68 research outputs found
Q-learning with censored data
We develop methodology for a multistage decision problem with flexible number
of stages in which the rewards are survival times that are subject to
censoring. We present a novel Q-learning algorithm that is adjusted for
censored data and allows a flexible number of stages. We provide finite sample
bounds on the generalization error of the policy learned by the algorithm, and
show that when the optimal Q-function belongs to the approximation space, the
expected survival time for policies obtained by the algorithm converges to that
of the optimal policy. We simulate a multistage clinical trial with flexible
number of stages and apply the proposed censored-Q-learning algorithm to find
individualized treatment regimens. The methodology presented in this paper has
implications in the design of personalized medicine trials in cancer and in
other life-threatening diseases.Comment: Published in at http://dx.doi.org/10.1214/12-AOS968 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
A Quantile Regression Model for Failure-Time Data with Time-Dependent Covariates
Since survival data occur over time, often important covariates that we wish
to consider also change over time. Such covariates are referred as
time-dependent covariates. Quantile regression offers flexible modeling of
survival data by allowing the covariates to vary with quantiles. This paper
provides a novel quantile regression model accommodating time-dependent
covariates, for analyzing survival data subject to right censoring. Our simple
estimation technique assumes the existence of instrumental variables. In
addition, we present a doubly-robust estimator in the sense of Robins and
Rotnitzky (1992). The asymptotic properties of the estimators are rigorously
studied. Finite-sample properties are demonstrated by a simulation study. The
utility of the proposed methodology is demonstrated using the Stanford heart
transplant dataset
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