The analysis of survival and longitudinal data from life-span carcinogenicity bioassay on Sprague-Dowley rats

Carcinogenicity bioassay are among the best instruments to strengthen the evidence on which regulatory agencies vase their decision to classify harmful agents as human carcinogens, so they are fundamental to protect public health. The statistical analysis is fundamental to validate the results from carcinogenicity bioassay. This work aims to propose and illustrate some methodologies for the analysis of non-cancer outcomes, in particular for the analysis of time-to-death and of longitudinal measurements of body weights. The data from an old experiment were used for this purpose: 4 experiments aimed at testing the carcinogenic potential of Coca-Cola on Sprague-Dawley rats of different ages (randomized males and females of 7, 30, 39, 55 weeks of age, and their non-randomized offspring, observed since birth) were re-analysed. Survival analysis aimed to verify the influence of the treatment, controlling for possible differences due to sex, age at beginning of observation and age of the dams at pregnancy. It was performed using Cox proportional hazards models for the rats of second generation, and accelerated failure-times models for those of first generation; the use of frailty terms was evaluated (univariate gamma frailty to account for unobserved heterogeneity applied to data from breeders; shared gamma frailty at the litter level applied to data from offspring). The analysis of longitudinal body weights of the offspring was aimed at verifying the relevance of treatment, controlling for physiological differences due to sex and age of the dams at gestation. It was performed using linear and nonlinear mixed-effects models to handle the hierarchical structure of the data. Linear models were fitted using log-transformation of time and polynomial terms of order 3; nonlinear models consisted of growth models, in particular the Berkey-Reed model, that is usually used to analyse human growth during infancy, was applied.