Efficient treatment allocation in 2 × 2 cluster randomized trials, when costs and variances are heterogeneous.

Typically, clusters and individuals in cluster randomized trials are allocated across treatment conditions in a balanced fashion. This is optimal under homogeneous costs and outcome variances. However, both the costs and the variances may be heterogeneous. Then, an unbalanced allocation is more efficient but impractical as the outcome variance is unknown in the design stage of a study. A practical alternative to the balanced design could be a design optimal for known and possibly heterogeneous costs and homogeneous variances. However, when costs and variances are heterogeneous, both designs suffer from loss of efficiency, compared with the optimal design. Focusing on cluster randomized trials with a 2 × 2 design, the relative efficiency of the balanced design and of the design optimal for heterogeneous costs and homogeneous variances is evaluated, relative to the optimal design. We consider two heterogeneous scenarios (two treatment arms with small, and two with large, costs or variances, or one small, two intermediate, and one large costs or variances) at each design level (cluster, individual, and both). Within these scenarios, we compute the relative efficiency of the two designs as a function of the extents of heterogeneity of the costs and variances, and the congruence (the cheapest treatment has the smallest variance) and incongruence (the cheapest treatment has the largest variance) between costs and variances. We find that the design optimal for heterogeneous costs and homogeneous variances is generally more efficient than the balanced design and we illustrate this theory on a trial that examines methods to reduce radiological referrals from general practices. Copyright © 2016 John Wiley & Sons, Ltd.

The effect of heterogeneous variance on efficiency and power of cluster randomized trials with a balanced 2 × 2 factorial design.

Sample size calculation for cluster randomized trials (CRTs) with a [Formula: see text] factorial design is complicated due to the combination of nesting (of individuals within clusters) with crossing (of two treatments). Typically, clusters and individuals are allocated across treatment conditions in a balanced fashion, which is optimal under homogeneity of variance. However, the variance is likely to be heterogeneous if there is a treatment effect. An unbalanced allocation is then more efficient, but impractical because the optimal allocation depends on the unknown variances. Focusing on CRTs with a [Formula: see text] design, this paper addresses two questions: How much efficiency is lost by having a balanced design when the outcome variance is heterogeneous? How large must the sample size be for a balanced allocation to have sufficient power under heterogeneity of variance? We consider different scenarios of heterogeneous variance. Within each scenario, we determine the relative efficiency of a balanced design, as a function of the level (cluster, individual, both) and amount of heterogeneity of the variance. We then provide a simple correction of the sample size for the loss of power due to heterogeneity of variance when a balanced allocation is used. The theory is illustrated with an example of a published 2 x2 CRT.

Optimal and maximin sample sizes for multicentre cost-effectiveness trials.

This paper deals with the optimal sample sizes for a multicentre trial in which the cost-effectiveness of two treatments in terms of net monetary benefit is studied. A bivariate random-effects model, with the treatment-by-centre interaction effect being random and the main effect of centres fixed or random, is assumed to describe both costs and effects. The optimal sample sizes concern the number of centres and the number of individuals per centre in each of the treatment conditions. These numbers maximize the efficiency or power for given research costs or minimize the research costs at a desired level of efficiency or power. Information on model parameters and sampling costs are required to calculate these optimal sample sizes. In case of limited information on relevant model parameters, sample size formulas are derived for so-called maximin sample sizes which guarantee a power level at the lowest study costs. Four different maximin sample sizes are derived based on the signs of the lower bounds of two model parameters, with one case being worst compared to others. We numerically evaluate the efficiency of the worst case instead of using others. Finally, an expression is derived for calculating optimal and maximin sample sizes that yield sufficient power to test the cost-effectiveness of two treatments.

Bayesian design for dichotomous repeated measurements with autocorrelation.

