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1

Chakraborty, Bibhas, and Susan A. Murphy. "Dynamic Treatment Regimes." Annual Review of Statistics and Its Application 1, no. 1 (January 3, 2014): 447–64. http://dx.doi.org/10.1146/annurev-statistics-022513-115553.

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2

Lavori, Philip W., and Ree Dawson. "Dynamic treatment regimes: practical design considerations." Clinical Trials 1, no. 1 (February 2004): 9–20. http://dx.doi.org/10.1191/1740774504cn002oa.

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Background Clinical management of chronic disease requires a dynamic treatment regime (DTR): rules for choosing the new treatment based on the history of response to past treatments. Estimating and comparing the effects of DTRs from a sample of observed trajectories of treatment and outcome depends on the untestable assumption that new treatments are assigned independently of potential future responses to treatment, conditional on the history of treatments and response to date (“sequential ignorability”). In longitudinal observational studies, sequential ignorability must be assumed, while randomization of dynamic regimes can guarantee it. Methods Using several clinical examples, we describe the simplest randomized experimental designs for comparing DTRs. We begin by considering an initial treatment A and a second treatment B, and discuss how a dynamic treatment regime that starts with A and leads (sometimes) to B, might be compared to either fixed treatment A or B. We also illustrate the problem of finding the optimal sequence of treatments in a DTR, when there are several choices. We describe and contrast two ways of incorporating randomization into studies to compare such regimes: baseline randomization among DTRs versus randomization at the decision points (sequentially randomized designs). Conclusions We discuss estimation and inference from both baseline randomized and sequentially randomized designs and conclude with a discussion of the differences between the experimental and observational approaches to optimizing and comparing dynamic treatment regimes.
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Murphy, S. A. "Optimal dynamic treatment regimes." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 65, no. 2 (April 25, 2003): 331–55. http://dx.doi.org/10.1111/1467-9868.00389.

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4

Zhang, Yichi, Eric B. Laber, Marie Davidian, and Anastasios A. Tsiatis. "Interpretable Dynamic Treatment Regimes." Journal of the American Statistical Association 113, no. 524 (October 2, 2018): 1541–49. http://dx.doi.org/10.1080/01621459.2017.1345743.

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Moodie, Erica E. M., Thomas S. Richardson, and David A. Stephens. "Demystifying Optimal Dynamic Treatment Regimes." Biometrics 63, no. 2 (February 26, 2007): 447–55. http://dx.doi.org/10.1111/j.1541-0420.2006.00686.x.

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6

Zhao, Ying-Qi, and Eric B. Laber. "Estimation of optimal dynamic treatment regimes." Clinical Trials: Journal of the Society for Clinical Trials 11, no. 4 (May 28, 2014): 400–407. http://dx.doi.org/10.1177/1740774514532570.

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7

Lavori, Philip W., and Ree Dawson. "Dynamic treatment regimes: practical design considerations." Clinical Trials 1, no. 1 (February 1, 2004): 9–20. http://dx.doi.org/10.1191/1740774s04cn002oa.

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8

Johnson, Brent A. "Treatment-competing events in dynamic regimes." Lifetime Data Analysis 14, no. 2 (September 9, 2007): 196–215. http://dx.doi.org/10.1007/s10985-007-9051-3.

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9

Lizotte, Daniel J., and Arezoo Tahmasebi. "Prediction and tolerance intervals for dynamic treatment regimes." Statistical Methods in Medical Research 26, no. 4 (July 11, 2017): 1611–29. http://dx.doi.org/10.1177/0962280217708662.

