SARS, lay epidemiology, and fear

Sir

Published online May 2, 2003 http://image.thelancet.com/extras/03cor4133web.pdf

Ann Falsey and Edward Walsh (published online April 8)¹ describe the fears that surround severe acute respiratory syndrome (SARS). In the past few weeks, our outpatient department in Germany has received numerous calls from worried doctors of companies doing business in Asia. These calls have increased since the claim was made that within 2 years every citizen of Hong Kong will be infected with SARS. A German newspaper² fitted an exponential curve to the cumulative number of probable SARS cases (as reported by WHO³), forecasting a progressively steeper increase in case numbers. Such predictions can have enormous economic repercussions, so they should be scientifically tenable; we do not believe they are.

To illustrate why, we have fitted curves to the cumulative cases reported from Hong Kong between Feb 21 and April 5, 2003. Microsoft Excel calculates an R ² of 0·98 for an exponential curve, indicating an excellent fit (figure, A ). Using the function of the curve, we can predict a total of 71 583 cases 60 days later. The exponential curve matches the dynamics of an epidemic in a closed population with a high basic reproductive number R₀, which corresponds to the average number of new cases that one infectious case is expected to produce. Under such conditions, almost everyone will become infected during the epidemic.⁴ However, a linear curve can be fitted to the same data, yielding an equally impressive R ² of 0.96, but predicting only 2410 cases 60 days later. Moreover, R ² statistics are invalid with cumulative data because the assumption that observations are independent is violated.

Figure.

Cumulative number (A) of reported cases of SARS in Hong Kong up to April 5, 2003, and daily number (B) of reported new SARS cases in Hong Kong up to April 26, 2003 (total n=1527)

Making predictions early in an outbreak by fitting simple curves is dubious for another reason–doing so ignores interventions to decrease contact rate and transmission probability. If successful, such efforts reduce R₀ and thereby case numbers.⁴ An emerging herd immunity would also reduce R₀. This effect might only be temporary, however, since antibody levels diminish rapidly in other coronavirus infections.⁵

Part B of the figure shows an alternative way of presenting the data, which we think is more informative. That there has not been a great increase in the average number of new cases per day in the past weeks becomes immediately apparent. Furthermore, the outbreak in a housing estate in late March is not followed by a pronounced peak of secondary cases 2–7 days later, as would be expected if R₀ was generally high. These data are compatible with the hypothesis of uncommon but effective modes of transmission, in combination with an overall R₀ that is not exceptionally high. Given the possibility of waning immunity, the data are also consistent with an emerging endemic situation in which a part of the population will be affected seasonally.4, 5

Attempts to model the dynamics of an epidemic early on can lead to untenable conclusions, especially when based on worst-case scenarios such as a persistently high R₀. Although we wholeheartedly support the policy to publish case numbers, a format that can be easier understood by lay people should be used–namely, daily case numbers instead of cumulative figures.