In medicine and health sciences, binary outcomes are often measured repeatedly to study their change over time. A problem for such studies is that designs with an optimal efficiency for some parameter values may not be efficient for other values. To handle this problem, we propose Bayesian designs which formally account for the uncertainty in the parameter values for a mixed logistic model which allows quadratic changes over time. Bayesian D-optimal allocations of time points are computed for different priors, costs, covariance structures and values of the autocorrelation. Our results show that the optimal number of time points increases with the subject-to-measurement cost ratio, and that neither the optimal number of time points nor the optimal allocations of time points appear to depend strongly on the prior, the covariance structure or on the size of the autocorrelation. It also appears that for subject-to-measurement cost ratios up to five, four equidistant time points, and for larger cost ratios, five or six equidistant time points are highly efficient. Our results are compared with the actual design of a respiratory infection study in Indonesia and it is shown that, selection of a Bayesian optimal design will increase efficiency, especially for small cost ratios.

Efficient treatment allocation in two-way nested designs.

Cluster randomized and multicenter trials sometimes combine two treatments A and B in a factorial design, with conditions such as A, B, A and B, or none. This results in a two-way nested design. The usual issue of sample size and power now arises for various clinically relevant contrast hypotheses. Assuming a fixed total sample size at each level (number of clusters or centers, number of patients), we derive the optimal proportion of the total sample to be allocated to each treatment arm. We consider treatment assignment first at the highest level (cluster randomized trial) and then at the lowest level (multicenter trial). We derive the optimal allocation ratio for various sets of clinically relevant hypotheses. We then evaluate the efficiency of each allocation and show that the popular balanced design is optimal or highly efficient for a range of research questions except for contrasting one treatment arm with all other treatment arms. We finally present simple equations for the total sample size needed to test each effect of interest in a balanced design, as a function of effect size, power and type I error α. All results are illustrated on a cluster-randomized trial on smoking prevention in primary schools and on a multicenter trial on lifestyle improvement in general practices.

Sample size calculation in cost-effectiveness cluster randomized trials: optimal and maximin approaches.

In this paper, the optimal sample sizes at the cluster and person levels for each of two treatment arms are obtained for cluster randomized trials where the cost-effectiveness of treatments on a continuous scale is studied. The optimal sample sizes maximize the efficiency or power for a given budget or minimize the budget for a given efficiency or power. Optimal sample sizes require information on the intra-cluster correlations (ICCs) for effects and costs, the correlations between costs and effects at individual and cluster levels, the ratio of the variance of effects translated into costs to the variance of the costs (the variance ratio), sampling and measuring costs, and the budget. When planning, a study information on the model parameters usually is not available. To overcome this local optimality problem, the current paper also presents maximin sample sizes. The maximin sample sizes turn out to be rather robust against misspecifying the correlation between costs and effects at the cluster and individual levels but may lose much efficiency when misspecifying the variance ratio. The robustness of the maximin sample sizes against misspecifying the ICCs depends on the variance ratio. The maximin sample sizes are robust under misspecification of the ICC for costs for realistic values of the variance ratio greater than one but not robust under misspecification of the ICC for effects. Finally, we show how to calculate optimal or maximin sample sizes that yield sufficient power for a test on the cost-effectiveness of an intervention.

Evaluation of the Hearing Aid Rehabilitation Questionnaire in Dutch: Examination of its Psychometric Properties and Potential Use as a Screening Instrument.

Items pertaining to hearing and hearing aids from the Hearing Aid Rehabilitation Questionnaire were applied to a heterogeneous sample of Dutch patients aged 55 years and more to evaluate their potential use in hearing screening. Subjects aged 55+ were recruited from a large general practitioners practice to participate. Three groups were formed: a group of 63 persons with a hearing aid, a group of 64 without a hearing aid but with sufficient hearing impairment to qualify for hearing aid reimbursement, and a group of 85 non-hearing impaired persons. Factor and reliability analyses revealed a structure with two scales regarding hearing, namely functionality and social hearing and three scales pertaining to hearing aids, namely hearing aid stigma, pressure to be assessed and not wanting a hearing aid. Scale validity was assessed with pure tone averages over the frequencies 1, 2 and 4 kHz and with a visual analogue scale for subjective hearing. The derived scales can be applied reliably in audiological assessment in an adult hearing screen setting to detect experienced hearing problems as well as attitudes related to hearing and hearing aids.

