627 328
Total Confirmed Cases 575 587 299
Age Analysis

Massachusetts Covid Breakdown by Age Part II: Case Analysis

In my previous post, I described my methodology for estimating the number of Covid cases, hospitalizations, and deaths by age cohort in Massachusetts. That post details the issues associated with determining these estimates because of lack of consistency and transparency in the data published by the state. This post begins the analysis based on these estimates.

Figure 1 shows an estimate of the weekly incidence of Covid cases for four different age cohorts (under 40, 40 to 59, 60 to 79, and 80 plus) starting May 30th. Prior to that, case incidences for people 80 and over are very large relative to current figures – this makes current trends less easy to discern on a graph. (The case incidence rate for people 80 plus in Massachusetts peaked at over 1,000 per 100,000 per week in late April, meaning that over 1% of people of that age were being diagnosed with Covid each week). The population estimates I use to calculate incidence rates are the same as those the state uses for its age cohort calculations in the weekly public health report.

Figure 1 clearly demonstrates the dramatic change in case incidence over time for those 80 and over, with a sharp decline through the middle of July so that this cohort now has low case rates compared to those under 60. The other age groups have similar rates through June, but these rates have diverged since, so that people between 60 and 79 now have low relative case incidences. In short, Figure 1 shows the both the shift in cases from older to younger populations, and the increase in cases for all age groups after Labor Day.

Figure 2 shows the percentage of confirmed and suspected cases for each age group, starting April 4th because there are no scaling issues here. It shows the shift to younger people in a different way – the percentage of cases in those under 40 grew from about 30% at the beginning of April to roughly 60% currently, while the percentage of cases for those 60 and older has declined from over 30% in April to just over 10% now. Figures 1 and 2 may seem contradictory for those 80 and over. However, over half the state is under 40, and only 4% is 80 and over – meaning that the case incidence rate for those over 80 could be very high, but cases in that age cohort remain a relatively small fraction of total cases.

Figure 3, which shows the ratio of the case percentages to population percentages for each cohort, illustrates this in a different way, essentially combining the information in Figures 1 and 2. For the state as a whole, this ratio must equal 100%, so a figure over 100% means that a particular age cohort has a higher share of the cases than one would expect based on its population, and a figure under 100% means that the age cohort has a lower share of the cases than one would expect based on its population. If cases were proportional to population for each age group, these ratios would be exactly 100%.

Figure 3 perhaps best shows the shift in the dynamics of cases by age, as cases for those those under 40 went from well below average in April to above average (and the most over-represented cohort) now. Conversely, those 80 and over, who at one point were 17% of cases with only 4% of the population, now have much lower relative risk for being diagnosed with Covid. That also holds to for those between 60 and 79, but the change has been less dramatic. This is presumably because seniors are now either less likely to be in situations where they can be infected by Covid, or because they take more stringent precautions when in these situations.


Massachusetts Covid Breakdown by Age Part I: Methodology

Since late August, I’ve wanted to perform an analysis of Covid cases, hospitalizations, and deaths by age cohort. Unfortunately, the reporting of this information by the state is (1) not transparent (2) internally inconsistent, and (3) sometimes clearly incorrect. I’ve spent time over the last month attempting to compile data from the weekly public health reports to which this information has been relegated. That work has been frustrating, to put it mildly.

The remainder of this post details the issues with the age cohort data provided by the state, and what I’ve done to calculate estimates of these important coronavirus statistics from the data provided. Parts of this post are technical in nature, so skip to the following posts for the bottom line.

Through August 11, the state provided a daily summary of cumulative cases, hospitalizations, and deaths by eight different age cohorts (and one group for unknown age) on its dashboard. Since then, all information by age cohort has been included only in the weekly public health report. In addition, the state dropped its cumulative reporting, and now provides age-based summaries for the prior two weeks only. This makes weekly tracking difficult, as one week rolls off and a new week is added to the summary in each report.

Fortunately, the state continues to provide a daily breakdown of cumulative cases, hospitalization, and death counts by race/ethnicity. Through August 11, the race/ethnicity total counts matched the total counts in the age cohort report as well as the aggregate totals for cases and deaths shown in the dashboard (confirmed and suspected).  After August 11, the state dropped the reporting of suspected cases and deaths from the daily dashboard as well. 

