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Evaluation of Viable Dynamic Treatment Regimes in a Sequentially Randomized Trial of Advanced Prostate Cancer
Open accessAbstract
We present new statistical analyses of data arising from a clinical trial designed to compare two-stage dynamic treatment regimes (DTRs) for advanced prostate cancer. The trial protocol mandated that patients were to be initially randomized among four chemotherapies, and that those who responded poorly were to be rerandomized to one of the remaining candidate therapies. The primary aim was to compare the DTRs' overall success rates, with success defined by the occurrence of successful responses in each of two consecutive courses of the patient's therapy. Of the one hundred and fifty study participants, forty seven did not complete their therapy per the algorithm. However, thirty five of them did so for reasons that precluded further chemotherapy; i.e. toxicity and/or progressive disease. Consequently, rather than comparing the overall success rates of the DTRs in the unrealistic event that these patients had remained on their assigned chemotherapies, we conducted an analysis that compared viable switch rules defined by the per-protocol rules but with the additional provision that patients who developed toxicity or progressive disease switch to a non-prespecified therapeutic or palliative strategy. This modification involved consideration of bivariate per-course outcomes encoding both efficacy and toxicity. We used numerical scores elicited from the trial's Principal Investigator to quantify the clinical desirability of each bivariate per-course outcome, and defined one endpoint as their average over all courses of treatment. Two other simpler sets of scores as well as log survival time also were used as endpoints. Estimation of each DTR-specific mean score was conducted using inverse probability weighted methods that assumed that missingness in the twelve remaining drop-outs was informative but explainable in that it only depended on past recorded data. We conducted additional worst-best case analyses to evaluate sensitivity of our findings to extreme departures from the explainable drop-out assumption.
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“For example, SMART has been used in oncology to develop medication algorithms to treat prostate cancer [36,52,53].”
From Introduction to SMART designs for the development of adaptive interventions: with application to weight loss research (2014) · cites this paper as [36]
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Cites
Docetaxel plus Prednisone or Mitoxantrone plus Prednisone for Advanced Prostate Cancer
Tannock, I. F., de Wit, R., Berry, W. R., Horti, J., Pluzanska, A., Chi, K. N., Oudard, S., Théodore, C., James, N. D., Turesson, I., et al. (2004) · New England Journal of Medicine · doi:10.1056/nejmoa040720 · Cited by 5,735 · cited 1×
“…and van der Laan 2007) and comparison of the regimens used in the trial to a particular combination chemotherapy reported in the medical literature while the trial was still ongoing (Tannock et al. 2004; Armstrong and Eisenberger 2006; Armstrong et al. 2007; Millikan, Logothetis, and Thall 2008).”
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“In IPTW estimation, efficiency can be improved by replacing the known treatment probabilities that form the factors in the weights ω by maximum likelihood estimates under correctly specified models (e.g., Robins, Rotnitzky, and Zhao 1994).”
MethodSelf-citationBayesian inference for causal effects: The role of randomization
Rubin, D. B. (1978) · The Annals of Statistics · doi:10.1214/aos/1176344064 · Cited by 2,503 · cited 1×
“To compare the different switch rules used in the trial, we apply the counterfactual framework for causal inference as originally developed by Rubin (1978) for time-independent treatments and later extended by Robins (1986, 1987) for time-dependent treatments in longitudinal studies.”
MethodRobins, J. (1986) · Mathematical Modelling · doi:10.1016/0270-0255(86)90088-6 · Cited by 2,451 · cited 8×
“To compare the different switch rules used in the trial, we apply the counterfactual framework for causal inference as originally developed by Rubin (1978) for time-independent treatments and later extended by Robins (1986, 1987) for time-dependent treatments in longitudinal studies.”
