Technical Notes: US Cancer Death Rates by State
Each cancer-site-specific section presents the death rate for the given cancer for each state and the District of Columbia, specifying the five highest and the five lowest death rates by state for the most recent 5-year period for all persons, males only, and females only. The rates are per 100,000 persons; they are age-adjusted to the 2000 US standard million population. (In some previous editions of the CSR, the 1970 US standard million population was used; death rates standardized to the 2000 US standard million population cannot be compared to death rates standardized to the 1970 US standard million population.)
The percent difference (PD) between a state rate and the rate for the total US is given by the formula:
PD = [(State Rate - Total US Rate)/Total US Rate] * 100
The standard error for each age-adjusted state death rate is calculated, based on the assumptions that:
- for each age-specific rate, the number of deaths is a Poisson random variable (Keyfitz, 1966) and
- the variance of the age-adjusted rate is a linear combination of the variances of the age-specific rates (Snedecor & Cochran, 1980; pp. 188-9).
The standard error of the difference (SEd) between a state rate and the total US rate is given by the formula
SEd = Square Root of [SES2 + SEU2 - 2 * Cov S,U]
where SES and SEU are the standard errors of a state rate and of the total US rate, respectively, and Cov S,U is the covariance between the two rates. The variance of each rate (i.e., the square of the standard error) and the covariance between the two rates are based on the Poisson assumption. The standard error does not represent the total error that may be present in the age-adjusted rate; it is merely the square root of the variance associated with the rates. In addition to this variance, there also exist potential biases and errors in the measurement of the rate that are difficult to assess accurately and probably impact differently on the error calculations for different states.
The difference between each age-adjusted state rate and the age-adjusted US rate is tested for statistical significance (see below) by calculating a Z (standard normal) statistic from the formula:
Z = (State rate - Total US rate) / SEd
Although the rates being compared are not independent because each state is part of the US, the statistical test may not be substantially affected if the state represents a small proportion of the total US. There is also an adjustment for multiple comparisons; see below under Statistical Significance.
