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Harrall KK, Muller KE, Starling AP, Dabelea D, Barton KE, Adgate JL, Glueck DH. Power and sample size analysis for longitudinal mixed models of health in populations exposed to environmental contaminants: a tutorial. BMC Med Res Methodol 2023; 23:12. [PMID: 36635621 PMCID: PMC9835314 DOI: 10.1186/s12874-022-01819-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2022] [Accepted: 12/13/2022] [Indexed: 01/14/2023] Open
Abstract
BACKGROUND When evaluating the impact of environmental exposures on human health, study designs often include a series of repeated measurements. The goal is to determine whether populations have different trajectories of the environmental exposure over time. Power analyses for longitudinal mixed models require multiple inputs, including clinically significant differences, standard deviations, and correlations of measurements. Further, methods for power analyses of longitudinal mixed models are complex and often challenging for the non-statistician. We discuss methods for extracting clinically relevant inputs from literature, and explain how to conduct a power analysis that appropriately accounts for longitudinal repeated measures. Finally, we provide careful recommendations for describing complex power analyses in a concise and clear manner. METHODS For longitudinal studies of health outcomes from environmental exposures, we show how to [1] conduct a power analysis that aligns with the planned mixed model data analysis, [2] gather the inputs required for the power analysis, and [3] conduct repeated measures power analysis with a highly-cited, validated, free, point-and-click, web-based, open source software platform which was developed specifically for scientists. RESULTS As an example, we describe the power analysis for a proposed study of repeated measures of per- and polyfluoroalkyl substances (PFAS) in human blood. We show how to align data analysis and power analysis plan to account for within-participant correlation across repeated measures. We illustrate how to perform a literature review to find inputs for the power analysis. We emphasize the need to examine the sensitivity of the power values by considering standard deviations and differences in means that are smaller and larger than the speculated, literature-based values. Finally, we provide an example power calculation and a summary checklist for describing power and sample size analysis. CONCLUSIONS This paper provides a detailed roadmap for conducting and describing power analyses for longitudinal studies of environmental exposures. It provides a template and checklist for those seeking to write power analyses for grant applications.
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Affiliation(s)
- Kylie K Harrall
- Lifecourse Epidemiology of Adiposity and Diabetes (LEAD) Center, University of Colorado - Anschutz Medical Campus, Aurora, CO, 80045, USA.
- Department of Epidemiology, Colorado School of Public Health, Aurora, CO, USA.
| | - Keith E Muller
- Health Outcomes & Biomedical Informatics, College of Medicine, University of Florida, Gainesville, FL, USA
| | - Anne P Starling
- Lifecourse Epidemiology of Adiposity and Diabetes (LEAD) Center, University of Colorado - Anschutz Medical Campus, Aurora, CO, 80045, USA
- Department of Epidemiology, Colorado School of Public Health, Aurora, CO, USA
- Department of Epidemiology, Gillings School of Global Public Health, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA
| | - Dana Dabelea
- Lifecourse Epidemiology of Adiposity and Diabetes (LEAD) Center, University of Colorado - Anschutz Medical Campus, Aurora, CO, 80045, USA
- Department of Epidemiology, Colorado School of Public Health, Aurora, CO, USA
- Department of Pediatrics, University of Colorado School of Medicine, Aurora, CO, USA
| | - Kelsey E Barton
- Department of Environmental and Occupational Health, Colorado School of Public Health, University of Colorado, Aurora, CO, USA
| | - John L Adgate
- Department of Environmental and Occupational Health, Colorado School of Public Health, University of Colorado, Aurora, CO, USA
| | - Deborah H Glueck
- Lifecourse Epidemiology of Adiposity and Diabetes (LEAD) Center, University of Colorado - Anschutz Medical Campus, Aurora, CO, 80045, USA
- Department of Pediatrics, University of Colorado School of Medicine, Aurora, CO, USA
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Moyer JC, Heagerty PJ, Murray DM. Analysis of multiple-period group randomized trials: random coefficients model or repeated measures ANOVA? Trials 2022; 23:987. [PMID: 36476294 PMCID: PMC9727985 DOI: 10.1186/s13063-022-06917-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2022] [Accepted: 11/11/2022] [Indexed: 12/12/2022] Open
Abstract
BACKGROUND Multiple-period parallel group randomized trials (GRTs) analyzed with linear mixed models can represent time in mean models as continuous or categorical. If time is continuous, random effects are traditionally group- and member-level deviations from condition-specific slopes and intercepts and are referred to as random coefficients (RC) analytic models. If time is categorical, random effects are traditionally group- and member-level deviations from time-specific condition means and are referred to as repeated measures ANOVA (RM-ANOVA) analytic models. Longstanding guidance recommends the use of RC over RM-ANOVA for parallel GRTs with more than two periods because RC exhibited nominal type I error rates for both time parameterizations while RM-ANOVA exhibited inflated type I error rates when applied to data generated using the RC model. However, this recommendation was developed assuming a variance components covariance matrix for the RM-ANOVA, using only cross-sectional data, and explicitly modeling time × group variation. Left unanswered were how well RM-ANOVA with an unstructured covariance would perform on data generated according to the RC mechanism, if similar patterns would be observed in cohort data, and the impact of not modeling time × group variation if such variation was present in the data-generating model. METHODS Continuous outcomes for cohort and cross-sectional parallel GRT data were simulated according to RM-ANOVA and RC mechanisms at five total time periods. All simulations assumed time × group variation. We varied the number of groups, group size, and intra-cluster correlation. Analytic models using RC, RM-ANOVA, RM-ANOVA with unstructured covariance, and a Saturated random effects structure were applied to the data. All analytic models specified time × group random effects. The analytic models were then reapplied without specifying random effects for time × group. RESULTS Results indicated the RC and saturated analytic models maintained the nominal type I error rate in all data sets, RM-ANOVA with an unstructured covariance did not avoid type I error rate inflation when applied to cohort RC data, and analytic models omitting time-varying group random effects when such variation exists in the data were prone to substantial type I error inflation unless the residual error variance is high relative to the time × group variance. CONCLUSION The time × group RC and saturated analytic models are recommended as the default for multiple period parallel GRTs.
