## About Age-Adjusted Rates, 95 Percent
Confidence Intervals and

Unstable Rates

### What is age-adjustment?

Age-adjustment is a statistical process applied to rates of disease, death, injuries or other health outcomes that allows communities with different age structures to be compared.

### Why do we do age-adjustment?

Almost all diseases or health outcomes occur at different times
in different age groups. Most chronic disease, including most
cancers, occurs more often among older people. Other outcomes, such
as many types of injuries, occur more often among younger people.
The age distribution determines what the most common health problems
in a community will be. One way of examining the pattern of health
outcomes in communities of different sizes is to calculate an
incidence or mortality rate, which is the number of new cases or
deaths divided by the size of the population. In chronic diseases
and injuries, rates are usually expressed in terms of the number of
cases/deaths per 100,000 people per year.

A community made up of more families with young children will have a
higher rate of bicycle injuries than a community with few young
children. A community with a larger number of older individuals will
have higher rates of cancer than one with younger individuals. This
is true even if the individuals in the two communities have the same
risk of developing cancer or being injured. Epidemiologists refer to
this as confounding. Confounding happens when the measurement of the
association between the exposure and the disease is mixed up with
the effects of some extraneous factor (a confounding variable).
Age-adjustment is a statistical way to remove confounding caused by
age.

### How is age-adjustment done?

Age confounding occurs when the two populations being compared have different age distributions and the risk of the disease or outcome varies across the age groups. The process of age-adjustment by the direct method changes the amount that each age group contributed to the overall rate in each community, so that the overall rates are based on the same age structure. Rates that are based on the same age distribution can be compared to each other without the presence of confounding by age. Adjustment is accomplished by first multiplying the age-specific rates of disease by age-specific weights. The weights used in the age-adjustment of cancer data are the proportion of the standard U.S. population within each age group. The weighted rates are then summed across the age groups to give the age-adjusted rate.

### What is a confidence interval?

A confidence interval is a range around a measurement that
conveys how precise the measurement is. Ninety five percent
confidence intervals are provided for the age-adjusted rates in data
released by the North Dakota Statewide Cancer Registry. These are
analogous to the margins of error that are provided for news polls.

In the simplest terms, an age-adjusted breast cancer incidence rate
of 132.6 cases per 100,000 women +/- 1.0 case per 100,000 means that
there is a 95 percent chance that the rate was between 131.6 and
133.6 cases per 100,000 women. Conversely, there is a 6 percent
chance that the rate was lower than 131.6 or higher than 133.6.

The precise statistical definition of the 95 percent confidence
interval is that if the measurement were conducted 100 times, 95
times the true value would be within the calculated confidence
interval and five times the true value would be either higher or
lower than the range of the confidence interval.

### What are confidence intervals used for?

Confidence intervals often are used in research that requires
that a measurement be taken on a sample of the population, such as a
survey. In that case, the confidence intervals are a way to measure
sampling error and are related to the size of the sample taken or
the number of people surveyed. The cancer incidence and mortality
rates derived from the Cancer Registry and the Division of Vital
Records are not samples and are, therefore, not subject to sampling
error. The rates are, however, subject to what is termed random
error, which arises from random fluctuations in the number of cases
over time or between different communities. The 95 percent
confidence intervals are an easily understood way to convey the
stability of the rates. A stable rate is one that would be close to
the same value if the measurement were repeated; e.g., if the rate
did not vary greatly from one year to the next. An unstable rate is
one that would vary from one year to the next due to change alone.
Wider confidence intervals in relation to the rate itself indicate
instability. For example, if a rate is five cases per 100,000
people, but the 95 percent confidence interval is plus or minus 2.5
cases per 100,000 people, then the rate is relatively unstable. In
one year, you might have a rate of three cases per 100,000 and in
the next year have six cases per 100,000. This would be a 100
percent increase in the rate but would still be within the range of
the confidence intervals.

On the other hand, narrow confidence intervals in relation to the
rate tell you that the rate is relatively stable and you would not
expect to see large fluctuations from year to year. If differences
are observed between stable rates (those with narrow confidence
intervals), then it is likely that the differences represent true
variations, rather than random fluctuations in the number of cases.

### How are confidence intervals calculated?

Confidence intervals are calculated based on the standard error
of the rate. The standard error, in turn, is based on the rate and
the number of cases or deaths. For crude rates, the formula for the
95 percent confidence intervals is as follows:

95% CI = +/- 1/96x se

= +/- 1/96x rate ÷ √cases

### Why are rates based on fewer than 20 cases marked as being unstable?

Annual rates based on fewer than 20 cases or five-year average
rates based on fewer than four cases per year are considered
unstable because they have a large relative standard error (RSE).
The RSE is the standard error as a percentage of the measure itself.
For age-adjusted incidence and mortality rates, the RSE is equal to
1÷ √cases. A RSE of 50 percent indicates that the standard error is
half the size of the rate.

The RSE of an incidence or mortality rate is based on the number of
cases or deaths, unlike the standard error and confidence intervals,
which are based on both the number of cases and the size of the
population.

Example:

If there are 20 testicular cancer deaths among males every year, the
rate of testicular cancer deaths is 0.4 per 100,000 males, and the
standard error is 0.09. The relative standard error is 22 percent.

If there are about 20 prostate cancer deaths in every year, the rate
is 21.9 deaths per 100,000 males and the standard error is 4.8.
Again, the relative standard error is 22 percent.

So, even though the standard error for the testicular cancer rate is
much smaller than the standard error for the prostate cancer rate,
both have the same magnitude relative to the rate itself. This means
that when there are only a few cases or deaths, small changes in the
number of cases or deaths have a much bigger effect than small
changes in a large number of cases or deaths.