Semiparametric model for semi-competing risks data with application to breast cancer study

Semiparametric copula-based regression modeling of semi-competing risks data

Semi-competing risks data often arise in medical studies where the terminal event (e.g., death) censors the non-terminal event (e.g., cancer recurrence), but the non-terminal event does not prevent the subsequent occurrence of the terminal event. This article considers regression modeling of semi-competing risks data to assess the covariate effects on the respective non-terminal and terminal event times. We propose a copula-based framework for semi-competing risks regression with time-varying coefficients, where the dependence between the non-terminal and terminal event times is characterized by a copula and the time-varying covariate effects are imposed on two marginal regression models. We develop a two-stage inferential procedure for estimating the association parameter in the copula model and time-varying regression parameters. We evaluate the finite sample performance of the proposed method through simulation studies and illustrate the method through an application to Surveillance, Epidemiology, and End Results-Medicare data for elderly women diagnosed with early-stage breast cancer and initially treated with breast-conserving surgery.

Semiparametric Model for Bivariate Survival Data Subject to Biased Sampling

To better understand the relationship between patient characteristics and their residual survival after an intermediate event such as the local cancer recurrence, it is of interest to identify patients with the intermediate event and then analyze their residual survival data. One challenge in analyzing such data is that the observed residual survival times tend to be longer than those in the target population, since patients who die before experiencing the intermediate event are excluded from the identified cohort. We propose to jointly model the ordered bivariate survival data using a copula model and appropriately adjusting for the sampling bias. We develop an estimating procedure to simultaneously estimate the parameters for the marginal survival functions and the association parameter in the copula model, and use a two-stage expectation-maximization algorithm. Using empirical process theory, we prove that the estimators have strong consistency and asymptotic normality. We conduct simulations studies to evaluate the finite sample performance of the proposed method. We apply the proposed method to two cohort studies to evaluate the association between patient characteristics and residual survival.

Dynamic prediction of repeated events data based on landmarking model: application to colorectal liver metastases data

BACKGROUND

In some clinical situations, patients experience repeated events of the same type. Among these, cancer recurrences can result in terminal events such as death. Therefore, here we dynamically predicted the risks of repeated and terminal events given longitudinal histories observed before prediction time using dynamic pseudo-observations (DPOs) in a landmarking model.

METHODS

The proposed DPOs were calculated using Aalen-Johansen estimator for the event processes described in the multi-state model. Furthermore, in the absence of a terminal event, a more convenient approach without matrix operation was described using the ordering of repeated events. Finally, generalized estimating equations were used to calculate probabilities of repeated and terminal events, which were treated as multinomial outcomes.

RESULTS

Simulation studies were conducted to assess bias and investigate the efficiency of the proposed DPOs in a finite sample. Little bias was detected in DPOs even under relatively heavy censoring, and the method was applied to data from patients with colorectal liver metastases.

CONCLUSIONS

The proposed method enabled intuitive interpretations of terminal event settings.