Ailin Fan

Precision medicine is a medical paradigm that focuses on finding the most effective treatment decision based on individual patient information. For many complex diseases, such as cancer, treatment decisions need to be tailored over time according to patients’ responses to previous treatments. Such an adaptive strategy is referred as a dynamic treatment regime. A major challenge in deriving an optimal dynamic treatment regime arises when an extraordinary large number of prognostic factors, such as patient’s genetic information, demographic characteristics, medical history and clinical measurements over time are available, but not all of them are necessary for making treatment decision. This makes variable selection an emerging need in precision medicine. In this paper, we propose a penalized multi-stage $A$-learning for deriving the optimal dynamic treatment regime when the number of covariates is of the nonpolynomial (NP) order of the sample size. To preserve the double robustness property of the $A$-learning method, we adopt the Dantzig selector, which directly penalizes the A-leaning estimating equations. Oracle inequalities of the proposed estimators for the parameters in the optimal dynamic treatment regime and error bounds on the difference between the value functions of the estimated optimal dynamic treatment regime and the true optimal dynamic treatment regime are established. Empirical performance of the proposed approach is evaluated by simulations and illustrated with an application to data from the STAR∗D study.

We propose a systematic method for testing and identifying a subgroup with an enhanced treatment effect. We adopts a change-plane technique to first test the existence of a subgroup, and then identify the subgroup if the null hypothesis on nonexistence of such a subgroup is rejected. A semiparametric model is considered for the response with an unspecified baseline function and an interaction between a subgroup indicator and treatment. A doubly robust test statistic is constructed based on this model, and asymptotic distributions of the test statistic under both null and local alternative hypotheses are derived. Moreover, a sample size calculation method for subgroup detection is developed based on the proposed statistic. The finite sample performance of the proposed test is evaluated via simulations. Finally, the proposed methods for subgroup identification and sample size calculation are applied to a data from an AIDS study.

ASTM Standard E2810 provides a methodology for establishing confidence in passing the USP Uniformity of Dosage Units (UDU) test, and provides acceptance limits for sample means and standard deviations that can be used as elements of lot release. These acceptance limits are quite conservative, however, due to both the nature and shape of an inverted triangular joint confidence region for the lot mean and standard deviation. We obtain improved (wider) acceptance limits by using a Bayesian approach that focuses on the posterior distribution of the probability of passing the USP UDU test. The Bayesian approach has good sampling properties, and the improvement in acceptance limits can be considerable. For example, for sample size of 10 units and sample means between 97 and 103, the Bayesian approach results in acceptance limits for sample standard deviations that are at least 25% greater than those in E2810. The impact of the improved acceptance limits is illustrated with operating characteristic curves.