Comparison of paired ordinal data with mis-classification and covariates adjustment

In this paper, we develop an estimation and testing procedure for comparing matched-pair ordinal outcomes in studies with confounding factors. The classification method for the categories of ordinal outcomes that is accessible for all units may be prone to mis-classification, and thus another error-free classification method that can only be affordable for a fraction of the units are used, resulting in a dataset with partial validation. The distribution of categorical variables is modelled using correlated bivariate Gaussian latent variables, and the confounding factors are adjusted as covariates. The mis-classification of ordinal outcomes is addressed by estimating the mis-classification probabilities through the partial validation structure of the dataset. The mis-classification probabilities and the other parameters are estimated by a two-stage maximum likelihood estimator, and the difference between the matched-pair ordinal outcomes are assessed by a Wald test statistic. Simulation studies were conducted to investigate the accuracy of the estimates of the model parameters, and the type I error rates and power of the proposed testing procedure. The motivating dataset from the Garki Project was analysed to demonstrate the applicability of the proposed approach.