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Objective: Researchers in Health Sciences and Medicine often use cohort designs to study treatment effects and changes of outcome variables over time period. The costs of these studies can be reduced by choosing an optimal number of repeated measurements over time and by selecting cohorts of subjects more efficiently with optimal design procedures. The objective of this study is to provide evidence on how to design large-scale cohort studies with budget constraints as efficiently as possible., Study Design and Setting: A linear cost function for repeated measurements is proposed, and this cost function is used in the optimization procedure. For a given budget/cost, different designs for linear mixed-effects models are compared by means of their efficiency., Results: We found that adding more repeated measures is only beneficiary if the costs of selecting and measuring a new subject are much higher than the costs of obtaining an additional measurement for an already recruited subject. However, this gain in efficiency and power is not very large., Conclusion: Adding more cohorts or repeated measurements do not necessarily lead to a gain in efficiency of the estimated model parameters. A general guideline for the optimal choice of a cohort design in practice is required and we offer this guideline., (Copyright © 2011 Elsevier Inc. All rights reserved.)

The design of a multi-subject fMRI experiment needs specification of the number of subjects and scanning time per subject. For example, for a blocked design with conditions A or B, fixed block length and block order ABN, where N denotes a null block, the optimal number of cycles of ABN and the optimal number of subjects have to be determined. This paper presents a method to determine the optimal number of subjects and optimal number of cycles for a blocked design based on the A-optimality criterion and a linear cost function by which the number of cycles and the number of subjects are restricted. Estimation of individual stimulus effects and estimation of contrasts between stimulus effects are both considered. The mixed-effects model is applied and analytical results for the A-optimal number of subjects and A-optimal number of cycles are obtained under the assumption of uncorrelated errors. For correlated errors with a first-order autoregressive (AR1) error structure, numerical results are presented. Our results show how the optimal number of cycles and subjects depend on the within- to between-subject variance ratio. Our method is a new approach to determine the optimal scanning time and optimal number of subjects for a multi-subject fMRI experiment. In contrast to previous results based on power analyses, the optimal number of cycles and subjects can be described analytically and costs are considered., (Copyright © 2011 Elsevier Inc. All rights reserved.)

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.

The D-optimality criterion is used to construct optimal designs for different numbers of independent cohorts, which constitute a number of repeated measurements per subject over time. A cost function for longitudinal data is proposed, and the optimality criterion is optimized taking into account the cost of the study. First, an optimal number of design points for a given number of cohorts and cost was identified. Then, an optimal number of cohorts is identified by comparing the relative efficiencies (REs). A numerical study shows that for models describing the trend of a continuous outcome over time by polynomials, the most efficient number of repeated measurements is equal to the sum of the total number of cohorts and the degree of the polynomial in the model. REs of a purely longitudinal cohort design with only one cohort, and mixed longitudinal and cross-sectional cohort designs with more cohorts are compared. The results show that a purely longitudinal cohort design with only one cohort of subjects measured at the optimal time points is the most efficient design. The findings in this paper show that one can obtain a highly efficient design for parameter estimation with only a few repeated measurements. The results of this study will reduce the cost of data collection and ease the logistical burdens in cohort studies.

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.

Cluster randomized and multicentre trials evaluate the effect of a treatment on persons nested within clusters, for instance, patients within clinics or pupils within schools. Optimal sample sizes at the cluster (centre) and person level have been derived under the restrictive assumption of equal sample sizes per cluster. This paper addresses the relative efficiency of unequal versus equal cluster sizes in case of cluster randomization and person randomization within clusters. Starting from maximum likelihood parameter estimation, the relative efficiency is investigated numerically for a range of cluster size distributions. An approximate formula is presented for computing the relative efficiency as a function of the mean and variance of cluster size and the intraclass correlation, which can be used for adjusting the sample size. The accuracy of this formula is checked against the numerical results and found to be quite good. It is concluded that the loss of efficiency due to variation of cluster sizes rarely exceeds 10 per cent and can be compensated by sampling 11 per cent more clusters., ((c) 2006 John Wiley & Sons, Ltd.)

The effect of number of repeated measures on the variance of the generalized least squares (GLS) treatment effect estimator is considered assuming a linearly divergent treatment effect, equidistant time-points and either a fixed number of subjects or a fixed study budget. The optimal combination of group sizes and number of repeated measures is calculated by minimizing this variance subject to a linear cost function. For a fixed number of subjects, the variance of the GLS treatment effect estimator can be decreased by adding intermediate measures per subject. This decrease is relatively large if a) the covariance structure is compound symmetric or b) the structure approaches compound symmetry and the correlation between two repeated measures does not exceed 0.80, or c) the correlation between two repeated measures does not exceed 0.60 if the time-lag goes to zero. In case the sample sizes and number of repeated measures are limited by budget constraints and the covariance structure includes a first-order auto-regression part, two repeated measures per subject yield highly efficient treatment effect estimators. Otherwise, it is more efficient to have more than two repeated measures. 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. The numerical results are illustrated by three examples.

In this article, the optimal selection and allocation of time points in repeated measures experiments is considered. D-optimal cohort designs are computed numerically for the first- and second-degree polynomial models with random intercept, random slope, and first-order autoregressive serial correlations. Because the optimal designs are locally optimal, it is proposed to use a maximin criterion. It is shown that, for a large class of symmetric designs, the smallest relative efficiency over the model parameter space is substantial.

In medical research the responses of patients to a number of items are often combined into a summary measure or total score for a more general patient characteristic, such as mobility. Clinical and statistical criteria exist for determining the weight of each question in the total score. The choice of weights may affect the differences between patients. The total score is often analysed statistically as if it had interval level of measurement, thereby allowing conclusions about the size of differences between patients, but it has merely an ordinal level. The incorrectness of the interval assumption may also affect differences between patients or patient groups. Finally, differences between patients are less dependent on the weighting of the items and on the assumption of an interval scale as the total score is based on more homogeneous items. Standard statistical software contains statistical methods for determining the homogeneity as well as the weights.