# Methods of Representation

## Table of Contents

## Age-Standardized Incidence and Mortality Rates

Data obtained from different districts and calendar years with varying population sizes and age structures can be made comparable by adjusting the rates for age to obtain "age-standardized mortality rates" (ASM). Mathematically, the ASM represents a weighted mean of age-specific mortality rates calculated for individual 5-year age ranges (AMR_{i}) and referred to a standard population (w_{i}). The ASM indicates in cases per 100 000 inhabitants the mortality that would exist in a region if the region had the age structure of the standard population.

To ensure optimum comparability of these data with the previous atlas and with other data published internationally, we again chose "Segi's world population" as the standard population (e.g., see Becker 1997). Analogously, the standardized incidence rates cited in the Atlas have been calculated. The "cumulative mortality rate" given in the previous edition, though quite useful as a direct indicator of risk, was omitted from the present edition due to space limitations.

## Standard Deviation

Standard deviations are shown in the mortality tables to provide a measure of the "accuracy" of the age-standardized mortality rates. The standard deviation (SE) is derived from the variance, which is calculated using the formula:

where n_{i} is the size of the resident population at mid-year, in each case for the i-th age range.

The SE is obtained by calculating the square root of the variance:

If the case numbers are sufficiently large (N ≥ 30), we can calculate a 95% confidence interval around the ASM using the formula:

(ASM - 1.96 × SE, ASM + 1.96 × SE).

For smaller case numbers, this method is not reliable. That is why the confidence interval is not stated directly in the tables (Estève 1994). Confidence intervals can be used to determine whether a statistically significant difference exists between two districts or between a district and a larger political division (e.g., a German state or Germany as a whole). If the two confidence intervals do not overlap, the difference is considered statistically significant. The problems involved in applying these concepts to the extensive volume of data in a cancer atlas are discussed in the concluding chapter.

## Cancer Maps

Two scaling methods - absolute and relative - are used in this book for mapping the regional distributions of cancer mortality.

#### Absolute Scaling

Age-standardized mortality rates in the state districts are color-coded according to the mathematical formula:

where ASM is the standardized mortality rate; I is twice the square root of the ASM, rounded to the nearest whole number; and c is the color value on a 20-step scale that is indicated by this calculation. Because the maps for all cancer sites and for both sexes use the same color scale, all the maps can be directly compared with one another. See Becker (1994) for the rationale and further explanation of this method.

The color scale is pictured at the bottom of each map page. Color bars above the scale indicate the range of mortality on the map and also the number of districts that display the particular color value. For each type of cancer, this scaling method is used to create separate mortality maps for each of the 5-year periods 1981-195 and 1986-1990.

This scheme cannot be used to represent total cancer mortality by adding together all the individual cancer rates. In this special case the color scale used for the individual cancer sites was applied to a different range of mortality rates; these data (below the color scale) should be checked before interpreting the map.

#### Relative Scaling

This method uses an ascending seven-step color scale to give a relative impression of the age-standardized district mortality rates for the entire 10-year period 1981-1990 for each type of cancer and both sexes using the following color codes: 5% (dark green), 10% (green), 15% (light green), 30% (yellow), 15% (orange), 10% (light red), and 5% (red) for the districts with the highest rates. The same seven colors are used for all the relative-scale maps, but as they represent a relative scale, they do not allow us to compare mortality rates on different maps. In plotting the maps, the respective function in the SAS graphics system was applied (SAS 1990).