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Life
Expectancy of Injured, Ill Elderly Most Often Badly Under-Estimated
Can Create Serious
Financial Problems
July 2, 2003 - A new
study says life expectancy is almost always under-estimated in elderly
persons who have been injured or suffer from life-threatening disease,
which can result in inadequate financial planning for their remaining
years.
“The example of
paraplegia (paralysis below the waist) is used for the purpose of the
article, but the under-estimation is seen with almost any disease that
shortens the life of an elderly person,” says Dr. Terence Anderson,
Professor Emeritus, Faculty of Medicine at the University of British
Columbia.
“The problem is the
result of a built-in bias in the traditional method of calculating
life expectancy,” he adds. “This is important information for seniors,
as well as for those who represent them.”
The study by Anderson and Dr. Stephen Marion was published in the May
2003 issue of the British Columbia Medical Journal.
Note: This problem was
first described in the book Life
Expectancy In Court, published by Teviot Press in 2002. A
copy of the book can be obtained from: (a) your local library or (b)
the UBC book shop at
http://www.bookstore.ubc.ca or (c) direct from the publisher at
http://www.teviotpress.com (quote ISBN 0-9689633-0-1)
The
Detailed Report Follows
(The complete report,
with tables, can by found by
clicking here.)
Underestimation of
life expectancy in elderly patients: The example of paraplegia
Conventional estimates
of life expectancy in elderly patients with life-shortening conditions
are almost always lower than they should be. An alternative approach
is suggested, based on the trend in proportional life expectancy from
younger ages.
Terence W. Anderson
BM, BCh, FRCPC, PhD and Stephen A. Marion, MD, FRCPC
Dr Anderson is
professor emeritus in the Department of Health Care and Epidemiology,
Faculty of Medicine, University of British Columbia. Dr Marion is a
professor in the Department of Health Care and Epidemiology, Faculty
of Medicine, UBC.
Abstract
Detailed tables of
life expectancy in patients with spinal cord injury have appeared in
recent reports from the US (1995) and England (1998). For patients
with paraplegia, both studies give estimates around 80% of normal at
age 20, but by age 80 the estimates are down to 50% of normal in one
study and 20% in the other. We show that all of the estimates at age
80 are too low, due to a downward bias in the conventional methods of
calculation. An alternative approach is suggested, based on the trend
in proportional life expectancy from younger ages. Support for this
approach is provided by a recent recalculation of data from the US
study.
Case
A
pedestrian-automobile accident has left Dorothy with paraplegia at
T10. Her future costs of care will be covered by the driver’s
insurance, but there is disagreement over her life expectancy. Dorothy
is currently 80 years old, at which age the average life expectancy
for a female is around 9 years (Canada 9.3; England 8.4; US 9.1). Two
experienced doctors have given their opinion on Dorothy’s life
expectancy: one has suggested 4.2 years; the other 1.8 years. Each
estimate was based on a different follow-up study, but both studies
were of high quality so there was little reason to choose one over the
other. The case has now been settled out of court, and a structured
settlement (life annuity) has been purchased to ensure that Dorothy
will receive regular payments for care until she dies, whatever her
actual length of survival.
As part of the
settlement, Dorothy’s life expectancy was assumed to be the average of
the two expert opinions, that is, 3 years, but we present evidence
that 6 years would be a more accurate figure. Because of the
underestimation of her life expectancy, the annual funding for
Dorothy’s care will now be approximately half what it should have
been.
Introduction
Doctors are often
asked to estimate life expectancy in patients who have survived a
serious accident or developed a life-threatening disease. Evidence
from epidemiological studies can be very helpful, but actual estimates
of life expectancy are rarely provided in published articles. Spinal
cord injury has been a notable exception, with some life expectancy
figures appearing in reports from a Canadian study as early as 1961
through to 1983.[1]
The first detailed
table was published in 1995, when DeVivo and colleagues provided life
expectancy estimates for four categories of spinal cord injury at
5-year intervals between ages 5 and 80.[2]
The top line of
Figure 1 shows the
proportional (or “relative”) life expectancy estimates from this
report for the category of paraplegia. Each point shows the life
expectancy at that age as a percentage of the normal value at the same
age. Thus at age 20 the estimated life expectancy of 44.8 years is 80%
of the normal value of 56.3 years.
There is little change
over the first 30 years, with a drop of only 6% by age 50 (to 74%;
21.2 years vs the normal figure of 28.6 years). The rate of decline
then accelerates, so that over the next 30 years the percentage figure
declines a further 22% by age 80 (to 52%; 4.2 years vs 8.1 years).
