Yunnan Key Laboratory of Statistical Modeling and Data Analysis, Yunnan University, Kunming 650091, P.R. China.
School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P.R. China.
Biometrics. 2024 Oct 3;80(4). doi: 10.1093/biomtc/ujae138.
With the advent of massive survival data with a cure fraction, large-scale regression for analyzing the effects of risk factors on a general population has become an emerging challenge. This article proposes a new probability-weighted method for estimation and inference for semiparametric cure regression models. We develop a flexible formulation of the mixture cure model consisting of the model-free incidence and the latency assumed by the semiparametric proportional hazards model. The susceptible probability assesses the concordance between the observations and the latency. With the susceptible probability as weight, we propose a weighted estimating equation method in a small-scale setting. Robust nonparametric estimation of the weight permits stable implementation of the estimation of regression parameters. A recursive probability-weighted estimation method based on data blocks with smaller sizes is further proposed, which achieves computational and memory efficiency in a large-scale or online setting. Asymptotic properties of the proposed estimators are established. We conduct simulation studies and a real data application to demonstrate the empirical performance of the proposed method.
随着带有治愈比例的大量生存数据的出现，分析风险因素对总体人群影响的大规模回归已成为一个新的挑战。本文提出了一种新的概率加权方法，用于半参数治愈回归模型的估计和推断。我们开发了一种灵活的混合治愈模型公式，其中包括无模型的发病率和半参数比例风险模型假设的潜伏期。易感性概率评估观察结果和潜伏期之间的一致性。我们以易感性概率为权重，在小规模环境中提出了一种加权估计方程方法。稳健的非参数权重估计允许对回归参数进行稳定的估计。进一步提出了一种基于较小数据块的递归概率加权估计方法，在大规模或在线环境中实现了计算和内存效率。建立了所提出估计器的渐近性质。我们进行了模拟研究和真实数据应用，以证明所提出方法的经验性能。
