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The Data: Observational Studies and Sequentially Randomized Trials

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Statistical Methods for Dynamic Treatment Regimes

Part of the book series: Statistics for Biology and Health ((SBH))

Abstract

The data for constructing (optimal) dynamic treatment regimes that we consider are obtained from either longitudinal observational studies or sequentially randomized trials. In this chapter, we review these two types of data sources, their advantages and drawbacks, and the assumptions required to perform valid analyses in each, along with some examples. We also discuss a basic framework of causal inference in the context of observational studies, and power and sample size issues in the context of randomized studies.

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Notes

  1. 1.

    In this book, we use the term treatment generically to denote either a medical treatment or an exposure (which is the preferred term in the causal inference literature and more generally in epidemiology).

  2. 2.

    While the term stage is commonly used in the randomized trial literature, the term interval is more popular in the causal inference literature. In this book, for consistency, we will use the term stage for both observational and randomized studies.

References

  • Almirall, D., Compton, S. N., Gunlicks-Stoessel, M., Duan, N., & Murphy, S. A. (2012a). Designing a pilot sequential multiple assignment randomized trial for developing an adaptive treatment strategy. Statistics in Medicine, 31, 1887–1902.

    Article  MathSciNet  Google Scholar 

  • Auyeung, S. F., Long, Q., Royster, E. B., Murthy, S., McNutt, M. D., Lawson, D., Miller, A., Manatunga, A., & Musselman, D. L. (2009). Sequential multiple-assignment randomized trial design of neurobehavioral treatment for patients with metastatic malignant melanoma undergoing high-dose interferon-alpha therapy. Clinical Trials, 6, 480–490.

    Article  Google Scholar 

  • Banerjee, A., & Tsiatis, A. A. (2006). Adaptive two-stage designs in phase II clinical trials. Statistics in Medicine, 25, 3382–3395.

    Article  MathSciNet  Google Scholar 

  • Berry, D. A. (2001). Adaptive clinical trials and Bayesian statistics in drug development (with discussion). Biopharmaceutical Report, 9, 1–11.

    Google Scholar 

  • Berry, D. A. (2004). Bayesian statistics and the efficiency and ethics of clinical trials. Statistical Science, 19, 175–187.

    Article  MathSciNet  MATH  Google Scholar 

  • Berry, D. A., Mueller, P., Grieve, A. P., Smith, M., Parke, T., Blazek, R., Mitchard, N., & Krams, M. (2001). Adaptive Bayesian designs for dose-ranging drug trials. In Gatsonis, C., Kass, R.E., Carlin, B., Carriquiry, A. Gelman, A. Verdinelli, I., and West, M. (Eds.), Case studies in Bayesian statistics (Vol. V, pp. 99–181). New York: Springer.

    Google Scholar 

  • Berzuini, C., Dawid, A. P., & Didelez, V. (2012). Assessing dynamic treatment strategies. In C. Berzuini, A. P. Dawid, & L. Bernardinelli (Eds.), Causality: Statistical perspectives and applications (pp. 85–100). Chichester, West Sussex, United Kindom.

    Chapter  Google Scholar 

  • Box, G. E. P., Hunter, W. G., & Hunter, J. S. (1978). Statistics for experimenters: An introduction to design, data analysis, and model building. New York: Wiley.

    MATH  Google Scholar 

  • Breiman, L. (1995). Better subset regression using the nonnegative garrote. Technometrics, 37, 373–384.

    Article  MathSciNet  MATH  Google Scholar 

  • Buhlmann, P., & Yu, B. (2002). Analyzing bagging. Annals of Statistics, 30, 927–961.

    Article  MathSciNet  Google Scholar 

  • Carlin, B. P., Kadane, J. B., & Gelfand, A. E. (1998). Approaches for optimal sequential decision analysis in clinical trials. Biometrics, 54, 964–975.

    Article  MATH  Google Scholar 

  • Chakraborty, B. (2011). Dynamic treatment regimes for managing chronic health conditions: A statistical perspective. American Journal of Public Health, 101, 40–45.