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We develop and evaluate tolerance interval methods for dynamic treatment regimes (DTRs) that can provide more detailed prognostic information to patients who will follow an estimated optimal regime. Although the problem of constructing confidence intervals for DTRs has been extensively studied, prediction and tolerance intervals have received little attention. We begin by reviewing in detail different interval estimation and prediction methods and then adapting them to the DTR setting. We illustrate some of the challenges associated with tolerance interval estimation stemming from the fact that we do not typically have data that were generated from the estimated optimal regime. We give an extensive empirical evaluation of the methods and discussed several practical aspects of method choice, and we present an example application using data from a clinical trial. Finally, we discuss future directions within this important emerging area of DTR research.
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Murphy, S. A., and D. Bingham. "Screening Experiments for Developing Dynamic Treatment Regimes." Journal of the American Statistical Association 104, no. 485 (March 2009): 391–408. http://dx.doi.org/10.1198/jasa.2009.0119.

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11

Henderson, Robin, Phil Ansell, and Deyadeen Alshibani. "Regret-Regression for Optimal Dynamic Treatment Regimes." Biometrics 66, no. 4 (December 9, 2009): 1192–201. http://dx.doi.org/10.1111/j.1541-0420.2009.01368.x.

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12

Laber, Eric B., Daniel J. Lizotte, Min Qian, William E. Pelham, and Susan A. Murphy. "Dynamic treatment regimes: Technical challenges and applications." Electronic Journal of Statistics 8, no. 1 (2014): 1225–72. http://dx.doi.org/10.1214/14-ejs920.

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13

Saarela, Olli, Elja Arjas, David A. Stephens, and Erica E. M. Moodie. "Predictive Bayesian inference and dynamic treatment regimes." Biometrical Journal 57, no. 6 (August 11, 2015): 941–58. http://dx.doi.org/10.1002/bimj.201400153.

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14

Wallace, Michael P., Erica E. M. Moodie, and David A. Stephens. "Reward ignorant modeling of dynamic treatment regimes." Biometrical Journal 60, no. 5 (May 30, 2018): 991–1002. http://dx.doi.org/10.1002/bimj.201700322.

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15

Goldberg, Yair, Moshe Pollak, Alexis Mitelpunkt, Mila Orlovsky, Ahuva Weiss-Meilik, and Malka Gorfine. "Change-point detection for infinite horizon dynamic treatment regimes." Statistical Methods in Medical Research 26, no. 4 (May 10, 2017): 1590–604. http://dx.doi.org/10.1177/0962280217708655.

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A dynamic treatment regime is a set of decision rules for how to treat a patient at multiple time points. At each time point, a treatment decision is made depending on the patient’s medical history up to that point. We consider the infinite-horizon setting in which the number of decision points is very large. Specifically, we consider long trajectories of patients’ measurements recorded over time. At each time point, the decision whether to intervene or not is conditional on whether or not there was a change in the patient’s trajectory. We present change-point detection tools and show how to use them in defining dynamic treatment regimes. The performance of these regimes is assessed using an extensive simulation study. We demonstrate the utility of the proposed change-point detection approach using two case studies: detection of sepsis in preterm infants in the intensive care unit and detection of a change in glucose levels of a diabetic patient.
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16

Ding, Juanjuan, Jiantao Zhao, Tonghua Pan, Linjie Xi, Jing Zhang, and Zhirong Zou. "Comparative Transcriptome Analysis of Gene Expression Patterns in Tomato Under Dynamic Light Conditions." Genes 10, no. 9 (August 29, 2019): 662. http://dx.doi.org/10.3390/genes10090662.

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Plants grown under highly variable natural light regimes differ strongly from plants grown under constant light (CL) regimes. Plant phenotype and adaptation responses are important for plant biomass and fitness. However, the underlying regulatory mechanisms are still poorly understood, particularly from a transcriptional perspective. To investigate the influence of different light regimes on tomato plants, three dynamic light (DL) regimes were designed, using a CL regime as control. Morphological, photosynthetic, and transcriptional differences after five weeks of treatment were compared. Leaf area, plant height, shoot /root weight, total chlorophyll content, photosynthetic rate, and stomatal conductance all significantly decreased in response to DL regimes. The biggest expression difference was found between the treatment with the highest light intensity at the middle of the day with a total of 1080 significantly up-/down-regulated genes. A total of 177 common differentially expressed genes were identified between DL and CL conditions. Finally, significant differences were observed in the levels of gene expression between DL and CL treatments in multiple pathways, predominantly of plant–pathogen interactions, plant hormone signal transductions, metabolites, and photosynthesis. These results expand the understanding of plant development and photosynthetic regulations under DL conditions by multiple pathways.
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17

TOPP, ANDREW S., GEOFFREY S. JOHNSON, and ABDUS S. WAHED. "Variants of double robust estimators for two-stage dynamic treatment regimes." Journal of Statistical Research 52, no. 1 (September 2, 2018): 91–113. http://dx.doi.org/10.47302/jsr.2018520106.

