Identifiability of Models for Multiple Diagnostic Testing in the Absence of a Gold Standard

Abstract

We discuss the issue of identifiability of models for multiple dichotomous diagnostic tests in the absence of a gold standard (GS) test. Data arise as multinomial or product-multinomial counts depending upon the number of populations sampled. Models are generally posited in terms of population prevalences, test sensitivities and specificities, and test dependence terms. It is commonly believed that if the degrees of freedom in the data meet or exceed the number of parameters in a fitted model then the model is identifiable. Goodman (1974, Biometrika 61, 215-231) established that this was not the case a long time ago. We discuss currently available models for multiple tests and argue in favor of an extension of a model that was developed by Dendukuri and Joseph (2001, Biometrics 57, 158-167). Subsequently, we further develop Goodman's technique, and make geometric arguments to give further insight into the nature of models that lack identifiability. We present illustrations using simulated and real data.

Diagnostic Performance Tests for Suspected Scaphoid Fractures Differ with Conventional and Latent Class Analysis

“…Therefore, the data violate the conditional independence assumption of standard latent class analysis, and require the use of a recently developed latent class analysis model based on Bayesian methods that allow for conditional dependence among multiple test results by relying on surgeon estimation of plausible dependencies between test results [21]. Johnson et al [20] provided Bayesian methods for the Hui-Walter model and Dendukuri and Joseph [12] extended the model to incorporate two additional dependence parameters (one for each latent class), in the case of two diagnostic tests.…”

Bayesian estimation of true prevalence, sensitivity and specificity of indirect ELISA, Rose Bengal Test and Slow Agglutination Test for the diagnosis of brucellosis in sheep and goats in Bangladesh

“…Jones et al (2010) proposed that in the construction of conditional dependence models, mainly simple extensions of the conditional independence model should be considered. Essentially, in the first set of simple parameterizations, the conditional dependence between iELISA and RBT, between iELISA and SAT and between RBT and SAT were each added in turn to the conditional independence model.…”

Flexible regression models for ROC and risk analysis, with or without a gold standard

“…In the more general case, with the two distributions being modeled nonparametrically, even the assumption of stochastic domination of one distribution over the other does not make the model identifiable. Moreover, in the area of medical classification with multiple binary tests, it is often the case that models either lack identifiability or require potentially strong assumptions in order to guarantee identifiability [21,22]. The approach taken here buys identifiability based on having additional information, including continuous test outcomes instead of dichotomous outcomes and covariate information that should be helpful in mitigating the lack of a gold standard.…”