Some New Random Effect Models for Correlated Binary Responses

• Autorzy: Fodé Tounkara , Louis-Paul Rivest
• Języki publikacji: EN

Abstrakty

EN

Exchangeable copulas are used to model an extra-binomial variation in Bernoulli experiments with a variable number of trials. Maximum likelihood inference procedures for the intra-cluster correlation are constructed for several copula families. The selection of a particular model is carried out using the Akaike information criterion (AIC). Profile likelihood confidence intervals for the intra-cluster correlation are constructed and their performance are assessed in a simulation experiment. The sensitivity of the inference to the specification of the copula family is also investigated through simulations. Numerical examples are presented.

Słowa kluczowe

EN

Multivariate exchangeable copulas; Exchangeable binary data; Profile interval; Maximum likelihood

Kategorie tematyczne

• 62H05: Characterization and structure theory

• Wydawca: De Gruyter Open
• Czasopismo: Dependence Modeling
• Rocznik: 2014
• Tom: 2
• Numer: 1

Daty

otrzymano

2014-05-12

zaakceptowano

2014-10-16

online

2014-12-01

Twórcy

autor

Fodé Tounkara

• Department of Mathematics and Statistics, Université Laval„ 1045 av. de la
  Médecine, Québec (Québec) G1V 0A6 Canada

autor

Louis-Paul Rivest

• Department of Mathematics and Statistics, Université Laval„ 1045 av. de la
  Médecine, Québec (Québec) G1V 0A6 Canada

Bibliografia

• [1] Ahmed, M. and Shoukri, M. (2010). A bayesian estimator of the intracluster correlation coefficient from correlated binary responses. J. Data Sci., 8:127–137.
• [2] Alanko, T. and Duffy, J. C. (1996). Compound binomial distribution for modeling consumption data. The Statistician, 45:269– 286. [Crossref]
• [3] Ananth, C. V. and Preisser, J. S. (1999). Bivariate logistic regression: Modeling the association of small for gestational age births in twin gestations. Stat. Med., 18:2011–2023. [Crossref]
• [4] Chakraborty, H., Moore, J., Carlo, W. A., Hartwell, T. D., and Wright, L. L. (2009). A simulation based technique to estimate intracluster correlation for a binary variable. Contemporary Clinical Trials, 30:71–80. [WoS][Crossref][PubMed]
• [5] Eldridge, S. and Kerry, S. (2012). A Practical Guide to Cluster Randomised Trials in Health Services Research. Wiley, New York.
• [6] Feng, Z. and Crizzle, J. E. (1992). Correlated binomial variates: Properties of estimators of intraclass correlation and its effect on sample size calculation. Stat. Med., 11:1600–1614.
• [7] Fleiss, J. L. and Cuzick, J. (1979). The reliability of dichotomous judgments: Unequal numbers of judges per subject. Appl. Psychol. Meas., 3:537–542. [Crossref]
• [8] Kuk, A. Y. C. (2004). A generalized estimating equation approach to modelling foetal response in developmental toxicity studies when the number of implants is dose dependent. J. Roy. Statist. Soc. Ser. C, 52:52–61.
• [9] Légaré, F., Labrecque, M., LeBlanc, A., Njoya, M., Laurier, C., Côté, L., Godin, G., Thivierge, R. L., O’Connor, A., and S., S.-J. (2011). Training family physicians in shared decision making for the use of antibiotics for acute respiratory infections: a pilot clustered randomized controlled trial. Health Expect., 1:96–110. [WoS][Crossref]
• [10] Liang, K. Y., Qaqish, B., and Zeger, S. (1992). Multivariate regression analyses for categorical data. J. Roy. Statist. Soc. Ser. B., 54:3–40.
• [11] Lipsitz, S. R., Laird, N. M., and Harrington, D. P. (1991). Generalized estimating equations for correlated binary data: using the odds ratio as a measure of association. Biometrika, 78:153–160. [Crossref]
• [12] Madsen, R. W. (1993). Generalized binomial distribution. Comm. Statist. Theory Methods, 22:3065–3086. [Crossref]
• [13] Mai, J.-M. and Scherer, M. (2012). Simulating Copulas; Stochastic Models, Sampling Algorithms and Applications. Series in Quantitative Finance: Volume 4. World Scientific Publishing Company, New York. [WoS]
• [14] Nikoloulopoulos, A. K. and Karlis, D. (2008). Multivariate logit copula model with an application to dental data. Stat. Med., 27:6393–6406. [PubMed][WoS][Crossref]
• [15] Ochi, Y. and Prentice, R. L. (1984). Likelihood inference in a correlated probit regression model. Biometrika, 71:531–542. [Crossref]
• [16] Pals, S. L., Beaty, B. L., Posner, S. F., and Bull, S. (2009). Estimates of intraclass correlation for variables related to behavioral hiv/std prevention in a predominantly african american and hispanic sample of young women. Health Education & Behavior, 36:182–194. [WoS]
• [17] Ridout, M. S., Demétrio, C. G. B., and Firth, D. (1999). Estimating intraclass correlation for binary data. Biometrics, 55:137– 148. [PubMed][Crossref]
• [18] Saha, K. K. (2012). Profile likelihood-based confidence interval of the intraclass correlation for binary outcome data sampled from clusters. Stat. Med., 31:3982–4002. [WoS][Crossref][PubMed]
• [19] Shoukri, M. M., Kumar, P., and Colak, D. (2011). Analyzing dependent proportions in cluster randomized trials: Modeling inter-cluster correlation via copula function. Comput. Statist. Data Anal., 55:1226–1235. [WoS][Crossref]
• [20] Stefanescu, C. and Turnbull, B. W. (2003). Likelihood inference for exchangeable binary data with varying cluster sizes. Biometrics, 59:18–24. [Crossref][PubMed]
• [21] Turner, R. M., Omar, R. Z., and Thompson, S. G. (2001). Bayesian methods of analysis for cluster randomized trials with binary outcome data. Stat. Med., 20:453–472. [Crossref][PubMed]
• [22] Turner, R. M., Omar, R. Z., and Thompson, S. G. (2006). Constructing intervals for the intracluster correlation coefficient using bayesian modelling, and application in cluster randomized trials. Stat. Med., 25:1443–1456. [PubMed][Crossref]
• [23] Williams, D. A. (1975). The analysis of binary response from toxicological experiments involving reproduction and teratogenicity. Biometrics, 31:949–952. [Crossref][PubMed]
• [24] Williams, D. A. (1982). Extra-binomial variation in logistic linear models. J. Appl. Statist., 31:305–309.
• [25] Zou, G. and Donner A., (2004). Confidence interval estimation of the intraclass correlation coefficient for binary outcome data. Biometrics., 60:807–811.[PubMed][Crossref]

Identyfikatory

DOI

10.2478/demo-2014-0006