BackgroundMethodInfluentialDoubly robust estimation in missing data and causal inference models
Bang, H., & Robins, J. M. (2005) · Biometrics · doi:10.1111/j.1541-0420.2005.00377.x · Cited by 1,998
Collins, L. M., Murphy, S. A., & Strecher, V. (2007) · American Journal of Preventive Medicine · doi:10.1016/j.amepre.2007.01.022 · Cited by 1,082
Optimal Dynamic Treatment Regimes
Murphy, S. A. (2003) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/1467-9868.00389 · Cited by 990 · cited 1×
“…of structural nested models (Robins 1986, 1989, 1993, 1997), some clever variations of g-estimation for optimal treatment regime estimation (Murphy 2003; Robins 2004) and inverse probability weighted estimation of marginal structural models (Murphy, van der Laan, Robins, and CPPRG 2001;…”
BackgroundSteyerberg, E. W., Eijkemans, M. J. C., Harrell, F. E., & Habbema, J. D. F. (2000) · Statistics in Medicine · doi:10.1002/(sici)1097-0258(20000430)19:8 · Cited by 789
Self-citationAn experimental design for the development of adaptive treatment strategies
Murphy, S. A. (2005) · Statistics in Medicine · doi:10.1002/sim.2022 · Cited by 746 · cited 7×
“A number of recent articles discuss design of randomized trials that aim at evaluating DTRs rather than individual treatments (Lavori and Dawson 2000, 2004; Thall, Millikan, and Sung 2000; Thall, Sung, and Estey 2002; Murphy 2005; Oetting et al. 2011).”
BackgroundInfluentialOptimal Structural Nested Models for Optimal Sequential Decisions
Robins, J. M. (2004) · Lecture notes in statistics · doi:10.1007/978-1-4419-9076-1_11 · Cited by 547 · cited 6×
“Our analyses differ from those in Thall et al. (2007) and Bembom and van der Laan 2007 in three important ways: (1) following the recommendation of Robins (1986, 2004), van der Laan and Petersen (2007), and Bembom and van der Laan (2008), we modify the definition of the candidate DTRs; (2) we study…”
BackgroundMethodInfluentialCausal Inference from Complex Longitudinal Data
Robins, J. M. (1997) · Lecture Notes in Statistics · doi:10.1007/978-1-4612-1842-5_4 · Cited by 510 · cited 1×
“Statistical methods include g-estimation of structural nested models (Robins 1986, 1989, 1993, 1997), some clever variations of g-estimation for optimal treatment regime estimation (Murphy 2003; Robins 2004) and inverse probability weighted estimation of marginal structural models (Murphy, van der…”
MethodA strategy for optimizing and evaluating behavioral interventions
Collins, L. M., Murphy, S. A., Nair, V. N., & Strecher, V. J. (2005) · Annals of Behavioral Medicine · doi:10.1207/s15324796abm3001_8 · Cited by 492
Randomized phase II clinical trials.
Simon, R. M., Wittes, R. E., & Ellenberg, S. S. (1985) · PubMed · Cited by 469
Marginal Mean Models for Dynamic Regimes
Murphy, S. A., van der Laan, M. J., Robins, J. M., & Conduct Problems Prevention Research Group (2001) · Journal of the American Statistical Association · doi:10.1198/016214501753382327 · Cited by 393 · cited 4×
“It follows from Murphy et al. (2001) that under unconfoundedness and positivity, E[Y(a,a∗)] = E( a,a ∗ωY ) E( a,a∗ω) = E( a,a∗ωY ).”
BackgroundMethodInfluentialArmstrong, A. J., Garrett-Mayer, E. S., Yang, Y.-C. O., de Wit, R., Tannock, I. F., & Eisenberger, M. A. (2007) · Clinical Cancer Research · doi:10.1158/1078-0432.ccr-07-1036 · Cited by 359 · cited 1×
“…and van der Laan 2007) and comparison of the regimens used in the trial to a particular combination chemotherapy reported in the medical literature while the trial was still ongoing (Tannock et al. 2004; Armstrong and Eisenberger 2006; Armstrong et al. 2007; Millikan, Logothetis, and Thall 2008).”
