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Technical Notes:

#### STEP 1: FINDING THE CORRECT NUMBER

#### STEP 2: MAKING THE NUMBER MEANINGFUL WITH RATES AND RATIOS

#### STEP 3: COMPARING TWO OR MORE NUMBERS

##### Chance variation

##### Small numbers

##### Changes in Measurement

##### Taking Age, Sex and Race into Account

#### STEP 4: ANALYZING THE DATA

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Last updated December 31, 2010

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- Technical Notes:

How to Use Vital Statistics*

Data users are diverse: public health officials evaluate a program using death data, demographers project school enrollments with birth data, and business people decide to open a formal-wear shop based on marriage data. Many of these users have a thorough knowledge of statistics, but others find the entire subject-matter confusing and intimidating. For either group, a misunderstanding of what vital statistics can mean could lead to wrong conclusions. Therefore, this section is included to provide an overview of how to use vital statistics. It is addressed to the person looking at vital events for the first time, but the experienced user may also find a review helpful.

The first step is to determine how many of a particular vital event took place during the year. This involves asking two questions.

1. Which event or events are appropriate?

BIRTHS

DEATHS

INFANT DEATHS

NEONATAL DEATHS

POSTNEONATAL DEATHS

FETAL DEATHS

LOW BIRTH WEIGHT INFANTS

PREGNANCIES

INDUCED ABORTIONS

MARRIAGES

DIVORCES

Deciding which events to use is important since sometimes the choice of one event over another can lead to vastly different conclusions.

This may be more complicated than it sounds because examining more than one type of event may be required. For example, a researcher who is concerned with teenage pregnancies will have to consider __abortions__ and __fetal death__s, not simply the number of __births__.

2. Who should be counted?

If you are a hospital planner who is deciding to expand or contract delivery services, you want to count the number of births which __occurred__ in your area, regardless of where the parents live. If you are projecting school enrollment, you want to count only how many children will potentially be __residing__ in your area.

OCCURRENCE DATA: The event (the death, birth, marriage, etc.) actually took place in the county or city. The person who is the focus of in the event may have lived in Davenport, Iowa.

RESIDENCE DATA: The person involved in the event lived in the geographic region mentioned, but the event itself may have taken place anywhere in the United States or Canada. In other words, a resident of the city of El Paso who died in an accident while on vacation in Hawaii has been added to the city of El Paso resident death figure.

When in doubt about which type of data to use, resident figures are usually the best choice. Most birth and death data are published by residence, which means that comparisons with other states, or to the United States as a whole, will be easier. Exceptions to this rule are listed in the individual sections.

Once the correct event has been determined, and the choice between occurrence and residence data has been made, the statistician can find the correct figures in the tables(s) in this book. If the needed table is not listed, contact the Center for Health Statistics (512-458-7509) for more information.

In many instances simply knowing the number of events is not sufficient. A. Bradford Hill expressed this important statistical concept: "It is well recognized that white sheep eat more than black sheep because there are more of them." For example, we know more people died in San Antonio than in Brownsville, because San Antonio has a much larger population. But what is the __likelihood__ of dying in each municipality?

In order to answer this question, statisticians calculate rates. This means that the number of events which occurred is compared to the population for which that event could have occurred, and the figure is then standardized to some number (such as 1,000 or 100,000) for convenience.

Here is an example:

CRUDE DEATH RATE = DEATHS X 1,000 (The number picked by vital statisticians to eliminate decimal points)/POPULATION (The number of people who could have died)

The more specifically a statistician can define the "population at risk" (the denominator or bottom part of the formula), the more meaningful the rate. For example, the crude birth rate, which compares the number of births to the population, is not nearly as informative as the general fertility rate, which uses only the number of women of childbearing-age (15-44) for comparative purposes. The general fertility rate is not distorted by changes in the number of men or pre-pubescent or post-menopausal women in the population.

