Improved population-based probability of developing cancer when direct estimates of the cancer-free population are available

Age-conditional probabilities of developing a first cancer represent the transition from being cancer-free to developing a first cancer. Natural inputs into their calculation are rates of first cancer per person-years alive and cancer-free. However these rates are not readily available because they require information on the cancer-free population. Instead rates of first cancer per person-years alive, calculated using as denominator the mid-year populations, available from census data, can be easily calculated from cancer registry data. Methods have been developed to estimate age-conditional probabilities of developing cancer based on these easily available rates per person-years alive that do not directly account for the cancer-free population. In the last few years models (Merrill et al., Int J Epidemiol 29(2):197-207, 2000; Mariotto et al., SEER Cancer Statistics Review, 2002; Clegg et al., Biometrics 58(3):684-688, 2002; Gigli et al., Stat Methods Med Res 15(3):235-253, 2006, and software (ComPrev:Complete Prevalence Software, Version 1.0, 2005) have been developed that allow estimation of cancer prevalence (DevCan: Probability of Developing or Dying of Cancer Software, Version 6.0, 2005). Estimates of population-based cancer prevalence allows for the estimation of the cancer-free population and consequently of rates per person-years alive and cancer-free. In this paper we present a method that directly estimates the age-conditional probabilities of developing a first cancer using rates per person-years alive and cancer-free obtained from prevalence estimates. We explore conditions when the previous and the new estimators give similar or different values using real data from the Surveillance, Epidemiology and End Results (SEER) program.