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H-likelihood Approach for Multivariate Survival Models with Random Effects


The department of Mathematics and Statistics at the University of Limerick invites you to a seminar by Prof. Il Do Ha (Pukyong National University):

Title: H-likelihood Approach for Multivariate Survival Models with Random Effects

Abstract: Multivariate survival data (or correlated time-to-event data) are frequently encountered in biomedical or econometrical research (e.g. multi-center clinical trial, twin/family genetic study, duration study of listed company or patent). Correlation and/or heterogeneity caused by clusters can be modelled by introducing unobserved frailty components (random effects) into the hazard function. Semi-parametric frailty models, generalizations of Cox's (1972) PH models, have now been widely used. However, current likelihood-based inference may encounter difficulties caused by (i) intractable integration required to obtain marginal likelihood (i.e. observed likelihood), (ii) incompleteness of data due to censoring and/or truncation and (iii) nuisance parameter problems for allowing non-parametric baseline hazard. Such challenging problems can be overcome by using the hierarchical likelihood (or h-likelihood; Lee and Nelder, 1996, Lee, Nelder, Pawitan, 2017).

In this talk, we present the h-likelihood methodologies which have been developed for various random-effect survival models (Ha, Jeong and Lee, 2017). We also show that the h-likelihood gives a unified framework for multivariate survival analysis. Furthermore, we introduce how the h-likelihood framework is extended to advanced survival analyses such as (i) interval estimation of individual random effects, (ii) model selection, (iii) penalized variable selection, (iv) competing risks modelling, and (v) joint modelling of different outcomes. The proposed methods are demonstrated with simulation studies and practical examples including a data set from multi-center clinical trials.

Key words: Competing-risks models, Frailty models, H-likelihood, Random effects, Joint models



Cox, D. R. (1972). Regression models and life tables (with Discussion). JRSS B 74: 187–220.

Lee, Y and Nelder, J. A. (1996). Hierarchical generalized linear models (with discussion). JRSS B 58: 619–678

Lee, Y., Nelder, J. A. and Pawitan, Y. (2017). Generalised linear models with random effects: unified analysis via h-likelihood. 2nd edn. Chapman and Hall: Boca Raton.

Ha, I.D., Jeong, J.-H. and Lee, Y. (2017). Statistical modelling of survival data with random effects: h-likelihood approach. Springer: Singapore.

This seminar will take place on Friday26th January, at 4 p.m, in  Room A2-002.

If you have any questions regarding this seminar, please direct them to Iain Moyles (061 233726,

A full list of upcoming seminars can be found at

Supported by Science Foundation Ireland funding, MACSI - the Mathematics Applications Consortium for Science and Industry (, centred at the University of Limerick, is dedicated to the mathematical modelling and solution of problems which arise in science, engineering and industry in Ireland.

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