Department of Epidemiology and Biostatistics, Netherlands Cancer Institute, Amsterdam, Netherlands.
Brandenburg Medical School Theodor Fontane, Institute of Biostatistics and Registry Research, Neuruppin, Germany.
Sci Rep. 2020 Jun 4;10(1):9143. doi: 10.1038/s41598-020-65767-7.
We consider mice experiments where tumour cells are injected so that a tumour starts to grow. When the tumour reaches a certain volume, mice are randomized into treatment groups. Tumour volume is measured repeatedly until the mouse dies or is sacrificed. Tumour growth rates are compared between groups. We propose and evaluate linear regression for analysis accounting for the correlation among repeated measurements per mouse. More specifically, we examined five models with three different variance-covariance structures in order to recommend the least complex method for small to moderate sample sizes encountered in animal experiments. We performed a simulation study based on data from three previous experiments to investigate the properties of estimates of the difference between treatment groups. Models were estimated via marginal modelling using generalized least squares and restricted maximum likelihood estimation. A model with an autoregressive (AR-1) covariance structure was efficient and unbiased retaining nominal coverage and type I error when the AR-1 variance-covariance matrix correctly specified the association between repeated measurements. When the variance-covariance was misspecified, that model was still unbiased but the type I error and the coverage rates were affected depending on the degree of misspecification. A linear regression model with an autoregressive (AR-1) covariance structure is an adequate model to analyse experiments that compare tumour growth rates between treatment groups.
我们考虑将肿瘤细胞注射到小鼠体内以诱导肿瘤生长的实验。当肿瘤达到一定体积时，将小鼠随机分配到治疗组。重复测量肿瘤体积，直到小鼠死亡或被处死。比较各组之间的肿瘤生长速率。我们提出并评估了线性回归分析方法，以考虑每只小鼠重复测量之间的相关性。更具体地说，我们检查了五个具有三种不同方差协方差结构的模型，以推荐在动物实验中遇到的小到中等样本量的最简单方法。我们基于三个先前实验的数据进行了模拟研究，以研究处理组之间差异估计量的性质。通过广义最小二乘法和限制最大似然估计，使用边缘模型对模型进行了估计。当自回归（AR-1）协方差结构正确指定重复测量之间的关联时，具有 AR-1 协方差结构的模型是有效且无偏的，保留了名义覆盖率和Ⅰ型错误率。当协方差结构被错误指定时，该模型仍然是无偏的，但Ⅰ型错误率和覆盖率会受到协方差结构错误指定程度的影响。具有自回归（AR-1）协方差结构的线性回归模型是分析比较治疗组之间肿瘤生长速率的实验的合适模型。
