### Abstract

Purpose: To investigate two statistical process control (SPC) metrics, the Hotelling (T^{2}) statistic and the input‐variable‐squared‐prediction‐error (Q^{(x)}), for predicting degradation in real‐time tumor displacement accuracy without explicit measurement of tumor displacement. Method and Materials: Independently but concurrently localized tumor and external surrogate positions from a database of Cyberknife Synchrony™ cases (130 treatment fractions from 63 lung tumors, 10 fractions from 5 liver tumors, and 48 fractions from 23 pancreas tumors) were analyzed. Each fraction consisted of 40–112 measurements obtained at an average rate of 0.018 Hz. The first 10 measured internal/external samples in each fraction were used to create fraction‐specific models of tumor displacement using external surrogates. The regression coefficients relating the 3D positions of the 3 skin markers to the 3D tumor positions were calculated using partial‐least‐squares (PLS) regression. The PLS model was applied to all subsequent localizations in the fraction. The T^{2}‐ and Q^{(x)}‐statistics in the training data were used to develop 90^{th}, 95^{th} and 99^{th} percentile ranges of expected T^{2} and Q^{(x)} values. The sensitivities and specificities of T^{2}, Q^{(x)}, T^{2}̆Q^{(x)}, and T^{2}̑Q^{(x)} for predicting real‐time tumor displacement errors greater than 3mm and 5mm were determined. Results: The T^{2}, Q^{(x)}, T^{2}̆Q^{(x)}, and T^{2}̑Q^{(x)} statistics' sensitivities and specificities varied with error threshold and acceptable percentile ranges of values. In general, the Q^{(x)} statistic was associated with high sensitivity and low specificity, while the T^{2} statistic was associated with moderate sensitivity and moderate specificity. For 90^{th} percentile T^{2}, 99^{th} percentile Q^{(x)} and 3 mm error, the sensitivities of T^{2}, Q^{(x)}, T^{2}̆Q^{(x)}, and T^{2}̑Q^{(x)} were 69%, 88%, 92%, and 64%, respectively, and the specificities were 62%, 37%, 28%, and 72%, respectively. Conclusion: This study illustrates the feasibility of SPC metrics for detecting breakdowns in tumor displacement prediction accuracy using external sensors.

Original language | English (US) |
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Number of pages | 1 |

Journal | Medical Physics |

Volume | 37 |

Issue number | 6 |

DOIs | |

State | Published - 2010 |

Externally published | Yes |

### ASJC Scopus subject areas

- Biophysics
- Radiology Nuclear Medicine and imaging

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## Cite this

*Medical Physics*,

*37*(6). https://doi.org/10.1118/1.3469402