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Maximum likelihood estimation in semiparametric regression models with censored data

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  • D. Zeng
  • D. Y. Lin

Abstract

Semiparametric regression models play a central role in formulating the effects of covariates on potentially censored failure times and in the joint modelling of incomplete repeated measures and failure times in longitudinal studies. The presence of infinite dimensional parameters poses considerable theoretical and computational challenges in the statistical analysis of such models. We present several classes of semiparametric regression models, which extend the existing models in important directions. We construct appropriate likelihood functions involving both finite dimensional and infinite dimensional parameters. The maximum likelihood estimators are consistent and asymptotically normal with efficient variances. We develop simple and stable numerical techniques to implement the corresponding inference procedures. Extensive simulation experiments demonstrate that the inferential and computational methods proposed perform well in practical settings. Applications to three medical studies yield important new insights. We conclude that there is no reason, theoretical or numerical, not to use maximum likelihood estimation for semiparametric regression models. We discuss several areas that need further research. Copyright 2007 Royal Statistical Society.

Suggested Citation

  • D. Zeng & D. Y. Lin, 2007. "Maximum likelihood estimation in semiparametric regression models with censored data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 507-564.
  • Handle: RePEc:bla:jorssb:v:69:y:2007:i:4:p:507-564
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    1. Fredriksson, Peter & Johansson, Per, 2004. "Dynamic Treatment Assignment – The Consequences for Evaluations Using Observational Data," IZA Discussion Papers 1062, Institute for the Study of Labor (IZA).
    2. de Luna, Xavier & Johansson, Per, 2007. "Matching estimators for the effect of a treatment on survival times," Working Paper Series 2007:1, IFAU - Institute for Evaluation of Labour Market and Education Policy.
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