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 TCF \(_2\) , 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 TCF \(_2\) , under the condition that the true class fractions for the first and third classes, TCF \(_1\) and TCF \(_3\) , 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 TCF \(_1\) and TCF \(_3\) . 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 TCF \(_2\) . Additionally, we present a method for estimating the covariate-adjusted TCF \(_2\) , maintaining fixed values for TCF \(_1\) and TCF \(_3\) . This measure represents the overall TCF \(_2\) when thresholds are adapted to covariates, ensuring that the corresponding TCF \(_1\) and TCF \(_3\) 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.