As an aside, the data aggregators covid tracking ( and worldometers ( began to use the race/ethnicity report to tabulate cases and deaths in Massachusetts, as it was only source of confirmed and suspected cases available on a daily basis. (The state added back probable cases and deaths to the daily Dashboard report in early September, but these data are no longer on the front page).

The race/ethnicity totals match the case and death totals reported by the state each day, but the two week totals in the weekly public health report by age cohort do not match the figures for the equivalent period in the race/ethnicity report. Table 1 shows these discrepancies starting August 8.

Table 1: Massachusetts Reporting of Total Cases, Hospitalizations and Deaths
Comparison of Weekly Public Health Reports to Daily Race/Ethnicity Report
August 8 to October 3, 2020
  From Daily Reports   From Weekly Reports
Two Weeks Ending Cases Hospitalized Deaths   Cases Hospitalized Deaths
8-Aug 5443 231 211   3912 116 14
15-Aug 5159 240 200   4856 107 180
22-Aug 4649 212 200   4728 82 200
29-Aug 4476 186 208   4398 78 200
5-Sep 4830 196 220   4716 91 190
12-Sep 4570 174 187   4785 81 176
19-Sep 4985 190 179   5126 97 184
26-Sep 5510 211 195   5947 124 202
3-Oct 7122 208 212   7672 133 223

Table 1 clearly shows the mismatch between the totals from the two reporting sources.  In particular, the death total for August 8 (this is not a typo), and the new hospitalization totals for the entire period stand out as particularly inconsistent.  Hospitalizations appear to be significantly under reported in the weekly report, both in comparison to the race/ethnicity report and to the new hospitalizations reported independently by hospitals (not shown here). 

Calculating accurate estimates is complicated by another factor: on September 2, the state changed its definition of probable cases and eliminated 8,050 cases, 26 deaths, and roughly 100 hospitalizations from the historical count.  Fortunately, the state did provide a back history for the changes in cases and deaths, so that these figures can be adjusted accordingly.  The state did not provide a back history for change in hospitalizations, so the 100 figure is an estimate. And while the state did provide a back history for total cases and deaths, it did not provide revised figures by age cohort.

This data definition change is why Table 1 is broken into three three-week periods.  The first period, through August 22nd, is before the state made the change, so the figures shown for those dates are the actual numbers as reported, not the adjusted numbers,  in order to show equivalent totals for comparisons between the two sources.  (In my estimates later, I do adjust all figures downward). 

The second period is a “transition period” that reflects these definition changes.  The August 29th figures from the weekly reported (released on September 2nd) were already adjusted, but the daily reports are not.  The following two weeks, through September 12th, contain data both before and after the definition change.  Therefore, the weekly data is as reported, and the daily data has been adjusted through September 1 to reflect the case definition changes. 

The figures for the he final three-week period are as reported, because the case definitions for both reports are aligned once again. (In this final period, the weekly reported figures for cases and deaths are always higher than the daily reported figures.  It almost appears that the state is erroneously using a 15 day total, rather than a 14 day total).

To reflect all of this, I used the following approach to estimate cases, hospitalizations, and deaths by age cohort.  First, all the data prior to September 2nd has been adjusted to reflect the definition change for probable cases.  Second, prior to and including August 8th, I derived weekly figures by simply summing daily figures.  (This means that I do not have to rely on the August 8th weekly public health report, as the 14 deaths reported there are clearly wrong).  Finally, starting August 15th, I used the following approach:

(1)  For each two week period, calculate the total number of cases, hospitalizations, and deaths over that period from the race/ethnicity report.

(2) Scale the age cohort figures in the weekly report for each statistic so that the totals calculated match that for the same period from the race/ethnicity report.  For example, suppose there are 200 total deaths over a two week period from the race/ethnicity report, but 160 deaths reported for that same period in the weekly age cohort report.  Furthermore, suppose there are 20 reported deaths for people aged 60 through 79.  This means that I calculate 24 deaths for that age cohort for that period (200 / 160 * 20).

