Abstract
PurposeCurrent normal tissue complication probability modeling using logistic regression suffers from bias and high uncertainty in the presence of highly correlated radiation therapy (RT) dose data. This hinders robust estimates of dose-response associations and, hence, optimal normal tissue—sparing strategies from being elucidated. Using functional data analysis (FDA) to reduce the dimensionality of the dose data could overcome this limitation.Methods and MaterialsFDA was applied to modeling of severe acute mucositis and dysphagia resulting from head and neck RT. Functional partial least squares regression (FPLS) and functional principal component analysis were used for dimensionality reduction of the dose-volume histogram data. The reduced dose data were input into functional logistic regression models (functional partial least squares—logistic regression [FPLS-LR] and functional principal component—logistic regression [FPC-LR]) along with clinical data. This approach was compared with penalized logistic regression (PLR) in terms of predictive performance and the significance of treatment covariate—response associations, assessed using bootstrapping.ResultsThe area under the receiver operating characteristic curve for the PLR, FPC-LR, and FPLS-LR models was 0.65, 0.69, and 0.67, respectively, for mucositis (internal validation) and 0.81, 0.83, and 0.83, respectively, for dysphagia (external validation). The calibration slopes/intercepts for the PLR, FPC-LR, and FPLS-LR models were 1.6/−0.67, 0.45/0.47, and 0.40/0.49, respectively, for mucositis (internal validation) and 2.5/−0.96, 0.79/−0.04, and 0.79/0.00, respectively, for dysphagia (external validation). The bootstrapped odds ratios indicated significant associations between RT dose and severe toxicity in the mucositis and dysphagia FDA models. Cisplatin was significantly associated with severe dysphagia in the FDA models. None of the covariates was significantly associated with severe toxicity in the PLR models. Dose levels greater than approximately 1.0 Gy/fraction were most strongly associated with severe acute mucositis and dysphagia in the FDA models.ConclusionsFPLS and functional principal component analysis marginally improved predictive performance compared with PLR and provided robust dose-response associations. FDA is recommended for use in normal tissue complication probability modeling.
Highlights
Normal tissue complication probability (NTCP) modeling uses radiation therapy (RT) dose data, often in combination with clinical and biological data, to construct statistical models of RT-induced toxicity
To input dose data into statistical models, the 3D dose distribution delivered to an organ at risk (OAR) is reduced to a single or series of scalar metrics, for example, maximum dose or mean dose, or multiple points sampled from the dose-volume histogram (DVH), such as the volume of an OAR receiving at least x cGy (Vx)
The functional principal component analysis (FPCA) components indicate that the variation between patients in the volume of OAR irradiated to a certain dose level increased with increasing dose level
Summary
Normal tissue complication probability (NTCP) modeling uses radiation therapy (RT) dose data, often in combination with clinical and biological data, to construct statistical models of RT-induced toxicity. There are 2 distinct aims of NTCP modeling: [1] accurate prediction of toxicity outcomes for individual patients; and [2] estimates of associations between treatment covariates and toxicity. Given the nature of the dose deposition within the patient, adjacent dose levels are very highly correlated [4] This is problematic for many statistical modeling methods, such as the commonly used logistic regression, which often exhibit biased regression coefficients with large standard errors in the presence of collinearity [5]. If the same or similar treatment techniques are used, this does not necessarily prevent the models from being able to accurately predict outcomes prospectively for new patients It does result in the regression coefficients of the dosimetric covariates being biased and having large standard errors. The apparent regression coefficients of the dosimetric covariates do not generalize well to new patients and, should not be used to determine the strength of associations between correlated dose metrics and toxicity, as is commonly done [6]
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