Modelos marginais para respostas binárias com estruturas hierárquicas de agrupamento

Abstract

Studies involving binary responses with hierarchical clustering are often found in different areas of knowledge. In regression models clustering structures should be properly handled, once they violate basic assumption of independence of observations. When the main focus of the study lies in the mean structure, first order Marginal Models , known as GEE1 proposed by Liang and Zeger (1986), has no distributional assumptions and offers an ease interpretation solution. However with GEE1 method, it is not possible satisfactorily accommodate hierarchical structures or multiple clustering structures, which may cause loss of efficiency in the mean structure. In order to satisfactorily accommodate hierarchical clustering, GEE1 been extended to the GEE2 (Prentice, 1988) by introducing a second estimation equation, allowing to estimate and make inferences for association parameters starting from covariates. When the main focus of the study lies in association structure and there is a hierarchical clustering structures, it is very common the presence of a large number of observations in the clusters. Numerical methods for GEE2 can be computationally infeasible if the number of observations within the clusters is large, and do not allow use of odds ratio for interpretation of association structure, being possible only the of correlation coefficient. With appropriate modification in the second equation estimation, Carey, Zeger and Diggle (1993) developed the ALR and Zink (2003) the ORTH, that requires less computational effort when compared with existing methods allows the use of odds ratio for interpretation of association structure. Here we report the comparison of marginal models (GEE2, ALR and ORTH) in simulations and real applications cases with hierarchical clustering in binary responses, with the research focus not only on the coefficients of the mean, but also in the association measures. Our results indicate that the methods ALR and ORTH proved to be effective for studies with binary responses in the presence of multiple hierarchical structures, especially in cases with a large number of observations in the clusters. Our results also indicate that when the primary purpose of the research is association structure, one should take special care in modeling the structure of the mean, because its misspecification may inconsistency of the association measures.