Improving Dose Volume Histogram (DVH) Based Analysis of Clinical Outcomes Using Modern Statistical Techniques: A Systematic Answer to Multiple Comparisons Concerns

Abstract

DVH constraints are essential in the clinical practice of radiation therapy. Historically, DVH constraints were found through sparse sampling of all possible DVH indices to find one that appeared to be most predictive for clinical toxicity. This approach can lead to inconsistent results among studies and to multiple comparison concerns. We aim to solve both problems by examining a full array of DVH indices using statistical methods that account for strong correlations among DVH indices and incorporate radiobiological knowledge constraints. We extracted a dense array of V%_D indices from a treatment planning system using ESAPI interface, with V%_D corresponding to the volume fraction irradiated to dose D, or higher. We used Fused Lasso as the base model to compensate for correlations among DVH indices because it applies a penalty on the difference between DVH variables with adjacent dose. The base model was augmented with additional constraints based on radiobiological considerations: the positivity constraint (beta_i > 0) which assumes that any tissue irradiation cannot reduce the risk of toxicity, and monotonicity constraint (beta_i+1 > = beta_i) which assumes that higher dose to a fixed volume fraction cannot be associated with a lower risk of toxicity. We called the hybrid model KC-Lasso (Knowledge Constrained Lasso) and applied it to two clinical examples: grade 2 acute rectal toxicity in conventionally fractionated RT for 79 prostate cancer patients (77.4 Gy + MR based boost to 81-83 Gy) and cardiac toxicity in conventionally fractionated RT for 119 locally advanced Non-small Cell Lung Cancer (NSCLC) patients (Median prescribed dose 62 Gy). We further examined alternative data driven models to determine the importance of knowledge constraints. KC-Lasso detected two distinct dose thresholds for grade 2 rectal toxicity, at 35 Gy and 78 Gy. A threshold of 51 Gy was detected for reduced overall survival due to cardiac irradiation in NSCLC patients. An examination of KC-Lasso models at varying step size suggested that a single mid-range index can be used as a treatment planning constraint while full model can be used for confirmatory, final plan evaluation. Alternative models which lack knowledge constraints show patterns of negative and isolated coefficients which are difficult to interpret and are not likely to be generalizable. A more systematic approach to the analysis of correlations between DVH constraints and clinical toxicity can lead to greater consistency of results among different studies, better understanding of true dose thresholds and results which are more generalizable.