Single-index models are becoming increasingly popular in many scientific applications as they offer the advantages of flexibility in regression modeling as well as interpretable covariate effects. In the context of survival analysis, the single-index hazards models are natural extensions of the Cox proportional hazards models. In this paper, we propose a novel estimation procedure for single-index hazard models under a monotone constraint of the index. We apply the profile likelihood method to obtain the semiparametric maximum likelihood estimator, where the novelty of the estimation procedure lies in estimating the unknown monotone link function by embedding the problem in isotonic regression with exponentially distributed random variables. The consistency of the proposed semiparametric maximum likelihood estimator is established under suitable regularity conditions. Numerical simulations are conducted to examine the finite-sample performance of the proposed method. An analysis of breast cancer data is presented for illustration.
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.