1
|
Watson SI, Girling A, Hemming K. Optimal study designs for cluster randomised trials: An overview of methods and results. Stat Methods Med Res 2023; 32:2135-2157. [PMID: 37802096 PMCID: PMC10683350 DOI: 10.1177/09622802231202379] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/08/2023]
Abstract
There are multiple possible cluster randomised trial designs that vary in when the clusters cross between control and intervention states, when observations are made within clusters, and how many observations are made at each time point. Identifying the most efficient study design is complex though, owing to the correlation between observations within clusters and over time. In this article, we present a review of statistical and computational methods for identifying optimal cluster randomised trial designs. We also adapt methods from the experimental design literature for experimental designs with correlated observations to the cluster trial context. We identify three broad classes of methods: using exact formulae for the treatment effect estimator variance for specific models to derive algorithms or weights for cluster sequences; generalised methods for estimating weights for experimental units; and, combinatorial optimisation algorithms to select an optimal subset of experimental units. We also discuss methods for rounding experimental weights, extensions to non-Gaussian models, and robust optimality. We present results from multiple cluster trial examples that compare the different methods, including determination of the optimal allocation of clusters across a set of cluster sequences and selecting the optimal number of single observations to make in each cluster-period for both Gaussian and non-Gaussian models, and including exchangeable and exponential decay covariance structures.
Collapse
|
2
|
Watson SI, Pan Y. Evaluation of combinatorial optimisation algorithms for c-optimal experimental designs with correlated observations. STATISTICS AND COMPUTING 2023; 33:112. [PMID: 37525745 PMCID: PMC10386961 DOI: 10.1007/s11222-023-10280-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/19/2022] [Accepted: 07/03/2023] [Indexed: 08/02/2023]
Abstract
We show how combinatorial optimisation algorithms can be applied to the problem of identifying c-optimal experimental designs when there may be correlation between and within experimental units and evaluate the performance of relevant algorithms. We assume the data generating process is a generalised linear mixed model and show that the c-optimal design criterion is a monotone supermodular function amenable to a set of simple minimisation algorithms. We evaluate the performance of three relevant algorithms: the local search, the greedy search, and the reverse greedy search. We show that the local and reverse greedy searches provide comparable performance with the worst design outputs having variance < 10 % greater than the best design, across a range of covariance structures. We show that these algorithms perform as well or better than multiplicative methods that generate weights to place on experimental units. We extend these algorithms to identifying modle-robust c-optimal designs. Supplementary Information The online version contains supplementary material available at 10.1007/s11222-023-10280-w.
Collapse
Affiliation(s)
- Samuel I. Watson
- Insitute of Applied Health Research, University of Birmingham, Birmingham, UK
| | - Yi Pan
- Insitute of Applied Health Research, University of Birmingham, Birmingham, UK
| |
Collapse
|
3
|
Optimal designs for semi-parametric dose-response models under random contamination. Comput Stat Data Anal 2023. [DOI: 10.1016/j.csda.2022.107615] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
|
4
|
Nikiforova ND, Berni R, López‐Fidalgo JF. Optimal approximate choice designs for a two‐step coffee choice, taste and choice again experiment. J R Stat Soc Ser C Appl Stat 2022. [DOI: 10.1111/rssc.12601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Nedka Dechkova Nikiforova
- Department of Statistics, Computer Science, Applications “G.Parenti” University of Florence Florence Italy
| | - Rossella Berni
- Department of Statistics, Computer Science, Applications “G.Parenti” University of Florence Florence Italy
| | | |
Collapse
|
5
|
Waite TW, Woods DC. Minimax Efficient Random Experimental Design Strategies With Application to Model-Robust Design for Prediction. J Am Stat Assoc 2022. [DOI: 10.1080/01621459.2020.1863221] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Timothy W. Waite
- Department of Mathematics, University of Manchester, Manchester, UK
| | - David C. Woods
- Statistical Sciences Research Institute, University of Southampton, Southampton, UK
| |
Collapse
|
6
|
Duarte BPM, Atkinson AC, Granjo JFO, Oliveira NMC. Optimal Design of Experiments for Implicit Models. J Am Stat Assoc 2022. [DOI: 10.1080/01621459.2020.1862670] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Belmiro P. M. Duarte
