The estimation of SARS incubation distribution from serial interval data using a convolution likelihood

The incubation period of SARS is the time between infection of disease and onset of symptoms. Knowledge about the distribution of incubation times is crucial in determining the length of quarantine period and is an important parameter in modelling the spread and control of SARS. As the exact time of infection is unknown for most patients, the incubation time cannot be determined. What is observable is the serial interval which is the time from the onset of symptoms in an index case to the onset of symptoms in a subsequent case infected by the index case. By constructing a convolution likelihood based on the serial interval data, we are able to estimate the incubation distribution which is assumed to be Weibull, and justifications are given to support this choice over other distributions. The method is applied to data provided by the Ministry of Health of Singapore and the results justify the choice of a ten-day quarantine period. The indirect estimate obtained using the method of convolution likelihood is validated by means of comparison with a direct estimate obtained directly from a subset of patients for whom the incubation time can be ascertained. Despite its name, the proposed indirect estimate is actually more precise than the direct estimate because serial interval data are recorded for almost all patients, whereas exact incubation times can be determined for only a small subset. It is possible to obtain an even more efficient estimate by using the combined data but the improvement is not substantial.