Technical Notes: Standard Errors of Rates
Survival rates: In the tables presenting survival rates, the magnitude of the standard error is given as a clue to the reliability of a given rate: the greater the standard error, the less reliable the rate. In addition, if there were fewer than 25 diagnoses in the first interval of the life table constructed to calculate survival, or if all cases became lost to follow-up within an interval, a valid survival rate could not be calculated, as is noted in the table footnotes.
The standard error (SE) of a relative survival rate is obtained as follows (Ederer et al., 1961):
SE(CRt) = CRt * square root of [q1/(e1-d1) + q2/(e2-d2) +... + qt/(et-dt)]
where CRt is the t-year relative survival rate, and for i=1, ... ,t,
qi is the probability of dying in year i after diagnosis,
ei is the effective number of patients at risk in year i after diagnosis, and
di is the number of deaths in year i after diagnosis.
Incidence and Mortality Rates
The standard errors of age-adjusted incidence and mortality rates are often not specified. However, the reader can approximate the SE of a particular incidence or mortality rate by the SE of a crude incidence or mortality rate (Keyfitz, 1966), that is, the SE can be approximated by the rate divided by the square root of the number of cancer cases (or the number of deaths).
Appendix tables provide numbers of cancer diagnoses within SEER areas and numbers of deaths in the entire US, respectively, by race and sex for the most recent 5-year period. These can be used to obtain approximations of the standard errors for associated age-adjusted rates for the same time period using the above formula. To approximate the standard error of a rate for a single year, use the formula but replace the number of cancer cases or deaths with the number of cancer cases or deaths divided by 5.
