Goodness of fit tests for estimating equations based on pseudo-observations

  • Klemen Pavlič
  • Torben Martinussen
  • Per Kragh Andersen
Article
  • 136 Downloads

Abstract

We study regression models for mean value parameters in survival analysis based on pseudo-observations. Such parameters include the survival probability and the cumulative incidence in a single point as well as the restricted mean life time and the cause-specific number of years lost. Goodness of fit techniques for such models based on cumulative sums of pseudo-residuals are derived including asymptotic results and Monte Carlo simulations. Practical examples from liver cirrhosis and bone marrow transplantation are also provided.

Keywords

Goodness-of-fit Pseudo-observations Survival probability Cumulative incidence function Restricted mean life time Years lost 

Supplementary material

10985_2018_9427_MOESM1_ESM.pdf (361 kb)
Supplementary material 1 (pdf 361 KB)

References

  1. Aalen OO (1989) A linear regression model for the analysis of life times. Stat Med 8:907–925CrossRefGoogle Scholar
  2. Andersen PK (2013) Decomposition of number of years lost according to causes of death. Stat Med 32:5278–5285MathSciNetCrossRefGoogle Scholar
  3. Andersen PK, Perme MP (2010) Pseudo-observations in survival analysis. Stat Methods Med Res 19:71–99MathSciNetCrossRefGoogle Scholar
  4. Andersen PK, Skovgaard LT (2010) Regression with linear predictors. Springer, New YorkCrossRefMATHGoogle Scholar
  5. Andersen PK, Klein JP, Rosthøj S (2003) Generalized linear models for correlated pseudo-observations, with applications to multi-state models. Biometrika 90:15–27MathSciNetCrossRefMATHGoogle Scholar
  6. Andersen PK, Hansen MG, Klein JP (2004) Regression analysis of restricted mean survival time based on pseudo-observations. Lifetime Data Anal 10:335–350MathSciNetCrossRefMATHGoogle Scholar
  7. Cox DR (1972) Regression models and life-tables. J Roy Stat Soc B 34:187–220MathSciNetMATHGoogle Scholar
  8. Eddelbuettel D, Francois R (2011) Rcpp: seamless R and C++ integration. J Stat Softw 40(8):1–18CrossRefGoogle Scholar
  9. Graw F, Gerds TA, Schumacher M (2009) On pseudo-values for regression analysis in competing risks models. Lifetime Data Anal 15:241–255MathSciNetCrossRefMATHGoogle Scholar
  10. Højsgaard S, Halekoh U, Yan J (2005) The R package geepack for generalized estimating equations. J Stat Softw 15(1):1–11Google Scholar
  11. Jacobsen M, Martinussen T (2016) A note on the large sample properties of estimators based on generalized linear models for correlated pseudo-observations. Scand J Stat 43:845–862MathSciNetCrossRefMATHGoogle Scholar
  12. Klein JP, Andersen PK (2005) Regression modeling of competing risks data based on pseudovalues of the cumulative incidence function. Biometrics 61:223–229MathSciNetCrossRefMATHGoogle Scholar
  13. Klein JP, Gerster M, Andersen PK, Tarima S, Perme MP (2008) SAS and R functions to compute pseudo-values for censored data regression. Comput Methods Programs Biomed 89:289–300CrossRefGoogle Scholar
  14. Li J, Scheike TH, Zhang MJ (2015) Checking fine and gray subdistribution hazards model with cumulative sums of residuals. Lifetime Data Anal 21(2):197–217MathSciNetCrossRefMATHGoogle Scholar
  15. Lin DY, Ying Z (1994) Semiparametric analysis of the additive risk model. Biometrika 81:61–71MathSciNetCrossRefMATHGoogle Scholar
  16. Lin DY, Wei LJ, Ying Z (1993) Checking the Cox model with cumulative sums of martingale-based residuals. Biometrika 80:557–572MathSciNetCrossRefMATHGoogle Scholar
  17. Lin DY, Wei LJ, Ying Z (2002) Model-checking techniques based on cumulative residuals. Biometrics 58:1–12MathSciNetCrossRefMATHGoogle Scholar
  18. Lombard M, Portmann B, Neuberger J, Williams R, Tygstrup N, Ranek L, Larsen HR, Rodes J, Navasa M, Trepo C, Pape G, Schou G, Badsberg JH, Andersen PK (1993) Cyclosporin A treatment in primary biliary cirrhosis. Results of a long-term placebo controlled trial. Gastroenterology 104:519–526CrossRefGoogle Scholar
  19. Martinussen T, Scheike TH (2006) Dynamic regression models for survival data. Springer, New YorkMATHGoogle Scholar
  20. McDaniel LS, Henderson NC, Rathouz PJ (2013) Fast pure R implementation of GEE: application of the matrix package. R J 5:181–187Google Scholar
  21. Overgaard M, Parner ET, Pedersen J (2017) Asymptotic theory of generalized estimating equations based on Jack-knife pseudo-observations. Ann Stat 45(5):1988–2015MathSciNetCrossRefMATHGoogle Scholar
  22. Perme MP, Andersen PK (2008) Checking hazard regression models using pseudo-observations. Stat Med 27:5309–5328MathSciNetCrossRefGoogle Scholar
  23. Scheike TH, Zhang MJ (2002) An additive-multiplicative Cox–Aalen model. Scand J Stat 28:75–88MathSciNetCrossRefMATHGoogle Scholar
  24. van der Vaart A (1998) Asymptotic statistics. Cambridge University Press, CambridgeCrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute for Biostatistics and Medical Informatics, Faculty of MedicineUniversity of LjubljanaLjubljanaSlovenia
  2. 2.Section of BiostatisticsUniversity of CopenhagenCopenhagen KDenmark

Personalised recommendations