(3) Subtract off the figures calculated for each age cohort for the prior week for each statistic to derive an estimate for the current week.  Because I have actual daily data from the race/ethnicity report for the week ending August 8th, I have a starting point for the August 15th calculation.

This approach ensures two things.  First, the percentages by age cohort for each statistic are preserved for each two-week period.  Second, total cases, hospitalizations, and deaths match the totals reported by the state for each two-week period. 

The third step, the subtraction, seems to lead to more volatile weekly changes than one might expect, and is probably the weakest part of the approach.  This is particularly true for hospitalizations, for which the weekly data is most suspect.  In fact, for the August 15th calculation, which blends together daily age data with weekly data, a naive implementation leads to negative hospitalizations and deaths for the 80 plus group for that week.  Quite simply, I fudged some numbers  there to make the numbers seem more reasonable.

The next several posts will use the estimates calculated this way to analyze information about cases, hospitalizations, and deaths by age cohorts.


Data Update

Massachusetts Data Update October 7, 2020

There are signs that we are stabilizing once again in Massachusetts, but unfortunately with higher test positivity rates than before. Positivity rates for newly tested individuals have been above 3% since September 26th, and the 7 day average rate is currently 3.6%. However, this  rate has not changed since the beginning of the month. The overall test positivity rate is still 1.1% (unchanged since September 28th), and positivity is at 0.2% for repeat testers (unchanged for a month). Testing remains dominated by repeat testers.


Table 1: Massachusetts Testing Statistics
7 Day  Trailing Average
October 7, 2020
Testing Statistic   Current 7 Days Ago 4 Weeks Ago
Test Positivity Rate (Individuals)   3.6% 3.5% 2.0%
Test Positivity Rate (Include Suspected)   3.9% 3.7% 2.1%
Test Positivity Rate (All Tests)   1.1% 1.1% 0.8%
Test Positivity Rate (Newly Tested)   3.6% 3.5% 2.0%
Test Positivity Rate (Repeat Testers)   0.2% 0.2% 0.2%
Percentage Repeat Testers   74.1% 72.7% 67.2%
Newly Tested (Lagged 1 Week)   15,990 14,300 21,520
All Tests (Lagged 1 Week)   58,675 55,480 46,364


As cases and positivity rates increased over the past few weeks, it is perhaps inevitable that hospitalizations would increase as well, but with a bit of a lag. The 7 day average of hospitalized patients and the number of intubated patients are both at their highest level since the end of July. The 7 day average of newly admitted patients is at its highest level since the beginning of July.


Table 2: Massachusetts Hospitalization Statistics
7 Day Trailing Average
October 7, 2020
Hospitalization Statistic   Current 7 Days Ago 4 Weeks Ago
Covid Patients Hospitalized   456 404 324
Covid Patients in ICU   82 84 53
Covid Patients Intubed   31 29 24
New Confirmed Patients   34 31 22
Percent ICU / Hospitalized   18% 21% 16%
Percent Intubated / ICU   38% 34% 45%


Deaths from Covid continue unabated. One anomaly in the statistics today is the percentage of deaths from long-term care facilities, which spiked to 87% of all deaths in the past week.  This is an artifact of the way data is reported in Massachusetts: on October 5th, the state reported an additional 43 deaths in long-term care facilities, but only 20 new deaths overall. 

Undoubtedly, the 43 long-term care deaths represent some sort of backdating of prior deaths, but it is unclear as to why this reporting isn’t reflected in the overall death figures.  This points out that short run trends may be somewhat unreliable – however, a salient statistic is that over 70% of deaths from Covid in Massachusetts since June 1 have been in long-term care facilities (looking at this percentage over a longer period removes short-term reporting anomalies) .  Cases continue upward, with higher positivity rates and overall testing that is flat.  We haven’t had this many cases since the end of May.


