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ABSTRACT Breast cancer patients may experience relapse or death after surgery during the follow‐up period, leading to dependent censoring of relapse. This phenomenon, known as semi‐competing risk, imposes challenges in analyzing treatment effects on breast cancer and necessitates advanced statistical tools for unbiased analysis. Despite progress in estimation and inference within semi‐competing risks regression, its application to causal inference is still in its early stages. This article aims to propose a frequentist and semi‐parametric framework based on copula models that can facilitate valid causal inference, net quantity estimation and interpretation, and sensitivity analysis for unmeasured factors under right‐censored semi‐competing risks data. We also propose novel procedures to enhance parameter estimation and its applicability in practice. After that, we apply the proposed framework to a breast cancer study and detect the time‐varying causal effects of hormone‐ and radio‐treatments on patients' relapse and overall survival. Moreover, extensive numerical evaluations demonstrate the method's feasibility, highlighting minimal estimation bias and reliable statistical inference. 

Steed et al . ( 1 ) illustrates the crucial impact that the quality of official statistical data products may exert on the accuracy, stability, and equity of policy decisions on which they are based. The authors remind us that data, however responsibly curated, can be fallible. With this comment, we underscore the importance of conducting principled quality assessment of official statistical data products. We observe that the quality assessment procedure employed by Steed et al . needs improvement, due to (i) the inadmissibility of the estimator used, and (ii) the inconsistent probability model it induces on the joint space of the estimator and the observed data. We discuss the design of alternative statistical methods to conduct principled quality assessments for official statistical data products, showcasing two simulation-based methods for admissible minimax shrinkage estimation via multilevel empirical Bayesian modeling. For policymakers and stakeholders to accurately gauge the context-specific usability of data, the assessment should take into account both uncertainty sources inherent to the data and the downstream use cases, such as policy decisions based on those data products. 

Abstract Heat storage change (HSC) is a crucial component of lake's thermal energy budget. Conventional temperature profile based models of HSC require location specific parameters such as lakebed topography. Based on the half‐order time‐derivative formula of heat fluxes, an analytical model was formulated for estimating HSC from water surface temperature and solar radiation without using geography dependent parameters. The proposed model was tested against field measurements at Poyang Lake, a shallow inland lake, which has pronounced seasonal variations in water level and lake area. Our analysis indicates that the model accurately simulates diurnal HSC with a coefficient of determination of 0.94 and a root mean squared error (RMSE) of 77.5 ± 21.6 Wm⁻²for the study period. Larger nighttime RMSE (75.0 ± 26.8 Wm⁻²) than the daytime value (55.1 ± 19.7 W m⁻²) is attributable to larger measurement errors of nighttime turbulent fluxes. The estimation of HSC independent of temperature profile and lake‐specific parameters by the proposed model facilitates remote sensing monitoring the HSC of global water bodies.