The effect of guiding questions on students' performance and attitude towards statistics.

BACKGROUND: In this study, the effect of guidance on students' performance was investigated. This effect was hypothesized to be manifested through a reduction of cognitive load and enhancement of self-explanations. AIM: The goal of this study was to investigate the effect of guiding questions on students' understanding of statistics. SAMPLE AND METHOD: In an experimental setting, two randomly selected groups of students (N= 49) answered achievement and transfer questions on statistics as a measure of performance. Students in the intervention condition were given guiding questions to direct their way of reasoning before they answered the achievement questions. The students in the control condition were asked to write down their way of thinking before they answered the same achievement questions. In this way, both groups were stimulated to self-explain, but only the reasoning processes of the students in the intervention condition were guided. RESULTS AND CONCLUSION: It was found that students in the intervention condition performed significantly better on achievement and transfer questions and that this effect of guidance was mediated by self-explanations. Attitude towards statistics was positively related to performance.

Optimal design for nonlinear estimation of the hemodynamic response function.

Subject-specific hemodynamic response functions (HRFs) have been recommended to capture variation in the form of the hemodynamic response between subjects (Aguirre et al., [ 1998]: Neuroimage 8:360-369). The purpose of this article is to find optimal designs for estimation of subject-specific parameters for the double gamma HRF. As the double gamma function is a nonlinear function of its parameters, optimal design theory for nonlinear models is employed in this article. The double gamma function is linearized by a Taylor approximation and the maximin criterion is used to handle dependency of the D-optimal design on the expansion point of the Taylor approximation. A realistic range of double gamma HRF parameters is used for the expansion point of the Taylor approximation. Furthermore, a genetic algorithm (GA) (Kao et al., [ 2009]: Neuroimage 44:849-856) is applied to find locally optimal designs for the different expansion points and the maximin design chosen from the locally optimal designs is compared to maximin designs obtained by m-sequences, blocked designs, designs with constant interstimulus interval (ISI) and random event-related designs. The maximin design obtained by the GA is most efficient. Random event-related designs chosen from several generated designs and m-sequences have a high efficiency, while blocked designs and designs with a constant ISI have a low efficiency compared to the maximin GA design.

The effect of directive tutor guidance on students' conceptual understanding of statistics in problem-based learning.

BACKGROUND: Education is aimed at students reaching conceptual understanding of the subject matter, because this leads to better performance and application of knowledge. Conceptual understanding depends on coherent and error-free knowledge structures. The construction of such knowledge structures can only be accomplished through active learning and when new knowledge can be integrated into prior knowledge. AIMS: The intervention in this study was directed at both the activation of students as well as the integration of knowledge. SAMPLE: Undergraduate university students from an introductory statistics course, in an authentic problem-based learning (PBL) environment, were randomly assigned to conditions and measurement time points. METHOD: In the PBL tutorial meetings, half of the tutors guided the discussions of the students in a traditional way. The other half guided the discussions more actively by asking directive and activating questions. To gauge conceptual understanding, the students answered open-ended questions asking them to explain and relate important statistical concepts. RESULTS AND CONCLUSIONS: Results of the quantitative analysis show that providing directive tutor guidance improved understanding. Qualitative data of students' misconceptions seem to support this finding. Long-term retention of the subject matter seemed to be inadequate.

Too many cohorts and repeated measurements are a waste of resources.

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.

Optimal design of multi-subject blocked fMRI experiments.

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.

ODmixed: a tool to obtain optimal designs for heterogeneous longitudinal studies with dropout.

ODMixed is a computer program to obtain optimal designs for linear mixed models of longitudinal studies. These designs account for heterogeneous correlated errors and for data with dropout. Designs are compared by using relative efficiencies, e.g., between a D-optimal design for homogeneous data and another for heterogeneous data or between a D-optimal design for complete data against another that optimizes designs when data is missing at random. Two examples are worked out to illustrate how researchers could use this computer program to profit of optimal design theory at the planning stage of longitudinal studies.

