ABSTRACT Scheike and Zhang [An additive-multiplicative Cox-Aalen regression model. Scand J Stat. 2002;29:75–88] proposed a flexible additive-multiplicative hazard model, called the Cox-Aalen model, by replacing the baseline hazard function in the well-known Cox model with a covariate-dependent Aalen model, which allows for both fixed and dynamic covariate effects. In this paper, based on left-truncated and mixed interval-censored (LT-MIC) data, we consider maximum likelihood estimation for the Cox-Aalen model with fixed covariates. We propose expectation-maximization (EM) algorithms for obtaining the conditional maximum likelihood estimators (cMLE) of the regression coefficients for the Cox-Aalen model. We establish the consistency of the cMLE. Numerical studies show that estimation via the EM algorithms performs well.

中文翻译：

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左截断和混合区间删失数据的 Cox-Aalen 模型

摘要 Scheike 和 Zhang [一个加法乘法 Cox-Aalen 回归模型。扫描 J 统计。2002;29:75-88] 提出了一种灵活的加法乘法风险模型，称为 Cox-Aalen 模型，通过用协变量依赖的 Aalen 模型替换众所周知的 Cox 模型中的基线风险函数，允许两个固定和动态协变量效应。在本文中，基于左截断和混合区间删失 (LT-MIC) 数据，我们考虑了具有固定协变量的 Cox-Aalen 模型的最大似然估计。我们提出了期望最大化 (EM) 算法，用于获得 Cox-Aalen 模型回归系数的条件最大似然估计量 (cMLE)。我们建立了 cMLE 的一致性。数值研究表明，通过 EM 算法的估计性能良好。