Density estimation of a biomedical variable subject to measurement error using an auxiliary set of replicate observations

Correcting for measurement error the density of a routinely collected biomedical variable is an important issue when describing reference values for both healthy and pathological states. The present work addresses the problem of estimating the density of a biomedical variable observed with measurement error without any \textit{a priori} knowledge on the error density. Assuming the availability of a sample of replicate observations, either internal or external, which is generally easily obtained in clinical settings, an estimator is proposed based on non-parametric deconvolution theory with an adaptive procedure for cut-off selection, the replicates being used for an estimation of the error density. This approach is illustrated in two applicative examples: i) the systolic blood pressure distribution density using the Framingham Study dataset and ii) the distribution of the timing of onset of pregnancy within the female cycle, using ultrasound measurements in the first trimester of pregnancy