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Biometrika Advance Access published online on November 22, 2007
Biometrika, doi:10.1093/biomet/asm063
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© 2007 London Mathematical Society

Article

Using Hierarchical Likelihood For Missing Data Problems

Yun Sung-Cheol

Department of Preventive Medicine, University of Ulsan College of Medicine, Seoul 138-736, Korea ysch97{at}amc.seoul.kr

Youngjo Lee

Department of Statistics, Seoul National University, Seoul 151-747, Korea youngjo{at}plaza.snu.ac.kr

Michael G. Kenward

London School of Hygiene and Tropical Medicine, London WC1E 7HT, U.K. mike.kenward{at}lshtm.ac.uk

Received for publication 1 June 2005. Revision received 1 March 2007.
  Abstract

Most statistical solutions to the problem of statistical inference with missing data involve integration or expectation. This can be done in many ways: directly or indirectly, analytically or numerically, deterministically or stochastically. Missing-data problems can be formulated in terms of latent random variables, so that hierarchical likelihood methods of Lee & Nelder (1996) can be applied to missing-value problems to provide one solution to the problem of integration of the likelihood. The resulting methods effectively use a Laplace approximation to the marginal likelihood with an additional adjustment to the measures of precision to accommodate the estimation of the fixed effects parameters. We first consider missing at random cases where problems are simpler to handle because the integration does not need to involve the missing-value mechanism and then consider missing not at random cases. We also study tobit regression and refit the missing not at random selection model to the antidepressant trial data analyzed in Diggle & Kenward (1994).

Key Words: Adjusted profile likelihood • Hierarchical likelihood • Marginal likelihood • Missing data • Restricted likelihood


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