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Statistical Models and Methods for Incomplete Data in Randomized Clinical Trials

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Developments in Statistical Evaluation of Clinical Trials

Abstract

In this chapter we discuss several models by which missing data can arise in clinical trials. The likelihood function is used as a basis for discussing different missing data mechanisms for incomplete responses in short-term and longitudinal studies, as well as for missing covariates. We critically discuss common ad hoc strategies for dealing with incomplete data, such as complete-case analyses and naive methods of imputation, and we review more broadly appropriate approaches for dealing with incomplete data in terms of asymptotic and empirical frequency properties. These methods include the EM algorithm, multiple imputation, and inverse probability weighted estimating equations. Simulation studies are reported which demonstrate how to implement these procedures and examine performance empirically.

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References

  1. Albert, P.S., Follmann, D.: Shared-parameter models. In: Fitzmaurice, G., Davidian, M., Verbeke, G., Molenberghs, G. (eds.) Longitudinal Data Analysis, Chapter 18, 433–452. CRC Press, Boca Raton, FL. (2009)

    Google Scholar 

  2. Barnard, J., Rubin D.B.: Miscellanea. small-sample degrees of freedom with multiple imputation. Biometrika 86(4), 948–955 (1999)

    Google Scholar 

  3. Chen, B., Cook, R.J.: Strategies for bias reduction in estimation of marginal means with data missing at random. Optimization and Data Analysis on Biomedical Informatics. Ed: Panos Pardalos. American Mathematics Society (2011)

    Google Scholar 

  4. Chen, B., Yi, G.Y., Cook, R.J.: Weighted generalized estimating functions for longitudinal response and covariate data that are missing at random. Journal of the American Statistical Associaton 105, 336–353 (2010)

    Google Scholar 

  5. Cook, R.J., Zeng, L., Yi, G.Y.: Marginal analysis of incomplete longitudinal binary data: a cautionary note on LOCF imputation. Biometrics 60(3), 820–828 (2004)

    Google Scholar 

  6. Cox, D.R.: The analysis of multivariate binary data. Applied Statistics 21, 113–120 (1972)

    Google Scholar 

  7. Crowder, M.: On the use of a working correlation matrix in using generalized linear models for repeated measures. Biometrika 82, 407–410 (1995)

    Google Scholar 

  8. Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via the EM algorithm (with discussion). Journal of the Royal Statistical Society: Series B 39, 1–38 (1977)

    Google Scholar 

  9. Fitzmaurice, G.M., Molenberghs, G., Lipsitz, S.R.: Regression models for longitudinal binary responses with informative drop-outs. Journal of the Royal Statistical Society. Series B (Methodological) 57(4), 691–704 (1995)

    Google Scholar 

  10. Glynn, R.J., Laird, N.M., Rubin, D.B.: Multiple imputation in mixture models for nonignorable nonresponse with followups. Journal of the American Statistical Associaton 88, 984–993 (1993)

    Google Scholar 

  11. Godambe, V.P.: Estimating Functions. Oxford University Press, USA (1991)

    Google Scholar 

  12. Gordon, K.B., Langley, R.G., Leonardi, C., Toth, D., Menter, M.A., Kang, S., Hefferman, M., Miller, B., Hamlin, R., Lim, L., Zhong, J., Hoffman, R., Okun, M.M.: Clinical response to adalimumab treatment in patients with moderate to severe psoriasis: Double-blind, randomized controlled trial and open-label extension study. Journal of the American Academy of Dermatology 55, 598–606 (2006)

    Google Scholar 

  13. Heagerty, P.J.: Marginalized transition models and likeliood inference for longitudinal categorical data. Biometrics 58, 342–351 (2002)

    Google Scholar 

  14. Heagerty, P.J., Zeger, S.L.: Marginalized multilevel models and likelihood inference. Statistical Science 15, 1–19 (2000)

    Google Scholar 

  15. Herzog, T., and Rubin, D.B.: Using multiple imputations to handle nonresponse in sample surveys. In: Madow, W.G., Olkin, I., Rubin, D.B. (eds.) Incomplete Data in Sample Surveys, Volume 2: Theory and Bibliography, 209–245. New York: Academic Press (1983)

    Google Scholar 

  16. Laupacis, A., Sackett, D.L., Roberts, R.S.: An assessment of clinically useful measures of the consequences of treatment. New England Journal of Medicine 318, 1728–1733 (1988)

    Google Scholar 

  17. Liang, K.Y., Zeger, S.: Longitudinal data analysis using generalized linear models. Biometrika 73, 13–22 (1986)

    Google Scholar 

  18. Little, R.J.A.: Pattern-mixture models for multivariate incomplete data. Journal of the American Statistical Associaton 88, 125–134 (1993)

    Google Scholar 

  19. Little, R.J.A.: Modeling the drop-out mechanism in repeated-measures studies. Journal of the American Statistical Associaton 90, 1112–1121 (1995)

    Google Scholar 

  20. Little, R.J.A., Rubin, D.B.: Statistical Analysis with Missing Data. Wiley, New York (1987)

    Google Scholar 

  21. Little, R.J.A., Rubin, D.B.: Statistical Analysis with Missing Data, Second Edition. Wiley, New York (2002)

    Google Scholar 

  22. Matthews, D.E., Farewell, V.T.: Using and Understanding Medical Statistics, 3rd Revised Edition. Karger, Basel, Switzerland (1996)

    Google Scholar 

  23. McCullagh, P., Nelder, J.A.: Generalized Linear Models, Second Edition. Chapman & Hall/CRC., London, UK (1989)

    Google Scholar 

  24. McIsaac, M.A., Cook, R.J.: Response-Dependent Sampling with Clustered and Longitudinal Data. In: ISS-2012 Proceedings Volume On Longitudinal Data Analysis Subject to Measurement Errors, Missing Values, and/or Outliers, 157–181. New York: Springer (2013)

