Reference-free Bayesian model for pointing errors of typein neurosurgical planning

Many neurosurgical planning tasks rely on identifying points of interest in volumetric images. Often, these points require significant expertise to identify correctly as, in some cases, they are not visible but instead inferred by the clinician. This leads to a high degree of variability between annotators selecting these points. In particular, errors of type are when the experts fundamentally select different points rather than the same point with some inaccuracy. This complicates research as their mean may not reflect any of the experts' intentions nor the ground truth.

We present a regularised Bayesian model for measuring errors of type in pointing tasks. This model is reference-free; in that it does not require a priori knowledge of the ground truth point but instead works on the basis of the level of consensus between multiple annotators. We apply this model to simulated data and clinical data from transcranial magnetic stimulation for chronic pain.

Our model estimates the probabilities of selecting the correct point in the range of 82.6[Formula: see text]88.6% with uncertainties in the range of 2.8[Formula: see text]4.0%. This agrees with the literature where ground truth points are known. The uncertainty has not previously been explored in the literature and gives an indication of the dataset's strength.

Our reference-free Bayesian framework easily models errors of type in pointing tasks. It allows for clinical studies to be performed with a limited number of annotators where the ground truth is not immediately known, which can be applied widely for better understanding human errors in neurosurgical planning.