Frailty Models and Survival Analysis in Cancer Research

描述(由申请人提供)：Kaplan Meier估计器、Iograne检验和比例风险模型在顶级医学期刊上的肿瘤学文章中报道的比例非常高。这种正统观点是有充分理由的。它们的理论属性被很好地理解，它们是健壮的，它们可以在标准统计软件中使用。遗憾的是，这些方法是基于强简化假设的，当这些假设被违反时，可能会出现困难。这项拟议的研究将调查癌症和其他慢性病研究中出现的三个这样的主题。统一的主题是半参数脆弱性模型的新应用，以解决现有方法的局限性。在实践中，通常的情况是，终止事件(死亡或退出)审查非终止事件(发病率)，但反之亦然。如果终止事件的审查是信息性的，则终止事件的Kaplan Meier估计器可能无效。在目标1中，我将使用脆弱性模型来估计事件的联合分布。该方法在评估代理端点的强度和边际分布方面具有一定的价值。在医学研究中，基于比例风险假设的预测模型总是被错误地指定。这可能包括预后因素，为了便于解释而被二分法，并可能省略科学上相关的协变量。在目标2中，我将考虑一类一般的单变量比例风险脆弱回归模型的推论的稳健性，这些模型比标准模型更灵活，但仍然可能被错误地指定。在以人群为基础的研究中，在控制了环境危险因素后，残留的家族相关性可能预示着一种遗传病因。通过比例风险假设合并协变量的多变量模型很受欢迎。然而，当回归模型不正确时，这种方法可能不合适，因为当重要的协变量被省略时就会发生这种情况。在目标3中，我将提出一类一般的多变量非比例风险脆弱回归模型，它们对这种错误说明是健壮的。在所有的目标中，现有的脆弱模型方法不适合所提出的应用，需要原始的方法或理论证明。

DESCRIPTION (provided by applicant): The Kaplan Meier estimator, the Iogrank test, and the proportional hazards model are reported in an extremely high percentage of oncology articles in the premier medical journals. There is good reason for this orthodoxy. Their theoretical properties are well understood, they are robust, and they are available in standard statistical software. Unfortunately, the methods are based on strong simplifying assumptions and difficulties may arise when the assumptions are violated. The proposed research will investigate three such topics arising in cancer and other chronic disease studies. The unifying theme is the novel application of semiparametric frailty models to address the limitations of the existing methods. In practice, it is often the case that a terminating event (death or drop out) censors a non terminating event (morbidity), but not vice versa. The Kaplan Meier estimator for the terminating event may not be valid if censoring by the terminating event is informative. In Aim 1, I will use a frailty model to estimate the joint distribution of the events. The approach is valuable in evaluating the strength and marginal distribution of surrogate endpoints. In medical studies, predictive models based on the proportional hazards assumption are invariably misspecified. The may include prognostic factors which are dichotomized for ease of interpretation and may omit covariates which are scientifically relevant. In Aim 2, I will consider the robustness of inferences for a general class of univariate proportional hazards frailty regression models which are more flexible than the standard model but may still be misspecified. In population based studies, residual familial correlations after controlling for environmental risk factors may be indicative of a genetic etiology. Multivariate models which incorporate covariates via proportional hazards assumptions are popular. However, the approach may not be appropriate when the regression model is incorrect, as occurs when important covariates are omitted. In Aim 3, I will propose a general class of multivariate non-proportional hazards frailty regression models which are robust to such misspecification. In all of the Aims, existing methods for frailty models are unsuitable for the proposed applications and original methodology or theoretical justification is needed.