Predicting future time-to-event outcomes is a foundational task in statistical learning. While various methods exist for generating point predictions, quantifying the associated uncertainties poses a more substantial challenge. In this study, we introduce an innovative approach specifically designed to address this challenge, accommodating dynamic predictors that may manifest as stochastic processes. Our investigation harnesses the forward intensity function in a novel way, providing a fresh perspective on this intricate problem. The framework we propose demonstrates remarkable computational efficiency, enabling efficient analyses of large-scale investigations. We validate its soundness with theoretical guarantees, and our in-depth analysis establishes the weak convergence of function-valued parameter estimations. We illustrate the effectiveness of our framework with two comprehensive real examples and extensive simulation studies.

OBJECTIVES: Electronic health records (EHR) are commonly used for the identification of novel risk factors for disease, often referred to as an association study. A major challenge to EHR-based association studies is phenotyping error in EHR-derived outcomes. A manual chart review of phenotypes is necessary for unbiased evaluation of risk factor associations. However, this process is time-consuming and expensive. The objective of this paper is to develop an outcome-dependent sampling approach for designing manual chart review, where EHR-derived phenotypes can be used to guide the selection of charts to be reviewed in order to maximize statistical efficiency in the subsequent estimation of risk factor associations. MATERIALS AND METHODS: After applying outcome-dependent sampling, an augmented estimator can be constructed by optimally combining the chart-reviewed phenotypes from the selected patients with the error-prone EHR-derived phenotype. We conducted simulation studies to evaluate the proposed method and applied our method to data on colon cancer recurrence in a cohort of patients treated for a primary colon cancer in the Kaiser Permanente Washington (KPW) healthcare system. RESULTS: Simulations verify the coverage probability of the proposed method and show that, when disease prevalence is less than 30%, the proposed method has smaller variance than an existing method where the validation set for chart review is uniformly sampled. In addition, from design perspective, the proposed method is able to achieve the same statistical power with 50% fewer charts to be validated than the uniform sampling method, thus, leading to a substantial efficiency gain in chart review. These findings were also confirmed by the application of the competing methods to the KPW colon cancer data. DISCUSSION: Our simulation studies and analysis of data from KPW demonstrate that, compared to an existing uniform sampling method, the proposed outcome-dependent method can lead to a more efficient chart review sampling design and unbiased association estimates with higher statistical efficiency. CONCLUSION: The proposed method not only optimally combines phenotypes from chart review with EHR-derived phenotypes but also suggests an efficient design for conducting chart review, with the goal of improving the efficiency of estimated risk factor associations using EHR data.

In statistical learning framework with regressions, interactions are the contributions to the response variable from the products of the explanatory variables. In high-dimensional problems, detecting interactions is challenging due to combinatorial complexity and limited data information. We consider detecting interactions by exploring their connections with the principal Hessian matrix. Specifically, we propose a one-step synthetic approach for estimating the principal Hessian matrix by a penalized M-estimator. An alternating direction method of multipliers (ADMM) is proposed to efficiently solve the encountered regularized optimization problem. Based on the sparse estimator, we detect the interactions by identifying its nonzero components. Our method directly targets at the interactions, and it requires no structural assumption on the hierarchy of the interactions effects. We show that our estimator is theoretically valid, computationally efficient, and practically useful for detecting the interactions in a broad spectrum of scenarios.