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

Correcting for measurement error when estimating 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 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, we propose an estimator based on the non-parametric deconvolution theory with an adaptive procedure for cutoff selection, the replicates being used for an estimation of the error density. We illustrate this approach in two applicative examples: (i) the systolic blood pressure distribution density, using the Framingham Study data set, and (ii) the distribution of the timing of onset of pregnancy within the female cycle, using ultrasound measurements in the first trimester of pregnancy.