Schmoor C, Sauerbrei W, Schumacher M
Institute of Medical Biometry and Medical Informatics, University of Freiburg, Stefan-Meier-Str. 26, D-79104 Freiburg, Germany.
Stat Med. 2000 Feb 29;19(4):441-52. doi: 10.1002/(sici)1097-0258(20000229)19:4<441::aid-sim349>3.0.co;2-n.
When the role of a new prognostic factor is investigated, careful planning of an appropriate study is required. This includes an assessment of the power of the study in terms of sample sizes. An adequate analysis of the independent prognostic effect of a new factor has to be adjusted for the existing standard factors. With survival time as endpoint this will usually be done with the Cox proportional hazards model. Sample size and power formulae in survival analysis have been developed by Schoenfeld for randomized treatment comparisons. In the analysis of prognostic factors the covariates included are expected to be correlated with the factor of primary interest. In this situation, the existing sample size and power formulae are not valid and may not be applied. In this paper, Schoenfeld's formula is first extended to the situation where a correlated factor is included in the analysis. The validity of the resulting approximate asymptotic formula is investigated for its asymptotic behaviour by numerical integration and for its finite behaviour by simulation. Second, an approximate formula for sample size and power is provided to detect an interaction between the interesting and a second correlated factor. This extends the formula for independent effects. Finally, the approach is illustrated by an example on the prognostic impact of DNA ploidy and other factors in advanced ovarian cancer.
在研究新的预后因素的作用时，需要对适当的研究进行精心规划。这包括根据样本量评估研究的效能。对新因素的独立预后效应进行充分分析时，必须对现有的标准因素进行校正。以生存时间作为终点，这通常使用Cox比例风险模型来完成。Schoenfeld已针对随机治疗比较开发了生存分析中的样本量和效能公式。在预后因素分析中，纳入的协变量预计与主要关注的因素相关。在这种情况下，现有的样本量和效能公式无效，可能无法应用。在本文中，Schoenfeld公式首先扩展到分析中包含相关因素的情况。通过数值积分研究所得近似渐近公式的渐近行为，并通过模拟研究其有限行为来检验其有效性。其次，提供了一个用于样本量和效能的近似公式，以检测感兴趣的因素与第二个相关因素之间的相互作用。这扩展了独立效应的公式。最后，通过一个关于DNA倍体和其他因素对晚期卵巢癌预后影响的例子来说明该方法。