    Article  Google Scholar 

  • Chakraborty, B., Murphy, S. A., & Strecher, V. (2010). Inference for non-regular parameters in optimal dynamic treatment regimes. Statistical Methods in Medical Research, 19, 317–343.

    Article  MathSciNet  Google Scholar 

  • Chakraborty, B., Laber, E. B., & Zhao, Y. (2013). Inference for optimal dynamic treatment regimes using an adaptive m-out-of-n bootstrap scheme. Biometrics, (in press).

    Google Scholar 

  • Chen, M.-H., Muller, P., Sun, D., & Ye, K. (Eds.). (2010). Frontiers of statistical decision making and Bayesian analysis: In Honor of James O. Berger. New York: Springer.

    MATH  Google Scholar 

  • Clemen, R. T., & Reilly, T. (2001). Making hard decisions. Pacific Grove: Duxbury.

    Google Scholar 

  • Cohen, J. (1988). Statistical power for the behavioral sciences (2nd ed.). Hillsdale: Erlbaum.

    MATH  Google Scholar 

  • Cole, S. R., & Frangakis, C. (2009). The consistency statement in causal inference: A definition or an assumption? Epidemiology, 20, 3–5.

    Article  Google Scholar 

  • Cole, S. A., & Hernán, M. A. (2008). Constructing inverse probability weights for marginal structural models. American Journal of Epidemiology, 168, 656–664.

    Article  Google Scholar 

  • Collins, L. M., Murphy, S. A., & Bierman, K. (2004). A conceptual framework for adaptive preventive interventions. Prevention Science, 5, 185–196.

    Article  Google Scholar 

  • Collins, L. M., Chakraborty, B., Murphy, S. A., & Strecher, V. J. (2009). Comparison of a phased experimental approach and a single randomized clinical trial for developing multicomponent behavioral interventions. Clinical Trials, 6, 5–15.

    Article  Google Scholar 

  • Cortes, C., & Vapnik, V. (1995). Support-vector networks. Machine Learning, 20, 273–297.

    MATH  Google Scholar 

  • Cox, D. R. (1958). Planning of experiments. New York: Wiley.

    MATH  Google Scholar 

  • Cox, D. R., & Oaks, D. (1984). Analysis of survival data. Boca Raton, Florida: Chapman & Hall/CRC.

    Google Scholar 

  • Dawson, R., & Lavori, P. W. (2010). Sample size calculations for evaluating treatment policies in multi-stage designs. Clinical Trials, 7, 643–652.

    Article  Google Scholar 

  • Dawson, R., & Lavori, P. W. (2012). Efficient design and inference for multistage randomized trials of individualized treatment policies. Biostatistics, 13, 142–152.

    Article  MATH  Google Scholar 

  • Dehejia, R. H. (2005). Program evaluation as a decision problem. Journal of Econometrics, 125, 141–173.

    Article  MathSciNet  Google Scholar 

  • Efron, B. (1979). Bootstrap methods: Another look at the jackknife. Annals of Statistics, 7, 1–26.

    Article  MathSciNet  MATH  Google Scholar 

  • Feng, W., & Wahed, A. S. (2009). Sample size for two-stage studies with maintenance therapy. Statistics in Medicine, 28, 2028–2041.

    Article  MathSciNet  Google Scholar 

  • Ferguson, T. S. (1996). A course in large sample theory. London: Chapman & Hall/CRC.

    MATH  Google Scholar 

  • Gao, H. (1998). Wavelet shrinkage denoising using the nonnegative garrote. Journal of Computational and Graphical Statistics, 7, 469–488.

    MathSciNet  Google Scholar 

  • Greenland, S., Pearl, J., & Robins, J. M. (1999). Causal diagrams for epidemiologic research. Epidemiology, 10, 37–48.

    Article  Google Scholar 

  • Guez, A., Vincent, R., Avoli, M., & Pineau, J. (2008). Adaptive treatment of epilepsy via batch-mode reinforcement learning. In Proceedings of the innovative applications of artificial intelligence (IAAI), Chicago.

    Google Scholar 

  • Hernán, M. A., & Taubman, S. L. (2008). Does obesity shorten life? The importance of well-defined interventions to answer causal questions. International Journal of Obesity, 32, S8–S14.