Table 3: Massachusetts Reported Case and Death Statistics
7 Day Trailing Average
October 7, 2020
Statistic   Current 7 Days Ago 4 Weeks Ago
Total Deaths Including Suspected   14 16 12
Total  Deaths Confirmed Only   14 15 12
Deaths in Long-Term Facilities (All Cases)   12 10 7
Percent from Long-Term Care   86% 67% 56%
Total Cases Including Suspected   625 515 289
Total Confirmed Cases   588 478 281



College Testing

Massachusetts College Testing Update October 5, 2020

Colleges and Universities are not driving the negative trends in cases and hospitalizations from Covid in Massachusetts. In fact, testing positivity rates for colleges are significantly below that for the state as a whole, and higher education testing is helping to keep positivity rates in check.

Table 1 shows updated cumulative testing and positive test percentages for twelve greater Boston area colleges and UMass Amherst through the end of last week. (This is an updated version of the table from an earlier post

Table 1: Greater Boston Area College Covid Testing
Cumulative Testing Results
October 4, 2020
  Results As Of Total Positive Positive
College/University Date Date Tests Tests Rate %
Babson 5-Aug 1-Oct 16,927 9 0.05%
Bentley 17-Aug 1-Oct 20,466 9 0.04%
Boston College 16-Aug 2-Oct 44,687 177 0.40%
Boston University 27-Jul 3-Oct 190,094 134 0.07%
Brandeis 12-Aug 2-Oct 35,566 12 0.03%
Emerson 6-Aug 1-Oct 21,909 19 0.09%
Harvard  1-Jun 2-Oct 89,371 54 0.06%
MIT 16-Aug 2-Oct 91,508 45 0.05%
Northeastern 17-Aug 2-Oct 197,836 103 0.05%
Suffolk 18-Sep 1-Oct 14,264 20 0.14%
Tufts 3-Aug 2-Oct 75,177 36 0.05%
UMass Amherst 6-Aug 2-Oct 70,111 121 0.17%
Wellesley 16-Aug 2-Oct 16,237 1 0.01%
Total     884,153 740 0.08%


Overall positivity rates remain very low, with cumulative rates above 0.1% only for Boston College, Suffolk, and UMass Amherst. Boston College appears to have brought its earlier small outbreak under control. Table 2 shows testing and positivity figures for the past week.

Table 2: Greater Boston Area College Covid Testing
Latest Weekly Results
October 4, 2020
    Average Weekly  
  As Of Daily Positive Positive Test
College/University Date Tests Tests Percent
Babson 1-Oct 337 1 0.04%
Bentley 1-Oct 121 3 0.35%
Boston College 2-Oct 941 9 0.14%
Boston University 3-Oct 3,790 1 0.03%
Brandeis 2-Oct 550 3 0.08%
Emerson 1-Oct 469 3 0.09%
Harvard  2-Oct 2,326 5 0.03%
MIT 2-Oct 2,272 12 0.08%
Northeastern 2-Oct 4,845 18 0.05%
Suffolk 1-Oct 434 4 0.13%
Tufts 2-Oct 2,117 5 0.03%
UMass Amherst 2-Oct 1,830 79 0.62%
Wellesley 2-Oct 545 0 0.00%
Total   20,577 143 0.12%

Note that the tests are shown on a daily basis so they can be compared across schools, but positive tests are for the entire prior week.  This table does point out the recent outbreak at UMass Amherst, at which cases began increasing on September 22nd.  Cases at UMass Amherst have increased even more over the past week.  Otherwise, positivity rates remain low.

The state has provided aggregate information on higher education testing for the past several weeks in its weekly public health reports. Figure 1 shows the average number of daily tests performed for higher education purposes relative to the total number of tests statewide from September 1st to 27th.  (Note that this report lags the data presented in Tables 1 and 2 by about a week, because of state reporting lags).

Figure 1 shows that higher education testing since September 1 has been slightly more than half of the testing in the entire state, indicating that higher education testing is now the most significant testing driver statewide. Over this period, higher education testing positivity rates have ranged between 0.05% and 0.11%. Because it is likely that much of the testing in higher education is repeated testing of the same individuals, these rates should probably be compared to the repeat tester rates statewide (which has been steady at 0.2% for several weeks). This indicates that test and case positivity rates outside of higher education are actually higher than they appear at first glance from the published statewide numbers. In fact, statewide test positivity rates outside of higher education ranged between 1.6% and 1.9%, compared to the 0.8% and 0.9% overall figure during September.

