Moment estimators for the beta-binomial distribution

R package to estimate intracluster correlation coefficient with confidence interval for binary data

BACKGROUND AND OBJECTIVE

The Intracluster Correlation Coefficient (ICC) is a major parameter of interest in cluster randomized trials that measures the degree to which responses within the same cluster are correlated. There are several types of ICC estimators and its confidence intervals (CI) suggested in the literature for binary data. Studies have compared relative weaknesses and advantages of ICC estimators as well as its CI for binary data and suggested situations where one is advantageous in practical research. The commonly used statistical computing systems currently facilitate estimation of only a very few variants of ICC and its CI. To address the limitations of current statistical packages, we developed an R package, ICCbin, to facilitate estimating ICC and its CI for binary responses using different methods.

METHODS

The ICCbin package is designed to provide estimates of ICC in 16 different ways including analysis of variance methods, moments based estimation, direct probabilistic methods, correlation based estimation, and resampling method. CI of ICC is estimated using 5 different methods. It also generates cluster binary data using exchangeable correlation structure.

RESULTS

ICCbin package provides two functions for users. The function rcbin() generates cluster binary data and the function iccbin() estimates ICC and it's CI. The users can choose appropriate ICC and its CI estimate from the wide selection of estimates from the outputs.

CONCLUSIONS

The R package ICCbin presents very flexible and easy to use ways to generate cluster binary data and to estimate ICC and it's CI for binary response using different methods. The package ICCbin is freely available for use with R from the CRAN repository (https://cran.r-project.org/package=ICCbin). We believe that this package can be a very useful tool for researchers to design cluster randomized trials with binary outcome.

Simultaneous confidence intervals for a success probability and intraclass correlation, with an application to screening mammography

This paper provides asymptotic simultaneous confidence intervals for a success probability and intraclass correlation of the beta-binomial model, based on the maximum likelihood estimator approach. The coverage probabilities of those intervals are evaluated. An application to screening mammography is presented as an example. The individual and simultaneous confidence intervals for sensitivity and specificity and the corresponding intraclass correlations are investigated. Two additional examples using influenza data and sex ratio data among sibships are also considered, where the individual and simultaneous confidence intervals are provided.

Intracluster correlation adjustments to maintain power in cluster trials for binary outcomes

Adequately powered sample size calculations for cluster randomized trials primarily depend on the event rate variability, effect size, average cluster size, and intracluster correlation (ICC). Furthermore, an ICC estimate depends on event rate variability among clusters, cluster size, and number of clusters. We evaluated the impact on ICC estimates of event rates, event rate variations, cluster size, and cluster size variations for different numbers of clusters. We also evaluated how the event rate changes at the end of the trial affect ICC estimates. We created one simulation exercise to investigate how different event rates, event rate variations, cluster size, and cluster size variations impact ICC estimates and 95% confidence intervals. A separate simulation exercise in four different trial scenarios examined the impact of an intervention or drug effect in the intervention group on ICC estimates, 95% confidence intervals, and on sample size. The first simulation results suggest that the ICC value depends upon the event rate and event rate variations in addition to the cluster size, cluster size variations, and number of clusters. The second simulation exercise suggested that adjusting the sample size will help to preserve the appropriate power at the end of the trial.

Interval estimation of generalized odds ratio in data with repeated measurements

When the underlying responses are on an ordinal scale, the generalized odds ratio (GOR), defined as the ratio of the proportions of concordant and discordant pairs, is a useful index to summarize the difference between two stochastically ordered distributions of an ordinal categorical variable. We discuss interval estimation of the GOR for ordinal data with repeated measurements. On the basis of the Dirichlet-multinomial model, we develop three asymptotic interval estimators of the GOR using Wald's test statistic, a logarithmic transformation, and a method analogous to Fieller's theorem, respectively. To evaluate and compare the finite-sample performance of these estimators, we apply Monte Carlo simulation. We find that when the number of subjects per group is not large, the coverage probability of interval estimator using Wald's test statistic is likely to be less than the desired confidence level. By contrast, the coverage probability of the other two estimators are approximately equal to or larger than the desired confidence level. When the number of subjects per group is small and the intraclass correlation between repeated measurements within subjects is large, we note that applying the interval estimator derived from a method analogous to Fieller's theorem can lose efficiency. We also note that the interval estimator using the logarithmic transformation is generally preferable to the other two estimators with respect to both the coverage probability and the average length. Finally, on the basis of a few preliminary simulations, we do find some robustness for all the estimators developed here. We include an example comparing the inflammation grade after lung transplant between surgeries to illustrate the use of the proposed interval estimators.

Tests for homogeneity of the risk ratio in a series of 2x2 tables

We often apply the risk ratio to measure the strength of a causal relationship between a suspected risk factor and a disease of interest. In this paper we consider testing the homogeneity of risk ratio over a series of 2x2 tables. In addition to the classical weighted least squares (CWLS) test procedure, we consider two test procedures using simple transformations of the CWLS statistic and develop three other asymptotically weighted test procedures. On the basis of Monte Carlo simulation, we conclude that the commonly-used CWLS test procedure is generally conservative, especially when the number of 2x2 tables is large and the mean group size per table is moderate or small. We further find that two of the test procedures discussed here can not only generally outperform the CWLS test procedure, but also perform well in a variety of situations considered in this paper. Finally, we illustrate the use of these testing procedures with an example of six randomized trials that assess the effects of aspirin on the prevention of death in post-myocardial infarction patients.

Estimating intraclass correlation for binary data

This paper reviews many different estimators of intraclass correlation that have been proposed for binary data and compares them in an extensive simulation study. Some of the estimators are very specific, while others result from general methods such as pseudo-likelihood and extended quasi-likelihood estimation. The simulation study identifies several useful estimators, one of which does not seem to have been considered previously for binary data. Estimators based on extended quasi-likelihood are found to have a substantial bias in some circumstances.