    Article  Google Scholar 

  • Hernán, M. A., Brumback, B., & Robins, J. M. (2000). Marginal structural models to estimate the causal effect of zidovudine on the survival of HIV-positive men. Epidemiology, 11, 561–570.

    Article  Google Scholar 

  • Hernán, M. A., Hernández-Díaz, S., & Robins, J. M. (2004). A structural approach to selection bias. Epidemiology, 15, 615–625.

    Article  Google Scholar 

  • Hernán, M. A., Cole, S. J., Margolick, J., Cohen, M., & Robins, J. M. (2005). Structural accelerated failure time models for survival analysis in studies with time-varying treatments. Pharmacoepidemiology and Drug Safety, 14, 477–491.

    Article  Google Scholar 

  • Huang, F., & Lee, M.-J. (2010). Dynamic treatment effect analysis of TV effects on child cognitive development. Journal of Applied Econometrics, 25, 392–419.

    Article  MathSciNet  Google Scholar 

  • Kaelbling, L. P., Littman, M. L., & Moore, A. (1996). Reinforcement learning: A survey. The Journal of Artificial Intelligence Research, 4, 237–385.

    Google Scholar 

  • Kaslow, R. A., Ostrow, D. G., Detels, R., Phair, J. P., Polk, B. F., & Rinaldo, C. R. (1987). The Multicenter AIDS Cohort Study: Rationale, organization, and selected characteristics of the participants. American Journal of Epidemiology, 126, 310–318.

    Article  Google Scholar 

  • Kramer, M. S., Aboud, F., Miranova, E., Vanilovich, I., Platt, R., Matush, L., Igumnov, S., Fombonne, E., Bogdanovich, N., Ducruet, T., Collet, J., Chalmers, B., Hodnett, E., Davidovsky, S., Skugarevsky, O., Trofimovich, O., Kozlova, L., & Shapiro, S. (2008). Breastfeeding and child cognitive development: New evidence from a large randomized trial. Archives of General Psychiatry, 65, 578–584.

    Article  Google Scholar 

  • Lavori, P. W., & Dawson, R. (2004). Dynamic treatment regimes: Practical design considerations. Clinical Trials, 1, 9–20.

    Article  Google Scholar 

  • Lavori, P. W., & Dawson, R. (2008). Adaptive treatment strategies in chronic disease. Annual Review of Medicine, 59, 443–453.

    Article  Google Scholar 

  • LeBlanc, M., & Kooperberg, C. (2010). Boosting predictions of treatment success. Proceedings of the National Academy of Sciences, 107, 13559–13560.

    Article  Google Scholar 

  • Levin, B., Thompson, J. L. P., Chakraborty, R. B., Levy, G., MacArthur, R., & Haley, E. C. (2011). Statistical aspects of the TNK-S2B trial of tenecteplase versus alteplase in acute ischemic stroke: An efficient, dose-adaptive, seamless phase II/III design. Clinical Trials, 8, 398–407.

    Article  Google Scholar 

  • Li, Z., & Murphy, S. A. (2011). Sampe size formulae for two-stage randomized trials with survival outcomes. Biometrika, 98, 503–518.

    Article  MathSciNet  MATH  Google Scholar 

  • Lieberman, J. A., Stroup, T. S., McEvoy, J. P., Swartz, M. S., Rosenheck, R. A., Perkins, D. O., Keefe, R. S. E., Davis, S., Davis, C. E., Lebowitz, B. D., & Severe, J. (2005). Effectiveness of antipsychotic drugs in patients with chronic schozophrenia. New England Journal of Medicine, 353, 1209–1223.

    Article  Google Scholar 

  • Moodie, E. E. M., Chakraborty, B., & Kramer, M. S. (2012). Q-learning for estimating optimal dynamic treatment rules from observational data. Canadian Journal of Statistics, 40, 629–645.

    Article  MathSciNet  Google Scholar 

  • Moodie, E. E. M., Dean, N., & Sun, Y. R. (2013). Q-learning: Flexible learning about useful utilities. Statistics in Biosciences, (in press).

    Google Scholar 

  • Murphy, S. A. (2005b). A generalization error for Q-learning. Journal of Machine Learning Research, 6, 1073–1097.

