The use of simple reparameterizations to improve the efficiency of Markov chain Monte Carol estimation for multilevel models with applications to discrete time survival models

In this paper we consider the application of MCMC estimation methods to random effects models and in particular the family of discrete-time survival models. Survival models can be used in many situations in the medical and social sciences and we illustrate their use through two examples that differ in terms of both substantive area and data structure. A multilevel discrete-time survival analysis involves expanding the dataset so that the model can be cast as a standard multilevel binary response model. For such models it has been shown that MCMC methods have advantages in terms of reducing estimate bias. However the data expansion results in very large datasets for which MCMC estimation is often slow and can produce chains that exhibit poor mixing. Any way of improving the mixing will result in both speeding up of the methods and more confidence in the estimates produced. The MCMC methodological literature is full of alternative algorithms designed to improve mixing of chains and we describe three reparameterisation techniques that are easy to implement in available software. We consider two examples of multilevel survival analysis: incidence of mastitis in dairy cattle and contraceptive use dynamics in Indonesia. For each application we show where the reparameterisation techniques can be used and assess their performance.