### 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) |
---|---|

Number of pages | 1 |

Journal | Medical Physics |

Volume | 37 |

Issue number | 6 |

DOIs | |

State | Published - 2010 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Biophysics
- Radiology Nuclear Medicine and imaging

### Cite this

*Medical Physics*,

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

**WE‐D‐204B‐05 : Online Monitoring and Error Detection of Real‐Time Tumor Displacement Prediction Accuracy Using Statistical Process Control.** / Malinowski, K. T.; mc Avoy, T. J.; George, R.; Dieterich, Sonja; D'souza, W. D.

Research output: Contribution to journal › Article

*Medical Physics*, vol. 37, no. 6. https://doi.org/10.1118/1.3469402

}

TY - JOUR

T1 - WE‐D‐204B‐05

T2 - Online Monitoring and Error Detection of Real‐Time Tumor Displacement Prediction Accuracy Using Statistical Process Control

AU - Malinowski, K. T.

AU - mc Avoy, T. J.

AU - George, R.

AU - Dieterich, Sonja

AU - D'souza, W. D.

PY - 2010

Y1 - 2010

N2 - Purpose: To investigate two statistical process control (SPC) metrics, the Hotelling (T2) 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 T2‐ and Q(x)‐statistics in the training data were used to develop 90th, 95th and 99th percentile ranges of expected T2 and Q(x) values. The sensitivities and specificities of T2, Q(x), T2̆Q(x), and T2̑Q(x) for predicting real‐time tumor displacement errors greater than 3mm and 5mm were determined. Results: The T2, Q(x), T2̆Q(x), and T2̑Q(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 T2 statistic was associated with moderate sensitivity and moderate specificity. For 90th percentile T2, 99th percentile Q(x) and 3 mm error, the sensitivities of T2, Q(x), T2̆Q(x), and T2̑Q(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.

AB - Purpose: To investigate two statistical process control (SPC) metrics, the Hotelling (T2) 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 T2‐ and Q(x)‐statistics in the training data were used to develop 90th, 95th and 99th percentile ranges of expected T2 and Q(x) values. The sensitivities and specificities of T2, Q(x), T2̆Q(x), and T2̑Q(x) for predicting real‐time tumor displacement errors greater than 3mm and 5mm were determined. Results: The T2, Q(x), T2̆Q(x), and T2̑Q(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 T2 statistic was associated with moderate sensitivity and moderate specificity. For 90th percentile T2, 99th percentile Q(x) and 3 mm error, the sensitivities of T2, Q(x), T2̆Q(x), and T2̑Q(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.

UR - http://www.scopus.com/inward/record.url?scp=85024811748&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85024811748&partnerID=8YFLogxK

U2 - 10.1118/1.3469402

DO - 10.1118/1.3469402

M3 - Article

VL - 37

JO - Medical Physics

JF - Medical Physics

SN - 0094-2405

IS - 6

ER -