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 (). 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.

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

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 ().

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 a Technical 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.

Technical Appendix

Open reading frames of African swine fever virus.