Determination of cell dose-survival relationships from endpoint dilution assays

Methods for fitting radiation survival curves to data obtained from endpoint-dilution assays are described. It is shown that for functional forms such as the linear-quadratic model the problem can be recast as a generalized linear model (GLM) and the data fitted using standard software. For functional forms which are not capable of being linearized, such as the multitarget model, the direct maximum likelihood (DML) techniques of Thames et al. (1986) can be used. Both these techniques produce exact maximum likelihood parameter estimates. Compared with the weighted least-squares (WLS) approach traditionally employed, these approaches avoid the need to approximate the binomial distribution of the number of negative wells by a normal distribution, and avoid the biases introduced by the need for arbitrary treatment of data points with 0 or 100% negative wells. The results of fittings using the novel GLM and DML approaches are compared with those obtained using the WLS method on a large series of datasets. For most datasets the WLS method performs well, compared with the exact method, but in a small number of cases the WLS predicted parameter estimates can be in error by as much as their estimated standard errors. A method for the use of a concurrent control to correct for interexperimental variation is outlined. The methods have been implemented in a Fortran computer program using the NAG subroutine library.