Frailty Models and Survival Analysis in Cancer Research

描述（由申请人提供）：Kaplan Meier估计器、Iogrank检验和比例风险模型在主要医学期刊的肿瘤学文章中报道的比例极高。这种正统观点是有充分理由的。它们的理论性质被很好地理解，它们是健壮的，并且在标准统计软件中可用。不幸的是，这些方法是基于强烈的简化假设，当这些假设被违反时，可能会出现困难。拟议的研究将调查癌症和其他慢性疾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，经常发生的情况是，一个终止事件（死亡或退学）审查了一个非终止事件（发病率），但反之亦然。如果终止事件的审查具有信息性，则终止事件的Kaplan Meier估计可能无效。在目标1中，我将使用一个脆弱性模型来估计事件的联合分布。该方法在评估替代终点的强度和边际分布方面是有价值的。在医学研究中，基于比例风险假设的预测模型总是指定错误。其中可能包括预后因素，为便于解释而将其二分类，并可能省略与科学相关的协变量。在目标2中，我将考虑一般类型的单变量比例风险脆弱回归模型的推断的稳健性，这些模型比标准模型更灵活，但仍可能被错误指定。在以人群为基础的研究中，在控制了环境风险因素后，剩余的家族相关性可能表明遗传病因。通过比例风险假设纳入协变量的多变量模型很受欢迎。然而，当回归模型不正确时，如省略重要协变量时，这种方法可能不合适。在目标3中，我将提出一类对这种错误规范具有鲁棒性的多元非比例风险脆弱性回归模型。在所有目标中，现有的脆弱性模型方法不适合提出的应用，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.