1. science
2. mathematics
3. statistics

JOURNAL OF INSURANCE MEDICINE
Copyright © 1998 By Journal of Insurance Medicine
ORIGINAL ARTICLE
How to Construct a Mortality Abstract (Number 497M-1 as an Example)
Richard B. Singer
Background: Since the 1976 publication of the first Medical Risks volu_me of analyses of mortality follow-up (FU) studies (called "mortality abstracts"), members of the American Academy of Insurance
Medicine have sought to extend this method of using FU studies in
the medical literature to produce comparative mortality data useful
for medical underwriting. Seminars on life table methodology started in 1977 and courses are now sponsored by the Board of insurance
Medicine. The Journal of Insurance Medicine has published many
mortality abstracts and methodology articles, and methodology is
further pursued by the Editor in this issue of the Journal.
Text: Retrieval of the source data (Annual Reports) is described and
the source tables are evaluated. These are related to a previous 1976
Abstract. The design of the Abstract is described: other sources,
tables, background, expected mortality, descriptive text, and comment. Aspects of life table methodology are used throughout the
description.
Address: Richard B. Singer, MD
52 Falmouth Road, #Cll, Falmouth,
ME 04105
Correspondence: Richard B. Singer,
MD, Consultant to AAIM.
Key Words: Life Table Methodology. Follow-up Studies, Comparative
Mortality, Cystic Fibrosis.
Received: January 1, 1998
Accepted: March 1, 1998
Journal of Insurance Medicine
1998; 30:28-38
Summary: The construction of the current Mortality Abstract 497M1 on mortality in cystic fibrosis is described in detail.
(Methodology Article 006M-5)
Introduction
the same volume, and from Chapter 4 of the
This article has been commissioned by the Edi- third edition of the text by Brackenridge and
tor to describe in detail the construction of a Elder.3
Mortality Abstract. I have responded to this
request by working with a current Abstract in The Mortality Abstract used as an example
the last issue of the Journal of Insurance Med- concerns secular change in the mortality of
icine, so the reader will not have to look far cystic fibrosis patients.4 Source material for this
afield for the sample Abstract used. However, Abstract includes the 1994 and 1995 Annual
the reader should secure copies of previously Reports of the Cystic Fibrosis (CF) Foundapublished material that is directly pertinent to tion,5 an address at the 1995 AAIM meeting by
this "how to" article, because the pattern of the Foundation’s Registry director, Dr. Fitsimconstruction is discussed in detail. The first mons,6 and a CF abstract in the 1976 Medical
article, "Guidelines for Evaluation of Follow- Risks reference volume.7
up Articles and Preparation of Mortality
Abstracts.’’1 appeared in the Journal of Insur- Medical directors involved in the inception of
ance Medicine in 1991, and was reprinted as the first Medical Risks volume7 desired to
Chapter 4 in Medical Risks - 1991 Compend of
expand the corpus of insurance mortality studMortality and Morbidity? Life table methodoloies then available, to extend the science and art
gy is another topic with which the reader of of risk classification for individual life insurthis article should be thoroughly familiar, and ance. Neither single company studies nor the
this is obtainable from Pokorski’s Chapter 22 in large cooperative impairment studies supplied
28
VOLUME 30 NUMBER 1 1998
JOURNAL OF INSURANCE MEDICINE
all of the results needed for comprehensive 1986, thanks to the efforts of editors such as Dr.
medical underwriting. It was believed that the Elder, Dr. Butz, and Dr. Roberts. However,
increasing numbers of follow-up studies pub- despite all of the efforts by members of AAIM,
lished in the medical literature after World abstract production remains on a limited and
War II might be analyzed and developed into strictly volunteer basis. Life table methodolotables of comparative mortality that would be gy is not as mysterious as it may appear to the
useful for improved medical underwriting. It uninitiated, and interested volunteers are
was recognized that such adaptation would be urgently need to increase the number of mora complex process for studies from non-insur- tality abstracts acceptable to the Editor of the
ance sources, because of the variety of popula- JIM. Creative writing brings great satisfaction!