One last point.  The thirteen institutions highlighted in Tables 1 and 2 appear to be doing most of the higher education testing statewide.  Adjusting for the lag in reporting at the state level and the individual college level, over 70% of the higher education tests and 65% of the higher education positive tests are associated with those thirteen schools.


Data Update

Massachusetts Data Update October 3, 2020

My data updates tend to be very table oriented. I find this a useful way to present information that can be easily and quickly grasped. But that approach can obscure longer term trends that provide context about the spread of Covid in Massachusetts. This data update provides graphical formulations of selected data from my usual coverage to better illustrate where we are compared to where we’ve been.

I’m starting these graphs on June 1st for two reasons. First, some of the information I present has only been published in the daily coronavirus updates provided by the Commonwealth since June 1st. Second, the scale of certain data prior to June 1st is so out-sized relative to current information that it obscures recent trends in the data. As an example, the number of reported hospitalizations peaked at almost 4,000 in late April, compared to 300 to 400 today. When a graph is scaled to include 4,000 hospitalizations, changes from 300 to 400 appear small. Relative to the beginnings of the outbreak, that change is indeed small, but in the current context that change may be significant.

Figure 1 shows test positivity rates through October 1st. The black line is the positivity rate for newly tested individuals. This is the rate the state emphasized through mid-August, when it switched its headline positivity number to the “all test” positivity number (shown in red). The black “new individuals” line clearly shows a decline in test positivity during June, shows that positivity rates were under control (under 2%) during July and August, and shows that rates began to increase near the end of August. As of the October 3rd update, this rate has climbed to 3.6%.

The blue line is the positivity rate for repeat testers. It demonstrates the changing composition of repeat testers over time. Through mid-July, repeat testers were likely individuals who had tested positive for coronavirus and were getting retested to see if they were clear. At that time, the positivity rates for repeat testers were higher than the rates for those newly tested. Starting sometime near the end of July, it appears that preventative testing (for front-line workers and college communities) became more prevalent among repeat testers, driving down the repeat testing positivity rate below the rate for newly tested individuals. It has been about 0.2% for several weeks.

We can also derive the mix of new testers and repeat testers. The “all test” line is a weighted average of the “new individuals” line and the “repeat tests” line. In June, the “all test” line is closer to the “new individuals” line, indicating that more of the tests were for new individuals (roughly a 75-25% mix). Over time, especially as the amount of college testing has increased dramatically, the “all test” line has moved closer to the “repeat tests” line (now roughly 75-25% but with the categories switched).

Figure 2 summarizes hospitalization information, also through October 1st. For clarity, the number of patients hospitalized (in black) is shown on the right axis, and the other statistics (ICU patients, intubated patients, and new admissions) or shown on the left axis. The scale ratio between the two axes is 4:1.

Hospitalization and ICU figures track each other well, with a relatively steep decline until the end of July, a roughly level period until around Labor Day, and a gradual increase since. It is a bit difficult to tell from the chart because hospitalized patients and ICU patients are shown on different scales, but the percentage of patients in the ICU has declined from about 25% at the beginning of June to about 20% now (although the percentage bottomed under 15% near the end of July).

The number of intubated patients as a percentage of ICU patients declined from about 70% at the beginning of June to about 35% currently. While intubations have increased slightly since Labor Day, the increase is smaller in percentage terms than the increase in the number of ICU patients, either because admitted patients are less ill than previously, or because treatment protocols have changed. The ratio of new admissions to total hospitalizations has been relatively constant since June 1 – between 4% and 7% until just about a week ago, when it went above 7% for the first time. That is perhaps a worrying trend.

Figure 3 shows the 7 day trailing average number of cases and deaths. Cases are shown in black on the right hand axis, deaths are in red and blue on the left hand axis. The scaling is 10:1.

As Figure 3 illustrates, the daily number of deaths declined rapidly through June and the beginning of July, but has been basically steady since then. The same is roughly true for deaths in long-term care facilities (LTC Deaths). About 70% of all (confirmed and suspected) deaths since June 1 have been in long-term care facilities. This ratio has been declining over the past month, but very slowly.

