Online monitoring and error detection of real-time tumor displacement prediction accuracy using control limits on respiratory surrogate statistics.

Purpose: To evaluate Hotelling’sT 2 statistic and the input variable squared prediction error (Q (X)) for detecting large respiratory surrogate-based tumor displacement prediction errors without directly measuring the tumor’s position. Methods: Tumor and external marker positions from a database of 188 Cyberknife Synchrony™ lung,liver, and pancreas treatment fractions were analyzed. The first ten measurements of tumor position in each fraction were used to create fraction-specific models of tumor displacement using external surrogates as input; the models were used to predict tumor position from subsequent external marker measurements. A partial least squares (PLS) model with four scores was developed for each fraction to determineT 2 and Q (X) confidence limits based on the first ten measurements in a fraction. The T 2 and Q (X) statistics were then calculated for every set of external marker measurements. Correlations between model error and both T 2 and Q (X) were determined. Receiver operating characteristic analysis was applied to evaluate sensitivities and specificities of T 2, Q (X), and T 2∪Q (X) for predicting real-time tumor localization errors >3 mm over a range of T 2 and Q (X) confidence limits. Results: Sensitivity and specificity of detecting errors >3 mm varied with confidence limit selection. At 95% sensitivity,T 2∪Q (X) specificity was 15%, 2% higher than either T 2 or Q (X) alone. The mean time to alarm for T 2∪Q (X) at 95% sensitivity was 5.3 min but varied with a standard deviation of 8.2 min. Results did not differ significantly by tumor site. Conclusions: The results of this study establish the feasibility of respiratory surrogate-based online monitoring of real-time respiration-induced tumor motion model accuracy for lung,liver, and pancreas tumors. TheT 2 and Q (X) statistics were able to indicate whether inferential model errors exceeded 3 mm with high sensitivity. Modest improvements in specificity were achieved by combining T 2 and Q (X) results.