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Li J, Li G, Zhang C. Weighted R-efficiency optimal design for experiments with mixture. COMMUN STAT-THEOR M 2022. [DOI: 10.1080/03610926.2022.2096901] [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]
Affiliation(s)
- Junpeng Li
- School of Economics and Statistics, Guangzhou University, Guangzhou, China
| | - Guanghui Li
- School of Science, Kaili University, Kaili, China
| | - Chongqi Zhang
- School of Economics and Statistics, Guangzhou University, Guangzhou, China
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2
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Zhou XD, Yue RX, Wang YJ. Optimal designs for the prediction of mixed effects in linear mixed models. STATISTICS-ABINGDON 2021. [DOI: 10.1080/02331888.2021.1975711] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Xiao-Dong Zhou
- School of Statistics and Information, Shanghai University of International Business and Economics, Shanghai, People's Republic of China
| | - Rong-Xian Yue
- College of Mathematics and Science, Shanghai Normal University, Shanghai, People's Republic of China
| | - Yun-Juan Wang
- School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai, People's Republic of China
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Qian T, Klasnja P, Murphy SA. Linear mixed models with endogenous covariates: modeling sequential treatment effects with application to a mobile health study. Stat Sci 2020; 35:375-390. [PMID: 33132496 PMCID: PMC7596885 DOI: 10.1214/19-sts720] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Abstract
Mobile health is a rapidly developing field in which behavioral treatments are delivered to individuals via wearables or smartphones to facilitate health-related behavior change. Micro-randomized trials (MRT) are an experimental design for developing mobile health interventions. In an MRT the treatments are randomized numerous times for each individual over course of the trial. Along with assessing treatment effects, behavioral scientists aim to understand between-person heterogeneity in the treatment effect. A natural approach is the familiar linear mixed model. However, directly applying linear mixed models is problematic because potential moderators of the treatment effect are frequently endogenous-that is, may depend on prior treatment. We discuss model interpretation and biases that arise in the absence of additional assumptions when endogenous covariates are included in a linear mixed model. In particular, when there are endogenous covariates, the coefficients no longer have the customary marginal interpretation. However, these coefficients still have a conditional-on-the-random-effect interpretation. We provide an additional assumption that, if true, allows scientists to use standard software to fit linear mixed model with endogenous covariates, and person-specific predictions of effects can be provided. As an illustration, we assess the effect of activity suggestion in the HeartSteps MRT and analyze the between-person treatment effect heterogeneity.
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Affiliation(s)
- Tianchen Qian
- Department of Statistics, Harvard University, Cambridge, MA 02138
- School of Information, University of Michigan, Ann Arbor, MI 48109
| | - Predrag Klasnja
- Department of Statistics, Harvard University, Cambridge, MA 02138
- School of Information, University of Michigan, Ann Arbor, MI 48109
| | - Susan A Murphy
- Department of Statistics, Harvard University, Cambridge, MA 02138
- School of Information, University of Michigan, Ann Arbor, MI 48109
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4
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Lee KM, Biedermann S, Mitra R. D-optimal designs for multiarm trials with dropouts. Stat Med 2019; 38:2749-2766. [PMID: 30912173 PMCID: PMC6563492 DOI: 10.1002/sim.8148] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2018] [Revised: 02/18/2019] [Accepted: 02/28/2019] [Indexed: 11/24/2022]
Abstract
Multiarm trials with follow-up on participants are commonly implemented to assess treatment effects on a population over the course of the studies. Dropout is an unavoidable issue especially when the duration of the multiarm study is long. Its impact is often ignored at the design stage, which may lead to less accurate statistical conclusions. We develop an optimal design framework for trials with repeated measurements, which takes potential dropouts into account, and we provide designs for linear mixed models where the presence of dropouts is noninformative and dependent on design variables. Our framework is illustrated through redesigning a clinical trial on Alzheimer's disease, whereby the benefits of our designs compared with standard designs are demonstrated through simulations.
