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% | |