Association of intracluster correlation measures with outcome prevalence for binary outcomes in cluster randomised trials

In cluster randomised trials, a measure of intracluster correlation such as the intraclass correlation coefficient (ICC) should be reported for each primary outcome. Providing intracluster correlation estimates may help in calculating sample size of future cluster randomised trials and also in interpreting the results of the trial from which they are derived. For a binary outcome, the ICC is known to be associated with its prevalence, which raises at least two issues. First, it questions the use of ICC estimates obtained on a binary outcome in a trial for sample size calculations in a subsequent trial in which the same binary outcome is expected to have a different prevalence. Second, it challenges the interpretation of ICC estimates because they do not solely depend on clustering level. Other intracluster correlation measures proposed for clustered binary data settings include the variance partition coefficient, the median odds ratio and the tetrachoric correlation coefficient. Under certain assumptions, the theoretical maximum possible value for an ICC associated with a binary outcome can be derived, and we proposed the relative deviation of an ICC estimate to this maximum value as another measure of the intracluster correlation. We conducted a simulation study to explore the dependence of these intracluster correlation measures on outcome prevalence and found that all are associated with prevalence. Even if all depend on prevalence, the tetrachoric correlation coefficient computed with Kirk’s approach was less dependent on the outcome prevalence than the other measures when the intracluster correlation was about 0.05. We also observed that for lower values, such as 0.01, the analysis of variance estimator of the ICC is preferred.

Familial aggregation and heritability: a nationwide family-based study of idiopathic inflammatory myopathies

ObjectivesThe magnitude of the genetic contribution to idiopathic inflammatory myopathies (IIMs) is unknown. In this project, we aimed to investigate the familial aggregation and heritability of IIM.MethodsThis is a family-based study using nationwide healthcare register data in Sweden. We matched each patient with IIM to individuals without IIM, identified their first-degree relatives and determined the IIM status among all first-degree relatives. We estimated the adjusted ORs (aORs) of familial aggregation of IIM using conditional logistic regression. In addition, we used tetrachoric correlation to estimate the heritability of IIM.ResultsWe included 7615 first-degree relatives of 1620 patients with IIM diagnosed between 1997 and 2016 and 37 309 first-degree relatives of 7797 individuals without IIM. Compared with individuals without IIM, patients with IIM were more likely to have ≥1 first-degree relative affected by IIM (aOR=4.32, 95% CI 2.00 to 9.34). Furthermore, the aOR of familial aggregation of IIM in full siblings was 2.53 (95% CI 1.62 to 3.96). The heritability of IIM was 22% (95% CI 12% to 31%) among any first-degree relatives and 24% (95% CI 12% to 37%) among full siblings.ConclusionsIIM has a familial component with a risk of aggregation among first-degree relatives and a heritability of about 20%. This information is of importance for future aetiological studies and in clinical counselling.

Differential Item Functioning Effect Size From the Multigroup Confirmatory Factor Analysis for a Meta-Analysis: A Simulation Study

This study presents a new approach to synthesizing differential item functioning (DIF) effect size: First, using correlation matrices from each study, we perform a multigroup confirmatory factor analysis (MGCFA) that examines measurement invariance of a test item between two subgroups (i.e., focal and reference groups). Then we synthesize, across the studies, the differences in the estimated factor loadings between the two subgroups, resulting in a meta-analytic summary of the MGCFA effect sizes (MGCFA-ES). The performance of this new approach was examined using a Monte Carlo simulation, where we created 108 conditions by four factors: (1) three levels of item difficulty, (2) four magnitudes of DIF, (3) three levels of sample size, and (4) three types of correlation matrix (tetrachoric, adjusted Pearson, and Pearson). Results indicate that when MGCFA is fitted to tetrachoric correlation matrices, the meta-analytic summary of the MGCFA-ES performed best in terms of bias and mean square error values, 95% confidence interval coverages, empirical standard errors, Type I error rates, and statistical power; and reasonably well with adjusted Pearson correlation matrices. In addition, when tetrachoric correlation matrices are used, a meta-analytic summary of the MGCFA-ES performed well, particularly, under the condition that a high difficulty item with a large DIF was administered to a large sample size. Our result offers an option for synthesizing the magnitude of DIF on a flagged item across studies in practice.

