Statistics and Its Interface

Volume 9 (2016)

Number 1

A copula approach to estimate reliability: an application to self-reported sexual behaviors among HIV serodiscordant couples

Pages: 57 – 67

DOI: http://dx.doi.org/10.4310/SII.2016.v9.n1.a6

Authors

Scarlett L. Bellamy (Department of Biostatistics and Epidemiology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Penn., U.S.A.)

Seunghee Baek (Department of Clinical Epidemiology and Biostatistics, Asan Medical Center, Ulsan College of Medicine, Seoul, Korea)

Andrea B. Troxel (Department of Biostatistics and Epidemiology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Penn., U.S.A.)

Thomas R. Ten Have (Department of Biostatistics and Epidemiology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Penn., U.S.A.)

John B. Jemmott, III (Annenberg School for Communication, Center for Health Behavior and Communication Research, University of Pennsylvania, Philadelphia, Penn., U.S.A.)

Abstract

Copula-based approaches can be useful in multivariate modeling settings where multivariate dependency is of primary interest, such as estimating the reliability of selfreported sexual behavior assessed independently for male and female partners (dyad) in a couple-based HIV risk reduction study. Specifically, we investigate the reliability of couple reports using copulas, adjusting for key individual baseline covariates. We propose applying a copula modeling approach to measure the reliability of self-reported, shared sexual behaviors from couples where measures are assessed independently from male and female partners. In particular, we estimate measures of dependence, such as the odds ratios and binary correlations, using mixtures of max-infinitely divisible copulas with a bivariate logit model. This approach is flexible in measuring the effect of covariates on dependence parameters and for estimating marginal probabilities for multiple outcomes simultaneously. In this paper, we focus on estimating these two dependencies and explore the influences of additional covariate information on the copula parameter.We provide simulation results comparing copulabased estimates to moment estimates of the generalized estimating equation (GEE) for the correlation coefficients with respect to bias and 95% coverage probability. We illustrate that copulas have better performance in terms of bias, while their performance is similar with respect to efficiency. The estimator of the marginal probability using copula methods is robust to the choice of copula family. The choice of copula may affect the estimator of dependency when the dependency of the outcomes is very low. We apply these methods to data from the Multisite HIV/STD Prevention Trial for African American Couples (AAC) Study.

Keywords

copula, reliability, bivariate

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