**Appendix A
Statistical Notes**

Death Rates

The cancer death rate is the number of deaths from cancer of a specific site or type occurring in a specified population during a year, expressed as the number of deaths per 100,000 population. This rate can be computed for each type of cancer, as well as for all cancers combined. In this report, Indiana cancer death rates for the years 1990-1994 are presented. These rates are age-standardized to the U.S. 1970 standard million population to allow for comparisons between groups (geographic or demographic) that have different age distributions.

Age-adjusted Rates

When comparing rates over time or across different populations, crude rates (the number of deaths due to cancer per 100,000 persons) can be misleading because differences in the age distributions of the various populations are not considered. Since cancer is age-dependent, the comparison of crude death rates from cancer can be especially deceptive.

Age-adjusted rates take into account the diverse age distributions of the populations. Valid comparisons between age-adjusted rates can be made, provided the same standard population and age groups have been used in the calculation of the rates. The direct method of adjustment was used to produce the age-adjusted rates for this report. In this method, the population is first divided into reasonably homogeneous age ranges and the age-specific rate is calculated for each age range; then each age-specific rate is weighted by multiplying it by the proportion of the standard population in the respective age group. The age-adjusted rate is the sum of the weighted age-specific rates.

Comparison of Rates

Rates based on small numbers of events over a given period of time or for sparsely
populated geographic areas should be viewed with caution. These rates show considerable
random variation, thus limiting their usefulness in comparisons and estimation of rare
occurrences. Multiple-year summary rates (average-annual rates based on five years of
data) were calculated to provide more stable rates for counties and** **to** **allow
for more valid comparisons between small geographic areas. Regardless, if the number of
deaths from cancer of any type is less than 20, the calculated rate is considered
unstable. A "u" will denote unstable rates in the tables.

An "s" denotes a county rate that differed significantly from the rate for Indiana as a whole. A comparison between rates was considered statistically significant if the difference between the rates would have occurred by chance less than five times out of 100 (i.e., p < 0.05). Statistical tests were conducted using the Z-score method, described in all basic statistics texts.

While the form of the Z test is similar, the calculation of the standard error for an
age-adjusted rate is not straightforward. The following formula can be used to approximate
the standard error of an age-adjusted rate^{1}:

SE_{(rate)} = rate / [events]^{1/2}

where, in this case, "events" is the number of deaths from cancer used to calculate the rate. Subsequently, the Z test for the difference between the state and county rates takes the form:

Z = (State rate - County rate) / SE_{(diff)}

where the SE_{(diff)} is defined as:

SE_{(diff)} = [(SE_{(s)})^{2} + (SE_{(c)})^{2}
]^{1/2}

where SE_{(s)} is the standard error of the state rate and SE_{(c)} is
the standard error of the county rate.

When testing the differences between the Indiana rate and the rate for each of the 92
counties for a given cancer the large number of comparisons increases the chance that a
rate would be statistically significant due to chance alone. To account for multiple
comparisons, based on Bonferroni's theory of inequalities,^{2} the significance
level for each individual comparison was set equal to 0.05/92, where 92 is the number of
comparisons made for each type of cancer. Thus, any individual comparison with an
associated "p" value less than 0.0002 (Z=3.48) was considered to be
statistically significant.

References