Comparisons of Dynamic Treatment Regimes using Observational Data

Transcription

1 Comparisons of Dynamic Treatment Regimes using Observational Data Bryan Blette University of North Carolina at Chapel Hill 4/19/18 Blette (UNC) BIOS 740 Final Presentation 4/19/18 1 / 15

2 Overview 1 Motivation 2 Methods 3 Discussion Blette (UNC) BIOS 740 Final Presentation 4/19/18 2 / 15

3 Motivation Randomized trials such as SMARTs are the gold standard for comparing dynamic treatment regimes (DTR) However, some randomized trials may be impractical or unethical to implement In addition, complex observational data such as open medical records are becoming more accessible to researchers Blette (UNC) BIOS 740 Final Presentation 4/19/18 3 / 15

4 Motivation Finally, DTRs can be defined very specifically; something like determining the right dosage of a medication or the right level of a biomarker to indicate start of treatment can involve dozens of relevant cutoffs- too many to include in a typical randomized trial Observational data may be an overlooked tool in dealing with these issues and uncovering effective dynamic treatment regimes Blette (UNC) BIOS 740 Final Presentation 4/19/18 4 / 15

5 Methods First we consider the method described by Hernan et. al. in 2006 This paper represents a two regime problem- among HIV patients, should HAART therapy be initiated when CD4 counts drop below 500 cells/µl or when they drop below 200 cells/µl (i.e. which regime results in better 5 year AIDS-free survival) To answer this question, a database of 2344 HIV-infected patients who had never received HAART were followed after their first CD4 measurement below 500. Blette (UNC) BIOS 740 Final Presentation 4/19/18 5 / 15

6 Methods The basic strategy is summarized here: 1 Define regimes of interest 2 Artificially censor individuals when they stop following a regime of interest 3 Estimate IPW to adjust for potential selection biased introduced by censoring 4 Compare survival among regimes by fitting an IPW-adjusted Cox proportional-hazards model with an indicator for regime membership and baseline confounders as covariates Blette (UNC) BIOS 740 Final Presentation 4/19/18 6 / 15

7 Methods Let N(t) denote an indicator of artificial censoring by not following a regime, C(t) be an indicator of censoring by loss to follow-up, L(t) be history of time-varying covariate CD4, A indicate regime membership, and V denote baseline covariates The time varying weights for the Cox model are SW N SW C where each weight component is defined as follows: SW N (t) = t P (N(k)=0 C(k)=0,N(k 1)=0,A,V ) k=0 SW C (t) = t k=0 P (N(k)=0 L(k),C(k)=0,N(k 1)=0,A,V ) P (C(k+1)=0 N(k)=0,C(k)=0,A,V ) P (C(k+1)=0 L(k),C(k)=0,N(k)=0,A,V ) The numerators act to stabilize the weights and reduce the variance of the estimates of the Cox model parameters. Each numerator and denominator weight can be estimated via pooled logistic regression Blette (UNC) BIOS 740 Final Presentation 4/19/18 7 / 15

8 Methods Finally we use the estimated weights to fit a weighted Cox model: λ T (t A, V ) = λ 0 (t)exp{β 1 A + β 2 (V )} Note that this approach requires the following assumptions: No unmeasured baseline confounding No unmeasured time-dependent selection bias (data on all joint risk factors for mortality and treatment initiation was collected) No model misspecification Blette (UNC) BIOS 740 Final Presentation 4/19/18 8 / 15

9 Extend to n possible treatment regimes Now, we consider the method developed in Cain et. al. (2010) This paper extends the previous method to n possible regimes Here, we consider the same analysis as before but with 31 possible treatment regimes of the form initiate treatment when CD4 decreases below x where x ranges from 200 to 500 in increments of 10 While the example in Hernan et. al. (2006) could have been studied as a randomized trial, this example can really only be studied using observational data Blette (UNC) BIOS 740 Final Presentation 4/19/18 9 / 15

10 Extend to n possible treatment regimes The general strategy is the same as before, but with the additional complication that a patient may be following several regimes at the same time For example, someone who enters the study at CD4 of 352 and does not initiate treatment could be following any of 16 regimes (initiate below 350,340,...,200) This needs to be accounted for by either randomly allocating such patients to one of the regimes they follow, or by allowing patients to follow more than one regime by replicating each of those individuals in our dataset, and then artifically censoring each replicate whenever that patient stops following the corresponding regime The latter is the more statistically efficient approach Blette (UNC) BIOS 740 Final Presentation 4/19/18 10 / 15

11 Extend to n possible treatment regimes Blette (UNC) BIOS 740 Final Presentation 4/19/18 11 / 15

12 Extend to n possible treatment regimes Blette (UNC) BIOS 740 Final Presentation 4/19/18 12 / 15

13 Extend to n possible treatment regimes After the analysis dataset is constructed, selection bias due to artificial censoring can be accounted for using IPW, as before. In this example, weights were truncated for further stabilization. Finally, a weighted Cox model can be fit to compare the 31 regimes. Selected results from the paper are presented below: Blette (UNC) BIOS 740 Final Presentation 4/19/18 13 / 15

14 Discussion I have shown two methods to use observational data in order to emulate randomized trials and compare dynamic treatment regimes The second paper, Cain et. al. (2010), also describes comparing regimes of the form treatment is initiated m months after CD4 drops below x where the method presented today represents the case when m = 0 For a more thorough formulation of these concepts, see Dynamic Regime Marginal Structural Mean Models for Estimation of Optimal Dynamic Treatment Regimes parts 1 and 2, by Orellana, Rotnitsky, and Robins (2010) Blette (UNC) BIOS 740 Final Presentation 4/19/18 14 / 15

15 Discussion Although this method is powerful, it does depend on strong assumptions, as do all causal analyses of observational studies The conclusions drawn from these studies should be confirmed by trials when possible, to rule out potential issues such as the presence on unmeasured confounding that can be controlled for by randomization Since SMART trials can be quite expensive and time-consuming, it might be a good idea for researchers to explore potential trial regime arms using observational data and narrow down to promising arms before the trial begins, when possible This process can make the trials more efficient by eliminating arms that are not promising and can also act as a proof-of-concept when applying for funding to implement a SMART Blette (UNC) BIOS 740 Final Presentation 4/19/18 15 / 15

16 References 1 Hernn, M. A., Lanoy, E., Costagliola, D., & Robins, J. M. (2006). Comparison of dynamic treatment regimes via inverse probability weighting. Basic & clinical pharmacology & toxicology, 98(3), Cain, L. E., Robins, J. M., Lanoy, E., Logan, R., Costagliola, D., & Hernn, M. A. (2010). When to start treatment? A systematic approach to the comparison of dynamic regimes using observational data. The international journal of biostatistics, 6(2). 3 Orellana, L., Rotnitzky, A., & Robins, J. M. (2010). Dynamic regime marginal structural mean models for estimation of optimal dynamic treatment regimes, part I: main content. The international journal of biostatistics, 6(2). Blette (UNC) BIOS 740 Final Presentation 4/19/18 16 / 15