In order to prove a small increment in a risk of concern in an epidemiological study, a large sample of a population is generally required. Since the background risk of an end point of interest, such as cancer mortality, is affected by various factors, such as lifestyle (diet, smoking, etc.), adjustment for such factors is necessary. However, it is impossible to inclusively and completely adjust for such factors; therefore, uncertainty in the background risk remains for control and exposed populations, indicating that there is a minimum limit to the lower bound for the provable risk regardless of the sample size. In this case study, we developed and discussed the minimum provable risk considering the uncertainty in background risk for hypothetical populations by referring to recent Japanese statistical information to grasp the extent of the minimum provable risk. Risk of fatal diseases due to radiation exposure, which has recently been the focus of radiological protection, was also examined by comparative assessment of the minimum provable risk for cancer and circulatory diseases. It was estimated that the minimum provable risk for circulatory disease mortality was much greater than that for cancer mortality, approximately five to seven times larger; circulatory disease mortality is more difficult to prove as a radiation risk than cancer mortality under the conditions used in this case study.