- Department of Chemical and Biological Engineering, Instituto Politécnico de Coimbra, Instituto Superior de Engenharia de Coimbra, Coimbra, Portugal
- CIEPQPF, Department of Chemical Engineering, University of Coimbra, Coimbra, Portugal
| | | | - José F. O. Granjo
- CIEPQPF, Department of Chemical Engineering, University of Coimbra, Coimbra, Portugal
| | - Nuno M. C. Oliveira
- CIEPQPF, Department of Chemical Engineering, University of Coimbra, Coimbra, Portugal
| |
Collapse
|
7
|
Rosa S, Harman R. Computing minimum-volume enclosing ellipsoids for large datasets. Comput Stat Data Anal 2022. [DOI: 10.1016/j.csda.2022.107452] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
|
8
|
Liu P, Gao LL, Zhou J. R-optimal designs for multi-response regression models with multi-factors. COMMUN STAT-THEOR M 2022. [DOI: 10.1080/03610926.2020.1748655] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Pengqi Liu
- Department of Statistics and Data Science, Yale University, New Haven, Connecticut, USA
| | - Lucy L. Gao
- Department of Biostatistics, University of Washington, Seattle, Washington, USA
| | - Julie Zhou
- Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada
| |
Collapse
|
9
|
Collins MD, Cui EH, Hyun SW, Wong WK. A model-based approach to designing developmental toxicology experiments using sea urchin embryos. Arch Toxicol 2022; 96:919-932. [PMID: 35022802 PMCID: PMC8850257 DOI: 10.1007/s00204-021-03201-1] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2021] [Accepted: 12/09/2021] [Indexed: 11/28/2022]
Abstract
The key aim of this paper is to suggest a more quantitative approach to designing a dose–response experiment, and more specifically, a concentration–response experiment. The work proposes a departure from the traditional experimental design to determine a dose–response relationship in a developmental toxicology study. It is proposed that a model-based approach to determine a dose–response relationship can provide the most accurate statistical inference for the underlying parameters of interest, which may be estimating one or more model parameters or pre-specified functions of the model parameters, such as lethal dose, at maximal efficiency. When the design criterion or criteria can be determined at the onset, there are demonstrated efficiency gains using a more carefully selected model-based optimal design as opposed to an ad-hoc empirical design. As an illustration, a model-based approach was theoretically used to construct efficient designs for inference in a developmental toxicity study of sea urchin embryos exposed to trimethoprim. This study compares and contrasts the results obtained using model-based optimal designs versus an ad-hoc empirical design.
Collapse
Affiliation(s)
- Michael D Collins
- Department of Environment Health Sciences and Molecular Toxicology Interdepartmental Program, University of California, Los Angeles, Los Angeles, CA, 90095, USA.
| | - Elvis Han Cui
- Department of Biostatistics, University of California, Los Angeles, Los Angeles, CA, 90095, USA
| | - Seung Won Hyun
- Research Biostatistics, Johnson and Johnson Medical Devices, Irvine, CA, 92618, USA
| | - Weng Kee Wong
- Department of Biostatistics, University of California, Los Angeles, Los Angeles, CA, 90095, USA.
| |
Collapse
|
10
|
Li Y, Deng X. On Efficient Design of Pilot Experiment for Generalized Linear Models. JOURNAL OF STATISTICAL THEORY AND PRACTICE 2021. [DOI: 10.1007/s42519-021-00222-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
|
11
|
The mixture design threshold accepting algorithm for generating $$\varvec{D}$$-optimal designs of the mixture models. METRIKA 2021. [DOI: 10.1007/s00184-021-00832-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
|
12
|
Pronzato L, Sagnol G. Removing inessential points in c-and A-optimal design. J Stat Plan Inference 2021. [DOI: 10.1016/j.jspi.2020.11.011] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
|
13
|
Model-Based Design of Experiments for High-Dimensional Inputs Supported by Machine-Learning Methods. Processes (Basel) 2021. [DOI: 10.3390/pr9030508] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Algorithms that compute locally optimal continuous designs often rely on a finite design space or on the repeated solution of difficult non-linear programs. Both approaches require extensive evaluations of the Jacobian Df of the underlying model. These evaluations are a heavy computational burden. Based on the Kiefer-Wolfowitz Equivalence Theorem, we present a novel design of experiments algorithm that computes optimal designs in a continuous design space. For this iterative algorithm, we combine an adaptive Bayes-like sampling scheme with Gaussian process regression to approximate the directional derivative of the design criterion. The approximation allows us to adaptively select new design points on which to evaluate the model. The adaptive selection of the algorithm requires significantly less evaluations of Df and reduces the runtime of the computations. We show the viability of the new algorithm on two examples from chemical engineering.
