Department of Biostatistics and Data Science, The University of Texas Health Science Center at Houston, Houston, Texas, USA.
Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston, Texas, USA.
Stat Med. 2022 Dec 20;41(29):5698-5714. doi: 10.1002/sim.9588. Epub 2022 Sep 27.
In medical research, it is often of great interest to have an accurate estimation of cure rates by different treatment options and for different patient groups. If the follow-up time is sufficiently long and the sample size is large, the proportion of cured patients will make the Kaplan-Meier estimator of survival function have a flat plateau at its tail, whose value indicates the overall cure rate. However, it may be difficult to estimate and compare the cure rates for all the subsets of interest in this way, due to the limit of sample sizes and curse of dimensionality. In the current literature, most regression models for estimating cure rates assume proportional hazards (PH) between different subgroups. It turns out that the estimation of cure rates for subgroups is highly sensitive to this assumption, so more flexible models are needed, especially when this PH assumption is clearly violated. We propose a new cure model to simultaneously incorporate both PH and non-PH scenarios for different covariates. We develop a stable and easily implementable iterative procedure for parameter estimation through maximization of the nonparametric likelihood function. The covariance matrix is estimated by adding perturbation weights to the estimation procedure. In simulation studies, the proposed method provides unbiased estimation for the regression coefficients, survival curves, and cure rates given covariates, while existing models are biased. Our model is applied to a study of stage III soft tissue sarcoma and provides trustworthy estimation of cure rates for different treatment and demographic groups.
在医学研究中，对于不同的治疗方案和不同的患者群体，准确估计治愈率通常非常重要。如果随访时间足够长且样本量足够大，则治愈患者的比例将使生存函数的 Kaplan-Meier 估计器在尾部出现平坦的高原，其值表示总体治愈率。然而，由于样本量的限制和维度的诅咒，可能难以以这种方式估计和比较所有感兴趣的亚组的治愈率。在当前的文献中，大多数用于估计治愈率的回归模型都假设不同亚组之间存在比例风险 (PH)。事实证明，亚组治愈率的估计对该假设非常敏感，因此需要更灵活的模型，特别是当明显违反此 PH 假设时。我们提出了一种新的治愈率模型，用于同时为不同协变量结合 PH 和非 PH 情况。我们通过最大化非参数似然函数来开发一种稳定且易于实施的参数估计迭代过程。通过向估计过程添加扰动权重来估计协方差矩阵。在模拟研究中，所提出的方法为给定协变量的回归系数、生存曲线和治愈率提供了无偏估计，而现有模型则存在偏差。我们的模型应用于 III 期软组织肉瘤的研究，并为不同治疗和人口统计学组提供了可靠的治愈率估计。