The second and third
lines in Figure 1 show the comparable figures from a report by Frankel
and colleagues published in 1998, which had the added feature of
separate estimates for males and females.[3]
The proportional life expectancy values are seen to be slightly higher
in females than males at all ages, and both sets of figures are close
to the DeVivo figures between ages 20 and 60. After age 60 the Frankel
figures decline more rapidly, and by age 80 they are down to only 22%
in females (1.8/8.3) and 17% in males (1.1/6.4).
The reason for these
much lower estimates in the Frankel data by age 80 is not immediately
obvious, since although the Frankel standardized mortality ratio (SMR)
is higher in the oldest age group (see the
Table: 3.68 vs 2.21)
this alone cannot explain such a large difference between the two
studies. This issue is explored further in later sections of this
article, where the results from each study are examined in more
detail.
Methods of estimation
The usual method of
calculating life expectancy is by means of a life table that follows a
hypothetical group of 100 000 newborn children, with current death
rates being applied at each year of age. By about age 110 the last
survivor has died, and the average life expectancy at each year of age
can then be calculated at each age by dividing the remaining
person-years of survival by the number alive at the start of the same
year.
In persons with a
life-shortening condition such as paraplegia, the life expectancy at
each age can be obtained in the same way, except that the annual rates
in the life table will need to be increased. This is usually done by
multiplying the normal rates in the life table by one or more
standardized mortality ratios derived from a suitable follow-up study,
thus converting the normal
expected rates of the life table to the
observed rates seen in the
study. A small follow-up study will often only supply a single SMR,
which is then applied to all ages in the life table.[4]
With larger studies there may be several age-specific SMRs available,
based on age groups such as 20–24, 25–29, and so on.
Singer and others have
suggested that in some situations a better method of changing the
rates in the life table would be to add the difference between
observed (O) and expected (E)—that is, adding O-E to the normal rate,
rather than using the SMR (the ratio O/E) to multiply the rates.[5]
In life expectancy studies this difference between observed and
expected rates is usually referred to as the excess death rate (EDR).
The effect of applying
a single EDR to the life table is almost the exact opposite of a
applying a single SMR. Thus when a single (constant) SMR is applied to
the whole life table the proportional life expectancy
declines with age, but
with a constant EDR it increases
with age. These trends are shown by the outer lines in the simplified
schematic diagram of
Figure 2.
The two inner lines of
Figure 2 show what can occur when age-specific SMRs and EDRs are
available below (say) age 50, leaving a final age group of 50 plus.
The life expectancy estimates are now very similar until age 50, but
the final age group now has a constant SMR or EDR from 50 to about
110, so the slopes again diverge and run parallel to the two outer
lines.
Results of DeVivo and colleagues (1995)
This report is from
the large US program of model care systems that began in 1973. By the
time of the 1995 report, the study had recruited over 17000 persons
with spinal cord injury, and follow-up was very good, with successful
tracing of 92% of the deaths and 99% of the survivors.[2]
Age-specific
standardized mortality ratios were calculated for four age groups, and
these are shown in the Table, together with the estimated overall SMR
for all ages combined.
In
Figure 3 the top
line shows the published life expectancy estimates as a percentage of
normal (as in Figure 1), while the second line shows the effect of
multiplying all the rates in the life table by the single all-age SMR
of 2.8.
The third line shows
the result of doubling this figure to 5.6, to illustrate that the size
of the SMR has little effect on the
shape of the curve.
Indeed, all three lines would be almost parallel if it were not for
the initial flattening of the top line, due to the three age-specific
SMRs at younger ages.
Note that this early
flattening of the curve was also seen in the third line in Figure 2
(the schematic diagram) due to the age-specific SMRs below age 50,
followed by a decline across the single age group beyond age 50. (No
EDR values were provided in the DeVivo report, but as in the second
line of Figure 2, if they had been available, the proportional life
expectancy would eventually start rising, and would be approaching 90%
by age 80.)
Results of Frankel and colleagues (1998)
The total follow-up
period in this study was a remarkable 50 years, and again the
follow-up was very good, with successful tracing of 92% of the
subjects. The study was based mainly on patients who had been treated
at the National Spinal Injuries Centre at Stoke Mandeville, with
additional data from the Regional Centre at Southport.[3]
Although the full report covered the years 1943–92, the authors
restricted the estimates of life expectancy to 1973–90 to reflect
recent mortality experience, and to allow for direct comparison with
the 1995 data from DeVivo and colleagues.
During the 1973–90
period a total of 1672 subjects were recruited, approximately 10% of
the 17000 in the DeVivo study, so that division of the data into the
same amount of detail led to some SMRs being based on relatively small
numbers. To reduce variations attributable to the resulting
instability of the SMRs, the authors explain that they applied
smoothing techniques “using a third degree polynomial regression.”
