Parametric Methods for Bivariate Quantile‐Partitioned Tables and the Efficiency of Corresponding Nonparametric Methods

Abstract

AbstractIn order to study the agreement between two continuous measurements on a sample of individuals, epidemiologists sometimes partition the original bivariate data into categories defined by the empirical quantiles of the two marginal distributions. The counts in the resulting two‐way contingency table have the empirical bivariate quantile‐partitioned (EBQP) distribution rather than the conventional multinomial distribution. BORKOWF et al. (1997) developed the asymptotic theory and inferential procedures for estimates of measures of agreement calculated from EBQP tables. In this paper, we develop parametric methods for bivariate quantile‐partitioned (BQP) tables. We use these methods to study the efficiency of nonparametric (EBQP) methods and to improve the precision of estimates of measures of agreement. We present computational methods for estimating certain measures of agreement (kappa, weighted kappa, and row proportions) together with their variances. Numerical studies and an example show that nonparametric (EBQP) estimates of kappa and certain row proportions tend to be quite inefficient compared to parametric estimates, whereas nonparametric estimates of weighted kappa can be relatively more efficient for some underlying distributions. Thus, investigators should weigh the efficiency advantages of parametric estimates against possible biases that can result from choosing an inappropriate parametric model when they employ BQP tables to study agreement.