Unobserved individual heterogeneity is a common challenge in population cancer survival studies. This heterogeneity is usually associated with the combination of model misspecification and the failure to record truly relevant variables. We investigate the effects of unobserved individual heterogeneity in the context of excess hazard models, one of the main tools in cancer epidemiology. We propose an individual excess hazard frailty model to account for individual heterogeneity. This represents an extension of frailty modelling to the relative survival framework. In order to facilitate the inference on the parameters of the proposed model, we select frailty distributions which produce closed-form expressions of the marginal hazard and survival functions. The resulting model allows for an intuitive interpretation, in which the frailties induce a selection of the healthier individuals among survivors. We model the excess hazard using a flexible parametric model with a general hazard structure which facilitates the inclusion of time-dependent effects. We illustrate the performance of the proposed methodology through a simulation study. We present a real-data example using data from lung cancer patients diagnosed in England, and discuss the impact of not accounting for unobserved heterogeneity on the estimation of net survival. The methodology is implemented in the R package IFNS.
翻译:在人口癌症生存研究中,常见的个别不观察异质是常见的挑战。这种异质性通常与模型的偏差和未能记录真正相关的变量相结合。我们调查在超危险模型(癌症流行病学的主要工具之一)中未观察到的个别异质效应。我们提出一个个人超过危险脆弱模型,以计算个人的异质性。这代表了脆弱模型与相对生存框架的延伸。为了便利对拟议模型参数的推断,我们选择了产生边际危险和生存功能封闭形式表达的脆弱分布,由此产生的模型可以进行直觉解释,即虚弱导致选择幸存者中较健康的个人。我们用一个灵活的超重危险模型来模拟超重危险,这种模型有助于纳入依赖时间的影响。我们通过模拟研究来说明拟议方法的绩效。我们用在英国诊断的肺癌病人的数据来进行真实数据示例,并讨论不考虑已实施的软件包的可靠性估算方法的影响。