The effect of heterogeneous variance on efficiency and power of cluster randomized trials with a balanced 2x2 factorial design

Sample size calculation for cluster randomized trials (CRTs) with a 2x2 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 2x2 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 2x2 CRT

Is left-handedness associated with a more pronounced age-related cognitive decline?

The effect of handedness on cognitive functioning has been the subject of much controversy. The influential "pathological left-handedness theory" posited by Coren and Halpern (1991) claims that left-handedness is probabilistically related to deviations from the neurological and cognitive norm. Many studies have failed to find negative effects of left-handedness on cognitive functioning, but most of these studies related handedness to cognition at one moment in time. Such studies do not exclude the possibility that sinistrality may be related to a more pronounced age-related longitudinal decline in cognitive functions. This hypothesis was tested in the present study. In a longitudinal study involving a large population sample of cognitively intact people aged at least 50 years at baseline, we evaluated the effect of handedness on age-related decline in four major cognitive domains: speed of information processing, verbal learning, long-term verbal memory, and executive functioning. The results failed to provide support for the hypothesis that sinistrality is associated with a more pronounced age-related cognitive decline. Recommendations for future studies are provided

Rey's verbal learning test: normative data for 1855 healthy participants aged 24-81 years and the influence of age, sex, education, and mode of presentation

The Verbal Learning Test (VLT; Rey, 1958) evaluates the declarative memory. Despite its extensive use, it has been difficult to establish normative data because test administration has not been uniform. The purpose of the present study was to gather normative data for the VLT for a large number (N = 1855) of healthy participants aged 24-81 years, using a procedure in which the words to be learned were presented either verbally or visually. The results showed that VLT performance decreased in an a.-e-dependent manner from an early age. The learning capacity of younger versus older adults differed quantitatively rather than qualitatively. Females and higher educated participants outperformed males and lower educated participants over the entire age range tested. Presentation mode affected VLT performance differently: auditory presentation resulted in a better recall on Trial 1 (a short-term or working memory measure), whereas visual presentation yielded a better performance on Trial 3, Trial 4, and Delta (a learning measure)

The impact of educational and environmental interventions in Dutch worksite cafeterias

Environmental interventions as labeling of healthy foods and an increased availability of healthy foods may help consumers to meet the guidelines for a healthy diet. This article describes a study into the effectiveness of two environmental programs to be used in worksite cafeterias along with an educational program. The aim of the interventions was to reduce fat intake and increase fruit and vegetable intake. In the 'Labeling Program', low fat products were labeled. The 'Food Supply Program' comprised an increased availability of low-fat products and fruits and vegetables in worksite cafeterias. The 'Educational Program' consisted of information about healthy nutrition through brochures, table tents, a self help manual and posters. The design consisted of a pretest-posttest experimental control group design, with four conditions: the Educational Program, the Food Supply Program plus Educational Program, the Labeling Program plus Educational Program and a control group. Seventeen worksites were randomly assigned to one of the four research conditions. Total fat, fruit, and vegetable intake was measured with a quantitative, self-administered food frequency questionnaire (35 questions). Intake during lunch was measured by asking respondents to write down which food items they had purchased during their last lunch in the cafeteria. Furthermore, sales data for some targeted product categories were collected (milk, butter, cheese, meat products, desserts). For the whole study population, no significant effects on consumption data were found for any of the programs. The data showed a beneficial significant treatment effect of the Labeling Program on total fat intake, for respondents who believe they eat a high fat diet. Sales data revealed a significant effect of the labeling program on desserts, but not for the other products

Effectiveness of the Assessment of Burden of Chronic Obstructive Pulmonary Disease (ABC) tool: Study protocol of a cluster randomised trial in primary and secondary care

Abstract Background Chronic Obstructive Pulmonary Disease (COPD) is a growing worldwide problem that imposes a great burden on the daily life of patients. Since there is no cure, the goal of treating COPD is to maintain or improve quality of life. We have developed a new tool, the Assessment of Burden of COPD (ABC) tool, to assess and visualize the integrated health status of patients with COPD, and to provide patients and healthcare providers with a treatment algorithm. This tool may be used during consultations to monitor the burden of COPD and to adjust treatment if necessary. The aim of the current study is to analyse the effectiveness of the ABC tool compared with usual care on health related quality of life among COPD patients over a period of 18 months. Methods/Design A cluster randomised controlled trial will be conducted in COPD patients in both primary and secondary care throughout the Netherlands. An intervention group, receiving care based on the ABC tool, will be compared with a control group receiving usual care. The primary outcome will be the change in score on a disease-specific-quality-of-life questionnaire, the Saint George Respiratory Questionnaire. Secondary outcomes will be a different questionnaire (the COPD Assessment Test), lung function and number of exacerbations. During the 18 months follow-up, seven measurements will be conducted, including a baseline and final measurement. Patients will receive questionnaires to be completed at home. Additional data, such as number of exacerbations, will be recorded by the patients’ healthcare providers. A total of 360 patients will be recruited by 40 general practitioners and 20 pulmonologists. Additionally, a process evaluation will be performed among patients and healthcare providers. Discussion The new ABC tool complies with the 2014 Global Initiative for Chronic Obstructive Lung Disease guidelines, which describe the necessity to classify patients on both their airway obstruction and a comprehensive symptom assessment. It has been developed to classify patients, but also to provide visual insight into the burden of COPD and to provide treatment advice. Trial registration Netherlands Trial Register, NTR3788

Optimal Experimental Design With Nesting of Persons in Organizations

This paper introduces optimal design of randomized experiments where individuals are nested within organizations, such as schools, health centers, or companies. The focus is on nested designs with two levels (organization, individual) and two treatment conditions (treated, control), with treatment assignment to organizations, or to individuals within organizations. For each type of assignment, a multilevel model is first presented for the analysis of a quantitative dependent variable or outcome. Simple equations are then given for the optimal sample size per level (number of organizations, number of individuals) as a function of the sampling cost and outcome variance at each level, with realistic examples. Next, it is explained how the equations can be applied if the dependent variable is dichotomous, or if there are covariates in the model, or if the effects of two treatment factors are studied in a factorial nested design, or if the dependent variable is repeatedly measured. Designs with three levels of nesting and the optimal number of repeated measures are briefly discussed, and the paper ends with a short discussion of robust design