X-Message-Number: 21547
Date: Sun, 6 Apr 2003 03:24:21 -0400 (EDT)
From: Charles Platt <>
Subject: SARS update, April 5, 2003

We now have three weeks of SARS data from the World Health Organization;
i.e. 18 data points (the bureaucrats at W.H.O. seem to feel no pressing
need--yet--to report data on Sundays). The obvious question is: Do the
data points constitute a trend?

An acquaintance of mine who shall remain nameless (mainly because I
wouldn't want to embarrass him) has spent a surprising amount of time
plotting curves on log paper in an attempt to measure the "doubling time"
of cases in nations where the virus is active. As I recall from my distant
educational past, if you have an exponential growth rate, the data should
appear as a smooth upward-trending curve on normal graph paper but will be
displayed as a straight line on log graph paper; and if you measure the
slope of the line, you can derive the doubling time.

Unfortunately, if you don't have an exponential growth rate but you are
pigheaded enough to plot the numbers on log graph paper anyway, the
squiggly lines are open to interpretation, and my acquaintance has seen
doubling times which I believe exist only in the eye of beholder. To prove
my point I have gone back to basics and plotted the numbers against a
normal, arithmetic scale. (Even this is liable to give misleading results
if the data are unreliable, but more on that below).

If you point your browser to


you will find four graphs showing the number of SARS cases in the USA,
Singapore, Hong Kong, and Canada. I have omitted other countries because
they have not yielded valuable data. Taiwan, for instance, currently
reports 17 cases, having started with 3 on March 18. I can't believe that
meaningful trends can be derived from such small numbers. Likewise France,
Germany, Italy, Ireland, Romania, Switzerland, Thailand, the UK,
Australia, Belgium, and Brazil are reporting a cumulative total of fewer
than 10 cases each. Clearly this is not the stuff of which epidemics are
made (yet), and you'd have to be extremely paranoid to conclude that there
is any significant problem in these nations (yet).

At the other extreme is China, which insisted it had a static number of
806 cases from March 27 through April 1, but then revised its total to
1190, and probably has a whole bunch more. Any trend derived from Chinese
numbers will be as unreliable as the numbers themselves.

Even the nations which supposedly have been cooperating with the W.H.O.
have shown sudden variations in their data. Hong Kong, for instance, went
from 530 cases to 685 cases in one day, when it decided that pretty much
everyone in a single apartment building probably had SARS. Are other
apartment buildings similarly infected, but as yet unreported? Maybe,
maybe not.

Data generally may be underestimated because cases have not been
diagnosed, diagnosed cases have not been officially reported, nations have
been reluctant to admit that they are infected, and infected people may be
in the incubation phase, which is asymptomatic.

Conversely, some data may be misleadingly alarming. This is especially
true in most Western nations where almost all the cases (so far) are
people who were infected elsewhere. According to the Centers for Disease
Control in Atlanta, only about 10 percent of cases in the USA are "home
grown." Thus the recent disturbing increase in US cases (averaging 15 per
day for the past three days) probably is an index of the number of people
who sought sanctuary here while inadvertantly bringing with them the
disease that they hoped to avoid. So long as they are isolated before they
can infect other people, they do not constitute a meaningful local trend.
Whether the isolation will be sufficiently prompt to prevent secondary
infection is not yet known, especially because we do not know, definitely,
if SARS can be transmitted during the incubation period.

Another factor affecting the data is that mild SARS cases are more likely
to be reported today than three weeks ago, simply because doctors have
been alerted to look for the symptoms, and people arriving on airplanes
are likewise being told to notify health authorities if they get sick.

Having said all that, it's still worth graphing the data for two reasons.
First, if a really powerful trend exists, it may be discernible despite
all the random factors mentioned above. Second, if a trend is not
discernible, this is useful information too--especially when other
observers are trying to convince us that such a thing as a "doubling time"

The GIF files at my web site speak for themselves. I challenge anyone to
draw a smooth, upward-trending curve through those erratic points.

So far as I can see, the growth rate has been more or less arithmetic, not
exponential; we do not have a measurable doubling time; and therefore we
do not have an epidemic (yet). However it is a salutary experience to
compare the sheer magnitude of the problem in Hong Kong with the
situations in Canada, the United States, and Singapore. A fifth graph at
my web site facilitates this comparison and illustrates that (for reasons
which remain unexplained) Hong Kong cases have proliferated about six or
seven times as fast as cases anywhere else. Thus the primary challenge
seems to be containing the Hong Kong problem in Hong Kong. Whether this is
possible will depend largely on political and regulatory issues.

I conclude that for the time being at least, graphs of SARS cases are of
no help whatsoever in predicting the future of the disease outside of


PS. For further confirmation that we don't have enough information to
determine what's happening, consider this notice from W.H.O.:

"The SARS outbreak in Hong Kong SAR has developed an unusual pattern of
transmission. This pattern is different from what is being seen in the
vast majority of other SARS outbreaks, and is not yet fully understood.
The number of cases is continuing to increase significantly, and there is
evidence that the disease has spread beyond the initial focus in

"These developments raise questions related to other routes of
transmission, in addition to well-documented face-to-face exposure to
droplets released when an infected person coughs or sneezes.
Epidemiologists are considering whether SARS is being transmitted in Hong
Kong by some environmental means for which no satisfactory explanation has
been found.

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