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Certain conditions and illnesses may necessitate multiple stages of treatment and thus require unique study designs to compare the efficacy of these interventions. Such studies are characterized by two or more stages of treatment punctuated by decision points where intermediate outcomes inform the choice for the next stage of treatment. The algorithm that dictates what treatments to take based on intermediate outcomes is referred to as a dynamic regime. This paper describes an efficient method of building double robust estimators of the treatment effect of different regimes. A double robust estimator utilizes both modeling of the outcome and weighting based on the modeled probability of receiving treatment in such a way that the resulting estimator is a consistent estimate of the desired population parameter under the condition that at least one of those models is correct. This new and more efficient double robust estimator is compared to another double robust estimator as well as classical regression and inverse probability weighted estimators. The methods are applied to estimate the regime effects in the STAR*D anti-depression treatment trial.
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18

Zhao, Ying-Qi. "Dynamic Treatment Regimes: Statistical Methods for Precision Medicine." Journal of the American Statistical Association 117, no. 537 (January 2, 2022): 527. http://dx.doi.org/10.1080/01621459.2022.2035159.

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19

Laber, Eric B., Daniel J. Lizotte, and Bradley Ferguson. "Set-valued dynamic treatment regimes for competing outcomes." Biometrics 70, no. 1 (January 8, 2014): 53–61. http://dx.doi.org/10.1111/biom.12132.

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20

Barrett, Jessica K., Robin Henderson, and Susanne Rosthøj. "Doubly Robust Estimation of Optimal Dynamic Treatment Regimes." Statistics in Biosciences 6, no. 2 (July 12, 2013): 244–60. http://dx.doi.org/10.1007/s12561-013-9097-6.

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21

Ertefaie, Ashkan, and Robert L. Strawderman. "Constructing dynamic treatment regimes over indefinite time horizons." Biometrika 105, no. 4 (September 17, 2018): 963–77. http://dx.doi.org/10.1093/biomet/asy043.

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22

Simoneau, Gabrielle, Erica E. M. Moodie, Jagtar S. Nijjar, Robert W. Platt, and the Scottish Early Rheumatoid Arthritis Inception Cohort Inv. "Estimating Optimal Dynamic Treatment Regimes With Survival Outcomes." Journal of the American Statistical Association 115, no. 531 (July 22, 2019): 1531–39. http://dx.doi.org/10.1080/01621459.2019.1629939.

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23

Zhang, B., A. A. Tsiatis, E. B. Laber, and M. Davidian. "Robust estimation of optimal dynamic treatment regimes for sequential treatment decisions." Biometrika 100, no. 3 (May 30, 2013): 681–94. http://dx.doi.org/10.1093/biomet/ast014.

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24

Rose, Eric J., Erica E. M. Moodie, and Susan Shortreed. "Using Pilot Data for Power Analysis of Observational Studies for the Estimation of Dynamic Treatment Regimes." Observational Studies 9, no. 4 (2023): 25–48. http://dx.doi.org/10.1353/obs.2023.a906627.

