Faculty of Medicine, Department of Clinical Sciences Lund, Oncology and Pathology, Lund University, Medicon Village Building 404, Scheelevägen 2, SE-223 81, Lund, Sweden.
Department of Pathology, Odense University Hospital, DK-5000, Odense, Denmark.
BMC Cancer. 2018 Dec 7;18(1):1226. doi: 10.1186/s12885-018-5123-x.
Prognostic factors in breast cancer are often measured on a continuous scale, but categorized for clinical decision-making. The primary aim of this study was to evaluate if accounting for continuous non-linear effects of the three factors age at diagnosis, tumor size, and number of positive lymph nodes improves prognostication. These factors will most likely be included in the management of breast cancer patients also in the future, after an expected implementation of gene expression profiling for adjuvant treatment decision-making.
Four thousand four hundred forty seven and 1132 women with primary breast cancer constituted the derivation and validation set, respectively. Potential non-linear effects on the log hazard of distant recurrences of the three factors were evaluated during 10 years of follow-up. Cox-models of successively increasing complexity: dichotomized predictors, predictors categorized into three or four groups, and predictors transformed using fractional polynomials (FPs) or restricted cubic splines (RCS), were used. Predictive performance was evaluated by Harrell's C-index.
Using FP-transformations, non-linear effects were detected for tumor size and number of positive lymph nodes in univariable analyses. For age, non-linear transformations did, however, not improve the model fit significantly compared to the linear identity transformation. As expected, the C-index increased with increasing model complexity for multivariable models including the three factors. By allowing more than one cut-point per factor, the C-index increased from 0.628 to 0.674. The additional gain, as measured by the C-index, when using FP- or RCS-transformations was modest (0.695 and 0.696, respectively). The corresponding C-indices for these four models in the validation set, based on the same transformations and parameter estimates from the derivation set, were 0.675, 0.700, 0.706, and 0.701.
Categorization of each factor into three to four groups was found to improve prognostication compared to dichotomization. The additional gain by allowing continuous non-linear effects modeled by FPs or RCS was modest. However, the continuous nature of these transformations has the advantage of making it possible to form risk groups of any size.
乳腺癌的预后因素通常在连续尺度上进行测量，但为了临床决策而进行分类。本研究的主要目的是评估是否考虑到诊断时年龄、肿瘤大小和阳性淋巴结数量这三个因素的连续非线性效应可以改善预后。这些因素很可能在未来也将被纳入乳腺癌患者的管理中，因为预计在做出辅助治疗决策时会采用基因表达谱分析。
4447 名和 1132 名原发性乳腺癌患者分别构成了推导集和验证集。在 10 年的随访期间，评估了这三个因素对远处复发对数风险的潜在非线性效应。使用 Cox 模型的复杂度依次增加：将预测因子二分类、将预测因子分类为三或四组、使用分数多项式（FP）或限制立方样条（RCS）对预测因子进行转换。使用 Harrell 的 C 指数评估预测性能。
使用 FP 转换，在单变量分析中检测到肿瘤大小和阳性淋巴结数的非线性效应。对于年龄，与线性恒等转换相比，非线性转换并没有显著改善模型拟合度。正如预期的那样，对于包含三个因素的多变量模型，随着模型复杂性的增加，C 指数也随之增加。通过允许每个因素有多个截断点，C 指数从 0.628 增加到 0.674。使用 FP 或 RCS 转换时，C 指数的额外增益适中（分别为 0.695 和 0.696）。在验证集中，基于推导集中相同的转换和参数估计，这些四个模型的 C 指数分别为 0.675、0.700、0.706 和 0.701。
将每个因素分为三到四个组比二分类更能提高预后。通过允许 FP 或 RCS 对连续非线性效应进行建模，获得的额外增益适中。然而，这些转换的连续性质具有可以形成任何大小的风险组的优势。
