Fig 1.
Detecting dispersion changes in case count time series.
a: Weekly incidence of COVID-19 in the United States, with time measured in weeks since January 4, 2020, showing an example of a randomly-selected 16-week period used as an incidence trend in simulation-based validation of the LRT test (red). b: Cases in one county (Douglas County, Nebraska) over the sample time period with estimated incidence trend (red) and estimated dispersion values on either side of the midpoint. c: Estimated versus true
in simulation studies combining a randomly-selected section of the national incidence curve with a random population size and set of dispersion values. Estimated values outside of tolerance plotted in purple (close to Poisson) and blue (close to collapsing to zero), and a line with an intercept of zero and a slope of one plotted in red. d: Statistical power of the LRT test with smooth function (red line) and a 99.7% confidence interval for predicted p (red shading).
Fig 2.
Dispersion analysis of weekly COVID-19 case data for Jefferson County, Alabama.
Results for all counties are shown in Fig 3. a: Weekly reported COVID-19 incidence. b: Estimated dispersion parameter () over time. c: Comparison of estimated dispersion (gray) with predicted values from the standard model
, where Ct is reported cases and
the reporting rate at time t. Predictions are shown for fixed
(black) and
(blue), chosen to encompass the range of
expected under variable
. d: Likelihood ratio test (LRT) statistic over time. Statistically significant changes in dispersion (red) correspond to p-values below the Bonferroni-corrected 5% threshold of a chi-square distribution with one degree of freedom.
Fig 3.
Incidence and dispersion between Jan 4, 2020 and March 18, 2023, in large counties in the US.
a: Mean COVID-19 cases of the 144 US counties over time (total cases over the counties divided by total population over the counties multiplied by 1,000). b: Mean of the 144 US counties over time. NAs produced by the method (see text) were removed from the average. c:
over time for each of the 144 counties, where county is the y-axis. d:
over time for each of the 144 counties. e: Expected value of
under the null model, assuming a reporting rate of 0.5 for each county. f: LRT p-values over time for each county.