Review of sample size determination methods for the intraclass correlation coefficient in the one-way analysis of variance model.

Reliability of measurement instruments providing quantitative outcomes is usually assessed by an intraclass correlation coefficient. When participants are repeatedly measured by a single rater or device, or, are each rated by a different group of raters, the intraclass correlation coefficient is based on a one-way analysis of variance model. When planning a reliability study, it is essential to determine the number of participants and measurements per participant (i.e. number of raters or number of repeated measurements). Three different sample size determination approaches under the one-way analysis of variance model were identified in the literature, all based on a confidence interval for the intraclass correlation coefficient. Although eight different confidence interval methods can be identified, Wald confidence interval with Fisher's large sample variance approximation remains most commonly used despite its well-known poor statistical properties. Therefore, a first objective of this work is comparing the statistical properties of all identified confidence interval methods-including those overlooked in previous studies. A second objective is developing a general procedure to determine the sample size using all approaches since a closed-form formula is not always available. This procedure is implemented in an R Shiny app. Finally, we provide advice for choosing an appropriate sample size determination method when planning a reliability study.

Optimal two-stage sampling for mean estimation in multilevel populations when cluster size is informative.

To estimate the mean of a quantitative variable in a hierarchical population, it is logistically convenient to sample in two stages (two-stage sampling), i.e. selecting first clusters, and then individuals from the sampled clusters. Allowing cluster size to vary in the population and to be related to the mean of the outcome variable of interest (informative cluster size), the following competing sampling designs are considered: sampling clusters with probability proportional to cluster size, and then the same number of individuals per cluster; drawing clusters with equal probability, and then the same percentage of individuals per cluster; and selecting clusters with equal probability, and then the same number of individuals per cluster. For each design, optimal sample sizes are derived under a budget constraint. The three optimal two-stage sampling designs are compared, in terms of efficiency, with each other and with simple random sampling of individuals. Sampling clusters with probability proportional to size is recommended. To overcome the dependency of the optimal design on unknown nuisance parameters, maximin designs are derived. The results are illustrated, assuming probability proportional to size sampling of clusters, with the planning of a hypothetical survey to compare adolescent alcohol consumption between France and Italy.

Effects of a Web-based tailored intervention to reduce alcohol consumption in adults: randomized controlled trial.

BACKGROUND: Web-based tailored interventions provide users with information that is adapted to their individual characteristics and needs. Randomized controlled trials assessing the effects of tailored alcohol self-help programs among adults are scarce. Furthermore, it is a challenge to develop programs that can hold respondents' attention in online interventions. OBJECTIVE: To assess whether a 3-session, Web-based tailored intervention is effective in reducing alcohol intake in high-risk adult drinkers and to compare 2 computer-tailoring feedback strategies (alternating vs summative) on behavioral change, dropout, and appreciation of the program. METHODS: A single-blind randomized controlled trial was conducted with an experimental group and a control group (N=448) in Germany in 2010-2011. Follow-up took place after 6 months. Drinking behavior, health status, motivational determinants, and demographics were assessed among participants recruited via an online access panel. The experimental group was divided into 2 subgroups. In the alternating condition (n=132), the tailored feedback was split into a series of messages discussing individual topics offered while the respondent was filling out the program. Participants in the summative condition (n=181) received all advice at once after having answered all questions. The actual texts were identical for both conditions. The control group (n=135) only filled in 3 questionnaires. To identify intervention effects, logistic and linear regression analyses were conducted among complete cases (n=197) and after using multiple imputation. RESULTS: Among the complete cases (response rate: 197/448, 44.0%) who did not comply with the German national guideline for low-risk drinking at baseline, 21.1% of respondents in the experimental group complied after 6 months compared with 5.8% in the control group (effect size=0.42; OR 2.65, 95% CI 1.14-6.16, P=.02). The experimental group decreased by 3.9 drinks per week compared to 0.4 drinks per week in the control group, but this did not reach statistical significance (effect size=0.26; beta=-0.12, 95% CI -7.96 to 0.03, P=.05). Intention-to-treat analyses also indicated no statistically significant effect. Separate analyses of the 2 experimental subgroups showed no differences in intervention effects. The dropout rate during the first visit to the intervention website was significantly lower in the alternating condition than in the summative condition (OR 0.23, 95% CI 0.08-0.60, P=.003). Program appreciation was comparable for the 2 experimental groups. CONCLUSIONS: Complete case analyses revealed that Web-based tailored feedback can be an effective way to reduce alcohol intake among adults. However, this effect was not confirmed when applying multiple imputations. There was no indication that one of the tailoring strategies was more effective in lowering alcohol intake. Nevertheless, the lower attrition rates we found during the first visit suggest that the version of the intervention with alternating questions and advice may be preferred. TRIAL REGISTRATION: International Standard Randomized Controlled Trial Number (ISRCTN): 91623132; http://www.controlled-trials.com/ISRCTN91623132 (Archived by WebCite at http://www.webcitation.org/6J4QdhXeG).

