Hypothesis Testing and Adaptive Treatment Strategies S.A. Murphy SCT May 2007.

Slides:



Advertisements
Similar presentations
Piloting and Sizing Sequential Multiple Assignment Randomized Trials in Dynamic Treatment Regime Development 2012 Atlantic Causal Inference Conference.
Advertisements

Treatment Effect Heterogeneity & Dynamic Treatment Regime Development S.A. Murphy.
11 Confidence Intervals, Q-Learning and Dynamic Treatment Regimes S.A. Murphy Time for Causality – Bristol April, 2012 TexPoint fonts used in EMF. Read.
Inference for Clinical Decision Making Policies D. Lizotte, L. Gunter, S. Murphy INFORMS October 2008.
Using Clinical Trial Data to Construct Policies for Guiding Clinical Decision Making S. Murphy & J. Pineau American Control Conference Special Session.
Experimenting to Improve Clinical Practice S.A. Murphy AAAS, 02/15/13 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.:
1 Dynamic Treatment Regimes Advances and Open Problems S.A. Murphy ICSPRAR-2008.
Methodology for Adaptive Treatment Strategies for Chronic Disorders: Focus on Pain S.A. Murphy NIH Pain Consortium 5 th Annual Symposium on Advances in.
Experiments and Dynamic Treatment Regimes S.A. Murphy Univ. of Michigan JSM: August, 2005.
SMART Designs for Constructing Adaptive Treatment Strategies S.A. Murphy 15th Annual Duke Nicotine Research Conference September, 2009.
Dynamic Treatment Regimes, STAR*D & Voting D. Lizotte, E. Laber & S. Murphy LSU ---- Geaux Tigers! April 2009.
Substance Abuse, Multi-Stage Decisions, Generalization Error How are they connected?! S.A. Murphy Univ. of Michigan CMU, Nov., 2004.
An Experimental Paradigm for Developing Dynamic Treatment Regimes S.A. Murphy Univ. of Michigan March, 2004.
Constructing Dynamic Treatment Regimes & STAR*D S.A. Murphy ICSA June 2008.
Screening Experiments for Developing Dynamic Treatment Regimes S.A. Murphy At ICSPRAR January, 2008.
SMART Designs for Developing Adaptive Treatment Strategies S.A. Murphy K. Lynch, J. McKay, D. Oslin & T.Ten Have CPDD June, 2005.
Dynamic Treatment Regimes: Challenges in Data Analysis S.A. Murphy Survey Research Center January, 2009.
Q-Learning and Dynamic Treatment Regimes S.A. Murphy Univ. of Michigan IMS/Bernoulli: July, 2004.
1 A Prediction Interval for the Misclassification Rate E.B. Laber & S.A. Murphy.
Sizing a Trial for the Development of Adaptive Treatment Strategies Alena I. Oetting The Society for Clinical Trials, 29th Annual Meeting St. Louis, MO.
Screening Experiments for Dynamic Treatment Regimes S.A. Murphy At ENAR March, 2008.
Experiments and Dynamic Treatment Regimes S.A. Murphy Univ. of Michigan Florida: January, 2006.
Hypothesis Testing and Dynamic Treatment Regimes S.A. Murphy Schering-Plough Workshop May 2007 TexPoint fonts used in EMF. Read the TexPoint manual before.
An Experimental Paradigm for Developing Adaptive Treatment Strategies S.A. Murphy Univ. of Michigan UNC: November, 2003.
1 A Confidence Interval for the Misclassification Rate S.A. Murphy & E.B. Laber.
Experiments and Dynamic Treatment Regimes S.A. Murphy Univ. of Michigan PSU, October, 2005 In Honor of Clifford C. Clogg.
Planning Survival Analysis Studies of Dynamic Treatment Regimes Z. Li & S.A. Murphy UNC October, 2009.
Statistical Issues in Developing Adaptive Treatment Strategies for Chronic Disorders S.A. Murphy Univ. of Michigan CDC/ATSDR: March, 2005.
SMART Experimental Designs for Developing Adaptive Treatment Strategies S.A. Murphy RWJ Clinical Scholars Program, UMich April, 2007.
Hypothesis Testing and Dynamic Treatment Regimes S.A. Murphy, L. Gunter & B. Chakraborty ENAR March 2007.
Dynamic Treatment Regimes, STAR*D & Voting D. Lizotte, E. Laber & S. Murphy ENAR March 2009.
Methodology for Adaptive Treatment Strategies R21 DA S.A. Murphy For MCATS Oct. 8, 2009.
An Experimental Paradigm for Developing Adaptive Treatment Strategies S.A. Murphy Univ. of Michigan ACSIR, July, 2003.
