Tumour size can have an impact on the outcomes of epidemiological studies on second cancers after radiotherapy

Obtaining a correct dose–response relationship for radiation-induced cancer after radiotherapy presents a major challenge for epidemiological studies. The purpose of this paper is to gain a better understanding of the associated uncertainties. To accomplish this goal, some aspects of an epidemiological study on breast cancer following radiotherapy of Hodgkin’s disease were simulated with Monte Carlo methods. It is demonstrated that although the doses to the breast volume are calculated by one treatment plan, the locations and sizes of the induced secondary breast tumours can be simulated and, based on these simulated locations and sizes, the absorbed doses at the site of tumour incidence can also be simulated. For the simulations of point dose at tumour site, linear and non-linear mechanistic models which predict risk of cancer induction as a function of dose were applied randomly to the treatment plan. These simulations provided for each second tumour and each simulated tumour size the predicted dose. The predicted-dose–response-characteristic from the analysis of the simulated epidemiological study was analysed. If a linear dose–response relationship for cancer induction was applied to calculate the theoretical doses at the simulated tumour sites, all Monte-Carlo realizations of the epidemiological study yielded strong evidence for a resulting linear risk to predicted-dose–response. However, if a non-linear dose–response of cancer induction was applied to calculate the theoretical doses, the Monte Carlo simulated epidemiological study resulted in a non-linear risk to predicted-dose–response relationship only if the tumour size was small (\u3c 1.5 cm). If the diagnosed breast tumours exceeded an average diameter of 1.5 cm, an applied non-linear theoretical-dose–response relationship for second cancer falsely resulted in strong evidence for a linear predicted-dose relationship from the epidemiological study realizations. For a typical distribution of breast cancer sizes, the model selection probability for a resulting predicted-dose linear model was 61% although a non-linear theoretical-dose–response relationship for cancer induction had been applied. The results of this study, therefore, provide evidence that the shapes of epidemiologically obtained dose–response relationships for cancer induction can be biased by the finite size of the diagnosed second tumour, even though the epidemiological study was done correctly