title: Bayesian Nonparametric Estimation for Dynamic Treatment Regimes with Sequential Transition Times.
abstract: We analyze a dataset arising from a clinical trial involving multi-stage chemotherapy regimes for acute leukemia. The trial design was a 2 × 2 factorial for frontline therapies only. Motivated by the idea that subsequent salvage treatments affect survival time, we model therapy as a dynamic treatment regime (DTR), that is, an alternating sequence of adaptive treatments or other actions and transition times between disease states. These sequences may vary substantially between patients, depending on how the regime plays out. To evaluate the regimes, mean overall survival time is expressed as a weighted average of the means of all possible sums of successive transitions times. We assume a Bayesian nonparametric survival regression model for each transition time, with a dependent Dirichlet process prior and Gaussian process base measure (DDP-GP). Posterior simulation is implemented by Markov chain Monte Carlo (MCMC) sampling. We provide general guidelines for constructing a prior using empirical Bayes methods. The proposed approach is compared with inverse probability of treatment weighting, including a doubly robust augmented version of this approach, for both single-stage and multi-stage regimes with treatment assignment depending on baseline covariates. The simulations show that the proposed nonparametric Bayesian approach can substantially improve inference compared to existing methods. An R program for implementing the DDP-GP-based Bayesian nonparametric analysis is freely available at https://www.ma.utexas.edu/users/yxu/.
authors.affiliation: Division of Statistics and Scientific Computing, The University of Texas at Austin, Austin, TX.
authors.forename: Yanxun
authors.initials: Y
authors.lastname: Xu
authors.affiliation: Department of Mathematics, The University of Texas at Austin, Austin, TX.
authors.forename: Peter
authors.initials: P
authors.lastname: Müller
authors.affiliation: Department of Biostatistics, University of Pittsburgh, Pittsburgh, PA.
authors.forename: Abdus S
authors.initials: AS
authors.lastname: Wahed
authors.affiliation: Department of Biostatistics, The University of Texas M.D. Anderson Cancer Center, Houston, TX.
authors.forename: Peter F
authors.initials: PF
authors.lastname: Thall
keywords: Dependent Dirichlet process; G-Computation; Gaussian process; In-verse probability of treatment weighting; Markov chain Monte Carlo