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Abstract: Significant attention has been given to developing data-driven methods for tailoring patient care based on individual patient characteristics. Dynamic treatment regimes formalize this approach through a sequence of decision rules that map patient information to a suggested treatment. The data for estimating and evaluating treatment regimes are ideally gathered through the use of Sequential Multiple Assignment Randomized Trials (SMARTs), though longitudinal observational studies are commonly used due to the potentially prohibitive costs of conducting a SMART. Observational studies are typically powered for simple comparisons of fixed treatment sequences; a priori power or sample size calculations for tailored strategies are rarely if ever undertaken. This has lead to many studies that fail to find a statistically significant benefit to tailoring treatment. We develop power analyses for the estimation of dynamic treatment regimes from observational studies. Our approach uses pilot data to estimate the power for comparing the value of the optimal regime, i.e., the expected outcome if all patients in the population were treated by following the optimal regime, with a known comparison mean. This allows for calculations that ensure a study has sufficient power to detect the need for tailoring, should it be present. Our approach also ensures the value of the estimated optimal treatment regime has a high probability of being within a range of the value of the true optimal regime, set a priori. We examine the performance of the proposed procedure with a simulation study and use it to size a study for reducing depressive symptoms using data from electronic health records.
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25

Hernan, Miguel A., Emilie Lanoy, Dominique Costagliola, and James M. Robins. "Comparison of Dynamic Treatment Regimes via Inverse Probability Weighting." Basic Clinical Pharmacology Toxicology 98, no. 3 (March 2006): 237–42. http://dx.doi.org/10.1111/j.1742-7843.2006.pto_329.x.

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26

Wallace, Michael P., Erica E. M. Moodie, and David A. Stephens. "Model selection for G‐estimation of dynamic treatment regimes." Biometrics 75, no. 4 (September 12, 2019): 1205–15. http://dx.doi.org/10.1111/biom.13104.

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27

Yavuz, Idil, Yu Chng, and Abdus S. Wahed. "Estimating the cumulative incidence function of dynamic treatment regimes." Journal of the Royal Statistical Society: Series A (Statistics in Society) 181, no. 1 (November 7, 2016): 85–106. http://dx.doi.org/10.1111/rssa.12250.

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28

Shi, Chengchun, Ailin Fan, Rui Song, and Wenbin Lu. "High-dimensional $A$-learning for optimal dynamic treatment regimes." Annals of Statistics 46, no. 3 (June 2018): 925–57. http://dx.doi.org/10.1214/17-aos1570.

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29

Goldberg, Yair, Rui Song, Donglin Zeng, and Michael R. Kosorok. "Comment on “Dynamic treatment regimes: Technical challenges and applications”." Electronic Journal of Statistics 8, no. 1 (2014): 1290–300. http://dx.doi.org/10.1214/14-ejs905.

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30

Hsu, Jesse Y., and Dylan S. Small. "Discussion of “Dynamic treatment regimes: Technical challenges and applications”." Electronic Journal of Statistics 8, no. 1 (2014): 1301–8. http://dx.doi.org/10.1214/14-ejs906.

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31

Banerjee, Moulinath. "Discussion of “Dynamic treatment regimes: Technical challenges and applications”." Electronic Journal of Statistics 8, no. 1 (2014): 1309–11. http://dx.doi.org/10.1214/14-ejs907.

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32

Robins, James, and Andrea Rotnitzky. "Discussion of “Dynamic treatment regimes: Technical challenges and applications”." Electronic Journal of Statistics 8, no. 1 (2014): 1273–89. http://dx.doi.org/10.1214/14-ejs908.

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33

Laber, Eric B., Daniel J. Lizotte, Min Qian, William E. Pelham, and Susan A. Murphy. "Rejoinder of “Dynamic treatment regimes: Technical challenges and applications”." Electronic Journal of Statistics 8, no. 1 (2014): 1312–21. http://dx.doi.org/10.1214/14-ejs920rej.

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34

Thitsa, Makhin, and Clyde Martin. "Dynamic treatment regimes: the mathematics of unstable switched systems." Communications in Information and Systems 16, no. 3 (2016): 185–202. http://dx.doi.org/10.4310/cis.2016.v16.n3.a3.

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35

Chen, Yuan, Yuanjia Wang, and Donglin Zeng. "Synthesizing independent stagewise trials for optimal dynamic treatment regimes." Statistics in Medicine 39, no. 28 (August 17, 2020): 4107–19. http://dx.doi.org/10.1002/sim.8712.