    Google Scholar 

  25. McIsaac, M.A., Cook, R.J., Poulin-Costello, M.: Incomplete data in randomized dermatology trials: Consequences and statistical methodology. Dermatology 226(1), 19–27 (2013). DOI 10.1159/ 000346247

    Google Scholar 

  26. Molenberghs, G., Kenward M.: Missing Data in Clinical Studies. John Wiley & Sons Ltd, West Sussex, England, UK (2007)

    Google Scholar 

  27. Prakash, A., Risser, R. C., Mallinckrodt, C. H.: The impact of analytic method on interpretaion of outcomes in longitudinal clinical trials. International Journal of Clinical Practice 62, 1147–1158 (2008)

    Google Scholar 

  28. Reich, K., Nestle, F.O., Papp, K., Ortonne, J.P., Evans, R., Guzzo, C., Dooley, L.T., Griffiths, C.E.M. for the EXPRESS Study Investigators: Infliximab induction and maintenance therapy for moderate-to-severe psoriasis: a phase III, multicentre, double-blind trial. Lancet 366, 1367–1374 (2005)

    Google Scholar 

  29. Reilly, M., Pepe, M.: The relationship between hot-deck multiple imputation and weighted likelihood. Statistics in Medicine 16, 5–19 (1997)

    Google Scholar 

  30. Robins, J.M., Ritov, Y.: Toward a curse of dimensionality approximate (CODA) asymptotic theory for semiparameric models. Statistics in Medicine 16, 285–319 (1997)

    Google Scholar 

  31. Robins, J.M., Hernan, M.A., Brumback, B. Marginal structural models and causal inference in epidemiology. Epidemiology 11(5), 550–560 (2000)

    Google Scholar 

  32. Robins, J.M., Rotnitzky, A., Zhao, L.P.: Analysis of semiparametric regression models for repeated outcomes in the presence of missing data. Journal of the American Statistical Association 90(429), 106–121 (1995)

    Google Scholar 

  33. Rothman, K.J., Greenland, S., eds: Modern Epidemiology, Second Edition. Lippincott Williams & Wilkins, Philadelphia (1998)

    Google Scholar 

  34. Rotnitzky, A., Wypij, D.: A note on the bias of estimators with missing data. Biometrics 50, 1163–1170 (1994)

    Google Scholar 

  35. Rubin, D.B.: Inference and missing data. Biometrika 63, 581–592 (1976)

    Google Scholar 

  36. Rubin, D.B.: Multiple Imputation for Nonresponse in Surveys. Wiley, New York (1987)

    Google Scholar 

  37. Saurat, J.H., Stingl, G., Dubertret, L., Papp, K., Langley, R.G., Ortonne, J.P., Unnebrink, K., Kaul, M., Camez, A., for the CHAMPION Study Investigators: Efficacy and safety results from the randomized controlled comparative study of adalimumab vs. methotrexate vs. placebo in patients with psoriasis (CHAMPION). British Journal of Dermatology 158, 558–566 (2007)

    Google Scholar 

  38. Schenker, N., Welsh, A.H.: Asymptotic results for multiple imputation. The Annals of Statistics 16(4), 1550–1566 (1988)

    Google Scholar 

  39. Sprott, D.A.: Statistical Inference in Science. Springer, New York (2000)

    Google Scholar 

  40. Sprott, D.A., Farewell, V.T.: Randomization in experimental science. Statistical Papers 34, 89–94 (1993)

    Google Scholar 

  41. Sutradhar, B.C., Das, K.: On the efficiency of regression estimators in generalised linear models for longitudinal data. Biometrika 86, 459–465 (1999)

    Google Scholar 

  42. Wang, N., Robins, J. M.: Large-sample theory for parametric multiple imputation procedures. Biometrika 85, 935–948 (1998)

    Google Scholar 

  43. White, H.A.: Maximum likelihood estimation of misspecified models. Econometrica 50, 1–25 (1982)

    Google Scholar 

  44. Yi, G.Y., Cook, R.J.: Marginal methods for incomplete longitudinal data arising in clusters. Journal of the American Statistical Association 97(460), 1071–1080 (2002)

    Google Scholar 

  45. Zhao, L.P., Prentice, R.L.: Correlated binary regression using a quadratic exponential model. Biometrika 77, 642–648 (1990)

    Google Scholar 

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Acknowledgements

This work was supported by a Post-Graduate Scholarship to Michael McIsaac from the Natural Sciences and Engineering Research Council (NSERC) of Canada and grants to Richard Cook from NSERC (Grant No. 101093) and the Canadian Institutes of Health Research (Grant No. 105099). Richard Cook is a Tier I Canada Research Chair in Statistical Methods for Health Research.

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Authors and Affiliations

  1. Department of Public Health Sciences, Queen’s University, Kingston, ON, Canada

    Michael A. McIsaac

  2. Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON, Canada

    Richard J. Cook

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  1. Michael A. McIsaac
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Correspondence to Michael A. McIsaac .

Editor information

Editors and Affiliations

  1. Department of Biostatistics, Erasmus Medical Center, Rotterdam, The Netherlands

    Kees van Montfort

  2. Behavioural Science Institute, University of Nijmegen, Nijmegen, The Netherlands

    Johan Oud

  3. Department of Hematology, Erasmus Medical Center, Rotterdam, The Netherlands

    Wendimagegn Ghidey

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McIsaac, M.A., Cook, R.J. (2014). Statistical Models and Methods for Incomplete Data in Randomized Clinical Trials. In: van Montfort, K., Oud, J., Ghidey, W. (eds) Developments in Statistical Evaluation of Clinical Trials. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55345-5_1

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