A flexible class of semiparametric partly linear frailty transformation models is considered for analyzing clustered interval-censored data, which arise naturally in complex diseases and dental research. This class of models features two nonparametric components, resulting in a nonparametric baseline survival function and a potential nonlinear effect of a continuous covariate. The dependence among failure times within a cluster is induced by a shared, unobserved frailty term. A sieve maximum likelihood estimation method based on piecewise linear functions is proposed. The proposed estimators of the regression, dependence, and transformation parameters are shown to be strongly consistent and asymptotically normal, whereas the estimators of the two nonparametric functions are strongly consistent with optimal rates of convergence. An extensive simulation study is conducted to study the finite-sample performance of the proposed estimators. We provide an application to a dental study for illustration.

中文翻译：

---

使用一类半参数部分线性脆弱变换模型分析聚类区间删失数据

考虑了一类灵活的半参数部分线性脆弱变换模型，用于分析在复杂疾病和牙科研究中自然出现的聚类区间删失数据。此类模型具有两个非参数组件，导致非参数基线生存函数和连续协变量的潜在非线性效应。集群内故障时间之间的依赖关系是由一个共享的、未观察到的脆弱项引起的。提出了一种基于分段线性函数的筛最大似然估计方法。所提出的回归、依赖和变换参数的估计量被证明是强一致且渐近正态的，而这两个非参数函数的估计量与最佳收敛速度是强一致的。进行了广泛的模拟研究以研究所提出的估计器的有限样本性能。我们提供了牙科研究的应用程序以进行说明。