Collapse
|
14
|
Support point of locally optimal designs for multinomial logistic regression models. J Stat Plan Inference 2020. [DOI: 10.1016/j.jspi.2020.03.006] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
|
15
|
Holland-Letz T, Kopp-Schneider A. The design heatmap: A simple visualization of D -optimality design problems. Biom J 2020; 62:2013-2031. [PMID: 33058202 DOI: 10.1002/bimj.202000087] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2020] [Revised: 07/30/2020] [Accepted: 09/12/2020] [Indexed: 01/03/2023]
Abstract
Optimal experimental designs are often formal and specific, and not intuitively plausible to practical experimenters. However, even in theory, there often are many different possible design points providing identical or nearly identical information compared to the design points of a strictly optimal design. In practical applications, this can be used to find designs that are a compromise between mathematical optimality and practical requirements, including preferences of experimenters. For this purpose, we propose a derivative-based two-dimensional graphical representation of the design space that, given any optimal design is already known, will show which areas of the design space are relevant for good designs and how these areas relate to each other. While existing equivalence theorems already allow such an illustration in regard to the relevance of design points only, our approach also shows whether different design points contribute the same kind of information, and thus allows tweaking of designs for practical applications, especially in regard to the splitting and combining of design points. We demonstrate the approach on a toxicological trial where a D -optimal design for a dose-response experiment modeled by a four-parameter log-logistic function was requested. As these designs require a prior estimate of the relevant parameters, which is difficult to obtain in a practical situation, we also discuss an adaption of our representations to the criterion of Bayesian D -optimality. While we focus on D -optimality, the approach is in principle applicable to different optimality criteria as well. However, much of the computational and graphical simplicity will be lost.
Collapse
Affiliation(s)
- Tim Holland-Letz
- German Cancer Research Center, Division of Biostatistics, Heidelberg, Germany
| | | |
Collapse
|
16
|
Li Y, Deng X. An efficient algorithm for Elastic I‐optimal design of generalized linear models. CAN J STAT 2020. [DOI: 10.1002/cjs.11571] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- Yiou Li
- Department of Mathematical Sciences DePaul University Chicago IL U.S.A
| | - Xinwei Deng
- Department of Statistics Virginia Tech Blacksburg VA U.S.A
| |
Collapse
|
17
|
Filová L, Harman R. Ascent with quadratic assistance for the construction of exact experimental designs. Comput Stat 2020. [DOI: 10.1007/s00180-020-00961-9] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
|
18
|
|
19
|
García-Ródenas R, García-García JC, López-Fidalgo J, Martín-Baos JÁ, Wong WK. A comparison of general-purpose optimization algorithms for finding optimal approximate experimental designs. Comput Stat Data Anal 2020. [DOI: 10.1016/j.csda.2019.106844] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
|
20
|
On Design and Analysis of Funnel Testing Experiments in Webpage Optimization. JOURNAL OF STATISTICAL THEORY AND PRACTICE 2020. [DOI: 10.1007/s42519-019-0068-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
|
21
|
Sverdlov O, Ryeznik Y, Wong WK. On Optimal Designs for Clinical Trials: An Updated Review. JOURNAL OF STATISTICAL THEORY AND PRACTICE 2019. [DOI: 10.1007/s42519-019-0073-4] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
|
22
|
Bayesian A-Optimal Design of Experiment with Quantitative and Qualitative Responses. JOURNAL OF STATISTICAL THEORY AND PRACTICE 2019. [DOI: 10.1007/s42519-019-0063-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
|
23
|
|
24
|
Optimal Design of Experiments for Liquid–Liquid Equilibria Characterization via Semidefinite Programming. Processes (Basel) 2019. [DOI: 10.3390/pr7110834] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Liquid–liquid equilibria (LLE) characterization is a task requiring considerable work and appreciable financial resources. Notable savings in time and effort can be achieved when the experimental plans use the methods of the optimal design of experiments that maximize the information obtained. To achieve this goal, a systematic optimization formulation based on Semidefinite Programming is proposed for finding optimal experimental designs for LLE studies carried out at constant pressure and temperature. The non-random two-liquid (NRTL) model is employed to represent species equilibria in both phases. This model, combined with mass balance relationships, provides a means of computing the sensitivities of the measurements to the parameters. To design the experiment, these sensitivities are calculated for a grid of candidate experiments in which initial mixture compositions are varied. The optimal design is found by maximizing criteria based on the Fisher Information Matrix (FIM). Three optimality criteria (D-, A- and E-optimal) are exemplified. The approach is demonstrated for two ternary systems where different sets of parameters are to be estimated.
