Bayesian optimal designs for cox regression model with random and nonrandom intercept based on type I censored data

Abstract

In this article, we aim to develop A and D-optimal designs for censored data via Bayesian strategy. In this regard, based on some different sorts of prior distributions for the unknown parameters, the appropriate designs are calculated. In the sequel, we define the random intercept model for the Cox regression model assuming the random intercept distributed normally. It is observed that the likelihood function of the observations cannot be acquired in a closed form. Thus, we obtain the quasi-information matrix based on the quasi-likelihood function. We then, use this matrix to obtain the A and D-optimal designs. It is seen that the Fisher information matrix depends on the unknown parameters as a result the locally optimal designs will be inefficient when the true guess about the parameters is failed. To overcome this problem, we propose the Bayesian strategy to obtain more robust optimal designs. Some numerical techniques such as Monte Carlo integration and numerical optimization methods are implemented to calculate the designs. Further, the generalized equivalence theorem is adapted to confirm the optimality of the proposed designs. All of the numerical results are done with R software. The results of this article will help to remove the weakness of the locally optimal designs that have been addressed in Schmidt and Schwabe when the parameters are misspecfied.