In this article, we introduce a long‐term survival model in which the number of competing causes of the event of interest follows the zero‐modified geometric (ZMG) distribution. Such distribution accommodates equidispersion, underdispersion, and overdispersion and captures deflation or inflation of zeros in the number of lesions or initiated cells after the treatment. The ZMG distribution is also an appropriate alternative for modeling clustered samples when the number of competing causes of the event of interest consists of two subpopulations, one containing only zeros (cure proportion), while in the other (noncure proportion) the number of competing causes of the event of interest follows a geometric distribution. The advantage of this assumption is that we can measure the cure proportion in the initiated cells. Furthermore, the proposed model can yield greater or lower cure proportion than that of the geometric distribution when modeling the number of competing causes. In this article, we present some statistical properties of the proposed model and use the maximum likelihood method to estimate the model parameters. We also conduct a Monte Carlo simulation study to evaluate the performance of the estimators. We present and discuss two applications using real‐world medical data to assess the practical usefulness of the proposed model.

中文翻译：

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一种具有灵活竞争原因的新治愈率模型，可应用于黑素瘤和移植数据。

在本文中，我们介绍了一个长期生存模型，其中关注事件的竞争原因数量遵循零修正几何（ZMG）分布。这种分布适应了等分散，欠分散和过度分散，并捕获了治疗后病变或起始细胞数量的零收缩或膨胀。当关注事件的竞争原因的数量由两个子群体组成，一个仅包含零（治愈比例），而另一个（非治愈比例）竞争原因的数量组成时，ZMG分布也是建模聚类样本的合适替代方法。感兴趣的事件遵循几何分布。这种假设的优点是我们可以测量起始细胞中的治愈率。此外，当建模竞争原因的数量时，所提出的模型可以产生比几何分布更大或更低的治愈比例。在本文中，我们介绍了所提出模型的一些统计性质，并使用最大似然法来估计模型参数。我们还进行了蒙特卡洛模拟研究，以评估估计器的性能。我们提出并讨论了使用实际医学数据评估所提出模型的实用性的两种应用。我们还进行了蒙特卡洛模拟研究，以评估估计器的性能。我们提出并讨论了使用实际医学数据评估所提出模型的实用性的两种应用。我们还进行了蒙特卡洛模拟研究，以评估估计器的性能。我们提出并讨论了使用实际医学数据评估所提出模型的实用性的两种应用。