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Affiliation(s)
- Jonathan C. Moyer
- Office of Disease Prevention, National Institutes of Health, Bethesda, MD USA
| | | | - David M. Murray
- Office of Disease Prevention, National Institutes of Health, Bethesda, MD USA
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Are Care-Recipient Outcomes Attributable to Improved Caregiver Well-Being? A Cluster-Randomized Controlled Trial of Benefit-Finding Intervention. Am J Geriatr Psychiatry 2022; 30:903-913. [PMID: 34563429 DOI: 10.1016/j.jagp.2021.08.009] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 07/10/2021] [Revised: 08/21/2021] [Accepted: 08/21/2021] [Indexed: 11/20/2022]
Abstract
OBJECTIVES The benefit-finding therapeutic (BFT) intervention, training cognitive reappraisal, and alternative thinking to construct positive aspects of caregiving have been found to reduce caregiver depression. This study examines BFT effects on care-recipient outcomes via reduced caregiver depression. DESIGN Cluster-randomized double-blind controlled trial. SETTING Social centers and clinics. PARTICIPANTS A total of 129 caregivers. Inclusion criteria were 1) primary caregiver aged 18+, 2) without cognitive impairment, 3) providing ≥14 care hours weekly to a relative with mild-to-moderate Alzheimer's disease, and 4) scoring ≥3 on the Hamilton Depression Rating Scale. Exclusion criterion was care-recipient having Parkinsonism or other forms of dementia. INTERVENTIONS BFT was evaluated against two forms of psychoeducation-standard and simplified (lectures only) psychoeducation. MEASUREMENTS Care-recipient outcomes included neuropsychiatric symptoms (NPS), functional impairment, and global dementia severity (Clinical Dementia Rating sum-of-box), measured at baseline, postintervention, and 4- and 10-month follow up. RESULTS Mixed-effects regressions showed a significant effect on NPS when compared with simplified psychoeducation only, with BFT participants reporting fewer NPS (especially mood symptoms) at 4-month follow-up (d = -0.52). Furthermore, longitudinal path analysis (using changes in caregiver depression scores at postintervention to predict changes in care-recipient NPS at follow-up) found that this effect was mediated by improved caregiver depression. No other intervention or mediation effects were found or were consistent across analyses. CONCLUSIONS Less depressed caregivers may be able to provide better care and more positive interactions, leading to reduced NPS in care-recipients. However, this benefit of BFT was limited to the comparison with simplified psychoeducation only.
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Zhou Y, Turner EL, Simmons RA, Li F. Constrained randomization and statistical inference for multi‐arm parallel cluster randomized controlled trials. Stat Med 2022; 41:1862-1883. [PMID: 35146788 PMCID: PMC9007899 DOI: 10.1002/sim.9333] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2021] [Revised: 01/12/2022] [Accepted: 01/14/2022] [Indexed: 12/17/2022]
Abstract
A practical limitation of cluster randomized controlled trials (cRCTs) is that the number of available clusters may be small, resulting in an increased risk of baseline imbalance under simple randomization. Constrained randomization overcomes this issue by restricting the allocation to a subset of randomization schemes where sufficient overall covariate balance across comparison arms is achieved. However, for multi-arm cRCTs, several design and analysis issues pertaining to constrained randomization have not been fully investigated. Motivated by an ongoing multi-arm cRCT, we elaborate the method of constrained randomization and provide a comprehensive evaluation of the statistical properties of model-based and randomization-based tests under both simple and constrained randomization designs in multi-arm cRCTs, with varying combinations of design and analysis-based covariate adjustment strategies. In particular, as randomization-based tests have not been extensively studied in multi-arm cRCTs, we additionally develop most-powerful randomization tests under the linear mixed model framework for our comparisons. Our results indicate that under constrained randomization, both model-based and randomization-based analyses could gain power while preserving nominal type I error rate, given proper analysis-based adjustment for the baseline covariates. Randomization-based analyses, however, are more robust against violations of distributional assumptions. The choice of balance metrics and candidate set sizes and their implications on the testing of the pairwise and global hypotheses are also discussed. Finally, we caution against the design and analysis of multi-arm cRCTs with an extremely small number of clusters, due to insufficient degrees of freedom and the tendency to obtain an overly restricted randomization space.
