This work proposes a model-based approach that optimizes model parameters, and evaluates first- and best-improvement algorithms, simulated annealing (SA), threshold accepting (TA), and two novel algorithms utilizing directional derivatives (dd) to guide exchanges.
Abstract
Because of time limitations or participation burden, the treatments in an experimental design can be too large for a single subject. Instead of addressing this using combinatorial incomplete block designs, we propose a model-based approach that optimizes model parameters. This offers distinct advantages: it incorporates subject-specific covariates to tailor treatment allocation to individual characteristics, allows for varying block sizes, and eliminates the equal-treatment replication requirement. Despite these benefits, model-based approaches are limited by a lack of software and prohibitively large search spaces, making exact optimization computationally intractable. Therefore, we present local search heuristic algorithms and compare them to existing methods. We evaluate first- and best-improvement algorithms, simulated annealing (SA), threshold accepting (TA), and two novel algorithms utilizing directional derivatives (dd) to guide exchanges. Serving as discrete versions of continuous gradient-based methods, these dd algorithms take smaller steps and avoid flat regions by prioritizing large-difference dd exchanges. Our broadly applicable approach uses item calibration in achievement tests as a comparative example to evaluate objective values and computational times. Results demonstrate that for larger problems, the dd algorithms achieve near-optimal solutions significantly faster than SA and TA. Due to computational efficiency, our algorithms offer a highly appealing approach for practical applications.
I study the optimal design and analysis of randomized experiments for estimating finite-population average treatment effects when potential outcomes are known to be bounded, as with binary outcomes. Among all assignment mechanisms and a broad class of affine estimators, worst-case mean-squared error (MSE) is minimized by independent random assignment and an unconventional regression of the support-midpoint-centered outcome on the recentered treatment, with no intercept. This contrasts with the usual prescription of balanced complete randomization and difference-in-means estimation: when outcomes are bounded, randomness in the realized treatment share is informative. The worst-case gain over full-sample complete randomization is asymptotically small, but gains can be first-order relative to other designs: complete within-pair randomization and pair-fixed-effect regression have twice the worst-case MSE. I extend the result to allow for arbitrary estimators. Independent random assignment remains optimal, and the generally-nonlinear optimal estimator can meaningfully reduce worst-case MSE.
The randomness, efficiency (power and variability), and desirable allocation proportions are important components for evaluating a response-adaptive design in clinical trials and conflicted demands in applications. The aim of this paper is to provide designs dealing with these dilemmas. We first give a general framework for efficient response-adaptive randomization procedures that attain the Cram\'er-Rao lower bounds of the allocation variances for any desired allocation proportions. The general framework is flexible for us to define new families of efficient designs with good properties for both two and multiple-treatment clinical trials. We also prove that, among all response-adaptive randomization procedures with the same limit allocation proportions, the selection biases and entropies as measures of the randomness of the designs have their optimal values. Basing on the theory on efficiency and randomness, we propose a new family of doubly adaptive biased coin designs for multi-treatment clinical trials that can target any allocation proportion and are asymptotically best in terms both the randomness and efficiency so that their randomness is asymptotic optimal and asymptotic allocation variance attains the Cram\'er-Rao lower bound. Theoretical properties, including the strong consistency, the asymptotic normality, and the functional central limit theorem for both the sample allocation proportions and the estimators of the distribution parameters, are developed by using the technique of Gaussian approximation and Gaussian comparing theorems.
Modern medical research, such as dose-finding studies, seamless trials, and shared control designs, often involves comparing multiple treatments simultaneously. Despite its wide applications, most research focuses on continuous endpoints, leaving the inference for general outcome types in high demand. In this article, we propose a new inference method for conducting multiple-treatment comparisons involving endpoints within the generalized linear model (GLM) framework under covariate-adaptive randomization (CAR). First, we investigate the asymptotic properties of the standard Wald z-statistics (z-scores) in multi-arm trials, highlighting issues when the working model is misspecified, particularly through omitted covariates. Our theoretical findings reveal that these \textcolor{black}{z-scores} do not consistently converge to a standard multivariate normal distribution, leading to either conservative or inflated Type I error rates, depending on the specific GLM endpoint. Second, based on these theoretical results, we develop adjusted test statistics to correct the distributional problems. To appropriately control the family-wise Type I error rate inherent in multi-arm comparisons, we incorporate our adjusted statistics with Simes-type multiple-testing procedures. This robust inference method can effectively control Type I error while potentially improving power. Extensive simulation studies and a real-world application to a metastatic breast cancer trial confirm the effectiveness and practicality of our approach.
The ranking and selection problem is a classic mathematical framework about identifying the best alternative from multiple alternatives through sampling them. However, the uncertainty about sampling distributions in the ranking and selection problem has been relatively overlooked, and related research is just starting to gain momentum recently. We propose a data-driven nonparametric tuning-free sequential budget allocation strategy under unknown light-tailed sampling distributions, which is theoretically proved to asymptotically achieve the exact large deviation–based optimal allocation as the sampling budget grows to infinity. Especially, we propose a new point estimation procedure for estimating the optimal large deviation rates in ranking and selection and theoretically demonstrate its validity.
History: Accepted by Bruno Tuffin, Area Editor for Simulation.
Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0895 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0895 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .
Yen-Chia Chen· INFORMS journal on computing· 0 citations
Sequential Multiple Assignment Randomized Trials (SMARTs) provide evidence for treatment sequences based on patient profiles, which is relevant in chronic disease settings. Sample size formulae implemented in calculators are the primary tool available to power SMARTs, though they require strong assumptions. We propose a simulation-based procedure omitting these assumptions, instead generating realistic synthetic SMART data by fitting models to real pilot data, to power SMARTs to compare treatment strategies. The proposed framework powers designs in two ways: by fixing the data generating mechanism and estimating effect size under different designs, or by fixing effect size and varying operational decisions within the SMART. Comparing our results to a calculator (SMARTsize), estimated sample sizes at varying power levels were similar at larger fixed effect sizes, whereas a discrepancy was apparent at smaller effect sizes due to differences between fixed and observed effect sizes in the simulated trials. The simulation-based procedure's ability to capture this effect size fluctuation is advantageous for smaller expected effect sizes, as it is essential to ensure adequate sample size to avoid a type II error. In providing flexible tools to power competing SMART designs, the full potential of SMARTs to build treatment sequences can be better realized.
Niki Z. Petrakos, Erica E. M. Moodie, Nicolas Savy et al.· 0 citations
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