Final answer:
The incidence density of prostate cancer in the study is calculated by dividing the total number of new cases (130) by the total person-time at risk, which accounts for how long each participant was followed before being diagnosed or censored.
Step-by-step explanation:
To calculate the incidence density of prostate cancer in the study group from Des Moines, Iowa, we need to consider the number of new cases during the study period and the amount of person-time the group was at risk. Incidence density takes into account the fact that not all participants are followed for the same length of time, especially in a study where participants can develop the condition at different times.
The total number of new cases of prostate cancer detected during the 4-year study is 20 + 25 + 40 + 45, which equals 130 cases. Now, rather than just using the full 4-year observation for all 5,000 men, we must calculate the amount of person-time at risk. This is done by adding the time each man remained in the study before getting diagnosed with prostate cancer or before being censored from the study (if they never developed prostate cancer).
For example, if none of the men were lost to follow-up or developed prostate cancer before the first year exam, they would contribute a combined total of 5,000 person-years in the first year. We would continue to add the person-years for each subsequent year, subtracting the men who develop prostate cancer in the previous years (since they are no longer 'at risk'). Once the total person-time is calculated, the incidence density is found by dividing the number of new cases (130) by the total person-time at risk.