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SAMSI Tutorial on Dynamic Treatment Regimes by Anastasios Tsiatis

SAMSI Tutorial on Dynamic Treatment Regimes by Anastasios Tsiatis. Dr. Gong Tang Wentao Feng Sachiko Miyahara. Introduction. Goal of Physicians : To give treatment to patients over time that will result in as favorable a clinical outcome as possible. Introduction (Cont.).

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SAMSI Tutorial on Dynamic Treatment Regimes by Anastasios Tsiatis

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  1. SAMSI Tutorial on Dynamic Treatment Regimes by Anastasios Tsiatis Dr. Gong Tang Wentao Feng Sachiko Miyahara

  2. Introduction Goal of Physicians: To give treatment to patients over time that will result in as favorable a clinical outcome as possible.

  3. Introduction (Cont.) When a new patient comes to a physician’s office, the physician needs to make many decisions such as: - Treatment Choice - Dose - When to switch => Complex and often difficult to know

  4. Goal of This Presentation To find the distribution of the responses, based on different treatment regimes, using observed data from: • a controlled intervention study • an observational study

  5. Notations For time point j= 0 to k, Lj = covariate information collected between time tj-1 and tj Aj = treatment assigned at time tj Y = Outcome

  6. Notations (Cont.) L0 L1 L2 Lk …… Ak Y …… A0 A1 A2 t0 t1 t2 tk

  7. Notations (cont.) = (L0, … Lj) The history of time dependent covariates = (A0, … Aj) The history of time dependent treatment decisions

  8. Treatment Regimes What is a treatment regime? an algorithm which dictates how each patient in the population treated possibly based on intervening covariate information. In formula: g(tj, ) = aj where and

  9. Treatment Regimes Example Example: HIV Study Let L1j = CD4 counts aj = 1 to give antiretroviral therapy 0 to not to give the therapy The treatment regime: g(tj, ) = I(CD4j <= 200)

  10. Methods What are the methods to estimate the distribution of Y for various g from the observed data? - G-computation algorithm - Inverse Probability Weighting Need to consider: 1. Concept of Potential Outcomes 2. Three assumptions

  11. Potential Outcomes • Denoted as Y*(g) • Y*( ) is the potential outcome of a randomly selected individual in our population if he/she hypothetically received treatment a0 at time t0, a1 at time t1…ak at time tk • L*( ) is also referred to as potential outcome • Also called “Counterfactuals”

  12. Potential Outcomes • The set of all potential outcomes denoted by: W ={L*0(g), L*1(g)… L*k(g), Y*(g)} where L*0(g) = L0 L*1(g) = L*1(g(t0, L0) … L*k(g) = L*k{g(t0, L0), …, g(tk-1, (g))} Y*(g) = Y*{g(t0, L0), …, g(tk-1, (g))}

  13. Three Assumptions 1. Consistency Assumptions 2. Sequential randomization assumption 3. Identification assumption

  14. 1. Consistency Assumptions • Assume: Y = Y*( ) Lk = L*( ) • In words, we assume that the potential outcome corresponds to observed outcome.

  15. 2. Sequential Randomization Assumption = No Unmeasured Confounder Assumption • Assume: {W _||_ Aj | ( , ) for all j = 0,…k} • In words, conditioning on the history of time dependent treatments and covariate information up to time tj, the treatment Aj is independent of the set of potential outcomes

  16. 3. Identification Assumption • Assume if every covariate-treatment history up to time tj that has a positive probability of observed, then there must be a positive probability that the corresponding treatment will be observed • Example: violated assumption case Lj shows an adverse event, so that no aj is given, then this assumption is violated.

  17. Purpose: To derive the distribution of potential outcomes From observed data: For example, if the potential outcome Y* is survival time, we may be interested in estimating or mean { }

  18. Inverse probability weighting

  19. Inverse weighting Inverse probability weighting (continued) The probability that a patient received regime is: So,

  20. Slide 27 of Tsiatis’s = Proof of consistency of inverse probability weighted estimator Consistency assumption =

  21. Defined by regime specify models G-computation algorithm

  22. Estimating procedure • Solve the estimating equation • to get the estimated parameters for the conditional distributions, • Then integrate out L’s to get the marginal distribution of • Compare the distribution of for different g’s.

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