The Use of Simple Reparameterizations to Improve the Efficiency of Markov Chain Monte Carlo Estimation for Multilevel Models with Applications to Discrete Time Survival Models

William J. Browne,Fiona Steele,Mousa Golalizadeh,Martin J. Green

doi:10.1111/j.1467-985x.2009.00586.x

Abstract

We consider the application of Markov chain Monte Carlo (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 data set 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 data sets 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 the methods and more confidence in the estimates that are produced. The MCMC methodological literature is full of alternative algorithms designed to improve mixing of chains and we describe three reparameterization 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 reparameterization techniques can be used and assess their performance.

Highlights

Survival analysis is widely used in the medical and social sciences to study the duration until the occurrence of events such as death, recovery from illness, unemployment, birth and divorce
In this paper we investigate three methods to increase the computational efficiency of Markov chain Monte Carlo (MCMC) estimation of multilevel discrete time survival models: hierarchical centring (Gelfand et al, 1995), orthogonal polynomials (e.g. Hills and Smith (1992)) and parameter expansion (Liu et al, 1998)
The data come from the 1997 Indonesia Demographic and Health Survey (Central Bureau of Statistics et al, 1998) which is a representative survey of all married women between the ages of 15 and 49 years

Summary

Introduction

Survival analysis (which is known as event history analysis) is widely used in the medical and social sciences to study the duration until the occurrence of events such as death, recovery from illness, unemployment, birth and divorce. J. Green multiple states between which individuals move (e.g. between employment and unemployment), an individual may be exposed to competing risks (e.g. different reasons for leaving a job) and there may be multiple correlated processes (e.g. the presence of children, outcomes of a birth history, may affect employment transitions and vice versa). Randomeffects or multilevel models are powerful tools for handling such features of survival data and have been proposed for the analysis of clustered durations (Clayton and Cuzick, 1985; Guo and Rodriguez, 1992; Sastry, 1997), competing risks and multiple states (Steele et al, 1996, 2004) and the simultaneous analysis of correlated event processes (Lillard, 1993)

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