Skip to main content
SpringerLink
Log in

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

  • Published:
Lifetime Data Analysis Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  • Aalen OO (1989) A linear regression model for the analysis of life times. Stat Med 8:907–925

    Article  Google Scholar 

  • Andersen PK (2013) Decomposition of number of years lost according to causes of death. Stat Med 32:5278–5285

    Article  MathSciNet  Google Scholar 

  • Andersen PK, Perme MP (2010) Pseudo-observations in survival analysis. Stat Methods Med Res 19:71–99

    Article  MathSciNet  Google Scholar 

  • Andersen PK, Skovgaard LT (2010) Regression with linear predictors. Springer, New York

    Book  MATH  Google Scholar 

  • Andersen PK, Klein JP, Rosthøj S (2003) Generalized linear models for correlated pseudo-observations, with applications to multi-state models. Biometrika 90:15–27

    Article  MathSciNet  MATH  Google Scholar 

  • Andersen PK, Hansen MG, Klein JP (2004) Regression analysis of restricted mean survival time based on pseudo-observations. Lifetime Data Anal 10:335–350

    Article  MathSciNet  MATH  Google Scholar 

  • Cox DR (1972) Regression models and life-tables. J Roy Stat Soc B 34:187–220

    MathSciNet  MATH  Google Scholar 

  • Eddelbuettel D, Francois R (2011) Rcpp: seamless R and C++ integration. J Stat Softw 40(8):1–18

    Article  Google Scholar 

  • Graw F, Gerds TA, Schumacher M (2009) On pseudo-values for regression analysis in competing risks models. Lifetime Data Anal 15:241–255

    Article  MathSciNet  MATH  Google Scholar 

  • Højsgaard S, Halekoh U, Yan J (2005) The R package geepack for generalized estimating equations. J Stat Softw 15(1):1–11

    Google Scholar 

  • 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 43:845–862

    Article  MathSciNet  MATH  Google Scholar 

  • Klein JP, Andersen PK (2005) Regression modeling of competing risks data based on pseudovalues of the cumulative incidence function. Biometrics 61:223–229

    Article  MathSciNet  MATH  Google Scholar 

  • 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 89:289–300

    Article  Google Scholar 

  • Li J, Scheike TH, Zhang MJ (2015) Checking fine and gray subdistribution hazards model with cumulative sums of residuals. Lifetime Data Anal 21(2):197–217

    Article  MathSciNet  MATH  Google Scholar 

  • Lin DY, Ying Z (1994) Semiparametric analysis of the additive risk model. Biometrika 81:61–71

    Article  MathSciNet  MATH  Google Scholar 

  • Lin DY, Wei LJ, Ying Z (1993) Checking the Cox model with cumulative sums of martingale-based residuals. Biometrika 80:557–572

    Article  MathSciNet  MATH  Google Scholar 

  • Lin DY, Wei LJ, Ying Z (2002) Model-checking techniques based on cumulative residuals. Biometrics 58:1–12

    Article  MathSciNet  MATH  Google Scholar 

  • 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 104:519–526

    Article  Google Scholar 

  • Martinussen T, Scheike TH (2006) Dynamic regression models for survival data. Springer, New York

    MATH  Google Scholar 

  • McDaniel LS, Henderson NC, Rathouz PJ (2013) Fast pure R implementation of GEE: application of the matrix package. R J 5:181–187

    Google Scholar 

  • Overgaard M, Parner ET, Pedersen J (2017) Asymptotic theory of generalized estimating equations based on Jack-knife pseudo-observations. Ann Stat 45(5):1988–2015

    Article  MathSciNet  MATH  Google Scholar 

  • Perme MP, Andersen PK (2008) Checking hazard regression models using pseudo-observations. Stat Med 27:5309–5328

    Article  MathSciNet  Google Scholar 

  • Scheike TH, Zhang MJ (2002) An additive-multiplicative Cox–Aalen model. Scand J Stat 28:75–88

    Article  MathSciNet  MATH  Google Scholar 

  • van der Vaart A (1998) Asymptotic statistics. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Biostatistics and Medical Informatics, Faculty of Medicine, University of Ljubljana, Vrazov trg 2, 1000, Ljubljana, Slovenia

    Klemen Pavlič

  2. Section of Biostatistics, University of Copenhagen, Ø. Farimagsgade 5, PB 2099, 1014, Copenhagen K, Denmark

    Torben Martinussen & Per Kragh Andersen

Authors
  1. Klemen Pavlič
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Torben Martinussen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Per Kragh Andersen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Per Kragh Andersen.

Additional information

Corresponding author has been updated to Dr. Per Kragh Andersen.

Klemen Pavlič—Deceased.

The work on this manuscript was conducted, primarily by the first author Dr. Klemen Pavlič, while he visited University of Copenhagen, Section of Biostatistics, in the spring of 2017. After the final acceptance of the manuscript, Dr. Pavlič sadly died in an accident in June 2018.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (pdf 361 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pavlič, K., Martinussen, T. & Andersen, P.K. Goodness of fit tests for estimating equations based on pseudo-observations. Lifetime Data Anal 25, 189–205 (2019). https://doi.org/10.1007/s10985-018-9427-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10985-018-9427-6

Keywords

Search

Navigation