The most common metric for comparing measured to calculated dose, such as for pretreatment quality assurance of intensity-modulated photon fields, is a pass rate (%) generated using percent difference (%Diff), distance-to-agreement (DTA), or some combination of the two (e.g., gamma evaluation). For many dosimeters, the grid of analyzed points corresponds to an array with a low areal density of point detectors. In these cases, the pass rates for any given comparison criteria are not absolute but exhibit statistical variability that is a function, in part, on the detector sampling geometry. In this work, the authors analyze the statistics of various methods commonly used to calculate pass rates and propose methods for establishing confidence intervals for pass rates obtained with low-density arrays.Methods:
Dose planes were acquired for 25 prostate and 79 head and neck intensity-modulated fields via diode array and electronic portal imaging device(EPID), and matching calculated dose planes were created via a commercial treatment planning system. Pass rates for each dose plane pair (both centered to the beam central axis) were calculated with several common comparison methods: %Diff/DTA composite analysis and gamma evaluation, using absolute dose comparison with both local and global normalization. Specialized software was designed to selectively sample the measuredEPID response (very high data density) down to discrete points to simulate low-density measurements. The software was used to realign the simulated detector grid at many simulated positions with respect to the beam central axis, thereby altering the low-density sampled grid. Simulations were repeated with 100 positional iterations using a 1 detector/cm2 uniform grid, a 2 detector/cm2 uniform grid, and similar random detector grids. For each simulation, %/DTA composite pass rates were calculated with various %Diff/DTA criteria and for both local and global %Diff normalization techniques.Results:
For the prostate and head/neck cases studied, the pass rates obtained with gamma analysis of high density dose planes were 2%–5% higher than respective %/DTA composite analysis on average (ranging as high as 11%), depending on tolerances and normalization. Meanwhile, the pass rates obtained via local normalization were 2%–12% lower than with global maximum normalization on average (ranging as high as 27%), depending on tolerances and calculation method. Repositioning of simulated low-density sampled grids leads to a distribution of possible pass rates for each measured/calculated dose plane pair. These distributions can be predicted using a binomial distribution in order to establish confidence intervals that depend largely on the sampling density and the observed pass rate (i.e., the degree of difference between measured and calculated dose). These results can be extended to apply to 3D arrays of detectors, as well.Conclusions:
Dose plane QA analysis can be greatly affected by choice of calculation metric and user-defined parameters, and so all pass rates should be reported with a complete description of calculation method. Pass rates for low-density arrays are subject to statistical uncertainty (vs. the high-density pass rate), but these sampling errors can be modeled using statistical confidence intervals derived from the sampled pass rate and detector density. Thus, pass rates for low-density array measurements should be accompanied by a confidence interval indicating the uncertainty of each pass rate.
II. METHOD AND MATERIALS
II.A. High-density dose plane acquisition
II.B. Pass rate calculation methods
II.C. Low-density sampling method
II.D. Confidence interval calculations for low-density pass rates
II.E. Analytical confidence interval simulations
III. RESULTS AND DISCUSSION
III.A. Effect of pass rate calculation method
III.B. Distribution of pass rates from low-density sampling
III.C. Establishing confidence intervals for low-density pass rates
III.D. Analytical confidence interval simulation results
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