A two-stage logistic regression model for analyzing inter-rater agreement

Studies of agreement commonly occur in psychiatric research. For example, researchers are often interested in the agreement among radiologists in their review of brain scans of elderly patients with dementia or in the agreement among multiple informant reports of psychopathology in children. In this paper, we consider the agreement between two raters when rating a dichotomous outcome (e.g., presence or absence of psychopathology). In particular, we consider logistic regression models that allow agreement to depend on both rater- and subject-level covariates. Logistic regression has been proposed as a simple method for identifying covariates that are predictive of agreement (Coughlin et al., 1992). However, this approach is problematic since it does not take account of agreement due to chance alone. As a result, a spurious association between the probability (or odds) of agreement and a covariate could arise due entirely to chance agreement. That is, if the prevalence of the dichotomous outcome varies among subgroups of the population, then covariates that identify the subgroups may appear to be predictive of agreement. In this paper we propose a modification to the standard logistic regression model in order to take proper account of chance agreement. An attractive feature of the proposed method is that it can be easily implemented using existing statistical software for logistic regression. The proposed method is motivated by data from the Connecticut Child Study (Zahner et al., 1992) on the agreement among parent and teacher reports of psychopathology in children. In this study, parents and teachers provide dichotomous assessments of a child's psychopathology and it is of interest to examine whether agreement among the parent and teacher reports is related to the age and gender of the child and to the time elapsed between parent and teacher assessments of the child.The authors thank the Associate Editor and the referees for their helpful comments and suggestions. We also thank Gwen Zahner for use of data from the Connecticut Child Study, which was conducted under contract to the Connecticut Department of Children and Youth Services. This research was supported by grants HL 69800, AHRQ 10871, HL52329, HL61769, GM 29745, MH 54693 and MH 17119 from the National Institutes of Health.