Results of a study of quantitative risk estimates of lung cancer incidence subsequent to exposure to radon daughters in 3366 caucasian uranium miners were reported. A previously developed power function risk model provided the best fit to data as measured by the log likelihood. Studies on exposure rates suggested that among groups of underground miners receiving equivalent cumulative exposures, those exposed to lower levels for longer periods of time were at increased risk compared with those exposed to higher doses for shorter periods of time. It was determined that a miner who received a total exposure below 834 units of cumulative exposure at a rate 0.1 times as great as another miner of the same age, smoking status and cumulative exposure, would have a 58 percent greater risk of lung cancer. For miners in the 834 to 10000 units of cumulative exposure range, the increased risk would only be 10 percent at the lower exposure rate. Age was shown to influence cancer risk. For example, a miner who was initially exposed 10 years later in life than another miner with the same radon daughter exposure and smoking history, was shown to have a 32 percent higher risk of lung cancer. Relative risk of lung cancer fell sharply in the years following cessation of exposure.