ResultQuality adjusted survival analysis
Glasziou, P., Simes, R. J., & Gelber, R. D. (1990) · Statistics in Medicine · doi:10.1002/sim.4780091106 · Cited by 319
The Multiphase Optimization Strategy for Engineering Effective Tobacco Use Interventions
Collins, L. M., Baker, T. B., Mermelstein, R. J., Piper, M. E., Jorenby, D. E., Smith, S. S., Christiansen, B. A., Schlam, T. R., Cook, J. W., & Fiore, M. C. (2011) · Annals of Behavioral Medicine · doi:10.1007/s12160-010-9253-x · Cited by 300
Web-Based Smoking-Cessation Programs
Strecher, V. J., McClure, J. B., Alexander, G. L., Chakraborty, B., Nair, V. N., Konkel, J. M., Greene, S. M., Collins, L. M., Carlier, C. C., Wiese, C. J., et al. (2008) · American Journal of Preventive Medicine · doi:10.1016/j.amepre.2007.12.024 · Cited by 266 · cited 1×
“highest estimated overall success rates, is more consistent with Thall et al. (2007), who used all patients in their first-line analysis based on the success/failure endpoint and concluded that the best initial chemo is TEC, while the worst initial chemo is CVD.”
ResultTargeted Maximum Likelihood Based Causal Inference: Part II
van der Laan, M. J. (2010) · The International Journal of Biostatistics · doi:10.2202/1557-4679.1241 · Cited by 239
A Distributional Approach for Causal Inference Using Propensity Scores
Tan, Z. (2006) · Journal of the American Statistical Association · doi:10.1198/016214506000000023 · Cited by 232
Dynamic treatment regimes: practical design considerations
Lavori, P. W., & Dawson, R. (2004) · Clinical Trials · doi:10.1191/1740774s04cn002oa · Cited by 229
A Design for Testing Clinical Strategies: Biased Adaptive Within-Subject Randomization
Lavori, P. W., & Dawson, R. (2000) · Journal of the Royal Statistical Society Series A (Statistics in Society) · doi:10.1111/1467-985x.00154 · Cited by 228 · cited 1×
“A number of recent articles discuss design of randomized trials that aim at evaluating DTRs rather than individual treatments (Lavori and Dawson 2000, 2004; Thall, Millikan, and Sung 2000; Thall, Sung, and Estey 2002; Murphy 2005; Oetting et al. 2011).”
BackgroundRobins, J. M. (1987) · Computers & Mathematics with Applications · doi:10.1016/0898-1221(87)90238-0 · Cited by 213 · cited 1×
“To compare the different switch rules used in the trial, we apply the counterfactual framework for causal inference as originally developed by Rubin (1978) for time-independent treatments and later extended by Robins (1986, 1987) for time-dependent treatments in longitudinal studies.”
MethodEstimation and extrapolation of optimal treatment and testing strategies
Robins, J., Orellana, L., & Rotnitzky, A. (2008) · Statistics in Medicine · doi:10.1002/sim.3301 · Cited by 208 · cited 1×
“…regime estimation (Murphy 2003; Robins 2004) and inverse probability weighted estimation of marginal structural models (Murphy, van der Laan, Robins, and CPPRG 2001; van der Laan 2006; van der Laan and Petersen 2007; Robins, Orellana, and Rotnitzky 2008; Orellana, Rotnitzky, and Robin 2010).”
