GEECORR: A SAS macro for regression models of correlated binary responses and within-cluster correlation using generalized estimating equations

BACKGROUND AND OBJECTIVES

Generalized estimating equations (GEE) provide population-averaged model inference for longitudinal and clustered outcomes via a generalized linear model for the effect of explanatory variables on the marginal mean, while intra-cluster correlations are ordinarily treated as nuisance parameters. Software to richly parameterize and conduct inference for complex correlation structures in the marginal modeling framework is scarce.

METHODS

A SAS macro, GEECORR, has been developed for the analysis of clustered binary data based on GEE to include additional estimating equations for modeling pairwise correlation between binary variates as a function of covariates.

RESULTS

We illustrate the macro in a surveillance study with repeated measures, a longitudinal study, and a study with biological clustering.

CONCLUSIONS

This article provides an overview of the GEE method consisting of a pair of estimating equations, describes the features and capabilities of the GEECORR macro including regression diagnostics and finite-sample bias-corrected covariance estimators, and demonstrates the macro usage for three studies.

Accurate confidence intervals for proportion in studies with clustered binary outcome

Clustered binary data are commonly encountered in many medical research studies with several binary outcomes from each cluster. Asymptotic methods are traditionally used for confidence interval calculations. However, these intervals often have unsatisfactory performance with regards to coverage for a study with a small sample size or the actual proportion near the boundary. To improve the coverage probability, exact Buehler's one-sided intervals may be utilized, but they are computationally intensive in this setting. Therefore, we propose using importance sampling to calculate confidence intervals that almost always guarantee the coverage. We conduct extensive simulation studies to compare the performance of the existing asymptotic intervals and the new accurate intervals using importance sampling. The new intervals based on the asymptotic Wilson score for sample space ordering perform better than others, and they are recommended for use in practice.

A novel confidence interval for a single proportion in the presence of clustered binary outcome data

Estimating the precision of a single proportion via a 100(1-α)% confidence interval in the presence of clustered data is an important statistical problem. It is necessary to account for possible over-dispersion, for instance, in animal-based teratology studies with within-litter correlation, epidemiological studies that involve clustered sampling, and clinical trial designs with multiple measurements per subject. Several asymptotic confidence interval methods have been developed, which have been found to have inadequate coverage of the true proportion for small-to-moderate sample sizes. In addition, many of the best-performing of these intervals have not been directly compared with regard to the operational characteristics of coverage probability and empirical length. This study uses Monte Carlo simulations to calculate coverage probabilities and empirical lengths of five existing confidence intervals for clustered data across various true correlations, true probabilities of interest, and sample sizes. In addition, we introduce a new score-based confidence interval method, which we find to have better coverage than existing intervals for small sample sizes under a wide range of scenarios.

Modeling clustered binary data with excess zero clusters

We establish a zero-inflated (random-effects) logistic-Gaussian model for clustered binary data in which members of clusters in one latent class have a zero response with probability one, and members of clusters in a second latent class yield correlated outcomes. Response probabilities in terms of random-effects models are formulated, and maximum marginal likelihood estimation procedures based on Gaussian quadrature are developed. Application to esophageal cancer data in Chinese families is presented.

Analysis of longitudinal multivariate outcome data from couples cohort studies: application to HPV transmission dynamics

We consider a specific situation of correlated data where multiple outcomes are repeatedly measured on each member of a couple. Such multivariate longitudinal data from couples may exhibit multi-faceted correlations which can be further complicated if there are polygamous partnerships. An example is data from cohort studies on human papillomavirus (HPV) transmission dynamics in heterosexual couples. HPV is a common sexually transmitted disease with 14 known oncogenic types causing anogenital cancers. The binary outcomes on the multiple types measured in couples over time may introduce inter-type, intra-couple, and temporal correlations. Simple analysis using generalized estimating equations or random effects models lacks interpretability and cannot fully utilize the available information. We developed a hybrid modeling strategy using Markov transition models together with pairwise composite likelihood for analyzing such data. The method can be used to identify risk factors associated with HPV transmission and persistence, estimate difference in risks between male-to-female and female-to-male HPV transmission, compare type-specific transmission risks within couples, and characterize the inter-type and intra-couple associations. Applying the method to HPV couple data collected in a Ugandan male circumcision (MC) trial, we assessed the effect of MC and the role of gender on risks of HPV transmission and persistence.