1,721,040 research outputs found
ANCOVA versus change from baseline: more power in randomized studies, more bias in nonrandomized studies
No full textBackground and Objective: For inferring a treatment effect from the difference between a treated and untreated group on a quantitative outcome measured before and after treatment, current methods are analysis of covariance (ANCOVA) of the outcome with the baseline as covariate, and analysis of variance (ANOVA) of change from baseline. This article compares both methods on power and bias, for randomized and nonrandomized studies. Methods: The methods are compared by writing both as a regression model and as a repeated measures model, and are applied to a nonrandomized study of preventing depression. Results: In randomized studies both methods are unbiased, but ANCOVA has more power. If treatment assignment is based on the baseline, only ANCOVA is unbiased. In nonrandomized studies with preexisting groups differing at baseline, the two methods cannot both be unbiased, and may contradict each other. In the study of depression, ANCOVA suggests absence, but ANOVA of change suggests presence, of a treatment effect. The methods differ because ANCOVA assumes absence of a baseline difference. Conclusion: In randomized studies and studies with treatment assignment depending on the baseline, ANCOVA must be used. In nonrandomized studies of preexisting groups, ANOVA of change seems less biased than ANCOVA, but two control groups and two baseline measurements are recommended
Optimal Experimental Design With Nesting of Persons in Organizations
No full textThis 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
ANCOVA Versus CHANGE From Baseline in Nonrandomized Studies: The Difference
No full textThe pretest-posttest control group design can be analyzed with the posttest as dependent variable and the pretest as covariate (ANCOVA) or with the difference between posttest and pretest as dependent variable (CHANGE). These 2 methods can give contradictory results if groups differ at pretest, a phenomenon that is known as Lord's paradox. Literature claims that ANCOVA is preferable if treatment assignment is based on randomization or on the pretest and questionable for preexisting groups. Some literature suggests that Lord's paradox has to do with measurement error in the pretest. This article shows two new things: First, the claims are confirmed by proving the mathematical equivalence of ANCOVA to a repeated measures model without group effect at pretest. Second, correction for measurement error in the pretest is shown to lead back to ANCOVA or to CHANGE, depending on the assumed absence or presence of a true group difference at pretest. These two new theoretical results are illustrated with multilevel (mixed) regression and structural equation modeling of data from two studies
Sample size adjustments for varying cluster sizes in cluster randomized trials with binary outcomes analyzed with second-order PQL mixed logistic regression
Full text linkAdjustments of sample size formulas are given for varying cluster sizes in cluster randomized trials with a binary outcome when testing the treatment effect with mixed effects logistic regression using second-order penalized quasi-likelihood estimation (PQL). Starting from first-order marginal quasi-likelihood (MQL) estimation of the treatment effect, the asymptotic relative efficiency of unequal versus equal cluster sizes is derived. A Monte Carlo simulation study shows this asymptotic relative efficiency to be rather accurate for realistic sample sizes, when employing second-order PQL. An approximate, simpler formula is presented to estimate the efficiency loss due to varying cluster sizes when planning a trial. In many cases sampling 14 per cent more clusters is sufficient to repair the efficiency loss due to varying cluster sizes. Since current closed-form formulas for sample size calculation are based on first-order MQL, planning a trial also requires a conversion factor to obtain the variance of the second-order PQL estimator. In a second Monte Carlo study, this conversion factor turned out to be 1.25 at most
Varying cluster sizes in trials with clusters on one treatment arm: sample size adjustments when testing treatment effects with linear mixed models.
Full text linkTrials in which treatments induce clustering of observations in one of two treatment arms, such as when comparing group therapy with pharmacological treatment or with a waiting-list group, are examined with respect to the efficiency loss caused by varying cluster sizes. When observations are (approximately) normally distributed, treatment effects can be estimated and tested through linear mixed model analysis. For maximum likelihood estimation, the asymptotic relative efficiency of unequal versus equal cluster sizes is derived. In an extensive Monte Carlo simulation for small sample sizes, the asymptotic relative efficiency turns out to be accurate for the treatment effect, but less accurate for the random intercept variance. For the treatment effect, the efficiency loss due to varying cluster sizes rarely exceeds 10 per cent, which can be regained by recruiting 11 per cent more clusters for one arm and 11 per cent more persons for the other. For the intercept variance the loss can be 16 per cent, which requires recruiting 19 per cent more clusters for one arm, with no additional recruitment of subjects for the other arm
Efficient design of cluster randomized and multicentre trials with unknown intraclass correlation
Full text linkFor cluster randomized and multicentre trials evaluating the effect of a treatment on persons nested within clusters, equations have been published to compute the optimal sample sizes at the cluster and person level as a function of sampling costs and intraclass correlation (ICC). Here, optimal means maximum power and precision for a given sampling budget, or minimum sampling costs for a given power and precision. However, the ICC is usually unknown, and the optimal sample sizes depend strongly on this ICC. To overcome this local optimality problem, this study presents Maximin designs (MMDs) based on relative efficiency (RE) and efficiency. These designs perform well over a range of possible ICC values either in terms of RE compared with the locally optimal designs, or in terms of minimum efficiency (maximum variance) of the treatment effect estimator. The use of MMDs is illustrated using information from many cluster randomized trials in primary care. It is concluded that MMDs and the optimal design for an ICC halfway its assumed range are efficient for a range of ICC values and recommendable for practical use. This requires that trial reports mention the study cost per cluster and person
Use of covariates in randomized controlled trials
No full textA recent discussion in this journal illustrates some recurrentmisunderstandings about the role of covariates in randomized controlledtrials (rcts). This letter aims at clarifying this role and at pointingout a pitfall in spss repeated measures anova. We hope that our commentarywill contribute to a further improvement in the use of advanced statisticsin neuropsychology
Optimal Design for Functional Magnetic Resonance Imaging Experiments: Methodology, Challenges, and Future Perspectives
No full textThis paper provides an overview of optimal design for functional magnetic resonance imaging (fMRI) studies. We present the main types of fMRI designs, namely blocked and event-related designs, and common objectives of fMRI experiments, for example, localization of task-related activity in the human brain. Furthermore, we present an introduction into the methodology for analysis and optimization of fMRI experiments, for instance common analysis models and applied optimality criteria. We outline some of the problems encountered when optimizing fMRI experiments, for example, the temporal autocorrelation between measurements in fMRI data. The most important results for optimization of blocked and event-related designs with regard to the different design objectives are presented and explained. Finally, we conclude with future perspectives and challenges for optimization of fMRI experiments
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