Atlas of Cancer Mortality -

Atlas of Cancer Mortality

Materials and Methods -- Calculation of age-adjusted cancer mortality rates

For each form of cancer, the age-adjusted (direct method, 1970 U.S. population standard--see Appendix Table 4) mortality rate R per 100,000 person-years was calculated by race, sex, and geographic area for each of the time periods 1970-94 and 1950-69, as follows: ^3,11,12

R= 100,000* SUM (w_ir_i) = 100,000* SUM (w_id_i/n_i) where

i= 18 age groups 0-4, 5-9,..., 85+
w_i= the proportion of the standard population in age group i
r_i= the age-specific rate d_i/n_i
d_i= the number of deaths in age group i
n_i= the person-years in age-group i

The binomial approximation to the variance of the age-adjusted rate was calculated as: var (R)= 100,000²* SUM [w_i²r_i(1-r_i)/n_i]. The 95 percent confidence limits of R were calculated from the square root of the variance as: Rą1.96[var(R)]^˝

A negative lower confidence limit was replaced by zero. For an area with zero deaths, the rate R was zero and the var (R) was estimated using the national rate. An area-specific age-adjusted rate was deemed significantly different statistically from the U.S. age-adjusted rate if their confidence limits did not overlap. Detailed area-specific data are not presented in this Atlas but are available from the NCI and from the NCI Atlas Static Web site.

Expected numbers of deaths from cancer for each geographic area by race and sex were the sums over age groups of the corresponding national age-specific rates times the age-specific person-years for each area by race and sex.

Male/female and black/white rate ratios (R₁/R₂) were calculated using the national age-adjusted rates rounded to two digits after the decimal point. The 95 percent confidence limits on the rate ratios are not presented but may be calculated as: ¹³

exp[ln(R₁/R₂)ą1.96 (1/D₁+1/D₂)^˝] where

exp[x]=ex,
ln[x]=the natural logarithm of x, and
D₁,D₂=the deaths associated with R₁,R₂ respectively

Maximum likelihood estimates of the relative risk standard deviations (RRSDs) and their standard errors (SEs) were calculated under the assumption of a mixed effects model. The RRSDs provide a measure of the standard deviation of the underlying area-specific relative risks and serve as quantitative indices to compare geographic variation across maps.¹⁴

References

3. Pickle LW, Mason TJ, Howard N, Hoover R, Fraumeni JF Jr. Atlas of U.S. cancer mortality among whites: 1950-1980. Washington, DC: U.S. Gov. Printing Office; 1987. DHHS Publ. No. (NIH) 87-2900.

11. Chiang CL. Standard error of the age-adjusted death rate. Vital Stat Selected Rep 1961;47:275-85.

12. Boyle P, Parkin DM. Statistical methods for registries. In: Jensen OM, Parkin DM, MacLennan R, et al., editors. Cancer registration: Principles and methods. Lyon, France: International Agency for Research on Cancer; 1991. p. 126-58. IARC Scientific Publ. No. 95.

13. Rothman KJ. Modern epidemiology. Boston: Little, Brown and Company; 1986.

14. Pennello GA, Devesa SS, Gail MH. Using a mixed model to estimate geographic variation in cancer rates. Biometrics 1999; 55:774-81.

Suggested Citation

Devesa SS, Grauman DG, Blot WJ, Pennello G, Hoover RN, Fraumeni JF Jr. Atlas of cancer mortality in the United States, 1950-94. Washington, DC: US Govt Print Off; 1999 [NIH Publ No. (NIH) 99-4564].