Prediction of risks of sequence of events using multistage proportional hazards model: a marginal-conditional modelling approach

  • Rafiqul I. Chowdhury
  • M. Ataharul IslamEmail author
Original Paper


In many studies, sequence of events may occur over time that produce repeated measures with censored observations. Multi-state models are commonly used, and the effect of risk factors on the transition from one state to another is assessed using the Cox proportional hazards model. In recent years, there is growing interest to predict the disease status at different stages and endpoints using multi-state models. Because of the complexity of existing methods their applications for prediction is limited. In this paper, a simple alternative method is proposed for risk prediction of the sequence of events using multistage modelling approach. The proposed method of prediction is a new development using a series of events in conditional setting arising from the beginning to the endpoint. The proposed method is based on marginal-conditional approach to link the events occurring in a trajectory. The probability of a trajectory can be calculated easily. The main improvement of proposed method for risk prediction is that it is a simple approach, compared to the existing ones, and this approach can easily be generalized to any number of events in the process to the endpoints. Two examples from real life data is illustrated in this paper using the proposed method for risk prediction.


Multi-state model Survival analysis Marginal-Conditional models Sequence of events Prediction 



We acknowledge gratefully that this study is supported by the HEQEP subproject 3293 of the University Grants Commission of Bangladesh and the World Bank. We also acknowledge the permission of Dr. Halida Hanum Akhter, Director, BIRPERHT, for using the data in the second example in this paper. The authors would like to thank Mahbub E Elahi K. Chowdhury and Arindom Sen, BIRPERHT for their assistance during different phases of this work. The authors are greatly indebted to the Ford Foundation for funding the data collection of the maternal morbidity study.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of Statistical Research and Training (ISRT)University of DhakaDhakaBangladesh

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