Robustness of optimal design of fMRI experiments with application of a genetic algorithm.

In this paper we apply the genetic algorithm developed by Kao et al. (2009) to find designs which are robust against misspecification of the error autocorrelation. Two common optimality criteria, the A-optimality criterion and the D-optimality criterion, based upon a general linear model are employed to obtain locally optimal designs for a given value of the autocorrelation. The maximin criterion is then used to obtain designs which are robust against misspecification of the autocorrelation. Furthermore, robustness depending on the choice of optimality criterion is evaluated. We show analytically and empirically that the A- and D-optimality criterion will result in different optimal designs, e.g. with different stimulus frequencies. Optimal stimulus frequency for the A-optimality criterion has been derived by Liu et al. (2004) whereas we derive here the optimal stimulus frequency for the D-optimality criterion. Conclusions about the robustness of an optimal design against misspecification of model parameters and choice of optimality criterion are drawn based upon our results.

A cluster-randomized trial of an educational intervention to reduce the use of physical restraints with psychogeriatric nursing home residents.

OBJECTIVES: To investigate the effects of an educational intervention on the use of physical restraints with psychogeriatric nursing home residents. DESIGN: Cluster-randomized trial. SETTING: Fifteen psychogeriatric nursing home wards in the Netherlands. PARTICIPANTS: In total, 432 psychogeriatric nursing home residents from 15 psychogeriatric nursing home wards in seven nursing homes were selected for participation; 404 consented, and 371 of these were available at baseline. Two hundred forty-one from 14 wards had complete data and were included in the data analyses. INTERVENTION: The nursing home wards were assigned at random to educational intervention or control status. The educational intervention consisted of an educational program for nursing staff combined with consultation with a nurse specialist (registered nurse (RN) level). MEASUREMENTS: Data were collected at baseline and 1, 4, and 8 months postintervention. At each measurement, the use of physical restraints was measured using observations of blinded, trained observers on four separate occasions over a 24-hour period. Other resident characteristics, such as cognitive status, were determined using the Minimum Data Set. RESULTS: Logistic and linear regression analyses showed no treatment effect on restraint status, restraint intensity, or multiple restraint use in any of the three postintervention measurements. Furthermore, only small changes occurred in the types of restraints used with residents in the experimental group. CONCLUSION: An educational program for nursing staff combined with consultation with a nurse specialist (RN level) had no effect on the use of physical restraints with psychogeriatric nursing home residents. In addition to restraint education and consultation, new measures to reduce the use of physical restraints with psychogeriatric nursing home residents should be developed.

An item response theory-based assessment of the pain assessment checklist for Seniors with Limited Ability to Communicate (PACSLAC).

UNLABELLED: Pain is often undetected in older people with dementia partly due to a deterioration of cognitive functioning. Observational scales enable the measurement of pain by registering physiological changes, facial expressions, or behaviors. Previous research showed that the Pain Assessment Checklist for Seniors with Limited Ability to Communicate (PACSLAC) is especially useful to measure pain in older people with dementia. PACSLAC was recently translated into Dutch and refined, thus forming PACSLAC-D. The current study uses a different approach to refining PACSLAC by (1) selecting items on the basis of ratings of nursing personnel and (2) applying confirmatory robust maximum likelihood factor analysis and (3) item response theory to investigate the psychometric properties of the selected items. Of the items that nursing personnel frequently registered, 18 valid and reliable items remained. Fourteen of these 18 items were also selected for PACSLAC-D, which confirms that these items are valid and reliable indicators of pain in older people with dementia. Confirmatory factor analysis showed that a 3-factor model is most adequate to describe the data. Differential item functioning analyses indicated that 2 items were biased. Ultimately, a refined version of PACSLAC was created that nursing personnel with different educational backgrounds might use to assess pain in older people with varying degrees of dementia. PERSPECTIVE: This article describes the selection of items of PACSLAC on the basis of ratings of nursing personnel. By comparing this item selection with the items selected for PACSLAC-D, one can confirm that certain items are sound indicators of pain, whereas others need some attention (eg, through the training of raters).

