Generalized estimating equation approach for analyzing the effects of metal-derived products on survival and hatching of zebrafish embryos

Zebrafish embryos are widely used as a model to monitor the effect of chemicals on their survival and hatching at different time epochs. This experimental design generates longitudinal data in which the observations for a given subject are correlated and they are statistically independent across the subjects. This particular nature of the observations suggests the use of generalized estimating equation (GEE) methodology for performing meaningful statistical analysis. However, it has been observed that the researchers working in this area have been routinely employing statistical methodologies such as analysis of variance (ANOVA) if the data are continuous and logit or probit models if the data are discrete. In our opinion, it is grossly incorrect to use these methods as they do not take into account the correlation structure mentioned above. The sole purpose of this article is to bring out this serious flaw clearly to the attention of the researchers. For illustration, we have studied the effects of two Ayurvedic bhasmas-Tamra bhasma and Suwarnamakshik bhasma-on survival and hatching of zebrafish embryos over certain time duration. The statistical analysis using GEE reveals a weak promotional effect of Suwarnamakshik bhasma and an inhibitory effect of Tamra bhasma on hatching.