Ewnetu Worku Biyadgie, Gijbels Irène, Verhasselt Anneleen
Department of Mathematics, KU Leuven, Celestijnenlaan 200 B, Leuven (Heverlee), 3001, Belgium.
Center for Statistics, Data Science Institute, Hasselt University, Agoralaan Building D, Diepenbeek, 3590, Belgium.
Int J Biostat. 2025 Apr 30;21(1):67-95. doi: 10.1515/ijb-2023-0153. eCollection 2025 May 1.
Cox proportional hazards model is widely used to study the relationship between the survival time of an event and covariates. Its primary objective is parameter estimation assuming a constant relative hazard throughout the entire follow-up time. The baseline hazard is thus treated as a nuisance parameter. However, if the interest is to predict possible outcomes like specific quantiles of the distribution (e.g. median survival time), survival and hazard functions, it may be more convenient to use a parametric baseline distribution. Such a parametric model should however be flexible enough to allow for various shapes of e.g. the hazard function. In this paper we propose flexible hazard-based models for right censored data using a large class of two-piece asymmetric baseline distributions. The effect of covariates is characterized through time-scale changes on hazard progression and on the relative hazard ratio; and can take three possible functional forms: parametric, semi-parametric (partly linear) and non-parametric. In the first case, the usual full likelihood estimation method is applied. In the semi-parametric and non-parametric settings a general profile (local) likelihood estimation approach is proposed. An extensive simulation study investigates the finite-sample performances of the proposed method. Its use in data analysis is illustrated in real data examples.
Cox比例风险模型被广泛用于研究事件生存时间与协变量之间的关系。其主要目标是在整个随访时间内假设相对风险恒定的情况下进行参数估计。因此，基线风险被视为一个干扰参数。然而，如果感兴趣的是预测可能的结果，如分布的特定分位数（例如中位生存时间）、生存函数和风险函数，那么使用参数化基线分布可能会更方便。不过，这样的参数模型应该足够灵活，以允许例如风险函数具有各种形状。在本文中，我们使用一大类两段式非对称基线分布，为右删失数据提出了灵活的基于风险的模型。协变量的影响通过时间尺度变化对风险进展和相对风险比的影响来表征；并且可以采用三种可能的函数形式：参数化、半参数化（部分线性）和非参数化。在第一种情况下，应用通常的全似然估计方法。在半参数化和非参数化设置中，提出了一种通用的轮廓（局部）似然估计方法。一项广泛的模拟研究调查了所提出方法的有限样本性能。通过实际数据示例说明了其在数据分析中的应用。