Self-citationOrellana, L., Rotnitzky, A., & Robins, J. M. (2010) · The International Journal of Biostatistics · doi:10.2202/1557-4679.1200 · Cited by 202
Self-citationRosenblum, M. (2011) · Springer series in statistics · doi:10.1007/978-1-4419-9782-1_9 · Cited by 181
Causal Effect Models for Realistic Individualized Treatment and Intention to Treat Rules
van der Laan, M. J., & Petersen, M. L. (2007) · The International Journal of Biostatistics · doi:10.2202/1557-4679.1022 · Cited by 175
A consistent estimator for the distribution of quality adjusted survival time
Zhao, H. (1997) · Biometrika · doi:10.1093/biomet/84.2.339 · Cited by 163
Improved double-robust estimation in missing data and causal inference models
Rotnitzky, A. G., Lei, Q., Sued, M., & Robins, J. M. (2012) · Biometrika · doi:10.1093/biomet/ass013 · Cited by 152
Self-citationCausality and Psychopathology: Finding the Determinants of Disorders and their Cures
Shrout, P. E., Keyes, K. M., & Ornstein, K. A. (2010) · Cited by 147
Lunceford, J. K., Davidian, M., & Tsiatis, A. A. (2002) · Biometrics · doi:10.1111/j.0006-341x.2002.00048.x · Cited by 145 · cited 1×
“…and Case Studies DOI: 10.1080/01621459.2011.641416 493 sequentially randomized (SR) designs with randomization probabilities that possibly can depend on past health status and covariates (Lunceford, Davidian, and Tsiatis 2002; Wahed and Tsiatis 2004, 2006; Bembom and van der Laan 2007, 2008).”
BackgroundInfluentialNon- and semi-parametric maximum likelihood estimators and the Von Mises method
Gill, R. D. (1986) · Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands · Cited by 119
Selecting Therapeutic Strategies Based on Efficacy and Death in Multicourse Clinical Trials
Thall, P. F., Sung, H., & Estey, E. H. (2002) · Journal of the American Statistical Association · doi:10.1198/016214502753479202 · Cited by 117
Self-citationDeveloping multicomponent interventions using fractional factorial designs
Chakraborty, B., Collins, L. M., Strecher, V. J., & Murphy, S. A. (2009) · Statistics in Medicine · doi:10.1002/sim.3643 · Cited by 107
Wahed, A. S., & Tsiatis, A. A. (2004) · Biometrics · doi:10.1111/j.0006-341x.2004.00160.x · Cited by 103 · cited 1×
“…and Case Studies DOI: 10.1080/01621459.2011.641416 493 sequentially randomized (SR) designs with randomization probabilities that possibly can depend on past health status and covariates (Lunceford, Davidian, and Tsiatis 2002; Wahed and Tsiatis 2004, 2006; Bembom and van der Laan 2007, 2008).”
BackgroundInfluentialHouédé, N., Thall, P. F., Nguyen, H. Q., Paolettí, X., & Kramar, A. (2009) · Biometrics · doi:10.1111/j.1541-0420.2009.01302.x · Cited by 96
Self-citationA flexible design for multiple armed screening trials
Sargent, D. J., & Goldberg, R. M. (2001) · Statistics in Medicine · doi:10.1002/sim.704 · Cited by 85
Collins, L. M., Chakraborty, B., Murphy, S. A., & Strecher, V. (2009) · Clinical Trials · doi:10.1177/1740774508100973 · Cited by 80
Thall, P. F., Wooten, L. H., Logothetis, C. J., Millikan, R. E., & Tannir, N. M. (2007) · Statistics in Medicine · doi:10.1002/sim.2894 · Cited by 75
Self-citationWahed, A. S., & Tsiatis, A. A. (2006) · Biometrika · doi:10.1093/biomet/93.1.163 · Cited by 73 · cited 1×
“…and Case Studies DOI: 10.1080/01621459.2011.641416 493 sequentially randomized (SR) designs with randomization probabilities that possibly can depend on past health status and covariates (Lunceford, Davidian, and Tsiatis 2002; Wahed and Tsiatis 2004, 2006; Bembom and van der Laan 2007, 2008).”
