## Thursday, August 21, 2008

### Accurately Calculating Age with Only One Line of Code

This tip was written by William Kreuter, a senior computer specialist at the University of Washington in Seattle. He has used SAS software in public health research since 1981, and now specializes in manipulating large data sets for the School of Public Health and the School of Medicine. He can be reached at billyk@u.washington.edu.

A frequent need of SAS software users is to determine a person's age, based on a given date and the person's birthday. Although no simple arithmetic expression can flawlessly return the age according to common usage, efficient code to do so can be written using SAS software's date functions. This article, by SAS software user William Kreuter, presents a one-line solution for this purpose.
Put SAS Date Functions to Work for You

Many kinds of work require the calculation of elapsed anniversaries. The most obvious application is finding a person's age on a given date. Others might include finding the number of years since any event has occurred, such as an index date for medical treatment or the start of a magazine subscription.

However, because of the way the modern Gregorian calendar is constructed, there is no straightforward arithmetic method that produces a person's age, stated according to common usage -- common usage meaning that a person's age should always be an integer that increases exactly on a birthday. (Persons born on a February 29 are a special case that will be addressed later.) It is often important to compute an age that exactly conforms to this usage, for example so that the data will be consistent with the age written on a medical record.

Exact computation of ages and elapsed anniversaries must take into account all rules governing lengths of months and lengths of years. While the rich set of functions and programming constructions available in the SAS DATA step language allows many possible solutions, this article presents a concise solution that relies on letting the SAS date functions do all the work.

What Doesn't Work

Often, SAS software users attempt to compute age using an expression such as:

age = (somedate - birth) / 365.25;

where somedate and birth are SAS date variables (or constants or expressions). Clearly this usually doesn't return an integer and therefore it is not stating an age according to colloquial usage. That problem can be addressed by:

age = floor( (somedate - birth) / 365.25);

Now we're at least getting integers. In fact, for most dates in a given year this statement does produce the correct result. But in most years, age will increment on the wrong day. To account for the Gregorian calendar's idiosyncrasies, some users make attempts such as:

age = floor( (somedate - birth) / 365.2422);

However, extending the denominator to any number of significant digits doesn't help. Astronomers define several kinds of "years" for various technical uses, but the Gregorian calendar uses a different concept of "year" in which there are always either 365 or 366 days. No algorithm of this kind perfectly models such an interval.

The Julian calendar, which was introduced in 46 BC, gave every fourth year 366 days. Because this slowly causes a discrepancy between the calendar and the seasons, Pope Gregory XIII proclaimed the Gregorian calendar in 1582. The new rule provided that every fourth year will have 366 days, except for years divisible by 100 but not 400. Thus the year 2000 will be a leap year, but 2100 will not.

How SAS Date Functions Can Help

As we've seen, the Gregorian calendar, and hence an integer count incremented on an anniversary date, cannot be modeled with simple arithmetic. A completely accurate approach requires coding all of the rules for which years are leap years and all the rules for the number of days in each month.

This is where SAS software's date functions help. Date functions such as intck and intnx have the needed rules built in. Particularly, intck returns intervals that correctly account for the idiosyncrasies of the Gregorian calendar. However, a little tweaking is necessary to get exactly what we need.

Because intck alone won't produce the number of years between successive anniversaries given an arbitrary birth date or starting date, a tweak is needed to find how old the person is in months. Then, simple arithmetic will turn this number into what we need -- years that always increment on the anniversary date.

Again, consistent with common usage, we want the number of months always to be an integer and we want it to increment exactly on the same day each month (or on the first day following a month that is too short for the same day to occur). Generally, the expression

intck('month',birth,somedate);

returns the number of times the first day of a month is passed between birth and somedate. An enhancement is needed to alter this into the number of times the same day of the starting month is passed. This simply consists of subtracting one month if the day number of somedate is earlier than the day number of birth. Although one could program this concept using a separate if-then statement, it can be calculated more concisely as a logical expression returning a 0 or 1 value. The 0 or 1 is then subtracted from the result of intck, as in the following example.

intck('month',birth,somedate) - (day(somedate) < day(birth));

This now gives exactly the correct number of months for any pair of dates.

A one-line solution

Converting months to years, we get:

age = floor((intck('month',birth,somedate)- (day(somedate) < day(birth))) / 12);

This can be conveniently set up as a macro:

%macro age(date,birth);
floor ((intck('month',&birth,&date)- (day(&date) < day(&birth))) / 12)
%mend age;

This is an example of how the macro is used in a SAS DATA step:

age = %age(somedate,birth);

For example, the following lines:

age = %age('28aug1998'd,'24mar1955'd);
put age=;
will cause the following message to be placed on the log:

AGE=43

When This Won't Work

There are only two instances where this approach might fail to yield the expected result.

1.The birthday is February 29, and during non-leap years the person celebrates the birthday on February 28. The solution described here would treat the birthday during non-leap years as March 1. In a random population this should affect at most one out of 1,461 persons, or less than 0.07 percent of the population. If desired, extra lines of code can accommodate this situation.

2.A person's age is to be calculated at a time in history when, in some particular country, the Gregorian calendar was not in use. Beginning with the earliest date that is valid in SAS software -- January 1, 1582 -- SAS software uses the Gregorian calendar. That is the year that France, Italy, Luxembourg, Portugal, and Spain replaced the Julian calendar with the Gregorian. (The Gregorian calendar was first implemented so that the day after October 4, 1582 was October 15, 1582. Nevertheless, SAS software recognizes 31 days in the month of October, 1582.) While the rest of Roman Catholic Europe switched shortly after1582, the United Kingdom and its colonies did not move to the Gregorian calendar until 1752. Many other countries switched even later, including the Soviet Union in 1918 and Greece in 1923. Some historic dates therefore might be handled in a misleading manner -- a problem which, it should be noted, is true of any use of SAS dates in such instances. Nevertheless, given likely scenarios, age will be computed correctly in every country and era.

#### 2 comments:

Anonymous said...

Very good
and important to me

Anonymous said...

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