Unfortunately, due to
the distribution of SMR values in the paraplegia data, this polynomial
equation generates very high SMRs at the older ages. This is
illustrated in
Figure 4, where the
smooth S-shaped curve passes through each of the four original SMR
values, but as it reaches the last SMR (at 3.68) the line is rising so
steeply that the SMR has almost doubled (to 7) by age 80, and is
approaching the ceiling value of 10 by age 85. (Here the normal death
rate is approximately 10% per year, so simple multiplication by 10
would give 100%—that is, no survivors. This would account for the very
steep decline in proportional life expectancy seen in Figure 1, where
both male and female lines appear to be headed for zero at around age
85.)
Using the trend from younger ages
The rapid drop in life
expectancy at the oldest ages in the Frankel study is the result of an
unusual problem, in which the process of smoothing has created
artificially high SMR values above age 70. In contrast, the
underestimation of life expectancy in the DeVivo study is less severe,
but it is a much more common problem, because in most cases only a
single (constant) age-specific standardized mortality ratio is
available for elderly subjects. The result is that the conventional
practice of using a fixed SMR above a certain age will almost always
lead to an unduly pessimistic estimate of life expectancy.
An alternative
approach has recently been suggested, based on the observation that
proportional life expectancy figures tend to remain constant with age,
or show only a slight upward or downward trend. This pattern has been
documented in several life-threatening conditions, and provides the
most intuitively simple solution to what is otherwise a very difficult
problem.[6]
In the present case,
this approach is illustrated in
Figure 5, where the
20–50 trend line in the DeVivo data has been extended to age 80, at
which point it reaches a value of 70%—equivalent to a life expectancy
of approximately 6 years (Canada 6.5; England 5.9; US 6.4).
It is, of course,
rarely possible to test the validity of this approach, because the
information that is needed is itself the source of the problem, that
is, most studies do not have enough elderly patients. However, the
large size of the US model systems study has enabled Strauss and
colleagues to calculate age-specific SMRs by 5-year age groups from
age 10 through to age 80.[7]
The results for paraplegia are shown by the top line in Figure 5,
which is almost parallel to the DeVivo trend line, and reaches a value
of 72% at age 80—virtually identical to the trend line prediction of
70%.
Discussion
Since they were
introduced in the 1980s, structured settlements have helped ensure
that many patients receive steady funding for the rest of their lives.
However, there is still a need for reasonably accurate estimations of
individual life expectancy. Thus in the example of Dorothy, her
structured settlement was purchased with a lump-sum award based on a
predicted 3 years of care. It is therefore providing her with
approximately half the annual amount that would have resulted from the
more realistic life expectancy of 6 years.
With current methods,
life expectancy in the elderly is underestimated when only a single
SMR is applied to the whole life table, or whenever age-specific SMRs
do not extend beyond the age of the patient. These errors are not
confined to persons with spinal cord injury, but will occur in the
presence of any life-shortening condition.
In the absence of
reliable age-specific SMRs (or EDRs) for older age groups, the simple
extrapolation of proportional life expectancy from younger ages will
usually provide the best estimate of life expectancy in an elderly
patient.
Table.
Paraplegia: Age-specific standardized mortality ratios in two reports.
|
Age |
0-30 |
31-45 |
46-60 |
61+ |
All ages |
|
DeVivo et al.[2]
1995
Frankel et al.[3]
1998 |
3.86
3.14 |
3.74
3.04 |
1.96
2.20 |
2.21
3.68 |
(estimated)
2.80
2.83 |
Acknowledgments
We thank Ian Karp,
Philip Steele, Keith Chambers, and Janet Heavyside for their helpful
comments and suggestions.
Competing interests
None declared.
References
1.
Geisler WO, Jousse AT, Wynne-Jones M, et al. Survival in traumatic
spinal cord injury. Paraplegia
1983;21:364-373.
PubMed Abstract
2.
DeVivo MJ, Stover SL. Long-term survival and causes of death. In
Spinal cord injury: Clinical Outcomes
from the Model Systems. Gaithersburg, MD: Aspen Publishers,
1995:289-316.
Full Text
3.
Frankel HL, Coll JR, Charlifue SW, et al. Long term survival in spinal
cord injury: A fifty year investigation.
Spinal Cord
1998;36:266-274.
Abstract
Full Text
4.
Smart CN, Sanders CR. The Costs of
Motor Vehicle Related SCI. Washington, DC: Insurance
Institute for Highway Safety, 1976.
5.
Singer RB. A method of relating life expectancy in the US population
life table to excess mortality. J
Insur Med 1992;24:32-41.
PubMed Citation
6.
Anderson TW. Life Expectancy in
Court. Vancouver, BC: Teviot Press, 2002.
7.
Strauss D, DeVivo MJ, Shavelle R. Long-term mortality risk after
spinal cord injury. J Insur Med
2000;32:11-16. |