BackgroundInfluentialThall, P. F., Logothetis, C., Pagliaro, L. C., Wen, S., Brown, M. A., Williams, D., & Millikan, R. E. (2007) · JNCI Journal of the National Cancer Institute · doi:10.1093/jnci/djm189 · Cited by 67 · cited 18×
“Bembom and van der Laan (2007) noted that the estimation strategy of Thall et al. (2007) was useful for identifying the chemotherapy that would give the best success rate in each course, but cannot identify the regime that gives the best overall success rate.”
BackgroundMethodResultInfluentialSelf-citationAnalytic Methods for Estimating HIV-Treatment and Cofactor Effects
Robins, J. M. (2002) · AIDS prevention and mental health · doi:10.1007/0-306-47137-x_12 · Cited by 60
Asymptotic Theory for Cross-validated Targeted Maximum Likelihood Estimation
Zheng, W., & van der Laan, M. J. (2010) · Collection of Biostatistics Research Archive (COBRA) · Cited by 59
Statistical Methodology for a SMART Design in the Development of Adaptive Treatment Strategies
Oetting, A. I., & Levy, J. A. (2011) · Oxford University Press eBooks · doi:10.1093/oso/9780199754649.003.0013 · Cited by 57
Efficient design and inference for multistage randomized trials of individualized treatment policies
Dawson, R., & Lavori, P. W. (2011) · Biostatistics · doi:10.1093/biostatistics/kxr016 · Cited by 44 · cited 1×
“Sample size calculations for SR trials are important to provide practical guidance (see Murphy 2005; Feng and Wahed 2009; Dawson and Lavori 2012).”
BackgroundScreening Experiments for Developing Dynamic Treatment Regimes
Murphy, S. A., & Bingham, D. (2009) · Journal of the American Statistical Association · doi:10.1198/jasa.2009.0119 · Cited by 41
Targeted Minimum Loss Based Estimator that Outperforms a given Estimator
Gruber, S., & van der Laan, M. J. (2012) · The International Journal of Biostatistics · doi:10.1515/1557-4679.1332 · Cited by 35
Bembom, O., & van der Laan, M. J. (2008) · Statistics in Medicine · doi:10.1002/sim.3268 · Cited by 35
Millikan, R. E., Thall, P. F., Pagliaro, L. C., Williams, D. L., Brown, M., & Logothetis, C. J. (2004) · Journal of Clinical Oncology · doi:10.1200/jco.2004.22.14_suppl.4561 · Cited by 33
Self-citationFeng, W., & Wahed, A. S. (2008) · Biometrika · doi:10.1093/biomet/asn025 · Cited by 32
Statistical Methods for Analyzing Sequentially Randomized Trials
Bembom, O., & van der Laan, M. J. (2007) · JNCI Journal of the National Cancer Institute · doi:10.1093/jnci/djm185 · Cited by 30
Proceedings of the Second Seattle Symposium in Biostatistics: Analysis Of Correlated Data
Lin, D. Y., & Heagerty, P. J. (2005) · Lecture notes in statistics · doi:10.1007/978-1-4419-9076-1 · Cited by 19
(2006) · CRC Press eBooks · doi:10.1201/9781420004656.ch1 · Cited by 19
Causal Effect Models for Intention to Treat and Realistic Individualized Treatment Rules
van der Laan, M. J. (2006) · Collection of Biostatistics Research Archive · Cited by 18
Knight, C. (2012) · Constructing knowledge: curriculum studies in action · doi:10.1007/978-94-6091-912-1_12 · Cited by 6
The International Journal of Biostatistics
van der Laan, M. V. (2017) · The International Journal of Biostatistics · doi:10.1515/ijb · Cited by 5
Millikan, R. E., Logothetis, C. J., & Thall, P. F. (2008) · JNCI Journal of the National Cancer Institute · doi:10.1093/jnci/djn105 · Cited by 1 · cited 1×
“…and van der Laan 2007) and comparison of the regimens used in the trial to a particular combination chemotherapy reported in the medical literature while the trial was still ongoing (Tannock et al. 2004; Armstrong and Eisenberger 2006; Armstrong et al. 2007; Millikan, Logothetis, and Thall 2008).”
