Statistical properties of shared-border ratios as a function of number of states

The chart above displays the average shared-border ratio as a function of number of states. More specifically, the shared-border ratio is averaged over all cancers, and the result is calculated for a list of the 10 states with highest cancer rates, 11 states with highest cancer rates, and so on, up to 20 states with highest cancer rates.

For example, for a list of the 10 states with highest cancer incidence rates of white men, the shared-border ratios are as follows (the methodologies used for calculating the shared-border ratios are described in the main article):

The average shared-border ratio of the list above is 87%, and the standard deviation (depicted in the section/chart below) is 28%.

Looking at all the combinations of gender, race/ethnicity, and incidence and mortality charts, the following conclusions are apparent (with few exceptions):

1. The average shared-border ratio is, generally, a monotonically increasing function of the number of states.
2. For every combination of gender and race/ethnicity (e.g. black men), the average shared-border ratios of mortality rates are generally higher than those of incidence rates.
3. Comparing the average shared-border ratios of white, black and Hispanic (men or women), the values for Hispanic origin are generally lower than those of white or black race/ethnicity.

The chart above displays the standard deviation of the shared-border ratios (among all cancers) as a function of number of states.

Since the shared-border ratio is expressed as a percentage, so is the standard deviation.

For a numerical example of a standard deviation, please see the section above.

The largest standard deviation in the entire dataset is 37% (black women mortality, using a list of 10 states with the highest cancer mortality rates).

Looking at all the combinations of gender, race/ethnicity, and incidence and mortality charts, there is no apparent correlation between the standard deviations and the number of states analyzed.

The chart above displays the maximum variations in the shared-border ratio of a single cancer (i.e. maximum among all cancers) when increasing the number of states with highest cancer rates by one (e.g. from a list of the 10 states with highest cancer rates to a list of 11 states with the highest cancer rates).

The largest variation in the entire dataset is 79% and occurs in white women mortality from melanoma. When moving from a list of 11 states with the highest melanoma mortality rates of white women to a list of 12 states, the shared-border ratio changes from 45% to 124% (i.e. a change of 79%).

The second largest variation in the entire dataset is 78% and occurs again in white women mortality, this time from myeloma. When moving from a list of 18 states with the highest myeloma mortality rates to a list of 19 states, the shared-border ratio changes from 94% to 172% (i.e. a change of 78%).

As stated in the main article, and as can be seen in the chart above for various combinations of gender, race/ethnicity, and incidence and mortality, the shared-border ratio (of a single cancer, as opposed to an average over all the cancers) as a function of number of states is inherently unstable since the addition (or removal) of a single state from the list can cause the value of the shared-border ratio to change considerably. However, I believe that searching for geographic clusters of states with high cancer incidence or mortality rates through shared borders, as has been done in this study, is viable and meaningful as exemplified by the results of this study.