tion or patient groups studied, and the variety
of methods used in presenting the results. Sur- Article Retrieval
vival curves and survival rates would have to In this case I retrieved the Annual Reportss as
be converted to mortality rates. Generally a deliberate attempt to update mortality expeobserved mortality was not matched with rience in CF patients, and compare current
expected mortality, and it was necessary to to rates with those reported in Abstract #785 in
develop the appropriate expected rates for all the 1976 Medical Risks volume.7 Aware of the
tables of comparative mortality. The results existence of the CF Foundation, in July, 1996 I
were designed to be presented in compact called the office of AAIM’s Executive Director,
units of a formalized text and tables called, for Russ Barker, and obtained staff assistance in
want of a better term, "Mortality Abstracts." securing the needed address and telephone
At the 1965 meeting of the Executive Council a number. A few health organizations do operate similar follow-up registries, and medical
proposal was presented to prepare a reference
volume, a mortality monograph, containing a directors should be aware of the help that may
large number of such mortality abstracts. The be obtained from our AAIM Executive DirecExecutive Council appointed a study commit- tor in pursuing any quest for additional infortee, which found the project feasible and pre- mation of this sort. After reaching the CF
sented a plan for preparation of such a vol- Foundation by phone I was referred to Dr.
ume. The study committee was reorganized as Stacy Fitzsimmons, who is in charge of the
a Mortality Monograph Committee, which Registry statistics, the annual report, and the
added members of the Society of Actuaries clinical research program. Dr. Fitzsimmons
(SOA), engaged a Project Director, and utilized sent me the 1994 Annual Report and several
funds from AAIM’s predecessor organization, reprints of hers, including the informative
ALIMDA (the Association of the Life Insur- address she gave at our 1995 annual meeting
ance Medical Directors of America), and, later, in Chicago. I was told that the 1995 Annual
from the research budget of the SOA, to pub- Report was nearing completion, and Dr.
Fitzsimmons sent this to me a few weeks later.
lish in 1976 the first Medical Risks volume.7 The
work of preparation of many mortality
abstracts proved to be arduous and time- conThese Annual Reports from the CF Foundasuming, but was even more lengthy in pro- tion constitute an exceptional type of source
duction of the second Medical Risks mono- for mortality follow-up data, but a type that
graph, published in two volumes in 1990.8
should not be neglected. Most studies are in
articles published in the medical literature, but
Life table methodology was included in the valuable information may also be found in
triennial course material, and in 1977 seminars periodic or occasional reports from private
were set up and offered to members of ALIM- health organizations such as the CF FoundaDA and others to encourage interest in the tion, or from agencies of the Federal governproduction of mortality abstracts. Occasional ment, such as data on End-Stage Renal Disabstracts appeared in the Journal of Insurance ease (ESRD), provided by HCFA (the Health
Medicine, and on a more regular basis after Care Financing Administration). Dr. Balakr29
VOLUME 30 NUMBER 1 1998
JOURNAL OF INSURANCE MEDICINE
ishna, formerly ~with the Travelers, was the years during 1995. The Registry of the CF
medical director who ferreted out the exis- Foundation was started in 1966, and it constitence of the ESRD reports, which formed the tutes, I believe, by far the largest and longest
basis of Abstract 637M-1,9 dealing with mor- follow-up record of CF patients in the world,
tality of patients on dialysis for renal failure, containing most of the patients resident in the
under the special Medicare program for such U.S. Deaths and exposures have been nearly
patients. Usually the medical director is apt to doubled by combining the data for two years
retrieve mortality follow-up articles from from the 1994 and 1995 Annual Reports which
scanning of the medical literature, or from a are similar in design.
planned search. We have also emphasized in
the past the need to read with care and utilize Source Data Presentation
the reference list of a good follow-up article, as Table I reproduces the life table data from page
the best single source of past mortality studies 20 of the 1995 Annual Report.s Five columns of
in the medical literature.
data are given: age (start-end for individual
ages 0-1 through 42-43 years, and ages 43 up);
Evaluation of Data Source
years of exposure to three decimal places; numAs indicated in the "Guidelines" article,1 ber of deaths; mortality rate (annual) to five
important features for evaluation of a follow- decimal places; and cumulative survival (rate)
up article include appropriateness of classifi- to five decimal places. At the bottom of the
cation of the condition studied, the size of the table data are given (in years) for the "median
series (numbers of entrants, exposures and cumulative survival," for all patients and for
deaths observed), the type of follow-up study, males and females. These are the ages at which
the formation of the series, demographic data each survival curve reaches the 50% level.