Collapse
|
25
|
Pokhilko V, Zhang Q, Kang L, Mays DP. D-Optimal Design for Network A/B Testing. JOURNAL OF STATISTICAL THEORY AND PRACTICE 2019. [DOI: 10.1007/s42519-019-0058-3] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
|
26
|
Wong WK, Yin Y, Zhou J. Optimal Designs for Multi-Response Nonlinear Regression Models With Several Factors via Semidefinite Programming. J Comput Graph Stat 2019; 28:61-73. [PMID: 31308618 DOI: 10.1080/10618600.2018.1476250] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
Abstract
We use semi-definite programming (SDP) to find a variety of optimal designs for multiresponse linear models with multiple factors, and for the first time, extend the methodology to find optimal designs for multi-response nonlinear models and generalized linear models with multiple factors. We construct transformations that (i) facilitate improved formulation of the optimal design problems into SDP problems, (ii) enable us to extend SDP methodology to find optimal designs from linear models to nonlinear multi-response models with multiple factors and (iii) correct erroneously reported optimal designs in the literature caused by formulation issues. We also derive invariance properties of optimal designs and their dependence on the covariance matrix of the correlated errors, which are helpful for reducing the computation time for finding optimal designs. Our applications include finding A-, A s -, c- and D-optimal designs for multi-response multi-factor polynomial models, locally c- and D-optimal designs for a bivariate E max response model and for a bivariate Probit model useful in the biosciences.
Collapse
Affiliation(s)
- Weng Kee Wong
- Department of Biostatistics, University of California, Los Angeles, Los Angeles, CA 90095-1772, USA
| | - Yue Yin
- Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada V8W 2Y2
| | - Julie Zhou
- Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada V8W 2Y2
| |
Collapse
|
27
|
Wong WK, Zhou J. CVX‐based algorithms for constructing various optimal regression designs. CAN J STAT 2019. [DOI: 10.1002/cjs.11499] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Weng Kee Wong
- Department of BiostatisticsUniversity of California Los Angeles CA 90095‐1772 U.S.A
| | - Julie Zhou
- Department of Mathematics and StatisticsUniversity of Victoria Victoria British Columbia Canada V8W 2Y2
| |
Collapse
|
28
|
|
29
|
Harman R, Filová L, Richtárik P. A Randomized Exchange Algorithm for Computing Optimal Approximate Designs of Experiments. J Am Stat Assoc 2019. [DOI: 10.1080/01621459.2018.1546588] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Radoslav Harman
- Comenius University in Bratislava, Slovakia
- Johannes Kepler University Linz, Austria
| | | | - Peter Richtárik
- King Abdullah University of Science and Technology, Kingdom of Saudi Arabia
- University of Edinburgh, UK
- Moscow Institute of Physics and Technology, Dolgoprudny, Russia
| |
Collapse
|
30
|
Hyun SW, Wong WK, Yang Y. Optimal designs for asymmetric sigmoidal response curves in bioassays and immunoassays. Stat Methods Med Res 2019; 29:421-436. [PMID: 30868935 DOI: 10.1177/0962280219832631] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The 5-parameter logistic (5PL) model is frequently used to model and analyze responses from bioassays and immunoassays which can be skewed. Various types of optimal experimental designs for 2, 3 and 4-parameter logistic models have been reported but not for the more complicated 5PL model. We construct different types of optimal designs for studying various features of the 5PL model and show that commonly used designs in bioassays and immunoassays are generally inefficient for statistical inference. To facilitate use of such designs in practice, we create a user-friendly software package to generate various tailor-made optimal designs for the 5PL model and evaluate robustness properties of a design under a variation of criteria, model forms and misspecification in the nominal values of the model parameters.
