Exact tests of the superiority under the Poisson distribution

Association of National Football League Fan Attendance With County-Level COVID-19 Incidence in the 2020-2021 Season

IMPORTANCE

The 2020-2021 National Football League (NFL) season had some games with fans and others without. Thus, the exposed group (ie, games with fans) and the unexposed group (games without fans) could be examined to better understand the association between fan attendance and local incidence of COVID-19.

OBJECTIVE

To assess whether NFL football games with varying degrees of in-person attendance were associated with increased COVID-19 cases in the counties where the games were held, as well as in contiguous counties, compared with games without in-person attendance for 7-, 14-, and 21-day follow-ups.

DESIGN, SETTING, AND PARTICIPANTS

This cross-sectional study used data for all 32 NFL teams across the entirety of the 2020-2021 season. Separate daily time-series of COVID-19 total cases and case rates were generated using 7-, 14-, and 21-day simple moving averages for every team and were plotted against the actuals to detect potential spikes (outliers) in incidence levels following games for the county in which games took place, contiguous counties, and a combination. Outliers flagged in the period following games were recorded. Poisson exact tests were evaluated for differences in spike incidence as well across games with different rates of attendance. The data were analyzed between February 2021 and March 2021.

EXPOSURES

Games with fan attendance vs games with no fan attendance, as well as the number of fans in attendance for games with fans.

MAIN OUTCOMES AND MEASURES

The main outcome was estimation of COVID-19 cases and rates at the county and contiguous county level at 7-, 14-, and 21-day intervals for in-person attended games and non-fan attended games, which was further investigated by stratifying by the number of persons in fan-attended games.

RESULTS

This included a total of 269 NFL game dates. Of these games, 117 were assigned to an exposed group (fans attended), and the remaining 152 games comprised the unexposed group (unattended). Fan attendance ranged from 748 to 31 700 persons. Fan attendance was associated with episodic spikes in COVID-19 cases and rates in the 14-day window for the in-county (cases: rate ratio [RR], 1.36; 95% CI, 1.00-1.87), contiguous counties (cases: RR, 1.31; 95% CI, 1.00-1.72; rates: RR, 1.41; 95% CI, 1.13-1.76), and pooled counties groups (cases: RR, 1.34; 95% CI, 1.01-1.79; rates: RR, 1.72; 95% CI, 1.29-2.28) as well as for the 21-day window in-county (cases: RR, 1.49; 95% CI, 1.21-1.83; rates: RR, 1.50; 95% CI, 1.26-1.78), in contiguous counties(cases: RR, 1.37; 95% CI, 1.14-1.65; rates: RR, 1.45; 95% CI, 1.24-1.71), and pooled counties groups (cases: RR, 1.41; 95% CI, 1.11-1.79; rates: RR, 1.70; 95% CI, 1.35-2.15). Games with fewer than 5000 fans were not associated with any spikes, but in counties where teams had 20 000 fans in attendance, there were 2.23 times the rate of spikes in COVID-19 (95% CI, 1.53 to ∞).

CONCLUSIONS AND RELEVANCE

In this cross-sectional study of the presence of fans at NFL home games during the 2020-2021 season, results indicated that fan attendance was associated with increased levels of COVID-19 in the counties in which the venues are nested within, as well as in surrounding counties. The spikes in COVID-19 for crowds of over 20 000 people suggest that large events should be handled with extreme caution during public health event(s) where vaccines, on-site testing, and various countermeasures are not readily available to the public.

Boundary problem in Simon's two-stage clinical trial designs

The activity of a new treatment in clinical trials with binary endpoints can be assessed by comparing the observed response rate to the target response rate. Traditionally, a one-sided hypothesis is used to make statistical inference, and the actual Type I error rate has to be computed over the parameter space of the null hypothesis. The monotonicity property is a fundamental property that guarantees the actual Type I error rate occurring at the boundary. One-arm two-stage designs are considered in this article. We theoretically proved this important property when the final threshold value of a design is less than the first-stage sample size together with another weak condition being satisfied. The method used in this article may finally lead to the final complete proof of this property in the future. We also numerically proved that the monotonicity property is satisfied for designs with the first-stage and the second-stage sample sizes from 10 to 100.