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We consider the effects of parameter uncertainty on the optimal radiation schedule in the context of the linear-quadratic model. Our interest arises from the observation that if inter-patient variations in OAR and tumor sensitivities to…
Two commonly used methods for improving precision and power in clinical trials are stratified randomization and covariate adjustment. However, many trials do not fully capitalize on the combined precision gains from these two methods, which…
With the emergence of precision medicine, estimating optimal individualized decision rules (IDRs) has attracted tremendous attention in many scientific areas. Most existing literature has focused on finding optimal IDRs that can maximize…
This paper proposes a novel criterion for the allocation of patients in Phase~I dose-escalation clinical trials aiming to find the maximum tolerated dose (MTD). Conventionally, using a model-based approach the next patient is allocated to…
We conduct a theoretical study of various solution methods for the adaptive fractionation problem. The two messages of this paper are: (i) dynamic programming (DP) is a useful framework for adaptive radiation therapy, particularly adaptive…
In developing products for rare diseases, statistical challenges arise due to the limited number of patients available for participation in drug trials and other clinical research. Bayesian adaptive clinical trial designs offer the…
Multi-arm trials are gaining interest in practice given the statistical and logistical advantages they can offer. The standard approach uses a fixed allocation ratio, but there is a call for making it adaptive and skewing the allocation of…
We consider the tuning parameter selection rules for nuclear norm regularized multivariate linear regression (NMLR) in high-dimensional setting. High-dimensional multivariate linear regression is widely used in statistics and machine…
Item response theory (IRT) is the statistical paradigm underlying a dominant family of generative probabilistic models for test responses, used to quantify traits in individuals relative to target populations. The graded response model…
When numerically solving partial differential equations, for a given problem and operating condition, adaptive mesh refinement (AMR) has proven its efficiency to automatically build a discretization achieving a prescribed accuracy at low…
Covariate-adjusted response-adaptive (CARA) designs have gained widespread adoption for their clear benefits in enhancing experimental efficiency and participant welfare. These designs dynamically adjust treatment allocations during interim…
Incentive design constitutes a foundational paradigm for influencing the behavior of strategic agents, wherein a system planner (principal) publicly commits to an incentive mechanism designed to align individual objectives with collective…
The optimal prophylaxis, and treatment if the prophylaxis fails, for a disease may be best evaluated using a sequential multiple assignment randomised trial (SMART). A SMART is a multi-stage study that randomises a participant to an initial…
This work considers the problem of binary classification: given training data $x_1, \dots, x_n$ from a certain population, together with associated labels $y_1,\dots, y_n \in \left\{0,1 \right\}$, determine the best label for an element $x$…
The choice of the parameter value for regularized inverse problems is critical to the results and remains a topic of interest. This article explores a criterion for selecting a good parameter value by maximizing the probability of the data,…
Self-Taught Reasoners (STaR), synonymously known as Rejection sampling Fine-Tuning (RFT), is an integral part of the training pipeline of self-improving reasoning Language Models (LMs). The self-improving mechanism often employs random…
One primary goal of precision medicine is to estimate the individualized treatment rules (ITRs) that optimize patients' health outcomes based on individual characteristics. Health studies with multiple treatments are commonly seen in…
Sequential multiple assignment randomized trials (SMARTs) have grown in popularity in recent years, and many of their study protocols propose conducting a cost effectiveness analysis of the adaptive strategies embedded within them. The cost…
Sequential Multiple Assignment Randomized Trials (SMARTs) are considered the gold standard for estimation and evaluation of treatment regimes. SMARTs are typically sized to ensure sufficient power for a simple comparison, e.g., the…
Recent development in the data-driven decision science has seen great advances in individualized decision making. Given data with individual covariates, treatment assignments and outcomes, policy makers best individualized treatment rule…