of the entrants, grouping of the subjects by
severity, age, or other criteria, details of the fol- The fact that exposure, E, is given to three declow-up, the derivation and presentation of the imal places is evidence that E was measured
results, and the statistical methods used. The by date for each individual in 1995, from Janu1995 Annual Report consists of a two-page ary I (or date of entry, if later) to date of death,
table of contents and 45 pages of tabular data date of loss to follow-up, or to December 31 for
(with one survival curve), and the four-page known survivors to the end of the year. Other
questionnaire used for reporting data on data in the report show an average of 4.6 visits
approximately 20,000 CF patients at 114 per patient, and 17,105 patients with ongoing
accredited clinical centers, constituting the care in 1995, 1,522 new patients (864 newly
Registry. There are 36 topics listed for sets of diagnosed, and 658 first visits for previously
tabular data, such as highlights, demographic, diagnosed patients), 385 deaths, 24 cases with
diagnostic, life table (page 20), death and sur- reversal of CF diagnosis, and 1,026 patients
vival, clinical, complication and hospitaliza- not seen in two years: With many patients
tion, test results, treatment, insurance cover- seen at more than one center, 22,026 patient
age, employment, etc. The detail of descriptive forms returned giving status as of December
data beyond the follow-up results is extraordi- 31 were utilized to eliminate duplications and
narily complete, although the age distribution provide information on 20,096 patients for
(by single years of age) is not differentiated by their 1995 history. Vital status was recorded as
sex. I would rate this as a source of the highest alive on December 31, death during 1995, with
value (A, as proposed in the "Guidelines"), date and cause of death, or vital status
because CF is a relatively uncommon disease, unknown. Exposures were derived for each
the series is nationwide and probably includes patient on the basis of such detailed informamost of the CF patients the U.S., with unusu- tion. As noted above, demographic and other
ally complete observation and 385 deaths data are given in much greater detail in these
recorded in a total exposure of 18,871 patient- reports than in most follow-up studies report3O
VOLUME 30 NUMBER 1 1998
JOURNAL OF INSURANCE MEDICINE
ed as articles.
Two features of the life table data I considered
to be of immediate importance: the absence of
expected mortality data, and the small numbers of deaths (fewer than 10) in a majority of
the single ages. It was apparent that expected
mortality would have to be supplied, and that
observed data by age should be combined into
a smaller number of age groups to increase the
exposures and deaths in each group, and thus
reduce the random error of the annual mortality rate. These are essential decisions that must
be made in designing abstract tables based on
life table data.. It should also be emphasized
that this is a follow-up study for a maximum
duration of a single year onl)~ for CF patients
by attained age, since entry age is equivalent
to the duration of their genetic disease. This is
quite different from the usual follow-up stud)4
in which a group of entrants is observed, of a
specified age distribution, for a period that
usually extends to a maximum of more than
five years. The best analogy is with the population life tables, which are based on census
data for the middle of a year, and a count of all
deaths during the year. Another important
decision in design of tables for the abstract was
to increase the exposures and particularly the
numbers of deaths by combining the data for
two years, from the 1994 and 1995 Annual
Reports. Such combination is easily accomplished, thanks to the detailed exposure and
death data in the source life tables.
Although there were only seven deaths in the
first year of life in the 1994-1995 experience, I
have chosen to keep this year separate, partly
because of its much higher expected mortality
rate. Otherwise the age grouping has
increased the deaths to a range from 21 at 1-5
years to a maximum of 156 at 20-25 years.
The standard format for tabular presentation
of comparative life table mortality gives the
following observed and derived data in
columns from left to right: age group, exposure (E), observed deaths (d), expected deaths
(d’=[E][q’]), mortality ratio (100d/d’),
observed annual mortality rate per 1,000 (q),
expected rate (q’), and excess rate (EDR =
[q-q’]). However, I have added an extra column next to the exposure, giving the percentage age distribution of E. The purpose of this
is to emphasize the very great change in age
distribution of CF patients in the Registry
from its earliest to recent years. Young and
mature adults over age 30 years are now present in large numbers, whereas too few
patients survived in 1966-1972 to justify any
attempt to calculate mortality rate. For any
mortality abstract the standard table format for
such data should be used, with a carefully
worded table heading, and both words and
symbols at the top of each column, with footnotes to give the basis for the expected mortality, and any other notes needed. Each table
must be numbered and should be self-explanatory to the reader, without reference to the text,
if this is possible. Table II reproduces Table i of
Abstract 497M-1, to illustrate the standard forAbstract Table Preparation
mat that has been developed for this type of
The first action I take in writing an abstract is abstract table (note that in this article tables are
to design and prepare the tables. The conden- identified with Roman numerals, to avoid consation of data by individual ages in the source fusion with the table numbers in the abstract).
table was accomplished by setting up 10 age
groups: 0-1, 1-5, 5-10, then quinquennial age At this point we should pause to consider the
groups through 35-40 years, and finally ages derivation of expected mortality rates, q’. This
40 years and up. This age grouping for the CF population is unselected and distributed
1994-1995 experience is compatible with what throughout the U.S. The U.S. Life Tables are
can be easily derived from Table 785d of the therefore the ones appropriate to use for
1976 abstract7, for the 1966-1972 combined expected mortality. Decennial tables cannot be
experience with CF patients (there are no data used, because, at the time of preparation of the
beyond age 30 years in this abstract). abstract (July, 1997) the 1989-91 Decennial U.S.
