STATISTICS IN MEDICINE Statist. Med. 2004; 23:2729–2744 (DOI: 10.1002/sim.1840) Modelling the distribution of ischaemic stroke-specic survival time using an EM-based mixture approach with random eects adjustment S. K. Ng 1; ∗; † , G. J. McLachlan 1 , Kelvin K. W. Yau 2 and Andy H. Lee 3 1 Department of Mathematics; University of Queensland; Brisbane; QLD 4072, Australia 2 Department of Management Sciences; City University of Hong Kong; Tat Chee Avenue; Kowloon; Hong Kong 3 Department of Epidemiology and Biostatistics; Curtin University of Technology; GPO Box U 1987; Perth; WA 6845; Australia SUMMARY A two-component survival mixture model is proposed to analyse a set of ischaemic stroke-specic mortality data. The survival experience of stroke patients after index stroke may be described by a subpopulation of patients in the acute condition and another subpopulation of patients in the chronic phase. To adjust for the inherent correlation of observations due to random hospital eects, a mixture model of two survival functions with random eects is formulated. Assuming a Weibull hazard in both components, an EM algorithm is developed for the estimation of xed eect parameters and variance components. A simulation study is conducted to assess the performance of the two-component survival mixture model estimators. Simulation results conrm the applicability of the proposed model in a small sample setting. Copyright ? 2004 John Wiley & Sons, Ltd. KEY WORDS: EM algorithm; GLMM; stroke-specic death; survival mixture; Weibull distribution 1. INTRODUCTION Mixture models have been widely used to model failure-time data in a variety of situations [1–5]. As a exible way of modelling data, the mixture approach is directly applicable in situations where the adoption of a single parametric family for the distribution of failure time is inadequate. For example, following open-heart surgery for heart valve replacement, the risk of death can be characterized by three merging phases [6]: an early phase immediately ∗ Correspondence to: Angus S. K. Ng, Department of Mathematics, University of Queensland, Brisbane, QLD 4072, Australia. † E-mail: skn@maths.uq.edu.au Contract=grant sponsor: Australian Research Council Contract=grant sponsor: Research Grants Council of Hong Kong Contract=grant sponsor: National Health and Medical Research Council of Australia Received June 2003 Copyright ? 2004 John Wiley & Sons, Ltd. Accepted December 2003