Spratt J A, von Fournier D, Spratt J S, Weber E E
Department of Surgery, Medical College of Virginia, Virginia Commonwealth University, Richmond.
Cancer. 1993 Mar 15;71(6):2013-9. doi: 10.1002/1097-0142(19930315)71:6<2013::aid-cncr2820710615>3.0.co;2-v.
Improved understanding of human breast cancer growth rates may have many clinical applications. Previous reports have used small numbers of patients and assumed an exponential growth rate.
The exponential equation and the most commonly used decelerating growth equations, the Gompertz equation and seven generalized forms of the logistic equation, were fitted to mammographic measurements of primary breast cancer using the least squares method. An average of 3.4 observations was made in 113 patients, whereas two measurements were made in another 335 patients. Tumors were assumed to originate as a single cell with the lethal tumor volume assumed to be 2(40) cells.
All decelerating equations tested provided a better fit than the exponential, whereas a form of the logistic equation provided the best fit to the data. Limitations in the number of tumor measurements, the assumption of maximal tumor size, and biases inherent in the method of data collection are reviewed. These observations suggest families of curves that characterize breast cancer growth during the early period of clinical observation.
Breast cancer growth in the early clinical period was modeled by a form of the logistic equation. The exponential equation fit the data least well.
对人类乳腺癌生长速率的深入了解可能具有许多临床应用价值。以往的报告所涉及的患者数量较少，且假定为指数生长速率。
使用最小二乘法将指数方程以及最常用的减速生长方程（Gompertz方程和逻辑斯蒂方程的七种广义形式）拟合到原发性乳腺癌的乳房X线测量数据上。113名患者平均进行了3.4次观察，另外335名患者进行了两次测量。假设肿瘤起源于单个细胞，致死肿瘤体积假定为2（40）个细胞。
所有测试的减速方程都比指数方程拟合得更好，而一种形式的逻辑斯蒂方程对数据的拟合最佳。本文回顾了肿瘤测量数量的局限性、最大肿瘤大小的假设以及数据收集方法中固有的偏差。这些观察结果提示了在临床观察早期表征乳腺癌生长的曲线族。
临床早期乳腺癌的生长可用一种形式的逻辑斯蒂方程来建模。指数方程对数据的拟合效果最差。