Dynamic Treatment Regimes, STAR*D & Voting D. Lizotte, E. Laber & S. Murphy Psychiatric Biostatistics Symposium May 2009.
An Experimental Paradigm for Developing Adaptive Treatment Strategies S.A. Murphy Univ. of Michigan February, 2004.
Experiments and Dynamic Treatment Regimes S.A. Murphy Univ. of Michigan Yale: November, 2005.
Methods for Estimating the Decision Rules in Dynamic Treatment Regimes S.A. Murphy Univ. of Michigan IBC/ASC: July, 2004.
1 Possible Roles for Reinforcement Learning in Clinical Research S.A. Murphy November 14, 2007.
Experiments and Dynamic Treatment Regimes S.A. Murphy Univ. of Michigan April, 2006.
SMART Designs for Developing Dynamic Treatment Regimes S.A. Murphy MD Anderson December 2006.
Exploratory Analyses Aimed at Generating Proposals for Individualizing and Adapting Treatment S.A. Murphy BPRU, Hopkins September 22, 2009.
SMART Experimental Designs for Developing Adaptive Treatment Strategies S.A. Murphy ISCTM, 2007.
1 A Prediction Interval for the Misclassification Rate E.B. Laber & S.A. Murphy.
1 Section IV Study Designs for Investigating Adaptive Treatment Strategies Murphy.
Experiments and Adaptive Treatment Strategies S.A. Murphy Univ. of Michigan Chicago: May, 2005.
Susan Murphy, PI University of Michigan Acknowledgements: MCAT network and NIH The Goal To facilitate methodological collaborations necessary for producing.
SMART Designs for Developing Dynamic Treatment Regimes S.A. Murphy Symposium on Causal Inference Johns Hopkins, January, 2006.
Experiments and Dynamic Treatment Regimes S.A. Murphy At NIAID, BRB December, 2007.
1 Machine/Reinforcement Learning in Clinical Research S.A. Murphy May 19, 2008.
Adaptive Treatment Strategies S.A. Murphy CCNIA Proposal Meeting 2008.
Adaptive Treatment Strategies S.A. Murphy Workshop on Adaptive Treatment Strategies Convergence, 2008.
Practical Application of Adaptive Treatment Strategies in Trial Design and Analysis S.A. Murphy Center for Clinical Trials Network Classroom Series April.
Experiments and Dynamic Treatment Regimes S.A. Murphy Univ. of Michigan January, 2006.
Revisiting an Old Topic: Probability of Replication D. Lizotte, E. Laber & S. Murphy Johns Hopkins Biostatistics September 23, 2009.
1 Variable Selection for Tailoring Treatment S.A. Murphy, L. Gunter & J. Zhu May 29, 2008.
Adaptive Treatment Strategies: Challenges in Data Analysis S.A. Murphy NY State Psychiatric Institute February, 2009.
Sample size calculations
Sequential, Multiple Assignment, Randomized Trials and Treatment Policies S.A. Murphy UAlberta, 09/28/12 TexPoint fonts used in EMF. Read the TexPoint.
Overview of Adaptive Treatment Regimes Sachiko Miyahara Dr. Abdus Wahed.
Sequential, Multiple Assignment, Randomized Trials and Treatment Policies S.A. Murphy MUCMD, 08/10/12 TexPoint fonts used in EMF. Read the TexPoint manual.
Simulation is the process of studying the behavior of a real system by using a model that replicates the behavior of the system under different scenarios.
Confidence intervals and hypothesis testing Petter Mostad
통계적 추론 (Statistical Inference) 삼성생명과학연구소 통계지원팀 김선우 1.
Motivation Using SMART research designs to improve individualized treatments Alena Scott 1, Janet Levy 3, and Susan Murphy 1,2 Institute for Social Research.
Sample Size Determination
An Experimental Paradigm for Developing Adaptive Treatment Strategies S.A. Murphy NIDA Meeting on Treatment and Recovery Processes January, 2004.
Statistical Inference Statistical inference is concerned with the use of sample data to make inferences about unknown population parameters. For example,
SMART Trials for Developing Adaptive Treatment Strategies S.A. Murphy Workshop on Adaptive Treatment Designs NCDEU, 2006.
Educational Research Inferential Statistics Chapter th Chapter 12- 8th Gay and Airasian.
Sample Size Determination
Presentation transcript:

