A systematic approach to statistical analysis in dosimetry and patient-specific IMRT plan verification measurements

PURPOSE In the presence of random uncertainties, delivered radiation treatment doses in patient likely exhibit a statistical distribution. The expected dose and variance of this distribution are unknown and are most likely not equal to the planned value since the current treatment planning systems cannot exactly model and simulate treatment machine. Relevant clinical questions are 1) how to quantitatively estimate the expected delivered dose and extrapolate the expected dose to the treatment dose over a treatment course and 2) how to evaluate the treatment dose relative to the corresponding planned dose. This study is to present a systematic approach to address these questions and to apply this approach to patient-specific IMRT (PSIMRT) plan verifications. METHODS The expected delivered dose in patient and variance are quantitatively estimated using Student T distribution and Chi Distribution, respectively, based on pre-treatment QA measurements. Relationships between the expected dose and the delivered dose over a treatment course and between the expected dose and the planned dose are quantified with mathematical formalisms. The requirement and evaluation of the pre-treatment QA measurement results are also quantitatively related to the desired treatment accuracy and to the to-be-delivered treatment course itself. The developed methodology was applied to PSIMRT plan verification procedures for both QA result evaluation and treatment quality estimation. RESULTS Statistically, the pre-treatment QA measurement process was dictated not only by the corresponding plan but also by the delivered dose deviation, number of measurements, treatment fractionation, potential uncertainties during patient treatment, and desired treatment accuracy tolerance. For the PSIMRT QA procedures, in theory, more than one measurement had to be performed to evaluate whether the to-be-delivered treatment course would meet the desired dose coverage and treatment tolerance. CONCLUSION By acknowledging and considering the statistical nature of multi-fractional delivery of radiation treatment, we have established a quantitative methodology to evaluate the PSIMRT QA results. Both the statistical parameters associated with the QA measurement procedure and treatment course need to be taken into account to evaluate the QA outcome and to determine whether the plan is acceptable and whether additional measures should be taken to reduce treatment uncertainties. The result from a single QA measurement without the appropriate statistical analysis can be misleading. When the required number of measurements is comparable to the planned number of fractions and the variance is unacceptably high, action must be taken to either modify the plan or adjust the beam delivery system.