The number of cases also dropped sharply through the end of June (with a low under 200 cases per day), but began to tick upward starting in July, leveled off during much of August, and then started its current sharp upward swing after Labor Day. Much of the recent increase is not from increased testing, but from higher positivity rates among those newly tested. Testing has increased from about 9,000 new individuals per day at the end of June to about 15,000 per day now (and peaked at about 20,000 near the end of August), but the newly tested positivity rate was already below 2% on June 30, compared to 3.6% today.

Community Testing

Community Spread in Massachusetts – Part II

What a day, as we learn Trump tested positive for the coronavirus. No further comment is necessary on that. But here’s a trivia question for you. Over the two week period ending September 26, what Massachusetts community had the highest per capita Covid testing rate? Stop. Before you read on, think about it. Is it Chelsea, or Everett, or Lowell, or another one of the hot spot communities in Massachusetts? Is it Boston, because of the many medical centers located there? No.

As Table 1 shows, the big winner is Williamstown, home to Williams College.  More than 4% of Williamstown’s population is being tested each day for coronavirus.  Of course, this figure is somewhat distorted, as many of those tested are presumably students who are not included in Williamstown’s stated population.  But even if one assumes that all of Williams College’s students (about 2,000) were back on campus, the per capita testing rate is astounding.

And there was even more testing being done in Williamstown for the two weeks ending September 19th, as it had the largest dropoff in testing from week to week.  In all, nine of the top ten per capita testing communities are home to college and universities. And even Somerville’s inclusion might partially reflect testing associated with Tufts. (In the original version of this post, I had stated that Dudley was a outlier, because I didn’t realize that it is home to Nichols College, which has done extensive testing.  Thanks to Jen for pointing out the error).


Table 1: Per Capita Massachusetts Testing Statistics
Most Testing and Largest Testing Changes
Week over Week Ending September 26,2020
Two Weeks Ending 9/26/20   Weekly Change Ending 9/26/20
City/Town Daily Tests per 100,000   City/Town Largest Increase in Daily Tests Per 100,000   City/Town Smallest Increase in Daily Tests Per 100,000
Williamstown 4,211   Southborough 431   Williamstown -796
Amherst 3,856   Cambridge 421   Nantucket -105
Cambridge 2,622   Newton 401   Somerset -10
Wellesley 2,328   North Andover 379   Charlton -8
Somerville 2,103   Boston 282   Peabody -7
North Andover 1,968   Somerville 263   Yarmouth -4
Norton 1,944   Dedham 259   Rowley -2
Boston 1,845   Brookline 250   N. Attleborough 4
Dudley 1,806   Wellesley 196   Wrentham 5
Waltham 1,684   Chelsea 158   Westport 6


One technical point. It is possible, although unlikely, that there are communities in Massachusetts with higher testing rates than shown here. Why? I am using population estimates that are embedded in the weekly report itself (it can be derived from the daily incident rate and the number of cases). But if there are fewer than five cases, the state suppresses the exact number, so I can’t derive a population estimate. In fact, of the 351 communities in Massachusetts covered in the report, I can’t calculate a population for over half. I could try to pull population estimates from other sources and integrate them into this analysis, but I think it highly unlikely this will add any community to the top ten list (and I’m lazy).

One other point related to the blog itself. As I noted when I first started, I’ve never blogged before. I’m learning as I go. And I noticed yesterday’s post via email, on a tablet, or on cell phone has strange formatting or the numbers weren’t visible through the colors. I am trying to learn how better to format the posts, but for now, if you flip your device to landscape mode, the posts become more readable (and I’ve bolded the numbers within colored cells).

Community Testing

Community Spread in Massachusetts September 26, 2020

As the Covid case rate and test positivity rate in Massachusetts begin to climb once again (albeit in a much more gradual and controlled fashion compared to the beginning of the outbreak), it is important to understand whether the increase is driven by just a few “hot-spot” communities or more widely distributed throughout the Commonwealth.  Fortunately, the state issues a weekly report that provides case rate and testing positivity information for each city and town within the state.

