Event time data under various censoring schemes arise in a variety of fields. The temporal dynamics of covariate effects on the occurrence of events can be flexibly studied in a partly functional regression model on the mean function of temporal processes defined by event times, with some covariate coefficients time-varying while others time-independent. Statistical inferences are challenging with the presence of multiple time-varying components, particularly when event times are not continuously but discretely observed, as under interval censoring. The investigator studies a unified semiparametric profile estimating function approach and an estimated version of it when the event times are only discretely observed. For continuously observed data, the model parameters are estimated from an algorithm that alternately updates the current estimate between an estimating equation for time-varying coefficients and an estimating equation for time-independent coefficients. For interval censored or doubly censored data, estimating functions will be estimated first using multiple imputation and then solved alternately. The methodology will be implemented in an R package under the quality assurance scheme of the R Project. The proposed approach provides a unified theoretical framework of dynamic regression models for event times, enabling a synthesized investigation of computing algorithms and statistical inferences. It allows efficient estimation and successive hypotheses test of covariate effects. Application of the method to a cystic fibrosis disease registry data will generate new knowledge on the temporal nature of the association between malnutrition and pulmonary disease progression.
The proposed method is motivated by the need of modeling temporal dynamics of covariate effects on the occurrence of certain events. Events of interests can be, for example, the recurrences of some chronic disease symptoms such as lung infection in cystic fibrosis patients, or the breakdowns of some engineering or electronic systems such as access failure of computer disks. A blend of time-varying effects and time-independent effects allows most flexibility in assessing the efficacy of a treatment of a disease or a design of new system over time. The method has an impact on the practice of event time data analysis when the temporal nature of covariate effects are of important interests. A publicly available software will get the methodology into the hands of those who will profit from using them, and, therefore, help to understand the temporal dynamics of covariate effects on event occurrences.