Study of Correlation the Implementation of Norms Small Happy and Prosperous Family with Difficulty Learning In 8th SMP Nurul Falah Srono Banyuwangi, East Java, Indonesia

Families have the role and primary responsibility for the care and protection of children from class SRONO culture, education, values and norms of community life begin in the family environment. For the perfect and harmonious development of children's personalities, they must grow in the family environment in a climate of happiness, love and understanding. What is the correlation between the implementation of the norms of happy and prosperous small families with learning difficulties in class VIII semester II SMP Nurul Falah Srono. This study uses a quantitative approach with the method used to analyze data using the tetrachoric correlation statistical method. The results of his research that there is a correlation between the norms of happy and prosperous small families with the learning difficulties of VIII semester II semester students of Nurul Falah Srono Middle School, the level of relationship obtained by 0.542 lies between 0.400 to 0.600 which means the level of correlation is sufficient.

A simple index of prediction accuracy in multiple regression analysis

Objectives Within the context of multiple regression the coefficient of determination can be converted to a probability of agreement between the actual and predicted outcomes, suitably dichotomized. Methods This probability of agreement can be used as a simple index of prediction accuracy to help capture the probability of a correct prediction in multiple regression. Results The simple index of prediction accuracy makes the multiple correlation comprehensible to statisticians and laypeople alike. Two examples are provided to demonstrate the application of the simple index. Conclusions In short, the paper introduces the simple index, its computation formula, and its theoretical affinity to the confusion matrix, binomial effect size, probit model, and tetrachoric correlation.

Methods for Determining the Tetrachoric Correlation Coefficient for Binary Variables

The tetrachoric correlation coefficient (rt) is a special case of the statistical covariation between two variables measured on a dichotomous scale, but assuming an underlying bivariate normal distribution. Our goal was to provide an analysis of seven different methods used to calculate rt. The rt approximation was then used to derive its standard error and its associated confidence interval. Computation of rt is not straightforward and is usually not available in standard statistical packages. This paper introduces seven methods for computing the rt value and three methods used to provide the standard error estimation {SE(rt)}. These methods were illustrated using data from questionnaires that were used to evaluate public awareness regarding Electronic Waste hazards. The different algorithmic/mathematical methods used to estimate rt and SE(rt) yielded values that were equal to (or very close to) each other and the estimates obtained from SAS statistical analysis software. Method 6 and Method 1 used to estimate rt and SE(rt) work very well, the equations are easy to understand, are computationally simple and are ideally suited for use. Additionally, the width of the confidence intervals for these methods are equal to (or closely approximates) the widths calculated by the SAS statistical analysis computer program.

Evaluating Psychometric Properties of an Instrument Addressing Comprehensiveness of Care Among Dentists

This study aimed to evaluate the psychometric properties of an instrument to assess comprehensiveness of care from dentists using a combination of classical test theory and item response theory. A 46-item instrument was developed and tested by a panel of experts, followed by a pilot test and administration to 187 primary care dentists in a large Brazilian city. The 46 items were evaluated using the following criteria: acceptability, internal consistency, temporal stability, inter-item correlation, and tetrachoric correlation. This evaluation led to a shortened version consisting of 11 items that met all the criteria previously described. The temporal stability was measured using Cohen’s kappa, and all 11 items presented values greater than 0.5. The Cronbach’s alpha value was 0.72. None of the 11 items had missing data on the distribution of responses, and the model considering the discrimination as varying fit the data better than the model considering discrimination as a constant parameter (p<0.001). Item characteristic curves showed that 54.5% of items could be considered difficult, i.e., only dentists with a good understanding of comprehensiveness responded favorably. The 11-item instrument to assess comprehensiveness of care by dentists is considered to have good psychometric properties.