Unravelling sensitivity: exploring covariate effects in early disease detection

Within the three-class ROC analysis framework for diagnostic tests, we address the problem of making inferences about a true class fraction (TCF), given the remaining two. More precisely, we propose a novel procedure to make inference about the covariate-specific TCF2, i.e., the covariate-specific probability of correct classification at the so-called early stage, when the values for the true class fractions at first and third classes are fixed. Our methodology focuses on both point and interval estimation for TCF2, under the condition that the true class fractions for the first and third classes, TCF1 and TCF3, are predetermined. The proposed approach integrates quantile regression techniques with a logistic regression model applied to a constructed“working”binary sample. Specifically, local quantile regressions are utilized to estimate covariate-specific thresholds corresponding to fixed values of TCF1 and TCF3. Using these threshold estimates, a “working” binary sample is generated for a given set of covariate values. Subsequently, a logistic regression model is employed to estimate the covariate-specific TCF2. Additionally, we present a method for estimating the covariate-adjusted TCF2, maintaining fixed values for TCF1 and TCF3. This measure represents the overall TCF2 when thresholds are adapted to covariates, ensuring that the corresponding TCF1 and TCF3 values align with fixed values in each covariate-specific subpopulation. The behaviour of the proposed techniques in finite samples is evaluated through several simulation experiments. In addition, an application to real data concerning Alzheimer’s disease shows the usefulness of our proposals in practical contexts.