Following the outbreak of COVID-19, various containment measures have been taken, including the use of quarantine. At present, the quarantine period is the same for everyone, since it is implicitly assumed that the incubation period distribution of COVID-19 is the same regardless of age or gender. For testing the effects of age and gender on the incubation period of COVID-19, a novel two-component mixture regression model is proposed. An expectation-maximization (EM) algorithm is adopted to obtain estimates of the parameters of interest, and the simulation results show that the proposed method outperforms the simple regression method and has robustness. The proposed method is applied to a Zhejiang COVID-19 dataset, and it is found that age and gender statistically have no effect on the incubation period of COVID-19, which indicates that the quarantine measure currently in operation is reasonable.