Collapse
Affiliation(s)
- Seung Won Hyun
- Research Biostatistics, Johnson and Johnson Medical Devices, Irvine, CA, USA
| | - Weng Kee Wong
- Department of Biostatistics, UCLA Fielding School of Public Health, Los Angeles, CA, USA
| | - Yarong Yang
- Department of Statistics, North Dakota State University, Fargo, ND, USA
| |
Collapse
|
31
|
Shen G, Hyun SW, Wong WK. Optimal designs based on the maximum quasi-likelihood estimator. J Stat Plan Inference 2017; 178:128-139. [PMID: 28163359 DOI: 10.1016/j.jspi.2016.07.002] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
Abstract
We use optimal design theory and construct locally optimal designs based on the maximum quasi-likelihood estimator (MqLE), which is derived under less stringent conditions than those required for the MLE method. We show that the proposed locally optimal designs are asymptotically as efficient as those based on the MLE when the error distribution is from an exponential family, and they perform just as well or better than optimal designs based on any other asymptotically linear unbiased estimators such as the least square estimator (LSE). In addition, we show current algorithms for finding optimal designs can be directly used to find optimal designs based on the MqLE. As an illustrative application, we construct a variety of locally optimal designs based on the MqLE for the 4-parameter logistic (4PL) model and study their robustness properties to misspecifications in the model using asymptotic relative efficiency. The results suggest that optimal designs based on the MqLE can be easily generated and they are quite robust to mis-specification in the probability distribution of the responses.
Collapse
Affiliation(s)
- Gang Shen
- Department of Statistics, North Dakota State University, Fargo, ND 58102, USA
| | - Seung Won Hyun
- Department of Statistics, North Dakota State University, Fargo, ND 58102, USA
| | - Weng Kee Wong
- Department of Biostatistics, University of California, Los Angeles, CA 90095, USA
| |
Collapse
|
32
|
Harman R, Benková E. Barycentric algorithm for computing D-optimal size- and cost-constrained designs of experiments. METRIKA 2016. [DOI: 10.1007/s00184-016-0599-3] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
|
33
|
Tian T, Yang M. Efficiency of the coordinate-exchange algorithm in constructing exact optimal discrete choice experiments. JOURNAL OF STATISTICAL THEORY AND PRACTICE 2016. [DOI: 10.1080/15598608.2016.1203842] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- T. Tian
- Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, Illionois, USA
| | - M. Yang
- Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, Illionois, USA
- College of Mathematics, Chongqing University of Science and Technology, Chongqing, China
| |
Collapse
|
34
|
Abstract
We consider the optimal design problem for a comparison of two regression curves, which is used to establish the similarity between the dose response relationships of two groups. An optimal pair of designs minimizes the width of the confidence band for the difference between the two regression functions. Optimal design theory (equivalence theorems, efficiency bounds) is developed for this non standard design problem and for some commonly used dose response models optimal designs are found explicitly. The results are illustrated in several examples modeling dose response relationships. It is demonstrated that the optimal pair of designs for the comparison of the regression curves is not the pair of the optimal designs for the individual models. In particular it is shown that the use of the optimal designs proposed in this paper instead of commonly used "non-optimal" designs yields a reduction of the width of the confidence band by more than 50%.
Collapse
Affiliation(s)
- Holger Dette
- Ruhr-Universität Bochum, Fakultät für Mathematik, 44780 Bochum, Germany
| | - Kirsten Schorning
- Ruhr-Universität Bochum, Fakultät für Mathematik, 44780 Bochum, Germany
| |
Collapse
|
35
|
Hyun SW, Wong WK. Multiple-Objective Optimal Designs for Studying the Dose Response Function and Interesting Dose Levels. Int J Biostat 2015; 11:253-71. [PMID: 26565557 DOI: 10.1515/ijb-2015-0044] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
We construct an optimal design to simultaneously estimate three common interesting features in a dose-finding trial with possibly different emphasis on each feature. These features are (1) the shape of the dose-response curve, (2) the median effective dose and (3) the minimum effective dose level. A main difficulty of this task is that an optimal design for a single objective may not perform well for other objectives. There are optimal designs for dual objectives in the literature but we were unable to find optimal designs for 3 or more objectives to date with a concrete application. A reason for this is that the approach for finding a dual-objective optimal design does not work well for a 3 or more multiple-objective design problem. We propose a method for finding multiple-objective optimal designs that estimate the three features with user-specified higher efficiencies for the more important objectives. We use the flexible 4-parameter logistic model to illustrate the methodology but our approach is applicable to find multiple-objective optimal designs for other types of objectives and models. We also investigate robustness properties of multiple-objective optimal designs to mis-specification in the nominal parameter values and to a variation in the optimality criterion. We also provide computer code for generating tailor made multiple-objective optimal designs.