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36

Huang, Xuelin, Jing Ning, and Abdus S. Wahed. "Optimization of individualized dynamic treatment regimes for recurrent diseases." Statistics in Medicine 33, no. 14 (February 9, 2014): 2363–78. http://dx.doi.org/10.1002/sim.6104.

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37

Chakraborty, Bibhas, Susan Murphy, and Victor Strecher. "Inference for non-regular parameters in optimal dynamic treatment regimes." Statistical Methods in Medical Research 19, no. 3 (July 16, 2009): 317–43. http://dx.doi.org/10.1177/0962280209105013.

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38

Tao, Yebin, Lu Wang, and Daniel Almirall. "Tree-based reinforcement learning for estimating optimal dynamic treatment regimes." Annals of Applied Statistics 12, no. 3 (September 2018): 1914–38. http://dx.doi.org/10.1214/18-aoas1137.

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39

Pollack, Ari H., Assaf P. Oron, Joseph T. Flynn, and Raj Munshi. "Using dynamic treatment regimes to understand erythropoietin-stimulating agent hyporesponsiveness." Pediatric Nephrology 33, no. 8 (April 4, 2018): 1411–17. http://dx.doi.org/10.1007/s00467-018-3948-9.

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40

Ertefaie, Ashkan, Tianshuang Wu, Kevin G. Lynch, and Inbal Nahum-Shani. "Identifying a set that contains the best dynamic treatment regimes." Biostatistics 17, no. 1 (August 3, 2015): 135–48. http://dx.doi.org/10.1093/biostatistics/kxv025.

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Abstract A dynamic treatment regime (DTR) is a treatment design that seeks to accommodate patient heterogeneity in response to treatment. DTRs can be operationalized by a sequence of decision rules that map patient information to treatment options at specific decision points. The sequential, multiple assignment, randomized trial (SMART) is a trial design that was developed specifically for the purpose of obtaining data that informs the construction of good (i.e. efficacious) decision rules. One of the scientific questions motivating a SMART concerns the comparison of multiple DTRs that are embedded in the design. Typical approaches for identifying the best DTRs involve all possible comparisons between DTRs that are embedded in a SMART, at the cost of greatly reduced power to the extent that the number of embedded DTRs (EDTRs) increase. Here, we propose a method that will enable investigators to use SMART study data more efficiently to identify the set that contains the most efficacious EDTRs. Our method ensures that the true best EDTRs are included in this set with at least a given probability. Simulation results are presented to evaluate the proposed method, and the Extending Treatment Effectiveness of Naltrexone SMART study data are analyzed to illustrate its application.
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41

Zhao, Ying-Qi, Donglin Zeng, Eric B. Laber, and Michael R. Kosorok. "New Statistical Learning Methods for Estimating Optimal Dynamic Treatment Regimes." Journal of the American Statistical Association 110, no. 510 (April 3, 2015): 583–98. http://dx.doi.org/10.1080/01621459.2014.937488.

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42

Murray, Thomas A., Ying Yuan, and Peter F. Thall. "A Bayesian Machine Learning Approach for Optimizing Dynamic Treatment Regimes." Journal of the American Statistical Association 113, no. 523 (July 3, 2018): 1255–67. http://dx.doi.org/10.1080/01621459.2017.1340887.

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43

Luckett, Daniel J., Eric B. Laber, Anna R. Kahkoska, David M. Maahs, Elizabeth Mayer-Davis, and Michael R. Kosorok. "Estimating Dynamic Treatment Regimes in Mobile Health Using V-Learning." Journal of the American Statistical Association 115, no. 530 (April 17, 2019): 692–706. http://dx.doi.org/10.1080/01621459.2018.1537919.

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44

Huang, Xuelin, Sangbum Choi, Lu Wang, and Peter F. Thall. "Optimization of multi-stage dynamic treatment regimes utilizing accumulated data." Statistics in Medicine 34, no. 26 (June 21, 2015): 3424–43. http://dx.doi.org/10.1002/sim.6558.

