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SARS Epidemiology
Dispatch
Multiple Contact Dates and
SARS Incubation Periods
Martin I. Meltzer*
*Centers for Disease Control and Prevention, Atlanta, Georgia, USA
Suggested citation:
for this article
Meltzer MI. Multiple contact dates and SARS incubation periods. Emerg
Infect Dis [serial online] 2004 Feb [date cited]. Available from:
URL: http://www.cdc.gov/ncidod/EID/vol10no2/03-0426.htm
Many severe acute
respiratory syndrome (SARS) patients have multiple possible incubation
periods due to multiple contact dates. Multiple contact dates cannot
be used in standard statistical analytic techniques, however. I present
a simple spreadsheet-based method that uses multiple contact dates to
calculate the possible incubation periods of SARS.
The appearance and rapid spread of severe acute respiratory syndrome
(SARS), caused by a previously unknown coronavirus (SARS-CoV) (1–3),
has already had a notable economic and social impact (4,5).
SARS has no definitive cure, although hospitalized patients have been
empirically treated with combinations of antibiotics, steroids, antiviral
drugs (typically ribavirin and oseltamivir), and mechanical ventilation
(6,7). No known drug can be used prophylactically, nor
is does a vaccine exist. Thus, to stop the spread of the disease, public
health officials have to rely almost completely on placing those who may
have been exposed to SARS-CoV under quarantine and isolating those with
suspected, probable, and confirmed SARS cases.
To make quarantine and isolation as effective as possible, knowing the
range of the possible incubation period of SARS is essential. Mathematical
modelers also need to know the characteristics of the incubation period
to provide estimates of possible spread and model the potential impact
of interventions. Many SARS patients often report more than one possible
date of contact with another known SARS patient (6,7),
however, which results in multiple dates of possible transmission and
infection (Table). These multiple dates prevent easy
identification of a discrete period of incubation for each patient, and
thus the data from such patients cannot be used in standard statistical
analytic techniques, such as regression analyses (unless the analyst chooses
a single incubation period from the possible choices) (8).
I present a simple method that allows a simulation of the frequency distribution,
including confidence intervals, of the possible incubation periods (in
days) for SARS. The method allows use of data from patients with multiple
potential incubation periods. One goal of the method was to keep it simple
by using common computer spreadsheet software, allowing for easy replication,
extension of the database and results, and rapid dissemination of the
method. The method can also be used to calculate when infectious persons
are most likely to have transmitted SARS to susceptible persons, even
when multiple days of possible transmission exist.
Methods
I used published data reporting possible incubation periods for 17 patients
(6,7) plus data from two case-patients in an unpublished database
maintained at the Centers for Disease Control and Prevention (CDC).
The data illustrate a common problem: many patients have multiple
possible incubation periods. I built a simulation model in a standard
computer spreadsheet (Excel 2000, Microsoft Corp, Redmond, WA) (see Appendix [Download
Excel 121 KB, 2 pages]).
I first listed each possible incubation period for every patient
for whom incubation period data were available (Table).
Then, for every patient, I assigned a random number generator (function
RAND in Excel software) to each possible incubation period. This
method is the equivalent of using a uniform distribution to select
an incubation period from all possible choices. Using a spreadsheet-based
simulation software package (@Risk, Palisade Corp., Newfield, NY),
I programmed the spreadsheet to run iterations of the model.
During a single iteration, for each patient, the programmed model selects
the incubation period with the highest random number for that iteration.
After a single iteration, the program calculates the frequency distribution
for the incubation periods. Then, the program assigns another set of random
numbers to each possible incubation period and selects and calculates
the frequency distribution. After numerous iterations, the program combines
all the frequency distributions from all iterations to provide a general
frequency distribution. From this final frequency distribution, descriptive
statistics can be obtained, such as the mean, median, 5th and 95th percentile
values. I ran approximately 10,000 iterations, at which point each additional
iteration caused the mean and the standard distribution for each possible
day of incubation to change by <1%.
Results
The three largest mean frequencies of incubation periods among the patients
examined were 2, 3, and 6 days (Figure 1). Incubation
periods of 1, 4, 5, and 10 days were the second highest mean frequencies
(Figure 1). However, the confidence intervals (5th
and 95th percentiles) for most of the potential incubation periods clearly
overlapped (Figure 1). This finding indicates that
with the given data set, an incubation period of 10 days is almost as
likely to occur as an incubation period of 6 days. Using the mean frequency
of each incubation period, I constructed a cumulative frequency graph
(Figure 2). The 95th percentile is 12 days, with
a median (50th percentile) of approximately 4 days.
Discussion
The incubation period for SARS is likely to be varied, with the frequency
distribution being nonnormal (Figure 1). Thus,
using mean incubation periods for activities such as mathematical modeling
will probably result in a misrepresentation of SARS transmission. The
type of analysis presented here can help public health officials determine
minimum quarantine periods for persons exposed to SARS, who are not yet
symptomatic. For example, public health authorities should be aware that
in a small percentage of case-patients, the incubation period might be
>10 days (Figure 2).