Collapse
|
36
|
Sagnol G, Harman R. Computing exact $D$-optimal designs by mixed integer second-order cone programming. Ann Stat 2015. [DOI: 10.1214/15-aos1339] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
37
|
Abstract
The problem of constructing Bayesian optimal discriminating designs for a class of regression models with respect to the T-optimality criterion introduced by Atkinson and Fedorov (1975a) is considered. It is demonstrated that the discretization of the integral with respect to the prior distribution leads to locally T-optimal discriminating design problems with a large number of model comparisons. Current methodology for the numerical construction of discrimination designs can only deal with a few comparisons, but the discretization of the Bayesian prior easily yields to discrimination design problems for more than 100 competing models. A new efficient method is developed to deal with problems of this type. It combines some features of the classical exchange type algorithm with the gradient methods. Convergence is proved and it is demonstrated that the new method can find Bayesian optimal discriminating designs in situations where all currently available procedures fail.
Collapse
Affiliation(s)
- Holger Dette
- Ruhr-Universität Bochum, Fakultät für Mathematik, 44780 Bochum, Germany,
| | - Viatcheslav B Melas
- St. Petersburg State University, Department of Mathematics, St. Petersburg, Russia,
| | - Roman Guchenko
- St. Petersburg State University, Department of Mathematics, St. Petersburg, Russia,
| |
Collapse
|
38
|
Wong WK, Chen RB, Huang CC, Wang W. A Modified Particle Swarm Optimization Technique for Finding Optimal Designs for Mixture Models. PLoS One 2015; 10:e0124720. [PMID: 26091237 PMCID: PMC4474858 DOI: 10.1371/journal.pone.0124720] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2014] [Accepted: 03/02/2015] [Indexed: 11/19/2022] Open
Abstract
Particle Swarm Optimization (PSO) is a meta-heuristic algorithm that has been shown to be successful in solving a wide variety of real and complicated optimization problems in engineering and computer science. This paper introduces a projection based PSO technique, named ProjPSO, to efficiently find different types of optimal designs, or nearly optimal designs, for mixture models with and without constraints on the components, and also for related models, like the log contrast models. We also compare the modified PSO performance with Fedorov's algorithm, a popular algorithm used to generate optimal designs, Cocktail algorithm, and the recent algorithm proposed by [1].
Collapse
Affiliation(s)
- Weng Kee Wong
- Department of Biostatistics, University of California, Los Angeles, USA
| | - Ray-Bing Chen
- Department of Statistics, National Cheng Kung University, Taiwan
| | - Chien-Chih Huang
- Department of Mathematics, National Taiwan University, Taipei, Taiwan
| | - Weichung Wang
- Institute of Applied Mathematical Sciences, National Taiwan University, Taiwan
- * E-mail:
| |
Collapse
|
39
|
Hu L, Yang M, Stufken J. Saturated locally optimal designs under differentiable optimality criteria. Ann Stat 2015. [DOI: 10.1214/14-aos1263] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
40
|
Hedayat A, Zhou Y, Yang M. Optimal designs for some selected nonlinear models. J Stat Plan Inference 2014. [DOI: 10.1016/j.jspi.2014.05.005] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
|
41
|
Lange MR, Schmidli H. Optimal design of clinical trials with biologics using dose-time-response models. Stat Med 2014; 33:5249-64. [DOI: 10.1002/sim.6299] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2013] [Revised: 07/31/2014] [Accepted: 08/20/2014] [Indexed: 12/23/2022]
Affiliation(s)
- Markus R. Lange
- Statistical Methodology, Development; Novartis Pharma AG; Basel Switzerland
- Hannover Medical School; Institute for Biometry; Hannover Germany
| | - Heinz Schmidli
- Statistical Methodology, Development; Novartis Pharma AG; Basel Switzerland
| |
Collapse
|