A result on a 2×2 survival experiment

Lifetime data classified according to categorical variables under the proportionality of the hazard functions of response variables for various treatment combinations is assumed. The proposed model is a combination of Coxʹs proportional hazards model and ANOVA model. The existence of a solution to the marginal likelihood function is examined for the case of 2×2 two-way classification. We provide an easily verifiable condition for the existence of a unique estimate.