Changes in skinfold thickness and waist circumference after 12 and 24 months resulting from the NHF-NRG In Balance-project.

BACKGROUND: More knowledge is needed regarding the effectiveness of weight gain prevention programmes. The present study tested the 12-and 24-month effectiveness of the 'Netherlands Research programme weight Gain prevention' (NHF-NRG)-In Balance-project, a worksite-based intervention aimed at the prevention of weight gain. METHODS: Twelve worksites (n = 553 participants) were matched and assigned to either intervention or control group. The worksites and employees of the intervention group received individual (i.e. pedometer, computer-tailored advice) and environmental (i.e. changes in worksite canteen) interventions, directed at physical activity and food intake over 1-year. Differences between the intervention and control group in changes in body weight, BMI, skinfold thickness and waist circumference at 12 and 24 months were examined using multilevel linear regression analyses adjusting for various baseline characteristics (age, gender, BMI, marital status, education and smoking status). RESULTS: A significant greater reduction in skinfold thickness was found in the intervention group than in the control group, both after 12-and 24 months (Unstandardized regression coefficients (B) = -2.52, 95% C.I. -4.58, -0.45; p = 0.018; B = -4.83, 95% C.I. 6.98, -2.67; p < 0.001 respectively). Significant differences were also observed for changes in waist circumferences both at 12 months (B = -1.50, 95% C.I. -2.35, -0.65; p < 0.001) and at 24 months (B = -1.30, 95% C.I. -2.18, -0.42; p = 0.005). No significant changes were observed for weight and BMI. CONCLUSIONS: The project was effective with regard to changes in skinfold thickness and waist circumference both at 12 and 24 months. It supports the usefulness of worksite-based prevention, especially regarding maintenance of behavioral changes.

Optimal designs for empirical bayes estimators of individual linear and quadratic growth curves in linear mixed models.

Many studies on optimal designs for linear mixed model analysis of repeated measures data have focussed on estimating the fixed effects. The present study investigates the optimal number of time points and subjects in case random effects have to be estimated. Linear mixed models with a linear or quadratic trend across equidistant time points are studied. Given a particular cost function, we examine which designs minimise the expected average squared prediction error. Robustness of the optimal design, important when one does not know the underlying model, is also treated.

Relative efficiency of unequal cluster sizes for variance component estimation in cluster randomized and multicentre trials.

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. Although equal sample sizes per cluster are generally optimal for parameter estimation, they are rarely feasible. This paper addresses the relative efficiency (RE) of unequal versus equal cluster sizes for estimating variance components in cluster randomized trials and in multicentre trials with person randomization within centres, assuming a quantitative outcome. Starting from maximum likelihood estimation, the RE is investigated numerically for a range of cluster size distributions. An approximate formula is presented for computing the RE as a function of the mean and variance of cluster sizes and the intraclass correlation. The accuracy of this approximation is checked and found to be good. It is concluded that the loss of efficiency for variance component estimation due to variation of cluster sizes rarely exceeds 20% and can be compensated by sampling 25% more clusters.