ResultSelf-citationArmstrong, A. J., & Eisenberger, M. A. (2006) · Nature Clinical Practice Urology · doi:10.1038/ncpuro0462 · Cited by 1 · cited 1×
“…and van der Laan 2007) and comparison of the regimens used in the trial to a particular combination chemotherapy reported in the medical literature while the trial was still ongoing (Tannock et al. 2004; Armstrong and Eisenberger 2006; Armstrong et al. 2007; Millikan, Logothetis, and Thall 2008).”
Result
Research works printed but not linked: 4
- Orellana L., 2010, International Journal of Biostatistics, 6
- Robins J. M., 1989, Health Service Research Methodology: A Focus on AIDS, 113
- Robins J. M., 1993, Methodological issues of AIDS Mental Health Research., 213
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Cited by
Sorted by citations
Almirall, D., Nahum-Shani, I., Sherwood, N. E., & Murphy, S. A. (2014) · Translational Behavioral Medicine · doi:10.1007/s13142-014-0265-0 · Cited by 453
“For example, SMART has been used in oncology to develop medication algorithms to treat prostate cancer [36, 52, 53].”
MethodChakraborty, B., & Murphy, S. A. (2013) · Annual Review of Statistics and Its Application · doi:10.1146/annurev-statistics-022513-115553 · Cited by 288
Assessing time-varying causal effect moderation in mobile health
Boruvka, A., Almirall, D., Witkiewitz, K., & Murphy, S. A. (2018) · Journal of the American Statistical Association · doi:10.1080/01621459.2017.1305274 · Cited by 152
“Conditioning on availability is related to the concept of viable or feasible dynamic treatment regimes (Robins 2004;Wang et al. 2012), in which one assesses only the causal effect of treatments that can actually be provided.”
Sample size calculations for micro‐randomized trials in mHealth
Liao, P., Klasnja, P., Tewari, A., & Murphy, S. A. (2015) · Statistics in Medicine · doi:10.1002/sim.6847 · Cited by 147
“The former conditional aspect of the definition is related to the concept of viable or feasible dynamic treatment regimes [20,21] in which one assesses only the causal effect of treatments that can actually be provided.”
BackgroundThall, P., Fox, P. S., & Wathen, J. K. (2015) · Annals of Oncology · doi:10.1093/annonc/mdv238 · Cited by 124
Self-citation
Metadata
- Authors
- Wang, L., Rotnitzky, A., Lin, X., Millikan, R. E., & Thall, P. F.
- Affiliations
- University of Michigan (US)
- Harvard University (US)
- The University of Texas MD Anderson Cancer Center (US)
- Corresponding author
- Thall, Peter F.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 2012-06
- Volume
- 107
- Issue
- 498
- Pages
- 493-508
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- PMC
- PMC3433243
- OpenAlex
- W2167371237
- Cited by
- 108
- References
- 62
- Citations by year
- 2026: 3 · 2025: 2 · 2024: 17 · 2023: 7 · 2022: 8 · 2021: 6 · 2020: 8 · 2019: 5 · 2018: 7 · 2017: 8 · 2016: 10 · 2015: 10 · 2014: 9 · 2013: 3 · 2012: 5
- FWCI
- 8.25
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Locations
- Journal of the American Statistical Association (publishedVersion)
- PubMed (publishedVersion)
- Europe PMC (PubMed Central) (acceptedVersion)
- PubMed Central (acceptedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- Funders
- National Cancer Institute (P50CA140388, P01CA049639, R37CA076404, R01CA083932, P30CA016672, R35CA197449)
- National Institute of General Medical Sciences (R01GM048704)
- National Institute of Allergy and Infectious Diseases (R01AI051164)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Keywords
- dynamic treatment regimes, advanced prostate cancer, chemotherapy, treatment switching, dropout, inverse probability weighting, efficacy-toxicity trade-off
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