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Affiliation(s)
- Yunji Zhou
- Department of Biostatistics and Bioinformatics Duke University Durham North Carolina USA
- Duke Global Health Institute Duke University Durham North Carolina USA
| | - Elizabeth L. Turner
- Department of Biostatistics and Bioinformatics Duke University Durham North Carolina USA
- Duke Global Health Institute Duke University Durham North Carolina USA
| | - Ryan A. Simmons
- Department of Biostatistics and Bioinformatics Duke University Durham North Carolina USA
- Duke Global Health Institute Duke University Durham North Carolina USA
| | - Fan Li
- Department of Biostatistics Yale School of Public Health New Haven Connecticut USA
- Center for Methods in Implementation and Prevention Science Yale School of Public Health New Haven Connecticut USA
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Cheng ST, Mak EPM, Kwok T, Fung H, Lam LCW. Benefit-Finding Intervention Delivered Individually to Alzheimer Family Caregivers: Longer-Term Outcomes of a Randomized Double-Blind Controlled Trial. J Gerontol B Psychol Sci Soc Sci 2020; 75:1884-1893. [PMID: 31556447 DOI: 10.1093/geronb/gbz118] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2019] [Indexed: 11/15/2022] Open
Abstract
OBJECTIVES To examine the longer-term effects of benefit-finding on caregivers' depressive symptoms (primary outcome), and global burden, role overload, psychological well-being, and positive aspects of caregiving (secondary outcomes). METHOD Ninety-six Hong Kong Chinese caregivers of relatives with Alzheimer's disease were randomly assigned to receive the benefit-finding intervention (BFT) or one of the two control conditions, namely, simplified psychoeducation (lectures only; SIM-PE) or standard psychoeducation (STD-PE). Caregivers received four biweekly one-to-one interventions of 3 hours each at their own homes. We focused on outcomes measured at 4- and 10-month follow-ups. The trajectories of intervention effects were modeled by BFT × time and BFT × time2 interaction terms. RESULTS Mixed-effects regression showed significant BFT × time2 interaction effects on depressive symptoms against both control conditions, suggesting diminishing BFT effects over time. Z tests showed that, compared with controls, BFT participants reported substantial reductions in depressive symptoms at 4-month follow-up (d = -0.85 and -0.75 vs. SIM-PE and STD-PE, respectively). For depressive symptoms measured at 10-month follow-up, BFT was indistinguishable from STD-PE, whereas a moderate effect was observed in comparison with SIM-PE (d = -0.52). Moreover, positive aspects of caregiving, but not other secondary outcomes, continued to show intervention effect up to 10-month follow-up. DISCUSSION Benefit-finding is an efficacious intervention for depressive symptoms in Alzheimer caregivers, with strong effects in the medium-term post-intervention and possible moderate effects in the longer-term post-intervention.
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Affiliation(s)
- Sheung-Tak Cheng
- Department of Health and Physical Education, The Education University of Hong Kong, Hong Kong.,Department of Clinical Psychology, Norwich Medical School, University of East Anglia, UK
| | - Emily P M Mak
- Department of Health and Physical Education, The Education University of Hong Kong, Hong Kong
| | - Timothy Kwok
- Department of Medicine and Therapeutics, Hong Kong
| | | | - Linda C W Lam
- Department of Psychiatry, The Chinese University of Hong Kong, Hong Kong
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Long-Term Outcomes of the Benefit-Finding Group Intervention for Alzheimer Family Caregivers: A Cluster-Randomized Double-Blind Controlled Trial. Am J Geriatr Psychiatry 2019; 27:984-994. [PMID: 31076215 DOI: 10.1016/j.jagp.2019.03.013] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 01/10/2019] [Revised: 03/18/2019] [Accepted: 03/18/2019] [Indexed: 11/20/2022]
Abstract
OBJECTIVES To examine the effects of the group benefit-finding therapeutic intervention (BFT) for Alzheimer family caregivers up to 10-month follow-up. METHODS This was a cluster-randomized double-blind controlled trial in social centers and clinics. Participants included 129 caregivers. Inclusion criteria were 1) primary caregiver aged 18 years and older and without cognitive impairment, 2) providing 14 or more care hours per week to a relative with mild-to-moderate Alzheimer disease, and 3) scoring 3 or more on the Hamilton Depression Rating Scale. Exclusion criterion was care-recipient having parkinsonism or other forms of dementia. BFT (using cognitive reappraisal to find positive meanings) was evaluated against two forms of psychoeducation as controls-standard and simplified (lectures only) psychoeducation. All interventions had eight weekly sessions of 2 hours each. Primary outcome was depressive symptoms, whereas secondary outcomes were global burden, role overload, and psychological well-being. Measures were collected at baseline, postintervention, and 4- and 10-month follow-up. RESULTS Mixed-effects regression showed that BFT's effect on depressive symptoms conformed to a curvilinear pattern, in which the strong initial effect leveled out after postintervention and was maintained up to 10-month follow-up; this was true when compared against either control group. The effect on global burden was less impressive but moderate effect sizes were found at the two follow-ups. For psychological well-being, there was an increase in the BFT group at 4-month follow-up and a return to baseline afterward. No effect on role overload was found. CONCLUSION Benefit-finding reduces depressive symptoms as well as global burden in the long-term and increases psychological well-being in the medium-term.
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Chi YY, Glueck DH, Muller KE. Power and Sample Size for Fixed-Effects Inference in Reversible Linear Mixed Models. AM STAT 2018; 73:350-359. [PMID: 32042203 DOI: 10.1080/00031305.2017.1415972] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Abstract
Despite the popularity of the general linear mixed model for data analysis, power and sample size methods and software are not generally available for commonly used test statistics and reference distributions. Statisticians resort to simulations with homegrown and uncertified programs or rough approximations which are misaligned with the data analysis. For a wide range of designs with longitudinal and clustering features, we provide accurate power and sample size approximations for inference about fixed effects in linear models we call reversible. We show that under widely applicable conditions, the general linear mixed-model Wald test has non-central distributions equivalent to well-studied multivariate tests. In turn, exact and approximate power and sample size results for the multivariate Hotelling-Lawley test provide exact and approximate power and sample size results for the mixed-model Wald test. The calculations are easily computed with a free, open-source product that requires only a web browser to use. Commercial software can be used for a smaller range of reversible models. Simple approximations allow accounting for modest amounts of missing data. A real-world example illustrates the methods. Sample size results are presented for a multicenter study on pregnancy. The proposed study, an extension of a funded project, has clustering within clinic. Exchangeability among participants allows averaging across them to remove the clustering structure. The resulting simplified design is a single level longitudinal study. Multivariate methods for power provide an approximate sample size. All proofs and inputs for the example are in the Supplementary Materials (available online).
