title: Fitting tumor control probability models to biopsy outcome after three-dimensional conformal radiation therapy of prostate cancer: pitfalls in deducing radiobiologic parameters for tumors from clinical data.
abstract: OBJECTIVE
  The goal of tumor control probability (TCP) models is to predict local control for inhomogeneous dose distributions. All existing fits of TCP models to clinical data have utilized summaries of dose distributions (e.g., prescription dose). Ideally, model fits should be based on dose distributions in the tumor, but usually only dose-volume histograms (DVH) of the planning target volume (PTV) are available. We fit TCP models to biopsy outcome after three-dimensional conformal radiation therapy of prostate cancer using either a dose distribution summary or the full DVH in the PTV. We discuss differences in the radiobiologic parameters and dose-response curves and demonstrate pitfalls in interpreting the results.
  
  
  METHODS
  Two mechanistic TCP models were fit with a maximum likelihood technique to biopsy outcome from 103 prostate patients treated at Memorial Sloan-Kettering Cancer Center. Fits were performed separately for different patient subgroups defined by tumor-related prognostic factors. Fits were based both on full DVHs, denoted TCP(DVH(calc)), and, alternatively, assuming a homogeneous PTV dose given by the mean dose (Dmean) of each DVH, denoted TCP(Dmean(calc)). Dose distributions for these patients were very homogeneous with any cold spots located on the periphery of the PTV. These cold spots were uncorrelated with biopsy outcome, likely because the low-dose regions may not contain tumor cells. Therefore, fits of TCP models that are potentially sensitive to cold spots (e.g., TCP(DVH(calc))) likely give biologic parameters that diminish this sensitivity. In light of this, we examined differences in fitted clonogenic cell number, N(C), or density, rho(C), surviving fraction after 2 Gy, SF(2), or radiosensitivity, alpha, and their standard deviations in the population, sigma(SF(2)) and sigma(alpha), resulting from fits based on TCP(DVH(calc)) and TCP(Dmean(calc)). Dose-response curves for homogeneous irradiation (characterized by TCD(50), the dose for a TCP of 50%) and differences in TCP predictions calculated from the DVH using alternatively derived parameters were evaluated.
  
  
  RESULTS
  Fits of TCP(Dmean(calc)) are better (i.e., have larger likelihood) than fits of TCP(DVH(calc)). For TCP(Dmean(calc)) fits, matching values of SF(2) and sigma(SF(2)) (or alpha and sigma(alpha)) exist for all N(C) (rho(C)) above a threshold that give fits of equal quality, with no maximum in likelihood. In contrast, TCP(DVH(calc)) fits have maximum likelihood for high SF(2) (low alpha) values that minimize effects of cold spots. Consequently, small N(C) (rho(C)) values are obtained to match the observed control rate. For example, for patients in low-, intermediate-, and high-risk groups, optimum values of SF(2) and N(C) are 0.771 and 3.3 x 10(3), 0.736 and 2.2 x 10(4), and 0.776 and 1.0 x 10(4), respectively. The TCD(50) of dose-response curves for intermediate-risk patients is 2.6 Gy lower using TCP(DVH(calc)) parameters (TCD(50) = 67.8 Gy) than for TCP(Dmean(calc)) parameters (TCD(50) = 70.4 Gy). TCP predictions calculated from the DVH using risk group-dependent TCP(Dmean(calc)) parameters are up to 53% lower than corresponding calculations with TCP(DVH(calc)) parameters.
  
  
  CONCLUSIONS
  For our data, TCP parameters derived from DVHs likely do not reflect true radiobiologic parameters in the tumor, but are a consequence of the reduced importance of low-dose regions at the periphery of the PTV. Deriving radiobiologic parameters from TCP(Dmean(calc)) fits is not possible unless one parameter is already known. TCP predictions using TCP(DVH(calc)) and TCP(Dmean(calc)) parameters may differ substantially, requiring consistency in the derivation and application of model parameters. The proper derivation of radiobiologic parameters from clinical data requires both substantial dose inhomogeneities and understanding of how these coincide with tumor location.
authors.affiliation: Department of Medical Physics, Memorial Sloan-Kettering Cancer Center, New York, NY, USA. s.levegruen@dkfz-heidelberg.de
authors.forename: S
authors.initials: S
authors.lastname: Levegrün
authors.forename: A
authors.initials: A
authors.lastname: Jackson
authors.forename: M J
authors.initials: MJ
authors.lastname: Zelefsky
authors.forename: M W
authors.initials: MW
authors.lastname: Skwarchuk
authors.forename: E S
authors.initials: ES
authors.lastname: Venkatraman
authors.forename: W
authors.initials: W
authors.lastname: Schlegel
authors.forename: Z
authors.initials: Z
authors.lastname: Fuks
authors.forename: S A
authors.initials: SA
authors.lastname: Leibel
authors.forename: C C
authors.initials: CC
authors.lastname: Ling
mesh_terms: D000230:Adenocarcinoma / Q000473:pathology* / Q000532:radiotherapy*; D000704:Analysis of Variance; D001706:Biopsy; D016001:Confidence Intervals; D004307:Dose-Response Relationship, Radiation; D006801:Humans; D016013:Likelihood Functions; D008297:Male; D009367:Neoplasm Staging; D011336:Probability; D011446:Prospective Studies; D011467:Prostate / Q000473:pathology*; D011471:Prostatic Neoplasms / Q000473:pathology* / Q000532:radiotherapy*; D011853:Radiobiology; D011879:Radiotherapy Dosage; D020266:Radiotherapy, Conformal