Institut für Statistik, Ludwig-Maximilians-Universität München, Germany.
Regul Toxicol Pharmacol. 2012 Oct;64(1):26-34. doi: 10.1016/j.yrtph.2012.06.014. Epub 2012 Jun 28.
Several doses and a control group can be compared under order restriction using the Williams procedure for normally distributed endpoints assuming variance homogeneity. Comparison of the survival functions represents a secondary endpoint in long-term in vivo bioassays of carcinogenicity. Therefore, a Williams-type procedure for the comparison of survival functions is proposed for the assumption of the Cox proportional hazards model or the general frailty Cox model to allow a joint analysis over sex and strains. Interpretation according to both statistical significance and biological relevance is possible with simultaneous confidence intervals for hazard ratios. Related survival data can be analyzed using the R packages survival, coxme, and multcomp. Together with the R packages MCPAN and nparcomp, Dunnett- or Williams-type procedures are now available for the statistical analysis of the following endpoint types in toxicology: (i) normally distributed, (ii) non-normally distributed, (iii) score (ordered categorical) data, (iv) crude proportions, (v) survival functions, and (vi) time-to-tumor data with and without cause-of-death information.
可以在有序限制下使用 Williams 程序比较多个剂量组和对照组，前提是正态分布的终点假设方差同质性。生存函数的比较是致癌性长期体内生物测定的次要终点。因此，对于 Cox 比例风险模型或一般脆弱 Cox 模型的假设，提出了一种用于生存函数比较的 Williams 型程序，以允许在性别和品系之间进行联合分析。通过同时进行危险比的置信区间，可以根据统计学意义和生物学相关性进行解释。使用 R 包 survival、coxme 和 multcomp 可以分析相关的生存数据。与 R 包 MCPAN 和 nparcomp 一起，现在可以为毒理学中的以下终点类型的统计分析提供 Dunnett 或 Williams 型程序：（i）正态分布，（ii）非正态分布，（iii）评分（有序分类）数据，（iv）原始比例，（v）生存函数，以及（vi）具有和不具有死亡原因信息的肿瘤时间数据。
