We present a computational framework to select the most accurate and precise method of measurement of a certain quantity, when there is no access to the true value of the measurand. A typical use case is when several image analysis methods are applied to measure the value of a particular quantitative imaging biomarker from the same images. The accuracy of each measurement method is characterized by systematic error (bias), which is modeled as a polynomial in true values of measurand, and the precision as random error modeled with a Gaussian random variable. In contrast to previous works, the random errors are modeled jointly across all methods, thereby enabling the framework to analyze measurement methods based on similar principles, which may have correlated random errors. Furthermore, the posterior distribution of the error model parameters is estimated from samples obtained by Markov chain Monte-Carlo and analyzed to estimate the parameter values and the unknown true values of the measurand. The framework was validated on six synthetic and one clinical dataset containing measurements of total lesion load, a biomarker of neurodegenerative diseases, which was obtained with four automatic methods by analyzing brain magnetic resonance images. The estimates of bias and random error were in a good agreement with the corresponding least squares regression estimates against a reference.
Keywords: Bayesian inference; Markov chain Monte-Carlo; Quantitative imaging biomarker; gold standard; linear regression.