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Affiliation(s)
- Yueh-Yun Chi
- Department of Biostatistics, University of Florida
| | - Deborah H Glueck
- Department of Biostatistics and Informatics, University of Colorado Denver
| | - Keith E Muller
- Department of Health Outcomes and Policy, University of Florida
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Cheng ST, Chan KL, Lam RWL, Mok MHT, Chen PP, Chow YF, Chung JWY, Law ACB, Lee JSW, Leung EMF, Tam CWC. A multicomponent intervention for the management of chronic pain in older adults: study protocol for a randomized controlled trial. Trials 2017; 18:528. [PMID: 29121961 PMCID: PMC5680817 DOI: 10.1186/s13063-017-2270-3] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2017] [Accepted: 10/21/2017] [Indexed: 11/10/2022] Open
Abstract
BACKGROUND Studies have shown that physical interventions and psychological methods based on the cognitive behavioral approach are efficacious in alleviating pain and that combining both tends to yield more benefits than either intervention alone. In view of the aging population with chronic pain and the lack of evidence-based pain management programs locally, we developed a multicomponent intervention incorporating physical exercise and cognitive behavioral techniques and examined its long-term effects against treatment as usual (i.e., pain education) in older adults with chronic musculoskeletal pain in Hong Kong. METHODS/DESIGN We are conducting a double-blind, cluster-randomized controlled trial. A sample of 160 participants aged ≥ 60 years will be recruited from social centers or outpatient clinics and will be randomized on the basis of center/clinic to either the multicomponent intervention or the pain education program. Both interventions consist of ten weekly sessions of 90 minutes each. The primary outcome is pain intensity, and the secondary outcomes include pain interference, pain persistence, pain self-efficacy, pain coping, pain catastrophizing cognitions, health-related quality of life, depressive symptoms, and hip and knee muscle strength. All outcome measures will be collected at baseline, postintervention, and at 3 and 6 months follow-up. Intention-to-treat analysis will be performed using mixed-effects regression to see whether the multicomponent intervention alleviates pain intensity and associated outcomes over and above the effects of pain education (i.e., a treatment × time intervention effect). DISCUSSION Because the activities included in the multicomponent intervention were carefully selected for ready implementation by allied health professionals in general, the results of this study, if positive, will make available an efficacious, nonpharmacological pain management program that can be widely adopted in clinical and social service settings and will hence improve older people's access to pain management services. TRIAL REGISTRATION Chinese Clinical Trial Registry, ChiCTR-IIR-16008387. Registered on 28 April 2016.
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Affiliation(s)
- Sheung-Tak Cheng
- Department of Health and Physical Education, The Education University of Hong Kong, 10 Lo Ping Road, Tai Po, New Territories, Hong Kong. .,Department of Clinical Psychology, Norwich Medical School, University of East Anglia, Norfolk, NR4 7TJ, UK.
| | - Ka Long Chan
- Department of Health and Physical Education, The Education University of Hong Kong, 10 Lo Ping Road, Tai Po, New Territories, Hong Kong
| | - Rosanna W L Lam
- Department of Health and Physical Education, The Education University of Hong Kong, 10 Lo Ping Road, Tai Po, New Territories, Hong Kong.,Department of Clinical Psychology, Norwich Medical School, University of East Anglia, Norfolk, NR4 7TJ, UK
| | - Monique H T Mok
- Department of Rehabilitation and Extended Care, Kowloon Hospital, 147A Argyle Street, Kowloon, Hong Kong
| | - Phoon Ping Chen
- Department of Anesthesiology & Operating Services, Alice Ho Miu Ling Nethersole Hospital, 11 Chuen On Road, Tai Po, New Territories, Hong Kong
| | - Yu Fat Chow
- Department of Anesthesiology & Operating Theatre Services, Queen Elizabeth Hospital, 30 Gascoigne Road, Kowloon, Hong Kong
| | - Joanne W Y Chung
- Department of Health and Physical Education, The Education University of Hong Kong, 10 Lo Ping Road, Tai Po, New Territories, Hong Kong
| | - Alexander C B Law
- Department of Medicine and Geriatrics, Princess Margaret Hospital, 2-10 Princess Margaret Hospital Road, Lai Chi Kok, Kowloon, Hong Kong
| | - Jenny S W Lee
- Department of Medicine, Alice Ho Miu Ling Nethersole Hospital, 11 Chuen On Road, Tai Po, New Territories, Hong Kong
| | - Edward M F Leung
- Department of Medicine and Geriatrics, United Christian Hospital, 130 Hip Wo Street, Kwun Tong, Kowloon, Hong Kong
| | - Cindy W C Tam
- Department of Psychiatry, North District Hospital, 9 Po Kin Road, Sheung Shui, New Territories, Hong Kong
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Amatya A, Bhaumik DK. Sample size determination for multilevel hierarchical designs using generalized linear mixed models. Biometrics 2017; 74:673-684. [PMID: 28901009 DOI: 10.1111/biom.12764] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2016] [Revised: 07/01/2017] [Accepted: 07/01/2017] [Indexed: 01/01/2023]
Abstract
A unified statistical methodology of sample size determination is developed for hierarchical designs that are frequently used in many areas, particularly in medical and health research studies. The solid foundation of the proposed methodology opens a new horizon for power analysis in presence of various conditions. Important features such as joint significance testing, unequal allocations of clusters across intervention groups, and differential attrition rates over follow up time points are integrated to address some useful questions that investigators often encounter while conducting such studies. Proposed methodology is shown to perform well in terms of maintaining type I error rates and achieving the target power under various conditions. Proposed method is also shown to be robust with respect to violation of distributional assumptions of random-effects.
