The delta and epsilon errors in the assessment of cancer clinical trials

The error probabilities alpha and beta are widely used to compute sample sizes and to analyze results of clinical trials. These errors are, however, not the only probabilities to consider when assessing results of clinical studies. The rate of false positive (delta) and false negative (epsilon) results allows one to determine if an experimental finding is likely to reflect the true situation in the population of interest. The delta error is generally high in randomized phase III and in early phase II clinical trials in cancer patients, whereas the epsilon error is relatively low in these settings. This is essentially due to the small probability of detecting a more effective treatment or a new chemotherapeutic agent active in cancer. The delta error could be considerably reduced by increasing the sample sizes and by restricting the allowance made for the alpha error, which should be set at a 1% level as a minimum requirement.