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JOURNAL OF INSURANCE MEDICINE
Life Tables were still in preparation and had to Expected Mortality, but no tables are given,
not been published. Even the Annual because the derivation of q’ is straightforward.
Abridged Tables are not being published until Tables III and IV are shown in this article to
five years after the calendar year. I made use of emphasize the importance of development of
the 1990 Abridged U.S: Life Tables for the expected mortality for use in the abstract
white population and calculated annual q’ tables. The q’ values derived above have been
rates from the table of annual survivors age 0 inserted in Tables I and 3 of abstract 497M-1. I
to 85 years, for both males and females. White will not detail the similar derivation of q’ from
population rates are valid because of the very the 1969-71 U.S. Life Tables in abstract 785 and
low CF prevalence in nonwhite patients. Table tables 2 and 3 of abstract 497M-1. However, I
III shows the derived q’ values by sex for the have recalculated the total d’ values by sex,
central age of each age group (d’ as the prod- used in in Table 3, because the ones shown in
uct of E and q’ was obtained by quinquennial Table 785f were erroneously underestimated.
age group instead of by individual ages, to
save the arithmetical labor). A direct mean of In addition to abstract Table I for the 1994-1995
the q’ values by sex was used instead of one experience and Table 2 for the 1966-1972 expeweighted.by the overall male/female ratio, rience, I designed two tables to provide a
which undoubtedly is not constant by age. An direct comparison of excess mortality in the
inspection of the q’ values will make it clear two periods about a quarter century apart.
that the error introduced is inconsequential for Table 3 has the exact same columnar arrangethe small q’ values that prevail except in the ment of data used in Tables 1 and 2, but it is
first year of life. The source life table does not restricted to totals and age subgroups 0-15
give any age distribution for those age 43 years years and 15 years up, not given in the previand up. However, another table in each Report ous tables. The 1966-1972 experience is given
gives the census distribution by individual in the upper part of the table, and the 1994ages, 40 to 71 (the highest reported). Table IV 1995 experience in the lower part. This
shows the derivation of mean q’, based on arrangement provides a secular comparison
numbers of patients by quinquennial age that still includes an age separation between
groups from the 1994 and 1995 Reports. A q’ children on the one hand, and young and
value, male and female combined for each cen- mature adults on the other. Overall life table
tral age, is multiplied by the total survivors, s, data by sex are also included for the 1966-1972
at the end of the year, to obtain the age-related experience; these are not available for the 1994expected deaths, d’. The mean q’, age 40 years 1995 experience.
up, is then calculated as the quotient, the sum
of the d’ values divided by the sum of the sur- Abstract Table 4 was designed to show the
vivors. Again, I should emphasize that this reduction in excess mortality as reduction in
accurate calculation of q’ for the open-ended EDR, from the 1966-1972 observation period to
age group 40 years up is only possible because the 1994-1995 period. A different arrangement
of the unusually complete age distribution of data is used: after the age group three sets of
published in the Reports; such detail is seldom columns show exposures, observed deaths,
available in published articles. Note that the and EDR values, one column of a pair giving
tabular age corresponding to the actual mean the 1962-1977 data and the second column, the
q’ is 47 years, two years over the mean age of 1994-1995 data. The last two columns give the
45.0 years. This relationship between mean age secular difference in EDR, first in absolute
and tabular age corresponding to mean q’ is an units (), and second, as a percentage of the iniimportant one; it is discussed in the references tial value. Overall, iX is (19-46) or -27 extra
cited.1,3
deaths per 1,000 per year and (100)(-27)/46 =
-59%. These differences are given for the indiIn abstract 497M-1 a section of text is devoted vidual age groups through 25-30 years, for
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JOURNAL OF INSURANCE MEDICINE
the survival curve has been given in the article. Credit for such additional data must be
included in the references. For abstract 497M1 it was not necessary to obtain any additional
data from Dr. Fitzsimmons. If the abstract
summarizes results from several source articles, text preparation is complicated. For
examples of this sort the reader should consult
the numerous abstracts on coronary bypass
surgery in Chapter 6 of the 1990 Medical Risks
monograph.8 Several summarizing abstracts
preceded the abstracts on individual source
articles, including a long one describing the
Preparation of Abstract Text
series and age/sex data from more than 16
To justify use of the term "Mortality Abstract," separate sources.
both tables and text should be prepared in the
standardized format. Initial completion of the Objective. A single sentence should be written
tables makes it easier write the text, especially setting forth the objective of the source followin the Results section. The text must be orga- up study or the abstract. If the objective of the
nized section by section in the order given abstract differs substantially from the objective
below, with each section containing its essen- of the source article(s), as it may~ the heading
tial information. Essential information mustshould be explicit as "Objective of This
be given in each section, and the nature of this Abstract."
can be learned by reading published abstracts.