Given that data from only 19 patients were available for this analysis,
some caution should be exercised when evaluating the results. Adding or
subtracting relatively small numbers of patients can cause estimates such
as the 95th percentile of the cumulative frequency to change. More data
concerning the possible incubation period of SARS patients are needed.
The advantage of the method used here is that such data need not be specific.
The method readily “accepts” data in which patients have multiple possible
incubation periods. More data will likely reduce the confidence intervals
for the frequencies of each incubation day (Figure
1), giving a clearer picture of the actual frequency distribution
of all incubation periods.
The method can also be readily adapted to examine other aspects of SARS
epidemiology when unambiguous data are scarce. For example, with
the appropriate data, this method can be used to examine the frequency
distribution of when an infectious person infects other people. (An
Excel workbook [Excel 2000, Microsoft, Corp, Redmond, WA] containing
the model used to calculate the results shown in Figures
1 and 2,
and using the data shown in the Table, is available
in the Appendix [Download
Excel 121 KB, 2 pages]). Also, distributions of incubation periods can be
used to examine whether an association exists between incubation period
and likelihood of hospitalization or death.
Dr. Meltzer is senior
health economist in the Office of Surveillance, National Center for
Infectious Diseases, Centers for Disease Control and Prevention. His
research interests include studying the economics of interventions to
control and prevent infectious diseases, and providing economic data
to aid the planning for catastrophic infectious disease events.
References
- Peiris JSM, Lai ST, Poon LLM, Guan Y, Yam LYC, Lim
W, et al. Coronavirus
as a possible cause of severe acute respiratory syndrome. Lancet
2003;361:1319–25.
- Ksiazek TG, Erdman D, Goldsmith CS, Zaki SR, Peret T, Emery S, et
al. A
novel coronavirus associated with severe acute respiratory syndrome.
N Engl J Med 2003;348:1953–66.
- Drosten C, Günther S, Preiser W, van der Werf S, Brodt H-R, Becker
S, et al. Identification
of a novel coronavirus in patients with severe acute respiratory syndrome.
N Engl J Med 2003;348:1967–76.
- Chew P, Coughlin P, Chambers J. S&P correct: respiratory disease
SARS chokes Asia-Pacific growth, but sovereign ratings are secure. [Accessed
April 29, 2003] Available from: URL: http://www.standardandpoors.com
- Special report: the SARS epidemic. The Economist 2003, April 26;367:18–20.
- Poutanen SM, Low DE, Henry B, Finkelstein S, Rose D, Green K, et al.
Identification
of severe acute respiratory syndrome in Canada. N Engl J Med 2003;348:1995–2005.
- Tsang KW, Ho PL, Ooi GC, Yee WK, Wang T, Chan-Yeung M, et al. A
cluster of severe acute respiratory syndrome in Hong Kong. N Engl
J Med 2003;348:1977–85.
- Donnelly CA, Ghani AC, Leung GM, Hedley AJ, Fraser C, Riley S, et
al. Epidemiological
determinants of spread of causal agent of severe acute respiratory syndrome
in Hong Kong. Lancet 2003;361:1761–6.
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Table. Patients with
severe acute respiratory syndrome (SARS) and possible incubation
periods |
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Patient source and no.a |
Possible incubation period of SARS
in days |
|
|
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
|
|
Canada 1 |
|
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
|
|
|
|
|
|
|
Canada 2 |
1 |
2 |
3 |
4 |
|
|
|
|
|
|
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|
|
|
|
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|
Canada 3 |
1 |
|
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4 |
|
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|
|
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Canada 4 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
|
|
|
|
|
|
|
|
Canada 5 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
|
|
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|
Canada 7 |
|
|
3 |
|
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|
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|
10 |
|
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Canada 8b |
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3 |
|
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Canada 10 |
1 |
2 |
3 |
4 |
5 |
6 |
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Hong Kong 2 |
|
2 |
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Hong Kong 3 |
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2 |
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Hong Kong 4 |
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6 |
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Hong Kong 5 |
|
2 |
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Hong Kong 6 |
1 |
2 |
3 |
4 |
5 |
6 |
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Hong Kong 7 |
|
|
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|
5 |
6 |
7 |
8 |
9 |
10 |
11 |
|
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Hong Kong 8 |
|
|
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|
5 |
6 |
7 |
8 |
9 |
10 |
11 |
|
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Hong Kong 9 |
1 |
2 |
3 |
4 |
5 |
|
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Hong Kong 10 |
|
2 |
3 |
4 |
5 |
6 |
7 |
|
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USA 1 |
|
|
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6 |
|
|
|
|
|
|
13 |
14 |
15 |
16 |
17 |
18 |
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USA 2 |
|
|
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|
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|
7 |
8 |
9 |
10 |
11 |
12 |
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| aPatient source: Canada refers
to patients reported in reference 6, Hong Kong to
patients reported in reference 7, and USA to patients
whose incubation periods were extracted from an unpublished database
held at CDC. I used the same patient numbers as used in the published
reports. |
| bPatient 9 from the Canadian
database (6) was excluded because the possible incubation
period was reported as <29 days. However, even with n =
20, adding patient Canada 9 would mean that possible incubation periods
between 19 and 29 days would each have very low frequencies (i.e.,
<0.01). |
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