Alternative Methods of Estimating an Incubation Distribution

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Abstract
Accurate and precise estimates of the incubation distribution of novel, emerging infectious diseases are vital to inform public health policy and to parameterize mathematical models. We discuss and compare different methods of estimating the incubation distribution allowing for interval censoring of exposures, using data from the severe acute respiratory syndrome (SARS) epidemic in 2003 as an example. Combining data on unselected samples of 149 and 168 patients with defined exposure intervals from Toronto and Hong Kong, respectively, we estimated the mean and variance of the incubation period to be 5.1 day and 18.3 days and the 95th percentile to be 12.9 days. We conducted multiple linear regression on the log incubation times and found that incubation was significantly longer in Toronto than in Hong Kong and in older compared with younger patients, while it was significantly shorter in healthcare workers than in other patients. Our findings suggest subtle but important heterogeneities in the incubation period of SARS among different strata of patients. Robust estimation of the incubation period should be independently carried out in different settings and subgroups for novel human pathogens using valid statistical methods.