Kim D K
Department of Biostatistics, Yonsei University College of Medicine, Seoul, Korea.
In Vitro Cell Dev Biol Anim. 1997 Apr;33(4):289-93. doi: 10.1007/s11626-997-0049-7.
Doubling time has been widely used to represent the growth pattern of cells. A traditional method for finding the doubling time is to apply gray-scaled cells, where the logarithmic transformed scale is used. As an alternative statistical method, the log-linear model was recently proposed, for which actual cell numbers are used instead of the transformed gray-scaled cells. In this paper, I extend the log-linear model and propose the extended log-linear model. This model is designed for extra-Poisson variation, where the log-linear model produces the less appropriate estimate of the doubling time. Moreover, I compare statistical properties of the gray-scaled method, the log-linear model, and the extended log-linear model. For this purpose, I perform a Monte Carlo simulation study with three data-generating models: the additive error model, the multiplicative error model, and the overdispersed Poisson model. From the simulation study, I found that the gray-scaled method highly depends on the normality assumption of the gray-scaled cells; hence, this method is appropriate when the error model is multiplicative with the log-normally distributed errors. However, it is less efficient for other types of error distributions, especially when the error model is additive or the errors follow the Poisson distribution. The estimated standard error for the doubling time is not accurate in this case. The log-linear model was found to be efficient when the errors follow the Poisson distribution or nearly Poisson distribution. The efficiency of the log-linear model was decreased accordingly as the overdispersion increased, compared to the extended log-linear model. When the error model is additive or multiplicative with Gamma-distributed errors, the log-linear model is more efficient than the gray-scaled method. The extended log-linear model performs well overall for all three data-generating models. The loss of efficiency of the extended log-linear model is observed only when the error model is multiplicative with log-normally distributed errors, where the gray-scaled method is appropriate. However, the extended log-linear model is more efficient than log-linear model in this case.
倍增时间已被广泛用于表示细胞的生长模式。一种传统的求倍增时间的方法是应用灰度细胞，其中使用对数变换尺度。作为一种替代的统计方法，最近提出了对数线性模型，该模型使用实际细胞数而非变换后的灰度细胞。在本文中，我扩展了对数线性模型并提出了扩展对数线性模型。此模型针对超泊松变异而设计，在这种情况下对数线性模型对倍增时间的估计不太合适。此外，我比较了灰度法、对数线性模型和扩展对数线性模型的统计特性。为此，我用三种数据生成模型进行了蒙特卡罗模拟研究：加性误差模型、乘性误差模型和过度分散泊松模型。从模拟研究中，我发现灰度法高度依赖于灰度细胞的正态性假设；因此，当误差模型是乘性的且误差服从对数正态分布时，此方法适用。然而，对于其他类型的误差分布，它的效率较低，尤其是当误差模型是加性的或误差服从泊松分布时。在这种情况下，倍增时间的估计标准误差不准确。当误差服从泊松分布或近似泊松分布时，发现对数线性模型是有效的。与扩展对数线性模型相比，随着过度分散的增加，对数线性模型的效率相应降低。当误差模型是加性的或与伽马分布误差乘性相关时，对数线性模型比灰度法更有效。扩展对数线性模型在所有三种数据生成模型中总体表现良好。仅当误差模型是乘性的且误差服从对数正态分布（此时灰度法适用）时，才观察到扩展对数线性模型的效率损失。然而，在这种情况下，扩展对数线性模型比对数线性模型更有效。
