Using latent class models to characterize and assess relative error in discrete measurements

Whenever a definitive standard is not available to mark accuracy in a classification process, discrete measurement error can be discussed only in relative terms. If strong assumptions concerning the underlying discrete processes can be made, latent class models allow one to characterize patterns of agreement/disagreement among raters while simultaneously producing "consensus" estimates of prevalence. A hypothetical definitive standard serves as the latent factor. The discrete data are treated as incomplete and log-linear models can be used to parameterize latent class models and extensions of latent class models. Data from the radiographic diagnosis of dental caries by five dentists were explored to estimate prevalence, assess relative error, and examine the validity of several traditional assumptions concerning diagnostic reliability. Latent class analysis allowed a more detailed description of diagnostic error than provided by commonly used summary statistics.