There are several issues with the report.  First, while it is issued weekly, it provides information for the trailing two weeks, so it is not possible to directly discern weekly trends (as a new week is added, an old week drops off).  Second, by the time the report is published on Wednesday evenings, it is a bit stale, as it contains information only up to the prior Saturday.  Nonetheless, it is what is available.

I’m concerned here with changes in case rates and changes in test positivity, not the absolute levels.  To do so, I look at the two week data published in the most recent report compared to the data in the report issued one week prior.  The rolling two week nature of the report can make the conclusions from this analysis misleading and mask short-term trends.  For example, if a really bad week rolls off the report, and is replaced with a more stable week, it can look as though trends are improving in a particular community when they really aren’t.  But this analysis can certainly provide insight, especially over the longer term.

The report includes new cases and case rates per 100,000 over the prior two weeks.  For the state in aggregate, the case rate is just the weighted average of the case rate in each community in the state, where the weights are equal to the population in that community divided by the population of the state.  Therefore, the change in the state case rate is just the weighted average of the case rate change in each community (with the population-derived weights).

We can then rank communities by their impact on the state case rate change by looking at the product of their case rate change and their population-derived weight.  What does this tell us?  A community is likely to be at the top of the list if (1) it is relatively large, or (2) it has had a relatively large change in case rates, either positive or negative.  Smaller communities with relatively stable case rates have little impact on the overall state figures.  In contrast, Boston, which has about 10% of the state’s population is likely to be at the top of the list even with small changes in its case rate.  Table 1, which shows the top ten biggest contributors to the increase in the state case rate, illustrates this point.


Table 1: Top Ten Contributors to Massachusetts Case Incidence Increase
Rolling Two-Week Case and Incidence Rates
Week over Week Ending September 26,2020
Two Weeks Ending 9/19/20 Two Weeks Ending 9/26/20
City/Town 14 Day Case Count Daily Case Rate per 100,000 14 Day Case Count Daily Case Rate per 100,000 % Contribution
Springfield 95 4.3 183 8.3 6.3%
North Andover 26 6.1 111 26.2 6.1%
Haverhill 52 5.6 129 14.0 5.5%
Boston 773 7.9 825 8.5 4.0%
Lowell 129 7.9 179 10.9 3.6%
Lawrence 273 22.1 313 25.4 2.9%
Methuen 59 7.9 94 12.5 2.5%
Plymouth 27 3.1 48 5.5 1.5%
Amherst 3 0.5 24 4.2 1.5%
Burlington 4 1.0 21 5.4 1.2%
Total/State 4823 4.9 5569 5.7 35.0%


Both Boston, with a relatively small increase in cases rates, and Amherst, with a population of about 40,000, are in the top ten negative contributors.  However, Amherst has had a significant case increase, presumably from an outbreak associated with UMass.  Note that all the communities in Table 1 moved up one color zone in the state’s three-tier color-coding system, with the exception of Lawrence, which was already in the red zone.

The last column is a measure of the percentage impact each community had on the state’s case rate increase.  The primary takeaway is that the impact is widely dispersed among these communities – there are not a few new “hot-spots” driving the case rate increase.

Table 2 is the equivalent report, but focused on the communities which have contributed the most to a decrease in the state’s case rate.  Because the overall rate is increasing, the impact on the overall rate is significantly smaller for these communities.  Also, only three of them (Newton, Somerville, and Wrentham) shifted down a color zone.  Newton had barely been in the yellow zone to start.