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45

Zhao, Ying‐Qi, Ruoqing Zhu, Guanhua Chen, and Yingye Zheng. "Constructing dynamic treatment regimes with shared parameters for censored data." Statistics in Medicine 39, no. 9 (April 30, 2020): 1250–63. http://dx.doi.org/10.1002/sim.8473.

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46

Sun, Hao, Ashkan Ertefaie, Xin Lu, and Brent A. Johnson. "Improved Doubly Robust Estimation in Marginal Mean Models for Dynamic Regimes." Journal of Causal Inference 8, no. 1 (January 1, 2020): 300–314. http://dx.doi.org/10.1515/jci-2020-0015.

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Abstract Doubly robust (DR) estimators are an important class of statistics derived from a theory of semiparametric efficiency. They have become a popular tool in causal inference, including applications to dynamic treatment regimes. The doubly robust estimators for the mean response to a dynamic treatment regime may be conceived through the augmented inverse probability weighted (AIPW) estimating function, defined as the sum of the inverse probability weighted (IPW) estimating function and an augmentation term. The IPW estimating function of the causal estimand via marginal structural model is defined as the complete-case score function for those subjects whose treatment sequence is consistent with the dynamic regime in question divided by the probability of observing the treatment sequence given the subject's treatment and covariate histories. The augmentation term is derived by projecting the IPW estimating function onto the nuisance tangent space and has mean-zero under the truth. The IPW estimator of the causal estimand is consistent if (i) the treatment assignment mechanism is correctly modeled and the AIPW estimator is consistent if either (i) is true or (ii) nested functions of intermediate and final outcomes are correctly modeled. Hence, the AIPW estimator is doubly robust and, moreover, the AIPW is semiparametric efficient if both (i) and (ii) are true simultaneously. Unfortunately, DR estimators can be inferior when either (i) or (ii) is true and the other false. In this case, the misspecified parts of the model can have a detrimental effect on the variance of the DR estimator. We propose an improved DR estimator of causal estimand in dynamic treatment regimes through a technique originally developed by [4] which aims to mitigate the ill-effects of model misspecification through a constrained optimization. In addition to solving a doubly robust system of equations, the improved DR estimator simultaneously minimizes the asymptotic variance of the estimator under a correctly specified treatment assignment mechanism but misspecification of intermediate and final outcome models. We illustrate the desirable operating characteristics of the estimator through Monte Carlo studies and apply the methods to data from a randomized study of integrilin therapy for patients undergoing coronary stent implantation. The methods proposed here are new and may be used to further improve personalized medicine, in general.
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47

Laber, Eric B., and Marie Davidian. "Dynamic treatment regimes, past, present, and future: A conversation with experts." Statistical Methods in Medical Research 26, no. 4 (May 8, 2017): 1605–10. http://dx.doi.org/10.1177/0962280217708661.

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We asked three leading researchers in the area of dynamic treatment regimes to share their stories on how they became interested in this topic and their perspectives on the most important opportunities and challenges for the future.
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48

Chakraborty, Bibhas. "Dynamic Treatment Regimes for Managing Chronic Health Conditions: A Statistical Perspective." American Journal of Public Health 101, no. 1 (January 2011): 40–45. http://dx.doi.org/10.2105/ajph.2010.198937.

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49

Fan, Yanqin, Ming He, Liangjun Su, and Xiao‐Hua Zhou. "A smoothed Q ‐learning algorithm for estimating optimal dynamic treatment regimes." Scandinavian Journal of Statistics 46, no. 2 (December 26, 2018): 446–69. http://dx.doi.org/10.1111/sjos.12359.

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50

Xu, Yanxun, Peter Müller, Abdus S. Wahed, and Peter F. Thall. "Bayesian Nonparametric Estimation for Dynamic Treatment Regimes With Sequential Transition Times." Journal of the American Statistical Association 111, no. 515 (July 2, 2016): 921–50. http://dx.doi.org/10.1080/01621459.2015.1086353.

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