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Affiliation(s)
- Anup Amatya
- Department of Public Health Sciences, New Mexico State University, 1335 International Mall, RM 102, Las Cruces, New Mexico 88011, U.S.A
| | - Dulal K Bhaumik
- Division of Epidemiology and Biostatistics, Department of Psychiatry, University of Illinois at Chicago, Chicago, Illinois 60612, U.S.A
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Turner EL, Li F, Gallis JA, Prague M, Murray DM. Review of Recent Methodological Developments in Group-Randomized Trials: Part 1-Design. Am J Public Health 2017; 107:907-915. [PMID: 28426295 PMCID: PMC5425852 DOI: 10.2105/ajph.2017.303706] [Citation(s) in RCA: 107] [Impact Index Per Article: 15.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 02/05/2017] [Indexed: 11/04/2022]
Abstract
In 2004, Murray et al. reviewed methodological developments in the design and analysis of group-randomized trials (GRTs). We have highlighted the developments of the past 13 years in design with a companion article to focus on developments in analysis. As a pair, these articles update the 2004 review. We have discussed developments in the topics of the earlier review (e.g., clustering, matching, and individually randomized group-treatment trials) and in new topics, including constrained randomization and a range of randomized designs that are alternatives to the standard parallel-arm GRT. These include the stepped-wedge GRT, the pseudocluster randomized trial, and the network-randomized GRT, which, like the parallel-arm GRT, require clustering to be accounted for in both their design and analysis.
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Affiliation(s)
- Elizabeth L Turner
- Elizabeth L. Turner and John A. Gallis are with the Department of Biostatistics and Bioinformatics, Duke University, Durham, NC, and the Duke Global Health Institute, Duke University. Fan Li is with the Department of Biostatistics and Bioinformatics, Duke University. Melanie Prague is with the Department of Biostatistics, Harvard T. H. Chan School of Public Health, Boston, MA, and Inria, project team SISTM, Bordeaux, France. David M. Murray is with the Office of Disease Prevention, Division of Program Coordination and Strategic Planning, and the Office of the Director, National Institutes of Health, Rockville, MD
| | - Fan Li
- Elizabeth L. Turner and John A. Gallis are with the Department of Biostatistics and Bioinformatics, Duke University, Durham, NC, and the Duke Global Health Institute, Duke University. Fan Li is with the Department of Biostatistics and Bioinformatics, Duke University. Melanie Prague is with the Department of Biostatistics, Harvard T. H. Chan School of Public Health, Boston, MA, and Inria, project team SISTM, Bordeaux, France. David M. Murray is with the Office of Disease Prevention, Division of Program Coordination and Strategic Planning, and the Office of the Director, National Institutes of Health, Rockville, MD
| | - John A Gallis
- Elizabeth L. Turner and John A. Gallis are with the Department of Biostatistics and Bioinformatics, Duke University, Durham, NC, and the Duke Global Health Institute, Duke University. Fan Li is with the Department of Biostatistics and Bioinformatics, Duke University. Melanie Prague is with the Department of Biostatistics, Harvard T. H. Chan School of Public Health, Boston, MA, and Inria, project team SISTM, Bordeaux, France. David M. Murray is with the Office of Disease Prevention, Division of Program Coordination and Strategic Planning, and the Office of the Director, National Institutes of Health, Rockville, MD
| | - Melanie Prague
- Elizabeth L. Turner and John A. Gallis are with the Department of Biostatistics and Bioinformatics, Duke University, Durham, NC, and the Duke Global Health Institute, Duke University. Fan Li is with the Department of Biostatistics and Bioinformatics, Duke University. Melanie Prague is with the Department of Biostatistics, Harvard T. H. Chan School of Public Health, Boston, MA, and Inria, project team SISTM, Bordeaux, France. David M. Murray is with the Office of Disease Prevention, Division of Program Coordination and Strategic Planning, and the Office of the Director, National Institutes of Health, Rockville, MD
| | - David M Murray
- Elizabeth L. Turner and John A. Gallis are with the Department of Biostatistics and Bioinformatics, Duke University, Durham, NC, and the Duke Global Health Institute, Duke University. Fan Li is with the Department of Biostatistics and Bioinformatics, Duke University. Melanie Prague is with the Department of Biostatistics, Harvard T. H. Chan School of Public Health, Boston, MA, and Inria, project team SISTM, Bordeaux, France. David M. Murray is with the Office of Disease Prevention, Division of Program Coordination and Strategic Planning, and the Office of the Director, National Institutes of Health, Rockville, MD
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Ali SM, Giordano R, Lakhani S, Walker DM. A review of randomized controlled trials of medical record powered clinical decision support system to improve quality of diabetes care. Int J Med Inform 2016; 87:91-100. [DOI: 10.1016/j.ijmedinf.2015.12.017] [Citation(s) in RCA: 48] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/11/2015] [Revised: 11/28/2015] [Accepted: 12/23/2015] [Indexed: 11/30/2022]
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Rutterford C, Copas A, Eldridge S. Methods for sample size determination in cluster randomized trials. Int J Epidemiol 2015; 44:1051-67. [PMID: 26174515 PMCID: PMC4521133 DOI: 10.1093/ije/dyv113] [Citation(s) in RCA: 212] [Impact Index Per Article: 23.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 06/02/2015] [Indexed: 11/14/2022] Open
Abstract
BACKGROUND The use of cluster randomized trials (CRTs) is increasing, along with the variety in their design and analysis. The simplest approach for their sample size calculation is to calculate the sample size assuming individual randomization and inflate this by a design effect to account for randomization by cluster. The assumptions of a simple design effect may not always be met; alternative or more complicated approaches are required. METHODS We summarise a wide range of sample size methods available for cluster randomized trials. For those familiar with sample size calculations for individually randomized trials but with less experience in the clustered case, this manuscript provides formulae for a wide range of scenarios with associated explanation and recommendations. For those with more experience, comprehensive summaries are provided that allow quick identification of methods for a given design, outcome and analysis method. RESULTS We present first those methods applicable to the simplest two-arm, parallel group, completely randomized design followed by methods that incorporate deviations from this design such as: variability in cluster sizes; attrition; non-compliance; or the inclusion of baseline covariates or repeated measures. The paper concludes with methods for alternative designs. CONCLUSIONS There is a large amount of methodology available for sample size calculations in CRTs. This paper gives the most comprehensive description of published methodology for sample size calculation and provides an important resource for those designing these trials.
