A family of estimators to diagnostic accuracy when candidate tests are subject to detection limits—Application to diagnosing early stage Alzheimer disease

In disease diagnosis, individuals are usually assumed to be one of the two basic types, healthy or diseased, as typically based on an established gold standard. Candidate markers for diagnosing a disease often are much cheaper and less invasive than the gold standard but must be evaluated against the gold standard for their sensitivity and specificity to accurately diagnose the disease. When candidate diagnostic markers are fully measured, receiver operating characteristic curves have been the standard approaches for assessing diagnostic accuracy. However, full measurements of diagnostic markers may not be available above or below certain limits due to various practical and technical limitations. For example, in the diagnosis of Alzheimer disease using cerebrospinal fluid biomarkers, the Roche Elecsys® immunoassays have a measuring range for multiple cerebrospinal fluid molecular concentrations. Many cognitive tests used in diagnosing dementia due to Alzheimer disease are also subject to detection limits, often referred to as the floor and ceiling effects in the neuropsychological literature. We propose a new statistical methodology for estimating the diagnostic accuracy when a diagnostic marker is subject to detection limits by dividing the entire study sample into two sub-samples by a threshold of the diagnostic marker. We then propose a family of estimators to the area under the receiver operating characteristic curve by combining a conditional nonparametric estimator and another conditional semi-parametric estimator derived from Cox's proportional hazards model. We derive the variance to the proposed estimators, and further, assess the performance of the proposed estimators as a function of possible thresholds through an extensive simulation study, and recommend the optimum thresholds. Finally, we apply the proposed methodology to assess the ability of several cerebrospinal fluid biomarkers and cognitive tests in diagnosing early stage Alzheimer disease dementia.