Bias reduction using surrogate endpoints as auxiliary variables

  • Yoshiharu Takagi
  • Yutaka Kano


Recently, it is becoming more active to apply appropriate statistical methods dealing with missing data in clinical trials. Under not missing at random missingness, MLE based on direct-likelihood, or observed likelihood, possibly has a serious bias. A solution to the bias problem is to add auxiliary variables such as surrogate endpoints to the model for the purpose of reducing the bias. We theoretically studied the impact of an auxiliary variable on MLE and evaluated the bias reduction or inflation in the case of several typical correlation structures.


Auxiliary variables Surrogate endpoints Direct-likelihood Not missing at random missingness data 


  1. Albert, P. S., Follmann, D. A. (2009). Shared-parameter models. In G. Fitzmaurice, M. Davidian, G. Verbeke, G. Molenberghs (Eds.), Longitudinal data analysis (pp. 433–452). Boca Raton, FL: Chapman & Hall/CRC Press.Google Scholar
  2. Anderson, T. W. (1957). Maximum likelihood estimates for a multivariate normal distribution when some observations are missing. Journal of American Statistical Association, 52(278), 200–203.MathSciNetCrossRefzbMATHGoogle Scholar
  3. Dawid, A. P. (1979). Conditional independence in statistical theory. Journal of the Royal Statistical Society Series B (Methodological), 41(1), 1–31.MathSciNetzbMATHGoogle Scholar
  4. Finkelstein, D., Shoenfeld, D. (1994). Analysing survival in the presense of an auxiliary variable. Statistics in Medicine, 13, 1747–1754.Google Scholar
  5. Fleming, T. R., DeMets, D. L. (1996). Surrogate end points in clinical trials: Are we being misled? Annals of Internal Medicine, 125, 605–613.Google Scholar
  6. Fleming, T. R., Prentice, R. L., Pepe, M. S., Glidden, D. (1994). Surrogate and auxiliary endpoints in clinical trials, with potential applications in cancer and AIDS research. Statistics in Medicine, 13, 955–968.Google Scholar
  7. Follmann, D., Wu, M. (1995). An approximate generalized linear model with random effects for informative missing data. Biometrics, 51, 151–168.Google Scholar
  8. Ibrahim, J. G., Lipsitz, S. R., Horton, N. (2001). Using auxiliary data for parameter estimation with non-ignorability missing outcomes. Applied Statistics, 50(3), 361–373.Google Scholar
  9. International Conference on Harmonisation E9 Expert Working Group. (1999). Statistical principles for clinical trials: ICH Harmonised Tripartite Guideline. Statistics in Medicine, 18, 955–968.Google Scholar
  10. Kano, Y. (2015). Developments in multivariate missing data analysis. A paper presented at International Meeting of the Psychometric Society (IMPS2015). Peking, China.Google Scholar
  11. Lauritzen, S. L. (1996). Graphical models. Oxford: Clarendon Press.zbMATHGoogle Scholar
  12. Li, Y., Taylor, J. M. G., Little, R. J. A. (2011). A shrinkage approach for estimating a treatment effect using intermediate biomarker data in clinical trials. Biometrics, 67, 1434–1441.Google Scholar
  13. Little, R. J. A., Rubin, D. B. (2002). Statistical analysis with missing data. New York: Wiley.Google Scholar
  14. Mallinckrodt, C. H., Clark, W. S., David, S. R. (2001). Accounting for dropout bias using mixed-effects models. Journal of Biopharmaceutical Statistics, 11(1&2), 9–21.Google Scholar
  15. National Research Council. (2010). The prevention and treatment of missing data in clinical trials (Panel on Handling Missing Data in Clinical Trials, Committee on National Statistics, Division of Behavioral and Social Sciences and Education). Washington, DC: The National Academies Press.Google Scholar
  16. O’Neill, R. T., Temple, R. (2012). The prevention and treatment of missing data in clinical trials: An FDA perspective on the importance of dealing with it. Clinical Pharmacology and Therapeutics, 91(3), 550–554.Google Scholar
  17. Pharmacological Therapy for Macular Degeneration Study Group. (1997). Interferon alpha-2a is ineffective for patients with choroidal neovascularization secondary to age-related macular degeneration. Archives of Ophthalmology, 115(7), 865–872.Google Scholar
  18. Prentice, R. L. (1989). Surrogate endpoints in clinical trials: Definition and operational criteria. Statistics in Medicine, 8, 431–440.CrossRefGoogle Scholar
  19. Rubin, D. B. (1976). Inference and missing data. Biometrika, 63(3), 581–592.MathSciNetCrossRefzbMATHGoogle Scholar
  20. Takai, K., Kano, Y. (2013). Asymptotic inference with incomplete data. Communications in Statistics—Theory and Methods, 42(17), 3174–3190.Google Scholar

Copyright information

© The Institute of Statistical Mathematics, Tokyo 2018

Authors and Affiliations

  1. 1.Biostatistics and ProgrammingSanofi K.K.TokyoJapan
  2. 2.Division of Mathematical Science, Graduate School of Engineering ScienceOsaka UniversityToyonakaJapan

Personalised recommendations