论文标题
具有线性危险的标准固化模型
The standard cure model with a linear hazard
论文作者
论文摘要
在本文中，我们为事件时间引入了具有线性危险速率回归模型的混合疗法模型。 CURE模型是事件时间的统计模型，这些模型考虑到一部分人口可能永远不会遇到感兴趣的事件，据说这部分是{`}固化的{'}。混合物治疗模型中的种群存活函数采用$ s（t）= 1 -π+π\ exp（ - \ int_0^tα（s）\，d s）$的形式，其中$π$是对正在研究的事件容易受到的事件的可能性，而$α（s）$是容易受到易于接受的危害。我们让$π$和$α$都取决于可能不同的协变量向量$ x $和$ z $。概率$π$被视为逻辑函数$π（x^{\ prime}γ）= 1/\ {1+ \ exp（-x^{\ prime}γ）\} $，而我们通过Aalen的线性危险利率回归模型来建模$ $α（s）$。该模型假设一个易感人具有危险率函数$α（t; z）=β_0（t） +β_1（t）z_1 + \ cdots + z__ {q-1}β_{q-1}β_{q-1}（t）$，以协值$ z_1，\ ldots，z_1，z_1，z___ {q-1} $。通过参数模型研究了我们估计器的大样本属性，这些模型倾向于将半参数模型作为参数$ k \ to \ infty $。对于参数模型序列中的每个模型，我们假设数据生成机制是参数，从而简化了估计器的推导以及一致性和限制正态性的证明。最后，我们使用连续性技术切换到假设数据源于半参数模型。以前已经研究并利用了非频率数据文献中的非和半参数设置中的估计量的技术，但在生存分析中似乎是新颖的。
In this paper we introduce a mixture cure model with a linear hazard rate regression model for the event times. Cure models are statistical models for event times that take into account that a fraction of the population might never experience the event of interest, this fraction is said to be {`}cured{'}. The population survival function in a mixture cure model takes the form $S(t) = 1 - π+ π\exp(-\int_0^tα(s)\,d s)$, where $π$ is the probability of being susceptible to the event under study, and $α(s)$ is the hazard rate of the susceptible fraction. We let both $π$ and $α(s)$ depend on possibly different covariate vectors $X$ and $Z$. The probability $π$ is taken to be the logistic function $π(X^{\prime}γ) = 1/\{1+\exp(-X^{\prime}γ)\}$, while we model $α(s)$ by Aalen's linear hazard rate regression model. This model postulates that a susceptible individual has hazard rate function $α(t;Z) = β_0(t) + β_1(t)Z_1 + \cdots + Z_{q-1}β_{q-1}(t)$ in terms of her covariate values $Z_1,\ldots,Z_{q-1}$. The large-sample properties of our estimators are studied by way of parametric models that tend to a semiparametric model as a parameter $K \to \infty$. For each model in the sequence of parametric models, we assume that the data generating mechanism is parametric, thus simplifying the derivation of the estimators, as well as the proofs of consistency and limiting normality. Finally, we use contiguity techniques to switch back to assuming that the data stem from the semiparametric model. This technique for deriving and studying estimators in non- and semiparametric settings has previously been studied and employed in the high-frequency data literature, but seems to be novel in survival analysis.
