Questions: Temporal Clustering and Seasonality Analysis

Question 1

Epidemiologists detect a sharp cluster of gastroenteritis cases over 3 days among attendees of a company picnic, with all cases appearing within one incubation period. A second similar cluster appears 3 weeks later among employees who had no contact with the first group. What does this temporal pattern most suggest?

• A. A propagated outbreak originating from the picnic, with secondary cases appearing after one generation interval
• B. Two separate point-source exposures — each cluster is narrow and contained within a single incubation period, suggesting two distinct contamination events
• C. Annual seasonal influenza following its typical bimodal winter pattern
• D. Person-to-person spread from a single index case at the picnic generating two waves of transmission

Answer: (B)

Each cluster is narrow (cases within a single incubation period) and the two groups had no contact — both features are inconsistent with propagated transmission, which would show successive waves at intervals matching the incubation period with continuous chain-of-contact. Two separate narrow clusters in isolated populations point to two distinct point-source exposures. A propagated epidemic (option D) would show a gradually broadening curve with new cases at each subsequent generation, and would require contact between the two groups.

Question 2

Kulldorff's temporal scan statistic is used in disease surveillance rather than simply comparing weekly counts to a historical average. What is the key methodological advantage of the scan statistic?

• A. It is computationally simpler and requires less historical data than baseline comparison methods
• B. It tests windows of variable width across the time series without requiring prior specification of when or how long an outbreak will last, while correcting for the multiple comparisons introduced by scanning many windows
• C. It eliminates seasonal variation automatically, making a separate seasonal adjustment model unnecessary
• D. It can detect clusters from just two data points, making it faster to deploy in early outbreak response

Answer: (B)

The key advantage of scan statistics is that they do not require the analyst to pre-specify the time window of interest. An outbreak of unknown start date and duration can still be detected because the scan statistic tests all possible window locations and widths simultaneously. The multiple-comparison correction (via Monte Carlo simulation of the null distribution) ensures that the overall false positive rate is controlled despite testing many windows. A fixed-window baseline comparison method would miss outbreaks that don't align with the pre-specified interval.

Question 3

A significant peak in the autocorrelation function (ACF) at a lag of 52 weeks, computed from weekly disease incidence data, is consistent with annual seasonality in that disease.

• T. True
• F. False

Answer: True

The ACF measures how strongly disease counts at time t are correlated with counts at time t+k (lag k). For a disease with annual seasonality, incidence at week 1 in any given year is correlated with incidence at week 1 the following year — which is a lag of 52 weeks. A significant ACF peak at lag 52 (in weekly data) directly identifies a recurring annual pattern. The ACF would show additional peaks at multiples of 52 (104, 156 weeks, etc.) for a strongly seasonal disease.

Question 4

A broad, multi-week epidemic curve with new case waves appearing at intervals approximately equal to one incubation period is most consistent with a point-source food contamination event.

• T. True
• F. False

Answer: False

This pattern is the hallmark of propagated (person-to-person) transmission. In a point-source exposure, all cases share the same exposure event, so onset dates cluster within a single incubation period producing a narrow, peaked curve. When new waves appear at intervals matching the incubation period, it indicates successive generations of transmission: infected people from one generation expose others, who develop illness one incubation period later. Distinguishing these patterns is critical for response: point-source outbreaks require identifying and eliminating the source, while propagated outbreaks require interrupting transmission chains.

Question 5

Explain how the temporal shape and width of a disease cluster helps narrow down whether the underlying cause is a point-source exposure versus person-to-person transmission, and why this distinction matters for the public health response.

Model answer: A point-source exposure (e.g., contaminated food at a single event) produces a narrow, unimodal cluster: all exposed individuals share the same exposure time, so their onset dates are spread only by variation in incubation period around a single central exposure. The cluster width approximates one incubation period. In contrast, propagated transmission produces a broader, multi-modal pattern: the index cases infect secondary cases who infect tertiary cases, with each generation separated by approximately one incubation period — the curve broadens and shows successive peaks. The distinction matters critically for response: a point-source outbreak requires identifying and removing the contaminated source (a food product, a water supply); a propagated outbreak requires interrupting transmission chains through isolation of cases, contact tracing, or vaccination. Responding to a propagated outbreak as if it were point-source (by searching for a contaminated food) would miss the actual mechanism and allow the chain of transmission to continue.

The epidemic curve shape was recognized as a diagnostic tool long before formal statistical methods existed — John Snow's original investigation of the 1854 Broad Street cholera outbreak used the time distribution of cases (concentrated around a single exposure event at the pump) to identify point-source transmission. Modern scan statistics and autocorrelation methods formalize this intuition into rigorous statistical tests, but the underlying conceptual logic — temporal pattern reveals transmission mechanism — is the same.