Analyses of two-way chronic studies

This paper proposes a method for analyzing tumor data from chronic studies when the experimental design includes combinations of two factors, for example, sex and dose. Both main effects and combined-effect (interaction) hypotheses are considered. A stratified log-rank statistic is presented for tests of no column or row (main) effects. The paper shows that when the numbers of animals in the cells are unequal and disproportional, the null distribution of the unstratified log-rank statistic does not have a chi-square distribution. Two simple models, additive and multiplicative, for representing the combined effect of row and column are considered under the proportional hazards model. A simple conservative statistic is proposed for testing the additivity of the row and column effects. A simulation experiment to examine the behavior of the null distribution of the combined-effect test statistic under the additive model and the power of the test against the multiplicative model is reported. The procedure is illustrated by analyzing mammary tumors induced by 7,12-dimethylbenz[a]anthracene (DMBA) in yellow and agouti F1 female mice from a laboratory experiment.