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Affiliation(s)
- Clare Rutterford
- Centre for Primary Care and Public Health, Barts and the London School of Medicine and Dentistry, Queen Mary University of London, London, UK and
| | - Andrew Copas
- Hub for Trials Methodology Research, MRC Clinical Trials Unit at University College London, London, UK
| | - Sandra Eldridge
- Centre for Primary Care and Public Health, Barts and the London School of Medicine and Dentistry, Queen Mary University of London, London, UK and
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Lam LCW, Chan WC, Leung T, Fung AWT, Leung EMF. Would older adults with mild cognitive impairment adhere to and benefit from a structured lifestyle activity intervention to enhance cognition?: a cluster randomized controlled trial. PLoS One 2015; 10:e0118173. [PMID: 25826620 PMCID: PMC4380493 DOI: 10.1371/journal.pone.0118173] [Citation(s) in RCA: 91] [Impact Index Per Article: 10.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2014] [Accepted: 01/05/2015] [Indexed: 12/01/2022] Open
Abstract
Background Epidemiologic evidence suggests that cognitive and physical activities are associated with better cognition in late life. The present study was conducted to examine the possible benefits of four structured lifestyle activity interventions and compare their effectiveness in optimizing cognition for older adults with mild cognitive impairment (MCI). Method and Findings This was a 12-month cluster randomized controlled trial. 555 community-dwelling Chinese older adults with MCI (295 with multiple-domain deficits (mdMCI), 260 with single-domain deficit (sdMCI)) were recruited. Participants were randomized into physical exercise (P), cognitive activity (C), integrated cognitive and physical exercise (CP), and social activity (S, active control) groups. Interventions comprised of one-hour structured activities three times per week. Primary outcome was Clinical Dementia Rating sum of boxes (CDR-SOB) scores. Secondary outcomes included Chinese versions of Alzheimer’s Disease Assessment Scale - Cognitive subscale (ADAS-Cog), delayed recall, Mini-Mental State Examination, Category Verbal Fluency Test (CVFT) and Disability Assessment for Dementia – Instrumental Activities of Daily Living (DAD-IADL). Percentage adherence to programs and factors affecting adherence were also examined. At 12th month, 423 (76.2%) completed final assessment. There was no change in CDR-SOB and DAD-IADL scores across time and intervention groups. Multilevel normal model and linear link function showed improvement in ADAS-Cog, delayed recall and CVFT with time (p<0.05). Post-hoc subgroup analyses showed that the CP group, compared with other intervention groups, had more significant improvements of ADAS-Cog, delayed recall and CVFT performance with sdMCI participants (p<0.05). Overall adherence rate was 73.3%. Improvements in ADAS-Cog and delayed recall scores were associated with adherence after controlling for age, education, and intervention groups (univariate analyses). Conclusions Structured lifestyle activity interventions were not associated with changes in everyday functioning, albeit with some improvements in cognitive scores across time. Higher adherence was associated with greater improvement in cognitive scores. Factors to enhance adherence should be specially considered in the design of psychosocial interventions for older adults with cognitive decline. Trial Registration ClinicalTrials.gov ChiCTR-TRC-11001359
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Affiliation(s)
- Linda Chiu-wa Lam
- Department of Psychiatry, The Chinese University of Hong Kong, Hong Kong
- * E-mail:
| | - Wai Chi Chan
- Department of Psychiatry, The University of Hong Kong, Hong Kong
| | - Tony Leung
- Department of Psychiatry, The Chinese University of Hong Kong, Hong Kong
| | - Ada Wai-tung Fung
- Department of Psychiatry, The Chinese University of Hong Kong, Hong Kong
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Heo M. Impact of subject attrition on sample size determinations for longitudinal cluster randomized clinical trials. J Biopharm Stat 2014; 24:507-22. [PMID: 24697555 DOI: 10.1080/10543406.2014.888442] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Abstract
Subject attrition is a ubiquitous problem in any type of clinical trial and, thus, needs to be taken into consideration at the design stage particularly to secure adequate statistical power. Here, we focus on longitudinal cluster randomized clinical trials (cluster-RCT) that aim to test the hypothesis that an intervention has an effect on the rate of change in the outcome over time. In this setting, the cluster-RCT assumes a three-level hierarchical data structure in which subjects are nested within a higher level unit such as clinics and are evaluated for outcome repeatedly over the study period. Furthermore, the subject-specific slopes can be modeled in terms of fixed or random coefficients in a mixed-effects linear model. Closed-form sample size formulas for testing the preceding hypothesis have been developed under an assumption of no attrition. In this article, we propose closed-form approximate samples size determinations with anticipated attrition rates by modifying those existing sample size formulas. With extensive simulations, we examine performances of the modified formulas under three attrition mechanisms: attrition completely at random, attrition at random, and attrition not at random. In conclusion, the proposed modification is very effective under fixed-slope models but yields biased, perhaps substantially so, statistical power under random slope models.
