Fitting Cox Models with Doubly Censored Data Using Spline-Based Sieve Marginal Likelihood

Regression analysis of doubly censored failure time data with ancillary information

Doubly censored failure time data occur in many areas and for the situation, the failure time of interest usually represents the elapsed time between two related events such as an infection and the resulting disease onset. Although many methods have been proposed for regression analysis of such data, most of them are conditional on the occurrence time of the initial event and ignore the relationship between the two events or the ancillary information contained in the initial event. Corresponding to this, a new sieve maximum likelihood approach is proposed that makes use of the ancillary information, and in the method, the logistic model and Cox proportional hazards model are employed to model the initial event and the failure time of interest, respectively. A simulation study is conducted and suggests that the proposed method works well in practice and is more efficient than the existing methods as expected. The approach is applied to an AIDS study that motivated this investigation.

Semiparametric regression analysis of doubly-censored data with applications to incubation period estimation

The incubation period is a key characteristic of an infectious disease. In the outbreak of a novel infectious disease, accurate evaluation of the incubation period distribution is critical for designing effective prevention and control measures . Estimation of the incubation period distribution based on limited information from retrospective inspection of infected cases is highly challenging due to censoring and truncation. In this paper, we consider a semiparametric regression model for the incubation period and propose a sieve maximum likelihood approach for estimation based on the symptom onset time, travel history, and basic demographics of reported cases. The approach properly accounts for the pandemic growth and selection bias in data collection. We also develop an efficient computation method and establish the asymptotic properties of the proposed estimators. We demonstrate the feasibility and advantages of the proposed methods through extensive simulation studies and provide an application to a dataset on the outbreak of COVID-19.

Semiparametric regression analysis of doubly censored failure time data from cohort studies

Doubly censored failure time data occur when the failure time of interest represents the elapsed time between two events, an initial event and a subsequent event, and the observations on both events may suffer censoring. A well-known example of such data is given by the acquired immune deficiency syndrome (AIDS) cohort study in which the two events are HIV infection and AIDS diagnosis, and several inference methods have been developed in the literature for their regression analysis. However, all of them only apply to limited situations or focus on a single model. In this paper, we propose a marginal likelihood approach based on a general class of semiparametric transformation models, which can be applied to much more general situations. For the implementation, we develop a two-step procedure that makes use of both the multiple imputation technique and a novel EM algorithm. The asymptotic properties of the resulting estimators are established by using the modern empirical process theory, and the simulation study conducted suggests that the method works well in practical situations. An application is also provided.