![](https://webarchive.library.unt.edu/eot2008/20090117144611im_/http://www.cdc.gov/ncidod/eid/images/spacer.gif)
|
![](https://webarchive.library.unt.edu/eot2008/20090117144611im_/http://www.cdc.gov/ncidod/eid/images/spacer.gif) |
Letter
Estimating SARS Incubation
Period
To the Editor: In a recent article, Meltzer described a simulation
method to estimate the incubation period for patients infected with SARS
with multiple contact dates (1). In brief, he assumed
a uniform distribution of all possible incubation periods derived from
these contact dates for each patient and randomly selected an incubation
period from all contact dates for each patient to obtain a distribution
of the incubation period for all 19 patients. The process is repeated
10,000 times to obtain an overall frequency distribution of the incubation
period.
Instead of using this cumbersome iterative approach, the same results
can be obtained by a simple method. When a uniform distribution is assumed
for all possible incubation periods, the expected frequency for a day
x as the incubation period is either 0 or 1/(total number of possible
days). Taking the first patient (Canada 1) in (1) as an example, the expected
frequency for 1, 2, 3, . . . , 18 days is 0, 1/11, 1/11, 1/11, 1/11, 1/11,
1/11, 1/11, 1/11, 1/11, 1/11, 1/11, 0, 0, . . . , 0. The expected frequencies
for the other patients are available in the Table.
The total expected frequency for each day is the sum of the expected
frequencies for all patients for that day. Therefore, the frequency distribution
of the incubation period is given by dividing each total expected frequency
by the sum of the total expected frequencies (x 100%) and is 7.6, 22.1,
14.2, 9.0, 6.5, 11.5, 4.6, 3.7, 3.7, 6.4, 3.7, 1.7, 1.1, 1.1, 0.7, 0.7,
0.7, 0.7. This is identical to the frequency distribution shown in Figure
1 of the paper by Meltzer (1).
Tze-wai Wong*
and Wilson Tam*
*The Chinese University of Hong Kong, Hong Kong
Suggested citation
for this article:
Wong TW, Tam W. Estimating SARS incubation period [letter]. Emerg Infect
Dis [serial on the Internet]. 2004 Aug [date cited]. Available
from: http://www.cdc.gov/ncidod/EID/vol10no8/04-0284_04-0427.htm
Reference
- Meltzer MI. Multiple
contact dates and SARS incubation periods. Emerg Infect Dis. 2004;10:207–9.
Table.
Expected frequency distribution of incubation period for SARS patient
with multiple contacts |
|
Patientsa
|
|
Days
|
|
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
13
|
14
|
15
|
16
|
17
|
18
|
|
Ca1
|
0
|
1/11
|
1/11
|
1/11
|
1/11
|
1/11
|
1/11
|
1/11
|
1/11
|
1/11
|
1/11
|
1/11
|
0
|
0
|
0
|
0
|
0
|
0
|
Ca2
|
1/4
|
1/4
|
1/4
|
1/4
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
Ca3
|
1/2
|
0
|
0
|
1/2
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
Ca4
|
1/11
|
1/11
|
1/11
|
1/11
|
1/11
|
1/11
|
1/11
|
1/11
|
1/11
|
1/11
|
1/11
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
Ca5
|
1/14
|
1/14
|
1/14
|
1/14
|
1/14
|
1/14
|
1/14
|
1/14
|
1/14
|
1/14
|
1/14
|
1/14
|
1/14
|
1/14
|
0
|
0
|
0
|
0
|
Ca7
|
0
|
0
|
1/2
|
0
|
0
|
0
|
0
|
0
|
0
|
1/2
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
Ca8
|
0
|
0
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
Ca10
|
1/6
|
1/6
|
1/6
|
1/6
|
1/6
|
1/6
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
HK2
|
0
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
HK3
|
0
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
HK4
|
0
|
0
|
0
|
0
|
0
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
HK5
|
0
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
HK6
|
1/6
|
1/6
|
1/6
|
1/6
|
1/6
|
1/6
|
1/6
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
HK7
|
0
|
0
|
0
|
0
|
1/7
|
1/7
|
1/7
|
1/7
|
1/7
|
1/7
|
1/7
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
HK8
|
0
|
0
|
0
|
0
|
1/7
|
1/7
|
1/7
|
1/7
|
1/7
|
1/7
|
1/7
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
HK9
|
1/5
|
1/5
|
1/5
|
1/5
|
1/5
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
HK10
|
0
|
1/6
|
1/6
|
1/6
|
1/6
|
1/6
|
1/6
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
US1
|
0
|
0
|
0
|
0
|
0
|
1/7
|
0
|
0
|
0
|
0
|
0
|
0
|
1/7
|
1/7
|
1/7
|
1/7
|
1/7
|
1/7
|
US2
|
0
|
0
|
0
|
0
|
0
|
0
|
1/6
|
1/6
|
1/6
|
1/6
|
1/6
|
1/6
|
0
|
0
|
0
|
0
|
0
|
0
|
Tot. exp. freq.
|
1.45
|
4.40
|
2.70
|
1.70
|
1.24
|
2.18
|
0.87
|
0.71
|
0.71
|
1.21
|
0.71
|
0.33
|
0.21
|
0.21
|
0.14
|
0.14
|
0.14
|
0.14
|
|
aCa, Canada; HK,
Hong Kong; US, United States |
Back to top
In Reply: Drs. Wong and Tam (1)
are correct in stating that their method of calculating mean frequencies
of possible incubation periods for patients with severe acute respiratory
syndrome (SARS) is simpler than the method that I presented (2).
However, their method cannot replicate the confidence intervals shown
in Figure 1 in my article. Their
suggested methodology can only replicate Figure
2 in my article, which shows the cumulative distribution of the mean
frequencies of individual incubation periods.
The comparative complexity of my method provides data that are essential
for making public health decisions. For example, public health officials
need to know incubation periods to determine appropriate periods of quarantine
and isolation and how long to conduct intensive (and expensive) surveillance
after the last clinical case has been reported. To reduce costs and to
enhance public support, public health officials may keep quarantine and
isolation periods to a minimum. They also need to know the risk for failure
of such interventions attributable to patients with relatively long incubation
periods. Both Figure 2 in my
article and Drs. Wong and Tam's data show that approximately 95% of the
mean incubation period will be <12 days (i.e., 5% will incubate
for 13 to 18 days). By summing the 95th percentiles for days 13 through
18 from my Figure 1, it can be
seen that there is a probability that <30% of patients will
have incubation periods >12 days (the actual probability of any given
percentage incubating for >12 days can be easily calculated by using
the spreadsheet which is an appendix to my article). Public health officials
need to understand the degree of variability associated with any data
used to make public health policies. Sole reliance on the mean incubation
periods (or mean frequencies) will hide more than is shown, which increases
the probability of failed public health interventions.
Martin I. Meltzer*![Comments](https://webarchive.library.unt.edu/eot2008/20090117144611im_/http://www.cdc.gov/ncidod/eid/images/email.gif)
*Centers for Disease Control and Prevention, Atlanta, Georgia, USA
Suggested citation
for this article:
Meltzer MI. Estimating SARS incubation periods [response to letter].
Emerg Infect Dis [serial on the Internet]. 2004 Aug [date cited].
Available from: http://www.cdc.gov/ncidod/EID/vol10no8/04-0284_04-0427.htm
References
- Wong TW, Tam W. Estimating SARS incubation period
[letter]. Emerg Infect Dis. 2004;10:1503–4.
- Meltzer MI. Multiple
contact dates and SARS incubation periods. Emerg Infect Dis. 2004;10:207–9.
|