Tratamento de dados perdidos em estudos longitudinais com respostas ordinais

Abstract

The main goal of this thesis is the treatment of missing data in longitudinal studies with ordinal response. In such studies missing data in the response and/or covariates can introduce bias and lead to misleading inferences about the regression parameters (Fitzmaurice et al., 2004). In this work, we adopt a proportional odds model for the longitudinal ordinal response and make use of Generalized Estimating Equations (Liang & Zeger, 1986) (GEE) to estimate the regression parameters. The GEE method presents computational simplicity and is intended to estimate fixed parameters without specifying the joint distribution for repeated measures. Nevertheless, in the presence of missing data, the standard GEE estimator is consistent only under the strong assumption of missing completely at random data. We propose a doubly robust GEE estimator for analysis of longitudinal ordinal data with intermittent missing response and covariate, both subject to a missing at random mechanism. The proposed method combines ideas of multiple imputation and the weighted GEE and it is attractive in the sense that, for consistency, it requires only the correct specification of one of its predictive models, but not necessarily both. First, independent estimating equations are assumed, which simplifies the iterative estimation process, and we focus on the bias of the proposed method compared to multiple imputation and the weighted GEE. Although the correlations between the longitudinal responses are usually treated as nuisance parameters, it is well known that in the presence of time-varying covariates the efficiency of the estimates can be improved by specifying the dependence structure. For this purpose, the proposed estimator is extended to accommodate the modeling of the association structure by means of the correlation coefficient as well as local odds ratio. Two real data sets from the medical field are used to illustrate the methods.