title: A comparison of four indices for combining distance and dose differences.
abstract: OBJECTIVE
  When one is comparing two dose distributions, a number of methods have been published to combine dose difference and distance to agreement into a single measure. Some have been defined as pass/fail indices and some as numeric indices. We show that the pass/fail indices can all be used to derive numeric indices, and we compare the results of using these indices to evaluate one-dimensional (1D) and three-dimensional (3D) dose distributions, with the aim of selecting the most appropriate index for use in different circumstances.
  
  
  METHODS
  The indices compared are the gamma index, the kappa index, the index in International Commission on Radiation Units & Measurements Report 83, and a box index. Comparisons are made for 1D and 3D distributions. The 1D distribution is chosen to have a variety of dose gradients. The 3D distribution is taken from a clinical treatment plan. The effect of offsetting distributions by known distances and doses is studied.
  
  
  RESULTS
  The International Commission on Radiation Units & Measurements Report 83 index causes large discontinuities unless the dose gradient cutoff is set to equal the ratio of the dose tolerance to the distance tolerance. If it is so set, it returns identical results to the kappa index. Where the gradient is very high or very low, all the indices studied in this article give similar results for the same tolerance values. For moderate gradients, they differ, with the box index being the least strict, followed by the gamma index, and with the kappa index being the most strict.
  
  
  CONCLUSIONS
  If the clinical tolerances are much greater than the uncertainties of the measuring system, the kappa index should be used, with tolerance values determined by the clinical tolerances. In cases where the uncertainties of the measuring system dominate, the box index will be best able to determine errors in the delivery system.
authors.affiliation: Department of Medical Physics, Addenbrooke's Hospital, Cambridge, England. simon.thomas@addenbrookes.nhs.uk
authors.forename: Simon J
authors.initials: SJ
authors.lastname: Thomas
authors.forename: Ian R
authors.initials: IR
authors.lastname: Cowley
mesh_terms: D000465:Algorithms; D011836:Radiation Tolerance; D011874:Radiometry / Q000379:methods*; D011879:Radiotherapy Dosage; D013679:Technology, Radiologic / Q000379:methods*