Regression models have a substantial impact on interpretation of treatments, genetic characteristics and other potential risk factors in survival analysis. In many applications, the description of censoring and survival curve reveals the presence of cure fraction on data, which leads to alternative modeling. The most common approach to introduce covariates under a parameter estimation is the cure rate model and its variations, although the use of defective distributions have introduced a more parsimonious and integrated approach. Defective distributions are given by a density function whose integration is not one after changing the domain of one of the parameters, making them appropriate for survival curves with an evident plateau. In this work, we introduce a new Bayesian defective regression model for long-term survival outcomes using the Marshall-Olkin Gompertz distribution. The estimation process is under the Bayesian paradigm. We evaluate the asymptotic properties of our proposal under the vague prior scheme in Monte Carlo studies. We present a motivating real-world application using data from patients diagnosed with testicular cancer in São Paulo, Brazil, in which long-term survivors were identified. Scenarios of cure with uncertainty estimates via credible intervals are provided to evaluate characteristics such as risk age, presence of treatment, and cancer stage.

翻译：回归模型在生存分析中对解释治疗效应、遗传特征及其他潜在风险因素具有重要影响。在许多应用中，删失数据的描述和生存曲线揭示了数据中存在治愈分数，这催生了替代性建模方法。在参数估计中引入协变量的最常见方法是治愈率模型及其变体，尽管有缺陷分布已提出了一种更简约且综合的方法。有缺陷分布通过一个密度函数定义，该函数在改变其中一个参数的定义域后积分值不等于1，使其适用于具有明显平台的生存曲线。本研究基于Marshall-Olkin Gompertz分布，提出了一种针对长期生存结局的新型贝叶斯有缺陷回归模型。估计过程遵循贝叶斯范式，并在蒙特卡洛研究中评估了在模糊先验方案下所提方法的渐近性质。我们以巴西圣保罗诊断的睾丸癌患者数据为实例，识别出长期幸存者，并基于贝叶斯后验分析论证了所提方法的优势。通过可信区间提供带不确定性估计的治愈场景，用以评估风险年龄、治疗存在与否及癌症分期等特征。