Unfortunately, we do not always have the correct denominator for the equation. In these situations a substitute is used. For example, how many people are at risk of getting divorced? The number of married people is only available for census years. As a substitute, the crude divorce rate is calculated using the total population regardless of marital status. In other situations, the event is simply compared to another related number. For instance, the abortion ratio compares the number of abortions to the number of births. This is easier and more accurate than trying to determine the true denominator, which is the total number of pregnant women.

When calculating rates and ratios, great care must be taken to make certain that the appropriate time periods, geographical boundaries and populations are used.

Numbers are more meaningful when they are converted into rates and ratios. But problems can arise when rates or ratios are compared for different geographical areas, different time periods, or different categories such as men versus women.

Statisticians expect a certain amount of chance variation and have methods to take this into account. The confidence interval uses the number of cases and their distributions to determine what the rate "really" is. If two rates have overlapping confidence intervals, then the difference between them may be due to this chance variation. In other words, the difference is not __statistically significant __. When comparing rates and ratios, differences should be tested for statistical significance.

Chance variation is a common problem when the numbers being used to calculate rates are extremely small. Large swings often occur in the rates which do not reflect real changes. Consider Maverick County's infant mortality rates for a five year period, shown below:

Year Births Infant Deaths Infant Mortality Rates 1988 868 5 5.8 1989 843 4 4.7 1990 900 9 10.0 1991 1,021 4 3.9 1992 1,165 2 1.7 __________________________________________________ 1988-92 4,797 24 5.0

The rates vary widely from year-to-year. Note that the 1991 infant death rate is double the 1992 rate, even though there were only two more infant deaths occurring in 1991 than there were in 1992.

Many rates based on small numbers are published in this book because readers demand them. However, anyone preparing to make important decisions based on these rates should be wary. Consider this rule of thumb: a rate based on 20 cases has a 95% confidence interval about as wide as itself (the interval for a rate of 50 is between 25 and 75). Even large differences between two rates based on 20 cases or less are probably not statistically significant.

If 20 are too few, how many cases are sufficient to say that a true difference exists? Unfortunately, we have no easy rules for this. To be safe, the vital statistician should always try to combine several years of data or consolidate geographical areas. Confidence intervals should be calculated, and differences should be tested for statistical significance.

Another problem is that the numbers being compared have not always been based on the same type of measurement. Definitions, population estimates, certificates, and coding procedures change from time to time as the need arises. This can create "artificial" differences which can disguise "real" differences. The cause-of-death item provides an excellent example of changes in comparability.

From 1980 to 1988, approximately 1,800 to 2,100 Texans died each year due to Diabetes. The range of annual crude death rates for these years is 11.7 to 13.1 per 100,000 residents. In 1990, 3,458 Texans died from this cause for a crude death rate of 20.4 per 100,000 residents.

It appears that the incidence of Diabetes increased. But actually, a revision to the death certificate resulted in more deaths being coded as due to that cause-of-death. In 1989, the cause-of-death section was expanded from three to four lines, which provides more room for describing multiple conditions leading to death.

Before comparing two places or two time periods always compare the population characteristics, such as age, sex and race, first. If discrepancies are noted in any relevant variables, than the rates should be adjusted or standardized in order to make the comparisons free of differences in the structure of the populations. An example of age-adjustment by the direct method of standardization is given in the Technical Appendix.

The first three steps have been fairly mechanical:

(1) Choose the correct events and the correct group to determine the number of events which took place for the geographical areas and time periods.

(2) Calculate the rates.

(3) Compare these rates to determine if the differences are statistically significant.

NOW the vital statistician must begin to ask the difficult questions. If we find that two rates are statistically significantly different, how can we find out why they're different? If the differences which we expected did not prove to be significant, is there another item which perhaps is making an actual difference? Frequently the statistician has to refine the research question and begin all over again.

**Technical Notes reprinted courtesy of the Oregon Center for Health Statistics; illustrative examples were changed to reflect Texas data.*

2006 Annual Report List of Tables and References

Annual Reports for Other Years

Center for Health Statistics