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Affiliation(s)
- Moonseong Heo
- a Division of Biostatistics, Department of Epidemiology and Population Health , Albert Einstein College of Medicine , Bronx , New York , USA
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Can leisure activities slow dementia progression in nursing home residents? A cluster-randomized controlled trial. Int Psychogeriatr 2014; 26:637-43. [PMID: 24411480 DOI: 10.1017/s1041610213002524] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 01/22/2023]
Abstract
BACKGROUND To examine the effects of complex cognitive (mahjong) and physical (Tai Chi) activities on dementia severity in nursing home residents with dementia. METHODS Cluster-randomized open-label controlled design. 110 residents were randomized by nursing home into three conditions: mahjong, Tai Chi, and simple handicrafts (control). Activities were conducted three times a week for 12 weeks. Clinical Dementia Rating (CDR) was taken at 0 (baseline), 3 (post-treatment), 6, and 9 months. The outcome measure was CDR sum-of-box, which is a composite measure of both cognitive and functional deterioration in dementia. RESULTS Intent-to-treat analyses were performed using multilevel regression models. Apolipoprotein E ε4 allele and education were included as covariates. Neither treatments had effects on the cognitive and functional components of the CDR, but mahjong had a significant interaction with time on the CDR sum-of-box total, suggesting a slower rate of global deterioration in the mahjong group as compared with the control group. CONCLUSIONS Mahjong led to a gradual improvement in global functioning and a slightly slower rate of dementia progression over time. The effect was generalized and was not specific to cognition or daily functioning.
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Heo M, Xue X, Kim MY. Sample size requirements to detect an intervention by time interaction in longitudinal cluster randomized clinical trials with random slopes. Comput Stat Data Anal 2013; 60:169-178. [PMID: 23459110 DOI: 10.1016/j.csda.2012.11.016] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Abstract
In longitudinal cluster randomized clinical trials (cluster-RCT), subjects are nested within a higher level unit such as clinics and are evaluated for outcome repeatedly over the study period. This study design results in a three level hierarchical data structure. When the primary goal is to test the hypothesis that an intervention has an effect on the rate of change in the outcome over time and the between-subject variation in slopes is substantial, the subject-specific slopes are often modeled as random coefficients in a mixed-effects linear model. In this paper, we propose approaches for determining the samples size for each level of a 3-level hierarchical trial design based on ordinary least squares (OLS) estimates for detecting a difference in mean slopes between two intervention groups when the slopes are modeled as random. Notably, the sample size is not a function of the variances of either the second or the third level random intercepts and depends on the number of second and third level data units only through their product. Simulation results indicate that the OLS-based power and sample sizes are virtually identical to the empirical maximum likelihood based estimates even with varying cluster sizes. Sample sizes for random versus fixed slope models are also compared. The effects of the variance of the random slope on the sample size determinations are shown to be enormous. Therefore, when between-subject variations in outcome trends are anticipated to be significant, sample size determinations based on a fixed slope model can result in a seriously underpowered study.
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Affiliation(s)
- Moonseong Heo
- Division of Biostatistics, Department of Epidemiology and Population Health, Albert Einstein College of Medicine, Bronx, New York, USA
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Cheng ST, Lau RWL, Mak EPM, Ng NSS, Lam LCW, Fung HH, Lai JCL, Kwok T, Lee DTF. A benefit-finding intervention for family caregivers of persons with Alzheimer disease: study protocol of a randomized controlled trial. Trials 2012; 13:98. [PMID: 22747914 PMCID: PMC3413525 DOI: 10.1186/1745-6215-13-98] [Citation(s) in RCA: 37] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2012] [Accepted: 07/02/2012] [Indexed: 12/13/2022] Open
Abstract
Background Caregivers of relatives with Alzheimer’s disease are highly stressed and at risk for physical and psychiatric conditions. Interventions are usually focused on providing caregivers with knowledge of dementia, skills, and/or support, to help them cope with the stress. This model, though true to a certain extent, ignores how caregiver stress is construed in the first place. Besides burden, caregivers also report rewards, uplifts, and gains, such as a sense of purpose and personal growth. Finding benefits through positive reappraisal may offset the effect of caregiving on caregiver outcomes. Design Two randomized controlled trials are planned. They are essentially the same except that Trial 1 is a cluster trial (that is, randomization based on groups of participants) whereas in Trial 2, randomization is based on individuals. Participants are randomized into three groups - benefit finding, psychoeducation, and simplified psychoeducation. Participants in each group receive a total of approximately 12 hours of training either in group or individually at home. Booster sessions are provided at around 14 months after the initial treatment. The primary outcomes are caregiver stress (subjective burden, role overload, and cortisol), perceived benefits, subjective health, psychological well-being, and depression. The secondary outcomes are caregiver coping, and behavioral problems and functional impairment of the care-recipient. Outcome measures are obtained at baseline, post-treatment (2 months), and 6, 12, 18 and 30 months. Discussion The emphasis on benefits, rather than losses and difficulties, provides a new dimension to the way interventions for caregivers can be conceptualized and delivered. By focusing on the positive, caregivers may be empowered to sustain caregiving efforts in the long term despite the day-to-day challenges. The two parallel trials will provide an assessment of whether the effectiveness of the intervention depends on the mode of delivery. Trial registration Chinese Clinical Trial Registry (http://www.chictr.org/en/) identifier number ChiCTR-TRC-10000881.
