A new proposal for multivariable modelling of time-varying effects in survival data based on fractional polynomial time-transformation
A new proposal for multivariable modelling of time-varying effects in survival data based on fractional polynomial time-transformation
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DOI：
10.1002/bimj.200610328
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发表时间：
2007-06-01
影响因子：
1.7
通讯作者：
Look, Maxime
中科院分区：
文献类型：
--
作者：
Sauerbrei, Willi;Royston, Patrick;Look, Maxime
考克斯比例风险模型已成为癌症和其他慢性疾病生存时间数据分析的标准。在大多数研究中，假设协变量效应为比例风险（PH）。长期随访时，可能违反PH假设，导致模型拟合不良。为了适应非PH效应，我们引入了一个新的程序，MFPT，多变量分数多项式（MFP）方法的扩展，做以下工作：（1）选择有影响力的变量;（2）确定一个合理的剂量反应函数的连续变量;（3）调查随时间变化的影响;（4）模型的连续规模上的这种随时间变化的影响。假设PH最初，我们从详细的模型构建步骤开始，包括搜索连续协变量的可能非线性函数。有时，如果在PH假设下对一段时间进行“平均”，具有强烈短期影响的变量可能会显得很弱或没有影响力。为了避免遗漏这些变量，我们在有限的时间间隔内重复分析。通过第二次分析确定的任何其他预后变量都被添加到我们的最终时间固定多变量模型中。使用前向选择算法，我们通过添加随时间变化的协变量来搜索拟合的可能改进。创建最终时间固定模型的第一部分不需要使用MFP。一个模型可能是从“外部”给出的，或者对于这一部分，不同的策略可能是首选的。这扩大了时变部分的范围。为了激励和说明的方法，我们创建了一个大型数据库的原发性乳腺癌患者的预后模型。孕激素受体状态和阳性淋巴结数量存在非线性时间固定效应。孕激素受体状态和肿瘤大小存在高度统计学显著的时变效应。
The Cox proportional hazards model has become the standard for the analysis of survival time data in cancer and other chronic diseases. In most studies, proportional hazards (PH) are assumed for covariate effects. With long-term follow-up, the PH assumption may be violated, leading to poor model fit. To accommodate non-PH effects, we introduce a new procedure, MFPT, an extension of the multivariable fractional polynomial (MFP) approach, to do the following: (1) select influential variables; (2) determine a sensible dose-response function for continuous variables; (3) investigate time-varying effects; (4) model such time-varying effects on a continuous scale. Assuming PH initially, we start with a detailed model-building step, including a search for possible non-linear functions for continuous covariates. Sometimes a variable with a strong short-term effect may appear weak or non-influential if 'averaged' over time under the PH assumption. To protect against omitting such variables, we repeat the analysis over a restricted time-interval. Any additional prognostic variables identified by this second analysis are added to create our final time-fixed multivariable model. Using a forward-selection algorithm we search for possible improvements in fit by adding time-varying covariates. The first part to create a final time-fixed model does not require the use of MFP. A model may be given from 'outside' or a different strategy may be preferred for this part. This broadens the scope of the time-varying part. To motivate and illustrate the methodology, we create prognostic models from a large database of patients with primary breast cancer. Non-linear time-fixed effects are found for progesterone receptor status and number of positive lymph nodes. Highly statistically significant time-varying effects are present for progesterone receptor status and tumour size.