Skip to main content
Log in

A Note on Postrandomization Adjustment of Covariates

  • Statistics
  • Published:
Drug information journal : DIJ / Drug Information Association Aims and scope Submit manuscript

Abstract

The adjustment for postrandomization variables has been widely used in practice to obtain additional information in randomized experiments despite its conceptual and statistical difficulties. To enhance the chance of more appropriate postrandomization adjustment analyses and interpretation, this paper systematically summarizes the potential problems of the conventional regression-based postrandomization adjustment method with its reliability, precision, and causality. Some available alternative methods that could possibly provide either more powerful, less biased evaluation or more appropriate assessment for causality are outlined. A working example is used to illustrate the application of the different postrandomization adjustment methods.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Senn S. Testing for baseline balance in clinical trials. Stat Med. 1994;13:1715–1726.

    Article  CAS  Google Scholar 

  2. Senn S. Letter to Editor: In defense of the analysis of covariance: a reply to Chambless and Roeback. Stat Med. 1995;14:2280–2283.

    Google Scholar 

  3. Smith F. Interpretation of adjusted treatment means and regressions in analysis of covariance. Biometrics. 1957;13:282–308.

    Article  Google Scholar 

  4. Snedecor GW, Cochran WG. Statistical Methods. 8th edition. Ames, IO: Iowa State University; 1998.

    Google Scholar 

  5. White I, Bamiss C, Hardy P, Pocock S, Warner J. Randomized clinical trials with added rescue medication: some approaches to their analysis and interpretation. Stat Med. 2001;20:2995–3008.

    Article  CAS  Google Scholar 

  6. Efron B, Feldman D. Compliance as an explanatory variable in clinical trials. J Am Stat Assoc. 1991;86:9–26.

    Article  Google Scholar 

  7. Lin DY, Fleming TR, Gruttola VDE. Estimating the proportion of treatment effect explained by a surrogate marker. Stat Med. 1997;16:1515–1527.

    Article  CAS  Google Scholar 

  8. Rochon J. Supplementing the intent-to-treat analysis; accounting for covariates observed post-randomization in clinical trials. J Am Stat Assoc. 1995;90:292–300.

    Article  Google Scholar 

  9. Rochon J. Issues in adjusting for covariates arising postrandomization in clinical trials. Drug Inf J. 1999;33:1219–1228.

    Article  Google Scholar 

  10. Frangakis C, Rubin D. Principal stratification in causal inference. Biometrics. 2002;58:21–29.

    Article  Google Scholar 

  11. Buyse M. The validation of surrogate endpoints in meta-analyses of randomized experiments. Biostatistics. 2000;1:49–67.

    Article  CAS  Google Scholar 

  12. Yang L, Tsiatis A. Efficiency study of estimators for a treatment effect in a pretest-posttest trial. Am Stat. 2001;55:314–321.

    Article  Google Scholar 

  13. MacKinnon D, Warsi G, Dwyer J. A simulation study of mediated effect measures. Multivariate Behav Res. 1995;30:41–62.

    Article  Google Scholar 

  14. Buyse M, Molenberghs G. Criteria for the validation of surrogate endpoints in randomized experiments. Biometrics. 1998;54:1014–1029.

    Article  CAS  Google Scholar 

  15. Joffe M,Golditz G. Restriction as a method for reducing bias in the estimation of direct effects. Stat Med. 1998;17:2233–2249.

    Article  CAS  Google Scholar 

  16. Crager M. Analysis of covariance in parallel-group clinical trials with pretreatment baselines. Biometrics. 1987;43:895–901.

    Article  CAS  Google Scholar 

  17. Li Z, Meredith M, Hoseyni M. A method to assess the proportion of treatment effect explained by a surrogate endpoint. Stat Med. 2001;20:3175–3188.

    Article  CAS  Google Scholar 

  18. Freedman L, Graubard B, Schatzkin A. Statistical validation of intermediate endpoints for chronic diseases, Stat Med. 1992;11:167–178.

    Article  CAS  Google Scholar 

  19. Freedman L. Confidence intervals and statistical power of the ‘Validation’ ratio for surrogate or intermediate endpoints. J Stat Plan Inf. 2001;96:143–153.

    Article  Google Scholar 

  20. Little RJA, Rubin DB. Statistical Analysis with Missing Data. New York: John Wiley & Sons; 2002.

    Book  Google Scholar 

  21. De Gruttola VG, Clax P, DeMets DL, et al. Considerations in the Evaluation of Surrogate Endpoints in Clinical Trials: Summary of a National Institutes of Health Workshop. Control Clin Trials. 2001;22:485–502.

    Article  Google Scholar 

  22. Helland I. On the interpretation and use of R2 in regression analysis. Biometrics. 1987;43:61–69.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xun Chen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, X., Liu, M. & Zhang, J. A Note on Postrandomization Adjustment of Covariates. Ther Innov Regul Sci 39, 373–383 (2005). https://doi.org/10.1177/009286150503900405

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1177/009286150503900405

Key Words

Navigation