Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
권호 표지

Regression Analysis of Longitudinal Data Based on M-estimates

  • Jung, Sin-Ho (Division of Statistics, Indiana University School of Medicine, Indianapolis) ;
  • Terry M. Therneau (Section of Biostatistics, Mayo Clinic, Rochester)
  • Published : 2000.06.01
Download PDF
⟨ Previous Next ⟩

Abstract

The method of generalized estimating equations (GEE) has become very popular for the analysis of longitudinal data. We extend this work to the use of M-estimators; the resultant regression estimates are robust to heavy tailed errors and to outliers. The proposed method does not require correct specification of the dependence structure between observation, and allows for heterogeneity of the error. However, an estimate of the dependence structure may be incorporated, and if it is correct this guarantees a higher efficiency for the regression estimators. A goodness-of-fit test for checking the adequacy of the assumed M-estimation regression model is also provided. Simulation studies are conducted to show the finite-sample performance of the new methods. The proposed methods are applied to a real-life data set.

Keywords

References

  1. Biometrika v.82 On the use of working correlation matrix in using generalized linear models for repeated measures Crowder, M.
  2. Statistics in Medicine v.10 Semi-parametric and non-parametric methods for the analysis of repeated measurements with applications to clinical trials Davis, C.S.
  3. Annals of Statistics v.10 On inconsistent M-estimators Freedman, D.A.;Diaconis, P.
  4. Biometrika v.74 A simple test of the proportional hazards assumption Gill R.;Schumacher M.
  5. Annals of Mathematical Statistics v.35 Robust estimation of a location parameter Huber P.J.
  6. Annals of Statistics v.1 Robust regression;Asymptotics, conjectures and Monte Carlo Huber P.J.
  7. Journal of the American Statistical Association v.91 Quasi-likelihood for median regression models Jung, S.H.
  8. Annals of Statistics v.22 A missing information principle and M-estimators in regression analysis with censored and truncated data Lai, T.L.;Ying Z.
  9. Biometrika v.73 Longitudinal data analysis using generalized linear models Liang K.Y.;Zeger, S.L.
  10. Journal of the American Statistical Association v.86 Goodness-of-fit analysis for the Cox regression model based on a class of parameter estimators Lin D.Y.
  11. Robust regression and outlier detection Rousseeuw P.J.;Leroy A.M.
  12. Biometrika v.63 Inference and missing data Rubin D.B.
  13. Biometrika v.86 On the efficiency of regression estimators in generalized linear models for longitudinal data Sutradhar, B.C.;Das, K.
  14. Biometrika v.79 M-estimation in censored linear models Zhou, M.