In this paper, we propose a generalization of the mixture (binary) cure rate model, motivated by the existence of a zero-modified (inflation or deflation) distribution, on the initial number of causes, under a competing cause scenario. This non-linear transformation cure rate model is in the same form of models studied in the past; however, following our approach, we are able to give a realistic interpretation to a specific class of proper transformation functions, for the cure rate modeling. The estimation of the parameters is then carried out using the maximum likelihood method along with a profile approach. A simulation study examines the accuracy of the proposed estimation method and the model discrimination based on the likelihood ratio test. For illustrative purposes, analysis of two real life data-sets, one on recidivism and another on cutaneous melanoma, is also carried out.

中文翻译：

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一类非线性变换治愈率模型

在本文中，我们提出了混合（二元）治愈率模型的推广，其动机是在竞争原因场景下，基于初始原因数量的零修正（通货膨胀或通货紧缩）分布的存在。这种非线性变换治愈率模型与过去研究的模型形式相同；然而，按照我们的方法，我们能够对特定类别的适当转换函数给出实际的解释，用于治愈率建模。然后使用最大似然方法和轮廓方法来执行参数的估计。模拟研究检验了所提出的估计方法的准确性和基于似然比检验的模型判别。出于说明目的，对两个现实生活数据集的分析，