In this work, we study the optimal design of two-armed clinical trials to maximize the accuracy of parameter estimation in a statistical model, where the interaction between patient covariates and treatment are explicitly incorporated to enable precision medication decisions. Such a modeling extension leads to significant complexities for the produced optimization problems because they include optimization over design and covariates concurrently. We take a min-max optimization model and minimize (over design) the maximum (over population) variance of the estimated interaction effect between treatment and patient covariates. This results in a min-max bilevel mixed integer nonlinear programming problem, which is notably challenging to solve. To address this challenge, we introduce a surrogate optimization model by approximating the objective function, for which we propose two solution approaches. The first approach provides an exact solution based on reformulation and decomposition techniques. In the second approach, we provide a lower bound for the inner optimization problem and solve the outer optimization problem over the lower bound. We test our proposed algorithms with synthetic and real-world data sets and compare them with standard (re)randomization methods. Our numerical analysis suggests that the proposed approaches provide higher-quality solutions in terms of the variance of estimators and probability of correct selection. We also show the value of covariate information in precision medicine clinical trials by comparing our proposed approaches to an alternative optimal design approach that does not consider the interaction terms between covariates and treatment. Summary of Contribution: Precision medicine is the future of healthcare where treatment is prescribed based on each patient information. Designing precision medicine clinical trials, which are the cornerstone of precision medicine, is extremely challenging because sample size is limited and patient information may be multidimensional. This work proposes a novel approach to optimally estimate the treatment effect for each patient type in a two-armed clinical trial by reducing the largest variance of personalized treatment effect. We use several statistical and optimization techniques to produce efficient solution methodologies. Results have the potential to save countless lives by transforming the design and implementation of future clinical trials to ensure the right treatments for the right patients. Doing so will reduce patient risks and reduce costs in the healthcare system.
more »
« less
Optimal Design of Controlled Experiments for Personalized Decision Making in the Presence of Observational Covariates
Controlled experiments are widely applied in many areas such as clinical trials or user behavior studies in IT companies. Recently, it is popular to study experimental design problems to facilitate personalized decision making. In this paper, we investigate the problem of optimal design of multiple treatment allocation for personalized decision making in the presence of observational covariates associated with experimental units (often, patients or users). We assume that the response of a subject assigned to a treatment follows a linear model which includes the interaction between covariates and treatments to facilitate precision decision making. We define the optimal objective as the maximum variance of estimated personalized treatment effects over different treatments and different covariates values. The optimal design is obtained by minimizing this objective. Under a semi-definite program reformulation of the original optimization problem, we use a YALMIP and MOSEK based optimization solver to provide the optimal design. Numerical studies are provided to assess the quality of the optimal design.
more »
« less
- Award ID(s):
- 1651912
- PAR ID:
- 10397881
- Date Published:
- Journal Name:
- The New England Journal of Statistics in Data Science
- ISSN:
- 2693-7166
- Page Range / eLocation ID:
- 1 to 8
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
more » « less
Personalized optimal decision making, finding the optimal decision rule (ODR) based on individual characteristics, has attracted increasing attention recently in many fields, such as education, economics, and medicine. Current ODR methods usually require the primary outcome of interest in samples for assessing treatment effects, namely, the experimental sample. However, in many studies, treatments may have a long‐term effect, and as such, the primary outcome of interest cannot be observed in the experimental sample due to the limited duration of experiments, which makes the estimation of ODR impossible. This paper is inspired to address this challenge by making use of an auxiliary sample to facilitate the estimation of ODR in the experimental sample. We propose an auGmented inverse propensity weighted Experimental and Auxiliary sample‐based decision Rule (GEAR) by maximizing the augmented inverse propensity weighted value estimator over a class of decision rules using the experimental sample, with the primary outcome being imputed based on the auxiliary sample. The asymptotic properties of the proposed GEAR estimators and their associated value estimators are established. Simulation studies are conducted to demonstrate its empirical validity with a real AIDS application.
-
We study the problem of learning to choose from $m$ discrete treatment options (e.g., news item or medical drug) the one with best causal effect for a particular instance (e.g., user or patient) where the training data consists of passive observations of covariates, treatment, and the outcome of the treatment. The standard approach to this problem is regress and compare: split the training data by treatment, fit a regression model in each split, and, for a new instance, predict all $m$ outcomes and pick the best. By reformulating the problem as a single learning task rather than $m$ separate ones, we propose a new approach based on recursively partitioning the data into regimes where different treatments are optimal. We extend this approach to an optimal partitioning approach that finds a globally optimal partition, achieving a compact, interpretable, and impactful personalization model. We develop new tools for validating and evaluating personalization models on observational data and use these to demonstrate the power of our novel approaches in a personalized medicine and a job training application.more » « less
-
Suppose an online platform wants to compare a treatment and control policy (e.g., two different matching algorithms in a ridesharing system, or two different inventory management algorithms in an online retail site). Standard experimental approaches to this problem are biased (due to temporal interference between the policies), and not sample efficient. We study optimal experimental design for this setting. We view testing the two policies as the problem of estimating the steady state difference in reward between two unknown Markov chains (i.e., policies). We assume estimation of the steady state reward for each chain proceeds via nonparametric maximum likelihood, and search for consistent (i.e., asymptotically unbiased) experimental designs that are efficient (i.e., asymptotically minimum variance). Characterizing such designs is equivalent to a Markov decision problem with a minimum variance objective; such problems generally do not admit tractable solutions. Remarkably, in our setting, using a novel application of classical martingale analysis of Markov chains via Poisson's equation, we characterize efficient designs via a succinct convex optimization problem. We use this characterization to propose a consistent, efficient online experimental design that adaptively samples the two Markov chains.more » « less
-
The activity that most distinguishes engineering from mathematics and the physical sciences is the design of technologically challenging devices, products and systems. But, while ABET recognizes design as a decision-making process, our current educational system treats engineers as problem-solvers and delivers a largely deterministic treatment of the sciences. Problem solving and decision making involve significantly different considerations, not the least of which is that all decision-making is done under uncertainty and risk. Secondly, effective choices among design alternatives demand an understanding of the mathematics of decision making, which rarely appears in engineering curricula. Specifically, we teach the sciences but not how to use them. Decision makers typically earn 50-200 percent more than problem-solvers. The objective of this paper is to make the case that this gap in engineering education lowers the value of an engineering education for both the students and the faculty, and to provide suggestions on how to fix it.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.51387/23-NEJSDS22