    MATH  Google Scholar 

  • Murphy, S. A., Van der Laan, M. J., Robins, J. M., & CPPRG (2001). Marginal mean models for dynamic regimes. Journal of the American Statistical Association, 96, 1410–1423.

    Google Scholar 

  • Murphy, S. A., Oslin, D., Rush, A. J., & Zhu, J. (2007b). Methodological challenges in constructing effective treatment sequences for chronic psychiatric disorders. Neuropsychopharmacology, 32, 257–262.

    Article  Google Scholar 

  • Nahum-Shani, I., Qian, M., Almiral, D., Pelham, W., Gnagy, B., Fabiano, G., Waxmonsky, J., Yu, J., & Murphy, S. (2012b). Q-learning: A data analysis method for constructing adaptive interventions. Psychological Methods, 17, 478–494.

    Article  Google Scholar 

  • Nankervis, J. C. (2005). Computational algorithms for double bootstrap confidence intervals. Computational Statistics & Data Analysis, 49, 461–475.

    Article  MathSciNet  MATH  Google Scholar 

  • Neugebauer, R., & Van der Laan, M. J. (2006). G-computation estimation for causal inference with complex longitudinal data. Computational Statistics & Data Analysis, 51, 1676–1697.

    Article  MathSciNet  MATH  Google Scholar 

  • Ng, A., & Jordan, M. (2000). PEGASUS: A policy search method for large MDPs and POMDPs.

    Google Scholar 

  • Olshen, R. A. (1973). The conditional level of the F-test. Journal of the American Statistical Association, 68, 692–698.

    MathSciNet  MATH  Google Scholar 

  • Pampallona, S., & Tsiatis, A. A. (1994). Group sequential designs for one and two sided hypothesis testing with provision for early stopping in favour of the null hypothesis. Journal of Statistical Planning and Inference, 42, 19–35.

    Article  MathSciNet  MATH  Google Scholar 

  • Parmigiani, G. (2002). Modeling in medical decision making: A Bayesian approach. New York: Wiley.

    MATH  Google Scholar 

  • Petersen, M. L., Deeks, S. G., & Van der Laan, M. J. (2007). Individualized treatment rules: Generating candidate clinical trials. Statistics in Medicine, 26, 4578–4601.

    Article  MathSciNet  Google Scholar 

  • Partnership for Solutions (2004). Chronic conditions: Making the case for ongoing care: September 2004 update. Baltimore: Partnership for Solutions, Johns Hopkins University.

    Google Scholar 

  • Politis, D. N., Romano, J. P., & Wolf, M. (1999). Subsampling. New York: Springer.

    Book  MATH  Google Scholar 

  • Rich, B., Moodie, E. E. M., and Stephens, D.A. (2013) Adaptive individualized dosing in pharmacological studies: Generating candidate dynamic dosing strategies for warfarin treatment. (submitted).

    Google Scholar 

  • Robins, J. M. (1997). Causal inference from complex longitudinal data. In M. Berkane (Ed.), Latent variable modeling and applications to causality: Lecture notes in statistics (pp. 69–117). New York: Springer.

    Chapter  Google Scholar 

  • Robins J. M. (1999a). Marginal structural models versus structural nested models as tools for causal inference. In: M. E. Halloran & D. Berry (Eds.) Statistical models in epidemiology: The environment and clinical trials. IMA, 116, NY: Springer-Verlag, pp. 95–134.

    Google Scholar 

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

    Article  Google Scholar 

  • Rosenbaum, P. R., & Rubin, D. B. (1983). The central role of the propensity score in observational studies for causal effects. Biometrika, 70, 41–55.

    Article  MathSciNet  MATH  Google Scholar 

  • Rubin, D. B. (1974). Estimating causal effects of treatments in randomized and nonrandomized studies. Journal of Educational Psychology, 66, 688–701.

    Article  Google Scholar 

  • Rubin, D. B. (1980). Discussion of “randomized analysis of experimental data: The Fisher randomization test” by D. Basu. Journal of the American Statistical Association, 75, 591–593.