Interactive computer program for optimal designs of longitudinal cohort studies.

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.

Optimal designs for one- and two-color microarrays using mixed models: a comparative evaluation of their efficiencies.

Comparative studies between the one- and two-color microarrays provide supportive evidence for similarities of results on differential gene expression. So far, no design comparisons between the two platforms have been undertaken. With the objective of comparing optimal designs of one- and two-color microarrays in their statistical efficiencies, techniques of design optimization were applied within a mixed model framework. A- and D-optimal designs for the one- and two-color platforms were sought for a 3 x 3 factorial experiment. The results suggest that the choice of the platform will not affect the "subjects to groups" allocation, being concordant in the two designs. However, under financial constraints, the two-color arrays are expected to have a slight upper hand in terms of efficiency of model parameters estimates, once the price of arrays is more expensive than that of subjects. This statement is especially valid for microarray studies envisaging class comparisons.

Preventing the use of physical restraints on residents newly admitted to psycho-geriatric nursing home wards: a cluster-randomized trial.

BACKGROUND: Although there is an urgent need for restraint-free care, the number of randomized clinical trials on preventing or reducing physical restraints has been limited. OBJECTIVES: To investigate the effectiveness of an educational intervention to prevent the use of physical restraints on residents newly admitted to psycho-geriatric nursing home wards. DESIGN: Cluster-randomized trial. SETTING: Fourteen Dutch psycho-geriatric nursing home wards. PARTICIPANTS: 138 residents admitted to 14 psycho-geriatric nursing home wards after baseline measurement of the trial were selected, out of which 33 residents died or informed consent had not been obtained. A total of 105 residents were included in the analyses. METHODS: The nursing home wards were randomly assigned to either educational intervention or control status. The educational intervention consisted of an educational programme for nurses combined with a nurse specialist's consultation. The data were collected at 1, 4 and 8 months post-intervention. The use of physical restraints was measured by blinded, trained observers on four separate occasions over a 24-h period. The Minimum Data Set was used to determine residents' characteristics, such as their cognitive status. RESULTS: During the study period, no statistically significant differences between the experimental group and the control group regarding restraint status, restraint intensity, multiple restraints and types of restraints were found. One month post-intervention, 38% of the residents newly admitted to the experimental wards were restrained. Bilateral bedrails were the most frequently used restraints at Post-test 1 (24%), Post-test 2 (23%) and Post-test 3 (28%), followed by the use of infrared systems at Post-tests 2 and 3. CONCLUSION: An educational programme combined with the consultation of a nurse specialist does not prevent the use of physical restraints on residents newly admitted to psycho-geriatric nursing home wards. Although other studies have shown promising results with the effectiveness of these types of intervention on restraint reduction, the development of additional interventions to prevent restraint usage is recommended.

The prevalence of pain in nursing home residents with dementia measured using an observational pain scale.

BACKGROUND: Studies on pain and pain prevalence in older people with dementia are limited compared to those on cognitively intact older people. Pain prevalence rates in older people with dementia are estimated to be between 28% and 83%. AIMS: This study aimed to explore pain prevalence in nursing home residents with dementia using observational scale PACSLAC-D, and to identify the association between pain prevalence and (dementia) demographic parameters such as cognitive status, gender, analgesic use and co-morbidity. METHODS: Using an observational study design, 117 residents were observed and assessed for pain during personal morning care. Prevalence data were calculated and regression analyses applied. RESULTS: This study showed that almost half of the participants (47%) experienced pain to some extent. However, overall pain intensity scores were relatively mild. Among the independent variables, co-morbidities, analgesic use and the adjusted interaction term 'co-morbidities+analgesic use' had the strongest associations with pain and were thus shown to be valid significant predictors. CONCLUSION: With its relatively new approach of measuring pain using an observational scale, this study confirms the expectation gleaned from other studies on less impaired older populations: namely, that pain prevalence in older residents with dementia in Dutch nursing homes is high.