In survival analysis, estimating the fraction of 'immune' or 'cured' subjects who will never experience the event of interest, requires a sufficiently long follow-up period. A few statistical tests have been proposed to test the assumption of sufficient follow-up, i.e. whether the right extreme of the censoring distribution exceeds that of the survival time of the uncured subjects. However, in practice the problem remains challenging. To address this, a relaxed notion of 'practically' sufficient follow-up has been introduced recently, suggesting that the follow-up would be considered sufficiently long if the probability for the event occurring after the end of the study is very small. All these existing tests do not incorporate covariate information, which might affect the cure rate and the survival times. We extend the test for 'practically' sufficient follow-up to settings with categorical covariates. While a straightforward intersection-union type test could reject the null hypothesis of insufficient follow-up only if such hypothesis is rejected for all covariate values, in practice this approach is overly conservative and lacks power. To improve upon this, we propose a novel test procedure that relies on the test decision for one properly chosen covariate value. Our approach relies on the assumption that the conditional density of the uncured survival time is a non-increasing function of time in the tail region. We show that both methods yield tests of asymptotically level $α$ and investigate their finite sample performance through simulations. The practical application of the methods is illustrated using a skin melanoma dataset.

翻译：在生存分析中，估计永远不会经历目标事件的"免疫"或"治愈"个体比例，需要足够长的随访期。已有若干统计检验被提出来检验充分随访的假设，即审查分布的右极端是否超过未治愈个体生存时间的右极端。然而，在实践中该问题仍然具有挑战性。为此，最近引入了"实际"充分随访的宽松概念，建议若研究结束后事件发生的概率非常小，则认为随访时间足够长。所有这些现有检验均未纳入协变量信息，而协变量可能影响治愈率和生存时间。我们将"实际"充分随访的检验扩展到包含分类协变量的场景。虽然简单的交并型检验仅当在所有协变量值下均拒绝不充分随访的原假设时才能拒绝该假设，但实践中这种方法过于保守且缺乏检验效能。为改进此问题，我们提出了一种新的检验程序，该程序依赖于针对一个适当选择的协变量值的检验决策。我们的方法基于以下假设：未治愈生存时间的条件密度在尾部区域是时间的非增函数。我们证明两种方法均产生渐近水平$α$的检验，并通过模拟研究其有限样本性能。最后使用皮肤黑色素瘤数据集展示了这些方法的实际应用。