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A Monte Carlo approach to the accuracy of cell-survival curves

Division of Biophysics, Institute of Cancer Research, Clifton Avenue, Sutton, Surrey

This excerpt was created in the absence of an abstract.

The application of statistics to biological problems can present considerable difficulties to the biologist particularly when the problem does not conform exactly to a standard textbook method. These difficulties can, to some extent, be circumvented using random numbers (Monte Carlo method) to provide a direct approach that does not involve a detailed mathematical knowledge of statistics and which provides useful quantitative information about the errors arising under specific conditions.

The method involves constructing a computer program that will generate artificial survival curves for any type of desired survival equation assuming particular values for the equation parameters; for instance, a simple multitarget equation with chosen values of D₀ and N. The exact survival values are calculated for specified radiation doses and then "experimental error" is introduced by altering the values calculated, in a random manner, in such a way that they conform to a particular probability distribution with a specified standard deviation. By generating many of these curves and obtaining estimates of the value of D₀ and N for each curve, using whichever curve-fitting method that is required, one can obtain a frequency distribution of the estimated values of D₀ and N. By this means one can quite straightforwardly investigate the importance of a wide variety of factors which influence the accuracy of the estimates of radiobiological parameters.

Received for publication October 1, 1975. Revision received January 1, 1976.