An extreme value paradigm for the effect of size of target volume on end results in radiation oncology

In clinical radiation oncology, it is commonly reported that complications of normal tissue occur more readily at larger field sizes for a given dose and recurrence of disease is observed more frequently from the larger tumors for a given dose. Cognate phenomena have long been observed in the study of the strength of materials. That is, the larger specimens will fracture under less applied stress, breakdown under less applied voltage, corrode in a shorter time, etc. The statistical theory of extreme values has provided both a rational explanation and a technique for exploitation of these "size effects" on the likelihood of specimen failure. This theory describes the relation which exists between the parameters (in particular, the location parameter) of the frequency distributions of the extreme values [smallest x(1) and largest x(n)] in a sample from a population of observations xi and the sample size n. It is shown in the present paper that the clinical failure phenomena are not inconsistent with the statistical theory of extreme values. The paper presents heuristic comparisons of the predictions of this theory with the received clinical observations of the effect of the size of the volume of irradiated tissues on the likelihood of occurrence of the misadventures of clinical radiation oncology: recurrence of disease and complication of normal tissue. The concordance of observations and predictions is acceptable. The quality and quantity of the currently available data have precluded the construction of any apodictic representations.