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Affiliation(s)
- Sheung-Tak Cheng
- Department of Psychological Studies, Hong Kong Institute of Education, 10 Lo Ping Road, Tai Po, NT, Hong Kong.
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Heo M, Leon AC. Sample size requirements to detect an intervention by time interaction in longitudinal cluster randomized clinical trials. Stat Med 2009; 28:1017-27. [PMID: 19153969 DOI: 10.1002/sim.3527] [Citation(s) in RCA: 69] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
Abstract
In designing a longitudinal cluster randomized clinical trial (cluster-RCT), the interventions are randomly assigned to clusters such as clinics. Subjects within the same clinic will receive the identical intervention. Each will be assessed repeatedly over the course of the study. A mixed-effects linear regression model can be applied in a cluster-RCT with three-level data to test the hypothesis that the intervention groups differ in the course of outcome over time. Using a test statistic based on maximum likelihood estimates, we derived closed-form formulae for statistical power to detect the intervention by time interaction and the sample size requirements for each level. Importantly, the sample size does not depend on correlations among second-level data units and the statistical power function depends on the number of second- and third-level data units through their product. A simulation study confirmed that theoretical power estimates based on the derived formulae are nearly identical to empirical estimates.
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Affiliation(s)
- Moonseong Heo
- Department of Epidemiology and Population Health, Albert Einstein College of Medicine, Bronx, NY, USA.
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Victor RG, Ravenell JE, Freeman A, Bhat DG, Storm JS, Shafiq M, Knowles P, Hannan PJ, Haley R, Leonard D. A barber-based intervention for hypertension in African American men: design of a group randomized trial. Am Heart J 2009; 157:30-6. [PMID: 19081393 PMCID: PMC2638989 DOI: 10.1016/j.ahj.2008.08.018] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 06/03/2008] [Accepted: 08/20/2008] [Indexed: 01/03/2023]
Abstract
BACKGROUND Barbershops constitute potential sites for community health promotion programs targeting hypertension (HTN) in African American men but such programs previously have not been formally evaluated. METHODS A randomized trial (ClinicalTrials.gov no. NCT00325533) will test whether a continuous HTN detection and medical referral program conducted by influential peers (barbers) in a receptive community setting (barbershops) can promote treatment-seeking behavior and thus lower blood pressure (BP) among the regular customers with HTN. Barbers will offer a BP check with each haircut and encourage appropriate medical referral using real stories of other customers modeling the desired behaviors. A cohort of 16 barbershops will go through a pretest/posttest group-randomization protocol. Serial cross-sectional data collection periods (10 weeks each) will be conducted by interviewers to obtain accurate snapshots of HTN control in each barbershop before and after 10 months of either barber-based intervention or no active intervention. The primary outcome is BP control: BP <135/85 mm Hg (nondiabetic subjects) and <130/80 mm Hg (diabetic subjects) measured in the barbershop during the 2 data collection periods. The multilevel analysis plan uses hierarchical models to assess the effect of covariates on HTN control and secondary outcomes while accounting for clustering of observations within barbershops. CONCLUSIONS By linking community health promotion to the health care system, this program could serve as a new model for HTN control and cardiovascular risk reduction in African American men on a nationwide scale.
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Affiliation(s)
- Ronald G Victor
- Division of Hypertension, Department of Internal Medicine, and Donald W Reynolds Clinical Research Center, University of Texas Southwestern Medical Center, Dallas, TX 75390-8586, USA.
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Electronic medical record-assisted design of a cluster-randomized trial to improve diabetes care and outcomes. J Gen Intern Med 2008; 23:383-91. [PMID: 18373134 PMCID: PMC2359510 DOI: 10.1007/s11606-007-0454-3] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
Abstract
BACKGROUND Electronic medical records (EMRs) have the potential to facilitate the design of large cluster-randomized trials (CRTs). OBJECTIVE To describe the design of a CRT of clinical decision support to improve diabetes care and outcomes. METHODS In the Diabetes Improvement Group-Intervention Trial (DIG-IT), we identified and balanced preassignment characteristics of 12,675 diabetic patients cared for by 147 physicians in 24 practices of 2 systems using the same vendor's EMR. EMR-facilitated disease management was system A's experimental intervention; system B interventions involved patient empowerment, with or without disease management. For our sample, we: (1) identified characteristics associated with response to interventions or outcomes; (2) summarized feasible partitions of 10 system A practices (2 groups) and 14 system B practices (3 groups) using intra-cluster correlation coefficients (ICCs) and standardized differences; (3) selected (blinded) partitions to effectively balance the characteristics; and (4) randomly assigned groups of practices to interventions. RESULTS In System A, 4,306 patients, were assigned to 2 groups of practices; 8,369 patients in system B were assigned to 3 groups of practices. Nearly all baseline outcome variables and covariates were well-balanced, including several not included in the initial design. DIG-IT's balance was superior to alternative partitions based on volume, geography or demographics alone. CONCLUSIONS EMRs facilitated rigorous CRT design by identifying large numbers of patients with diabetes and enabling fair comparisons through preassignment balancing of practice sites. Our methods can be replicated in other settings and for other conditions, enhancing the power of other translational investigations.
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