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Affiliation(s)
- Kim May Lee
- MRC Biostatistics Unit, School of Clinical MedicineUniversity of CambridgeCambridgeUK
| | | | - Robin Mitra
- Department of Mathematics and StatisticsLancaster UniversityLancasterUK
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5
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Affiliation(s)
- Rong-Xian Yue
- Department of Mathematics, Shanghai Normal University, and Scientific Computing Key Laboratory of Shanghai Universities, Shanghai, China
| | - Xiao-Dong Zhou
- School of Statistics and Information, Shanghai University of International, Business and Economics, Shanghai, China
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7
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Application of Linear Mixed-Effects Models in Human Neuroscience Research: A Comparison with Pearson Correlation in Two Auditory Electrophysiology Studies. Brain Sci 2017; 7:brainsci7030026. [PMID: 28264422 PMCID: PMC5366825 DOI: 10.3390/brainsci7030026] [Citation(s) in RCA: 52] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/31/2016] [Revised: 02/15/2017] [Accepted: 02/24/2017] [Indexed: 01/08/2023] Open
Abstract
Neurophysiological studies are often designed to examine relationships between measures from different testing conditions, time points, or analysis techniques within the same group of participants. Appropriate statistical techniques that can take into account repeated measures and multivariate predictor variables are integral and essential to successful data analysis and interpretation. This work implements and compares conventional Pearson correlations and linear mixed-effects (LME) regression models using data from two recently published auditory electrophysiology studies. For the specific research questions in both studies, the Pearson correlation test is inappropriate for determining strengths between the behavioral responses for speech-in-noise recognition and the multiple neurophysiological measures as the neural responses across listening conditions were simply treated as independent measures. In contrast, the LME models allow a systematic approach to incorporate both fixed-effect and random-effect terms to deal with the categorical grouping factor of listening conditions, between-subject baseline differences in the multiple measures, and the correlational structure among the predictor variables. Together, the comparative data demonstrate the advantages as well as the necessity to apply mixed-effects models to properly account for the built-in relationships among the multiple predictor variables, which has important implications for proper statistical modeling and interpretation of human behavior in terms of neural correlates and biomarkers.
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van Breukelen GJP. Optimal Experimental Design With Nesting of Persons in Organizations. ZEITSCHRIFT FUR PSYCHOLOGIE-JOURNAL OF PSYCHOLOGY 2013. [DOI: 10.1027/2151-2604/a000143] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
Abstract
This paper introduces optimal design of randomized experiments where individuals are nested within organizations, such as schools, health centers, or companies. The focus is on nested designs with two levels (organization, individual) and two treatment conditions (treated, control), with treatment assignment to organizations, or to individuals within organizations. For each type of assignment, a multilevel model is first presented for the analysis of a quantitative dependent variable or outcome. Simple equations are then given for the optimal sample size per level (number of organizations, number of individuals) as a function of the sampling cost and outcome variance at each level, with realistic examples. Next, it is explained how the equations can be applied if the dependent variable is dichotomous, or if there are covariates in the model, or if the effects of two treatment factors are studied in a factorial nested design, or if the dependent variable is repeatedly measured. Designs with three levels of nesting and the optimal number of repeated measures are briefly discussed, and the paper ends with a short discussion of robust design.
