Advantages of Binomial Likelihood Maximization for Analyzing and Modeling Cell Survival Curves.

Mathematical analysis of cell survival allows parameter estimation for radiobiological models and selection of an appropriate model. To our knowledge, no rigorous comparisons on the accuracy of various methods used for such analysis have been performed. In this study we compared three methods: 1. maximization of binomial log-likelihood (BLL); 2. minimization of sum of squares (SS); and 3. method 2 using log-transformed data (SSlog). Analysis of Monte Carlo simulated data (A) generated from the linear-quadratic (LQ) model showed that model parameter estimates from the BLL method were more accurate and less affected by "noise" than those from other methods. Analysis of actual breast cancer cell data showed substantial differences among LQ parameters estimated by the three methods (B). To select among radiobiological models, we used: 1. Sample size-corrected Akaike information criterion (AICc), calculated from BLL method-generated log-likelihood values; and 2. Adjusted coefficient of determination (R(2)), calculated from SS/SSlog method-generated SS values. Analysis of data simulated from the repair-misrepair (RMR) formalism (C) showed that the first approach outperformed the second approach at identifying the true data-generating model. Examples of how the first approach discriminates between several models were explored using actual mouse (H2AX-proficient and -deficient) and human [DNA-dependent protein kinase (DNA-PK)-proficient and -deficient] cell data (D). Based on this work, we concluded that BLL maximization combined with AICc-based model selection constitutes an effective method for analyzing cell survival data.