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Methodology

The basic steps in computing an individual's life table are fairly simple:

  1. If nothing is known about the individual except the age and sex, a standard government life table applies (National Center for Health Statistics, 1997). The life table will specify the mortality rate m(x) for each age x.
  2. Certain risk factors have a known effect on mortality. For example, heavy alcohol consumption increases mortality by amounts that have been well documented in the medical literature. The increases are excess death rates, or EDRs. Thus if we know that the individual is a heavy drinker we can increase the age-specific rates m(x) appropriately.
  3. This new schedule of mortality rates can be used to construct a new life table, from which the life expectancy and other quantities of interest can at once be obtained.
  4. In some cases the medical literature specifies how the excess risk changes over the lifetime. For example, patients with acute renal failure or cancer have a very large EDR during the first few post-onset years, but these gradually diminish if the patient survives long enough. The point is that a whole schedule of age- specific EDRs is needed, not just the EDR at the current age.
  5. It should be noted that the EDRs can be negative. This will occur for persons with healthy life styles -- for example, those who are slightly underweight or who exercise regularly.
  6. In most cases there will be several factors to consider simultaneously. For example, a diabetic patient may also be a smoker. The literature specifies EDRs for each factor, but how should they be combined?

In general there is no fully satisfactory answer. The answer ultimately depends on:

  1. Whether the two factors tend to co-occur. If they do then adding EDRs may "double count" the risk. For example, smoking is the main cause of chronic obstructive pulmonary disease, so if a patient has both it would probably be inappropriate to count both conditions. Here the sum of the EDRs would overestimate the risk.
  2. Some risk factors "co-operate", so having both is much more dangerous than either separately. In that case case, the sum of the EDRs would underestimate the risk.

It is not feasible to cover all the possible combinations of risk factors in a computer program, and the user is encouraged to input various scenarios so as to obtain a plausible range of life expectancies. In the software we have followed the widespread actuarial practice of simply adding the EDRs, which is probably a suitable default option.

  1. We have consulted hundreds of medical and actuarial articles to determine the EDRs for the various risk factors. This is an ongoing process, however, as new data and medical research findings are constantly being published. The sources currently used for the software's schedules of EDRs are given in the references.
  2. Once the schedule of EDRs is determined, and the corresponding life table computed, all other quantities of interest are immediately available. For example, the expected present value of payments and services specified by a life care plan can be computed from the life table.

Smoking, Race and Education

This trio of factors deserves separate consideration here. They need to be considered simultaneously because they are strongly interrelated. For example, college educated persons are much less likely to smoke than persons with high school education or less, and the college educated include much lower proportions of Hispanics and Blacks (Richards & Abele 1999, pp. 38 and 43). Thus if, for instance, the increased mortality associated with smoking and with low education were simply added there would be some double counting.

Each of the three factors is related to mortality. Smoking results in a substantial increase in death rates, as has been documented by a large research literature (see summaries in Singer 1976, pp.38-40, and Lew & Gajewski 1990, pp.3-7 to 3-11). Mortality rates also vary by race, the difference being sufficient that the National Center for Health Statistics (NCHS) publishes race-specific life tables (NCHS 1997, Anderson 1999). Finally, it has been shown that mortality rates differ according to education level, the most educated groups having the lowest mortality rates (Richards & Barry 1999). This is not surprising because education often serves as a proxy for socioeconomic status.

There do not seem to be published tables on the "three way interaction" -- i.e., broken down by smoking, education and race simultaneously (for each age and sex). Some assumption must therefore be made. The most plausible appears to be that race and smoking have independent effects once education is controlled for. Under this assumption the appropriate procedure is to make adjustments for race and education simultaneously, then for smoking and education simultaneously, and to combine the two adjustments. This procedure has been followed here.

1. Smoking and Education

In the current version of the software, three smoking categories are recognized: current smokers, former smokers, and never smokers. This grouping is often used by insurance company underwriters. Educational categories are: less than high school, high school diploma, some college, college graduate, and graduate school.

a. Both smoking and educational level known.

The relative risk for current, former and never smokers were obtained from page 39 of Richards & Abele (1999). These risks were relative to mortality rates for all persons of a given educational level, as provided on pages 145-146. The relative risks were then converted to excess death rates (EDRs).

b. Smoking status known, educational level unknown.

Age- and sex-specific relative risks (RRs) for current and former smokers were obtained from Richards & Abele (1999, p. 37). These RRs are relative to mortality rates for the never smokers.

The relative risks determine the mortality rates for each smoking category, except for an unknown multiplying factor. The latter is determined from the fact that the average mortality over the 3 smoking categories, weighted by the proportion of persons in each category, is the known overall mortality rate. Age-, sex- and smoking-specific mortality rates were thus obtained. The EDRs were computed as the difference between these rates and those of the United States general population of the same age and sex.

c. Smoking status unknown.

The EDRs for the effect of smoking are taken to be zero. The effect of education, if known, is addressed below in Race & Education. 

2. Race and Education

Four race groups were used: White, Black, Hispanic and Other.

a. Both race and educational level known.

Age-, sex-, race- and education-specific mortality probabilities were obtained from pages 147-151 of Richards & Abele (1999). These were converted to mortality rates as using methods described in the life table section. Data was not provided for ages over 84, so an adjustment was necessary: excess death rates for a given race or educational level (with the other factor held constant) were obtained, and jointly added to the sex-specific general population mortality rates for ages 85 and older. EDRs were computed as the difference between these rates and those of the United States general population of the same age and sex.

b. Race known, educational level unknown.

Age- and sex-specific mortality rates by race were obtained as follows:

  1. Values for whites and blacks were obtained from the National Center For Health Statistics (Anderson 1999).
  2. Values for Hispanics were converted from page 151 of Richards & Abele (1999) as follows. First, mortality probabilities were converted to mortality rates. Second, because data over age 84 was not available, the procedure described immediately above was followed. Lastly, the education-specific rates were averaged over the known educational attainment levels of Hispanics (U.S. Department of Commerce, 1993).

EDRs were then computed as the difference between these rates and those of the United States general population of the same age and sex.

c. Race unknown, education known.

Mortality probabilities on pages 145 and 146 of Richards & Abele (1999) were converted to mortality rates using methods described in the life table section. Data was not provided for ages over 84, so the procedure described above was followed. EDRs were computed as the difference between these rates and those of the United States general population of the same age and sex.

d. Race unknown, education unknown.

These mortality rates are given by the National Center For Health Statistics (Anderson 1999). As there is no race or education effect to consider, the EDRs are equal to zero.


References

Anderson RN (1999). United States life tables, 1997. National vital statistics reports; vol 47 no 28. Hyattsville, Maryland: National Center for Health Statistics.

Lew EA, Gajewski (Eds.) (1990). Medical risks: Trends in mortality by use and time elapsed. New York: Praeger.

National Center For Health Statistics (1997). U.S. decennial life tables for 1989-1991, volume 1, number 1. Hyattsville, Maryland: Author.

Richard H, Barry R (1998). U.S. life tables for 1990 by sex, race, and education. Journal of Forensic Economics, 11:9-26.

Richards H, Abele JR (1999). Life and worklife expectancies. Tucson: Lawyers & Judges.

Singer RB (Ed.) (1976). Medical risks: Patterns of mortality and survival. Lexington, Massachusetts: Lexington Books.

Schoen R (1988). Modeling multigroup populations, chapter 1. New York: Plenum Press.

U.S. Department of Commerce (1993). 1990 Census of Population. Persons of Hispanic Origin in the United States, 1990 CP-3-3.