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Affiliation(s)
- Gerard J. P. van Breukelen
- Faculty of Psychology and Neuroscience, and CAPHRI School for Public Health and Primary Care, Maastricht University, The Netherlands
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9
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Smucker BJ, del Castillo E, Rosenberger JL. Model-Robust Two-Level Designs Using Coordinate Exchange Algorithms and a Maximin Criterion. Technometrics 2012. [DOI: 10.1080/00401706.2012.694774] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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10
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Tekle FB, Tan FES, Berger MPF. Interactive computer program for optimal designs of longitudinal cohort studies. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2009; 94:168-176. [PMID: 19131139 DOI: 10.1016/j.cmpb.2008.11.002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/29/2008] [Revised: 10/28/2008] [Accepted: 11/06/2008] [Indexed: 05/27/2023]
Abstract
Many large scale longitudinal cohort studies have been carried out or are ongoing in different fields of science. Such studies need a careful planning to obtain the desired quality of results with the available resources. In the past, a number of researches have been performed on optimal designs for longitudinal studies. However, there was no computer program yet available to help researchers to plan their longitudinal cohort design in an optimal way. A new interactive computer program for the optimization of designs of longitudinal cohort studies is therefore presented. The computer program helps users to identify the optimal cohort design with an optimal number of repeated measurements per subject and an optimal allocations of time points within a given study period. Further, users can compute the loss in relative efficiencies of any other alternative design compared to the optimal one. The computer program is described and illustrated using a practical example.
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Affiliation(s)
- Fetene B Tekle
- University of Maastricht, Department of Methodology and Statistics, P.O. Box 616, 6200 MD, Maastricht, The Netherlands.
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11
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Wong WK, Zhu W. Optimum treatment allocation rules under a variance heterogeneity model. Stat Med 2009; 27:4581-95. [PMID: 18563794 DOI: 10.1002/sim.3318] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
We provide optimal treatment allocation schemes when the outcome variance varies across the treatment groups and our objectives are to estimate treatment effects with equal or unequal interest. Unlike other optimal designs, such as A-optimal designs, the proposed designs can be found without an iterative scheme. We evaluate robustness properties of the optimal designs to mis-specification in the expected variance from each group and identify situations when popular allocation schemes have poor efficiencies. An application to design a randomized rheumatoid arthritis trial is discussed, along with a potential application to design a cancer screening trial when the main outcome is a continuous variable.
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Affiliation(s)
- Weng Kee Wong
- Department of Biostatistics, School of Public Health, University of California at Los Angeles, 10833 Le Conte Ave., Los Angeles, CA 90095, USA.
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12
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Ortega-Azurduy SA, Tan FES, Berger MPF. Highly Efficient Designs to Handle the Incorrect Specification of Linear Mixed Models. COMMUN STAT-SIMUL C 2008. [DOI: 10.1080/03610910802379152] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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13
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Winkens B, Schouten HJA, van Breukelen GJP, Berger MPF. Optimal designs for clinical trials with second-order polynomial treatment effects. Stat Methods Med Res 2007; 16:523-37. [PMID: 17698939 DOI: 10.1177/0962280206071847] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
The effect of adding intermediate measures on the efficiency of treatment effect estimation is considered for a second-order polynomial treatment effect, equidistant time-points, different covariance structures and two optimality criteria, assuming either a fixed sample size or a fixed budget. The benefit of adding intermediate measures (at the expense of subjects) depends strongly on the assumed covariance structure and is hardly affected by the two used optimality criteria (Ds or c). For a fixed sample size, the increase in efficiency by adding intermediate measures is large for a compound symmetric structure and small for a first-order auto-regressive structure. For a first-order auto-regressive structure with measurement error, the results depend on the covariance parameter values. For a fixed budget and linear cost function, the design with only three measures per subject is often highly efficient. If the structure resembles compound symmetry and the cost per subject is eight or more times larger than the cost per repeated measure, however, more than three measures are required to obtain highly efficient treatment effect estimators. If the covariance structure is unknown, the optimal design based on a first-order auto-regressive structure with measurement error is preferable in terms of robustness against misspecification of the covariance structure. Given a design with three repeated measures and a second-order polynomial treatment effect, equidistant time-points are either optimal (Ds-) or highly efficient (c-optimality criterion). The results are illustrated by a practical example.
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Affiliation(s)
- Bjorn Winkens
- Department of Methodology and Statistics, University of Maastricht, Maastricht, The Netherlands.
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