Multi-threshold proportional hazards model and subgroup identification

Renewable risk assessment of heterogeneous streaming time-to-event cohorts

The analysis of streaming time-to-event cohorts has garnered significant research attention. Most existing methods require observed cohorts from a study sequence to be independent and identically sampled from a common model. This assumption may be easily violated in practice. Our methodology operates within the framework of online data updating, where risk estimates for each cohort of interest are continuously refreshed using the latest observations and historical summary statistics. At each streaming stage, we introduce parameters to quantify the potential discrepancy between batch-specific effects from adjacent cohorts. We then employ penalized estimation techniques to identify nonzero discrepancy parameters, allowing us to adaptively adjust risk estimates based on current data and historical trends. We illustrate our proposed method through extensive empirical simulations and a lung cancer data analysis.

Frailty model with change points for survival analysis

We propose a novel frailty model with change points applying random effects to a Cox proportional hazard model to adjust the heterogeneity between clusters. In the specially focused eight Empowered Action Group (EAG) states in India, there are problems with different survival curves for children up to the age of five in different states. Therefore, when analyzing the survival times for the eight EAG states, we need to adjust for the effects among states (clusters). Because the frailty model includes random effects, the parameters are estimated using the expectation-maximization (EM) algorithm. Additionally, our model needs to estimate change points; we thus propose a new algorithm extending the conventional estimation algorithm to the frailty model with change points to solve the problem. We show a practical example to demonstrate how to estimate the change point and the parameters of the distribution of random effect. Our proposed model can be easily analyzed using the existing R package. We conducted simulation studies with three scenarios to confirm the performance of our proposed model. We re-analyzed the survival time data of the eight EAG states in India to show the difference in analysis results with and without random effect. In conclusion, we confirmed that the frailty model with change points has a higher accuracy than the model without a random effect. Our proposed model is useful when heterogeneity needs to be taken into account. Additionally, the absence of heterogeneity did not affect the estimation of the regression parameters.

Survival analysis with a random change-point

Contemporary works in change-point survival models mainly focus on an unknown universal change-point shared by the whole study population. However, in some situations, the change-point is plausibly individual-specific, such as when it corresponds to the telomere length or menopausal age. Also, maximum-likelihood-based inference for the fixed change-point parameter is notoriously complicated. The asymptotic distribution of the maximum-likelihood estimator is non-standard, and computationally intensive bootstrap techniques are commonly used to retrieve its sampling distribution. This article is motivated by a breast cancer study, where the disease-free survival time of the patients is postulated to be regulated by the menopausal age, which is unobserved. As menopausal age varies across patients, a fixed change-point survival model may be inadequate. Therefore, we propose a novel proportional hazards model with a random change-point. We develop a nonparametric maximum-likelihood estimation approach and devise a stable expectation-maximization algorithm to compute the estimators. Because the model is regular, we employ conventional likelihood theory for inference based on the asymptotic normality of the Euclidean parameter estimators, and the variance of the asymptotic distribution can be consistently estimated by a profile-likelihood approach. A simulation study demonstrates the satisfactory finite-sample performance of the proposed methods, which yield small bias and proper coverage probabilities. The methods are applied to the motivating breast cancer study.