The mean past lifetime provides the expected time elapsed since the failure of a subject given that he/she has failed before the time of observation. In this paper, we propose the proportional mean past lifetime model to study the association between the mean past lifetime function and potential regression covariates. In the presence of left censoring, martingale estimating equations are developed to estimate the model parameters, and the asymptotic properties of the resulting estimators are studied. To assess the adequacy of the model, a goodness of fit test is also investigated. The proposed method is evaluated via simulation studies and further applied to a data set.

中文翻译：

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比例平均过去生命模型的半参数推断

鉴于他/她在观察时间之前已经失败，平均过去寿命提供了自受试者失败以来经过的预期时间。在本文中，我们提出了比例平均过去寿命模型来研究平均过去寿命函数与潜在回归协变量之间的关联。在存在左删失的情况下，开发了鞅估计方程来估计模型参数，并研究了所得估计量的渐近性质。为了评估模型的充分性，还研究了拟合优度检验。所提出的方法通过模拟研究进行评估，并进一步应用于数据集。