To estimate the impact of early detection of cancer, knowledge of how quickly primary tumors grow and at what size they shed lethal metastases is critical. We developed a natural history model of cancer to estimate the probability of disease-specific cure as a function of tumor size, the tumor volume doubling time (TVDT), and disease-specific mortality reduction achievable by screening. The model was applied to non-small-cell lung carcinoma (NSCLC) and invasive ductal carcinoma (IDC), separately. Model parameter estimates were based on Surveillance Epidemiology and End Results (SEER) cancer registry datasets and validated on screening trials. Compared to IDC, NSCLC is estimated to have a lower probability of disease-specific cure at the same detected tumor size, shed lethal metastases at smaller sizes (median: 19 mm for IDC versus 8 mm for NSCLC), have a TVDT that is almost half as long (median: 252 days for IDC versus 134 days for NSCLC). Consequently, NSCLC is associated with a lower mortality reduction from screening at the same screen detection threshold and screening interval. In summary, using a similar natural history model of cancer, we quantify the disease-specific curability attributable to screening for breast cancer, and separately lung cancer, in terms of the TVDT and onset of lethal metastases.