    Google Scholar 

  • Rubin, D. B., & Shenker, N. (1991). Multiple imputation in health-case data bases: An overview and some applications. Statistics in Medicine, 10, 585–598.

    Article  Google Scholar 

  • Saarela, O., Moodie, E. E. M., Stephens, D. A., & Klein, M. B. (2013a). On Bayesian estimation of marginal structural models (submitted).

    Google Scholar 

  • Schulte, P. J., Tsiatis, A. A., Laber, E. B., & Davidian, M. (2012). Q- and A-learning methods for estimating optimal dynamic treatment regimes. arXiv, 1202.4177v1.

    Google Scholar 

  • Strecher, V., McClure, J., Alexander, G., Chakraborty, B., Nair, V., Konkel, J., Greene, S., Collins, L., Carlier, C., Wiese, C., Little, R., Pomerleau, C., & Pomerleau, O. (2008). Web-based smoking cessation components and tailoring depth: Results of a randomized trial. American Journal of Preventive Medicine, 34, 373–381.

    Article  Google Scholar 

  • Stroup, T. S., McEvoy, J. P., Swartz, M. S., Byerly, M. J., Glick, I. D., Canive, J. M., McGee, M., Simpson, G. M., Stevens, M. D., & Lieberman, J. A. (2003). The National Institute of Mental Health Clinical Antipschotic Trials of Intervention Effectiveness (CATIE) project: Schizophrenia trial design and protocol deveplopment. Schizophrenia Bulletin, 29, 15–31.

    Article  Google Scholar 

  • Thall, P. F., Millikan, R. E., & Sung, H. G. (2000). Evaluating multiple treatment courses in clinical trials. Statistics in Medicine, 30, 1011–1128.

    Article  Google Scholar 

  • Thall, P. F., Sung, H. G., & Estey, E. H. (2002). Selecting therapeutic strategies based on efficacy and death in multicourse clinical trials. Journal of the American Statistical Association, 97, 29–39.

    Article  MathSciNet  MATH  Google Scholar 

  • Thall, P. F., Wooten, L. H., Logothetis, C. J., Millikan, R. E., & Tannir, N. M. (2007a). Bayesian and frequentist two-stage treatment strategies based on sequential failure times subject to interval censoring. Statistics in Medicine, 26, 4687–4702.

    Article  MathSciNet  Google Scholar 

  • Van der Laan, M. J., & Robins, J. M. (2003). Unified methods for censored longitudinal data and causality. New York: Springer.

    Book  MATH  Google Scholar 

  • Wagner, E. H., Austin, B. T., Davis, C., Hindmarsh, M., Schaefer, J., & Bonomi, A. (2001). Improving chronic illness care: Translating evidence into action. Health Affairs, 20, 64–78.

    Article  Google Scholar 

  • Wahed, A. S., & Tsiatis, A. A. (2006). Semiparametric efficient estimation of survival distributions in two-stage randomisation designs in clinical trials with censored data. Biometrika, 93, 163–177.

    Article  MathSciNet  MATH  Google Scholar 

  • Wald, A. (1949). Statistical decision functions. New York: Wiley.

    Google Scholar 

  • Wang, L., Rotnitzky, A., Lin, X., Millikan, R. E., & Thall, P. F. (2012). Evaluation of viable dynamic treatment regimes in a sequentially randomized trial of advanced prostate cancer. Journal of the American Statistical Association, 107, 493–508.

    Article  MathSciNet  MATH  Google Scholar 

  • Wathen, J. K., & Thall, P. F. (2008). Bayesian adaptive model selection for optimizing group sequential clinical trials. Statistics in Medicine, 27, 5586–5604.

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Biostatistics, Columbia University, New York, USA

    Bibhas Chakraborty

  2. Department of Epidemiology, Biostatistics, and Occupational Health, McGill University, Montreal, Québec, Canada

    Erica E. M. Moodie

Authors
  1. Bibhas Chakraborty
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  2. Erica E. M. Moodie
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Chakraborty, B., Moodie, E.E.M. (2013). The Data: Observational Studies and Sequentially Randomized Trials. In: Statistical Methods for Dynamic Treatment Regimes. Statistics for Biology and Health. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7428-9_2

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