Abstract
When an outcome of interest in a clinical trial is late-occurring or difficult to obtain, good surrogate markers can reliably extract information about the effect of the treatment on the outcome of interest. Surrogate measures are obtained post-randomization, and thus the surrogate–outcome relationship may be subject to unmeasured confounding. Thus Frangakis and Rubin (Biometrics 58:21–29, 2002) suggested assessing the causal effect of treatment within “principal strata” defined by the counterfactual joint distribution of the surrogate marker under the treatment arms. Li et al. (Biometrics 66:523–531, 2010) elaborated this suggestion for binary markers and outcomes, developing surrogacy measures that have causal interpretations and utilizing a Bayesian approach to accommodate non-identifiability in the model parameters. Here we extend this work to accommodate missing data under ignorable and non-ignorable settings, focusing on latent ignorability assumptions (Frangakis and Rubin, Biometrika 86:365–379, 1999; Peng et al., Biometrics 60:598–607, 2004; Taylor and Zhou, Biometrics 65:88–95, 2009). We also allow for the possibility that missingness has a counterfactual component, one that might differ between the treatment and control due to differential dropout, a feature that previous literature has not addressed.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
AGIS Investigators.: The Advanced Glaucoma Intervention Study (AGIS) 7: The relationship between control of intraocular pressure and visual field deterioration. American Journal of Ophthalmology. 130, 429–440 (2000)
Burzykowski, T., Molenberghs, G. and Buyse, M.: The Evaluation of Surrogate Endpoints. Springer-Verlag, New York (2005)
Buyse, M., Molenberghs, G., Burzykowski, T., Renard, D. and Geys, H.: The validation of surrogate endpoints in meta-analyses of randomized experiments. Biostatistics 1, 49–67 (2000)
Chen, T.T., Simon, R.M., Korn, E.L., Anderson, S.J., Lindblad, A.S., Wieand, H.S., Douglass, H.O. Jr, Fisher, B., Hamilton, J.M. and Friedman, M.A.: Investigation of disease-free survival as a surrogate endpoint for survival in cancer clinical trials. Communications in Statistics: Theory and Methods 27, 1363–1378 (1998)
Elliott, M.R., Raghunathan, T.E. and Li, Y.: Bayesian inference for causal mediation effects using principal stratification with dichotomous mediators and outcomes. Biostatistics 11, 353–372 (2010)
Frangakis C. and Rubin D.B.: Addressing complications of intention-to-treat analysis in the combined presence of all-or-none treatment-noncompliance and subsequent missing outcomes. Biometrika 86, 365–379, 1999
Frangakis, C. and Rubin, D.B.: Principal stratification in causal inference. Biometrics 58, 21–29 (2002)
Gilbert, P.B. and Hudgens, M.G.: Evaluating candidate principal surrogate endpoints. Biometrics 64, 1146–1154 (2008)
Gustafson, P.: Bayesian inference for partially identified models. The International Journal of Biostatistics. 6:17 (2010)
Li, Y., Taylor, J.M.G. and Elliott, M.R.: A Bayesian approach to surrogacy assessment using principal stratification in clinical trials. Biometrics 66, 523–531 (2010)
Li, Y., Taylor, J.M.G., Elliott, M.R. and Sargent D.J.: Causal assessment of surrogacy in a meta-analysis of colorectal cancer trials. Biostatistics 12, 478–492 (2011)
Lin, D.Y., Fischl, M.A. and Schoenfeld, D.A.: Evaluating the role of CD4-lymphocyte counts as surrogate endpoints in Human Immunodeficiency Virus clinical trials. Statistics in Medicine 12, 835–842 (1993)
Musch D.C., Lichter P.R., Guire K.E., Standardi C.L. and CIGTS Investigators.: The Collaborative Initial Glaucoma Treatment Study (CIGTS): Study design, methods, and baseline characteristics of enrolled patients. Ophthalmology 106, 653–662. (1999)
Peng, Y., Little, R.J.A. and Raghunathan, T.E.: An extended general location model for causal inferences from data subject to noncompliance and missing values. Biometrics 60, 598–607 (2004)
Prentice R.L.: Surrogate endpoints in clinical trials: Definition and operational criteria. Statistics in Medicine 8, 431–440 (1989)
Robins, J.M. and Greenland, S.: Identifiability and exchangeability for direct and indirect effects. Epidemiology 3, 143–155 (1992)
Rosenbaum, P.R.: The consequences of adjustment for a concomitant variable that has been affected by the treatment. Journal of the Royal Statistical Society A147, 656–666 (1984)
Rubin D.B.: Formal modes of statistical inference for causal effects. Journal of Statistical Planning and Inference 25, 279–292 (1990)
Spiegelhalter, D.J., Best, N.G., Carlin, B.P. and Van Der Linde, A.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society B64, 583–639 (2002)
Taylor, J.M.G., Wang, Y. and Thiébaut, R.: Counterfactual links to the proportion of treatment effect explained by a surrogate marker. Biometrics 61, 1102–1111 (2005)
Taylor, L. and Zhou, X. H.: Multiple imputation methods for treatment noncompliance and nonresponse in randomized clinical trials. Biometrics 65, 88–95 (2009)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media New York
About this paper
Cite this paper
Elliott, M.R., Li, Y., Taylor, J.M.G. (2013). Missing Data in Principal Surrogacy Settings. In: Hu, M., Liu, Y., Lin, J. (eds) Topics in Applied Statistics. Springer Proceedings in Mathematics & Statistics, vol 55. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7846-1_8
Download citation
DOI: https://doi.org/10.1007/978-1-4614-7846-1_8
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-7845-4
Online ISBN: 978-1-4614-7846-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)