Table 2: Top Ten Contributors to Massachusetts Case Incidence Decrease
Rolling Two-Week Case and Incidence Rates
Week over Week Ending September 26,2020
Two Weeks Ending 9/19/20 Two Weeks Ending 9/26/20
City/Town 14 Day Case Count Daily Case Rate per 100,000 14 Day Case Count Daily Case Rate per 100,000 % Contribution
Newton 52 4.0 33 2.6 -1.4%
Chelsea 118 22.4 99 18.8 -1.4%
Lynn 160 11.3 143 10.1 -1.2%
Framingham 130 12.5 116 11.1 -1.0%
Worcester 238 8.9 224 8.3 -1.0%
Nantucket 42 26.5 30 18.9 -0.9%
Somerville 53 4.9 41 3.8 -0.9%
Hingham 25 7.5 14 4.2 -0.8%
Brockton 92 6.7 82 6.0 -0.7%
Wrentham 19 12.0 11 7.0 -0.6%
Total/State 4823 4.9 5569 5.7 -9.7%


The state also provides testing counts and positivity rates by community.   Here, the state provides the data for the lower “all testing” positivity rate (which it has been emphasizing since mid-August), not the individual case positivity rate.  The testing positivity rate was essentially unchanged between the two reports. The statewide positivity rate is just a weighted average of each community’s positivity rate, but the weights are now the number of tests for each community divided by the total number of tests.  Also, unlike population-based weights, the weights for each community can vary from report to report as testing counts change.


Table 3: Top Ten Contributors to Massachusetts Test Positivity Increase
Rolling Two-Week Test and Positivity Rates
Week over Week Ending September 26,2020
Two Weeks Ending 9/19/20 Two Weeks Ending 9/26/20
City/Town 14 Day Test Count Test Positivity Rate (%) 14 Day Test Count Test Positivity Rate (%) Relative Impact (%)
North Andover 6,730 0.40 8,335 1.43 11.4%
Springfield 10,714 1.10 11,488 1.92 11.3%
Haverhill 3,732 1.77 4,466 3.27 9.2%
Methuen 3,237 2.41 3,745 2.99 3.1%
Lowell 6,785 2.24 7,196 2.71 3.0%
Plymouth 2,474 1.21 2,919 1.75 2.2%
Burlington 1,457 0.41 1,616 1.42 2.1%
Amherst 21,102 0.05 21,862 0.12 1.9%
Middleton 421 1.43 529 3.78 1.7%
Webster 1,087 0.28 1,197 1.34 1.6%
State 693,958 0.86% 782,320 0.87%


The communities dominating the positivity rate tables are either those with large changes in positivity rates or those performing many tests.  Table 3 shows the top ten contributors based on increases in the positivity rate.  For example, Amherst, which has a very low positivity rate, is a very big tester relative to its population presumably because of UMass.  It is testing at almost eight times the rate of Springfield.

Table 4 shows the top ten communities contributing to a decrease in positivity rates.  Boston is on this list, even with a very small positivity rate decrease, because of its large number of tests (almost 23% of the state total for the last two weeks).  This might appear to contradict the inclusion of Boston as a top ten contributor to an increase in the case rate in Table 1.

However, it does not.  First, case rates and test positivity rates are measuring different things (case rates focus on individuals and test positivity rates are just measuring tests including repeat testers).  Second, the increase in the case rate in Boston can easily be a result of increases in newly tested individuals (impossible to discern from this report), as overall testing increased by 18% from one period to the next.   In other words, there can be both increases in case rates and decreases in positivity rates if more testing is being done.

Table 4: Top Ten Contributors to Massachusetts Test Positivity Decrease
Rolling Two-Week Case and Incidence Rates
Week over Week Ending September 26,2020
Two Weeks Ending 9/19/20 Two Weeks Ending 9/26/20
City/Town 14 Day Test Count Test Positivity Rate (%) 14 Day Test Count Test Positivity Rate (%) Relative Impact (%)
Lynn 5,641 4.11 6,068 3.33 -8.5%
Worcester 34,906 0.86 36,092 0.79 -7.6%
Chelsea 3,858 4.02 4,690 2.75 -6.6%
Revere 4,636 4.31 5,031 3.82 -4.8%
Boston 152,051 0.60 179,475 0.56 -4.7%
Newton 14,336 0.44 19,485 0.21 -4.4%
Framingham 4,426 3.32 5,511 2.49 -4.1%
Brockton 5,324 2.27 5,623 1.97 -3.6%
Somerville 19,717 0.35 22,532 0.26 -2.8%
Nantucket 1,127 3.73 961 3.23 -2.3%
State 693,958 0.86% 782,320 0.87%