Hypothesis Testing and Adaptive Treatment Strategies S.A. Murphy SCT May 2007

2 Collaborators Lacey Gunter A. John Rush Bibhas Chakraborty

3 Outline Adaptive treatment strategies Constructing and addressing questions regarding an optimal adaptive treatment strategy A solution to non-regularity? Example using STAR*D.

4 Adaptive treatment strategies are individually tailored treatments, with treatment type and dosage changing according to patient outcomes. Operationalize clinical practice. k Stages for one individual Observation available at j th stage Action at j th stage (usually a treatment)

5 Goal : Construct decision rules that input information available at each stage and output a recommended decision; these decision rules should lead to a maximal mean Y where Y is a function of The adaptive treatment strategy is the sequence of two decision rules: k=2 Stages

6 Data for Constructing the Adaptive Treatment Strategy: Subject data from sequential, multiple assignment, randomized trials. At each stage subjects are randomized among alternative options. A j is a randomized action with known randomization probability. binary actions with P[A j =1]=P[A j =-1]=.5

7

8 A natural approach: Myopic Decisions Evaluate each stage of treatment in isolation; the dependent variable is 1 if remission in that stage, 0 otherwise. In stage 3 there are two treatment actions for those who prefer a switch in treatment (Mirtazapine or Nortriptyline) and two treatment actions for those who prefer an augment (Lithium or Thyroid). Compare the two switches in treatment according to the remission rate achieved by end of stage 3. Do the same for the two augments.

9 Need an alternative This is not a good idea if we want to evaluate the sequence of treatments (e.g. adaptive treatment strategies). Some of the stage 3 non-remitters went on to have a remission in stage 4; these people have an dependent variable equal to 0 in the myopic analysis. the remission or lack of remission in stage 4 may be partially attributable to the stage 3 treatment. Patching together the separate analyses of the stages requires unnecessary causal assumptions.

10 Need an alternative for the stage 3 dependent variable What should the value of the stage 3 dependent variable be for those that move to stage 4? We should not use a stage 3 dependent variable of Y=1 for those people who remit in stage 4. We should not use an stage 3 dependent variable of Y=0 for those people who remit in stage 4. The dependent variable should be something in between.

11 Regression-based methods for constructing decision rules Q-Learning (Watkins, 1989) (a popular method from computer science) A-Learning or optimal nested structural mean model (Murphy, 2003; Robins, 2004) The first method is an inefficient version of the second method when each stages’ covariates include the prior stages’ covariates and the actions are coded to have conditional mean zero.

12 There is a regression for each stage. A Simple Version of Q-Learning – Stage 4 regression: Regress Y on to obtain Stage 3 regression: Regress on to obtain

13 for patients entering stage 4: is the estimated probability of remission in stage 4 as a function of variables that may include or be affected by stage 3 treatment. is the estimated probability of remission assuming the “best” treatment is provided at stage 4 (note max in formula). will be the dependent variable in the stage 3 regression for patients moving to stage 4

14 A Simple Version of Q-Learning – Stage 4 regression, (using Y as dependent variable) yields Stage 3 regression, (using as dependent variable) yields

15 Decision Rules:

16 Non-regularity

17 Non-regularity

18 Non-regularity – Replace hard-max by soft-max

19 STAR*D Stages 3 & 4 Regression at stage 3: α 3 T S 3 ' + β 3 T S 3 A 3 S 3 ' = (1, X 3 ) X 3 is a vector of variables available at or prior to stage 3 S 3 = ((1-Aug), Aug, Aug*Qids 2 ) We are interested in the β 3 coefficients as these are used to form the decision rule at stage 3.

20 STAR*D Stages 3 & 4 Decision Rule at stage 3: If patient prefers a Switch then if offer Mirtazapine, otherwise offer Nortriptyline. If patient prefers an Augment then if offer Lithium, otherwise offer Thyroid Hormone.

21 STAR*D Stages 3 & 4 Regression at stage 4: α 4 T S 4 ' + β 4 S 4 A 4 S 4 ' =(1,X 4, (1-Aug)*A 3, Aug*A 3, Aug*A 3 *Qids 2 ), (X 4 is a vector of variables available at or prior to stage 4, Aug is 1 if patient preference is augment and 0 otherwise) S 4 = 1 Decision rule: Choose TCP if, otherwise offer Mirtazapine + Venlafaxine XR

22 Switch-.11(.07)-1.6 Augment.47(.25)1.9 Augment*QIDS (.02)-2.3 Stage 3 Coefficients

23

24 = means not significant in two sided test at.05 level < means significant in two sided test at.05 level

25 Discussion We replace the hypothesis test concerning a non- regular parameter, β 3 by a hypothesis test concerning a near-by regular parameter. These multi-stage regression methods need to be generalized to survival analysis. This is work in progress!

26 Discussion Robins (2004) proposes several conservative confidence intervals for β 3. Ideally to decide if the two stage 3 treatments are equivalent, we would evaluate whether the choice of stage 3 treatment influences the mean outcome resulting from the use of the adaptive treatment strategy. We did not do this here. Constructing “evidence-based” strategies is of great interest in clinical research and there is much to be done by statisticians.

27 This seminar can be found at: seminars/SCT0507.ppt me with questions or if you would like a copy!

28