However, the reader should be reassured that Background. This section heading is usually
useful comparative mortality information can not needed, but was included in abstract 497Mbe presented in a "Mortality Article," not sub- I because of the special nature of cystic fibrosis
ject to the format constraints of the Abstract as a disease and the nature of the Registry of the
format. Examples may be found in recent CF Foundation. Dr. Fitzsimmons’ address to
issues of the Journal of Insurance Medicine.
AAIM5 was the chief source for this section.
subtotals 0-15 years and 15 years up, and for
the total experience. No differences can be
shown for age 30 years up, because there are
no 1966-1972 data for ages over 30 years. Since
the secular changes are uniformly a reduction,
all of the data in these last two columns bear a
negative sign. Table 4 thus provides a comparative display of the observed E and d data, the
derived EDR rates, and the negative differences in EDR in both absolute and relative
terms. Table 4 also accomplishes the objective
given in the title of the abstract.
Abstract Title. A brief but informative title
should be written, such as "Comparative Mortality in [name of condition studied]." To pack
in as much information as possible, the title
chosen for abstract 497M-1 was "Secular
Change, 1972 to 1995, in the Comparative
Mortality of Patients Observed in the Registry
of the Cystic Fibrosis Foundation."
Subjects Studied. This is a description, as
detailed as feasible, of the condition studied
and of the make-up, source and location of the
series studied, its distribution by age, sex and
race, its grouping by diagnosis, severity or
other features, and other salient characteristics. Sometimes a small age/sex distribution
table may be given in this section. In abstract
497M-1 a description is given of some of the
collateral data in the Annual Reports of the CF
Foundation.
References. Contrary to usual custom, these
are placed first in the Abstract, for the purpose
of "giving credit where credit is due." It is
explained in the Guidelines article that the Follow-up. Methods, duration and time peripreparer may find it necessary to write to the od of follow-up are given in this section. As
author of the source article, to request addi- noted above, this study is unusual in presenttional information, such as the age distribu- ing follow-up data for a single year in each
tion when only a mean age is given, or the Report, from a Registry large enough to pronumerical survival rates when only a graph of vide nearly 400 deaths per year.
33
JOURNAL OF INSURANCE MEDICINE
VOLUME 30 NUMBER 1 1998
Expected Mortality. The text should be adequate to explain the reason for selection of the
source tables of expected mortality, and how
the rates were derived for use in the tables. If
the derivation is complicated it may be desirable to present a special table or tables for this
purpose. There are two common problems
associated with derivation of expected mortality for series with all ages combined when only
the mean age is given: (1) estimating the firstyear mean q’ with only a mean age given; (2)
progression of q’ by duration at a rate lower
than normally anticipated. These problems are
not present in abstract 497M-1, but they are frequently encountered, and they are thoroughly
discussed in the Guidelines article.’
Results. The most important features of the
comparative mortality results are described in
words, citing the Tables in irder. It should be
remembered that some readers prefer a word
description with a few numbers embedded in
the text to all of the data presented in a table.
This section is intended to cater to their needs,
and to emphasize any patterns of comparative
mortality, by age, sex, duration, severity or
other characteristic. In abstract 497M-1 attention is devoted to the age pattern in excess
mortality. There are no data by duration, but
secular changes in EDR and age distribution
of the Registry patients are also described. As
discussed in the Guidelines article,’ because of
wide variation in expected mortality, q’, by
age and sex, there are reasons to prefer use of
EDR to use of the Mortality Ratio in discussing
trends in excess mortality between groups.
Comment. This is a final optional section
reserved for any discussion that the preparer
of the abstract considers desirable. It often
happens that results of interest are given in the
source article that are not relevant to the mortality data used in the abstract. Some of these
may be listed to call them to the attention of
the reader. The first topic discussed in the
Comment section of abstract 497M-1 is my
opinion that CF remains a declinable disease
because of the EDR levels and the age trend in
EDR. The second topic concerns standard
34
methods of therapy that have been so successful in reducing excess mortality since 19661972, and newer, experimental modes of therap~ including gene therapy. Both topics were
considered to be of potential interest to readers
of the Journal of Insurance Medicine.
Coding. A final step in completion of a mortality abstract or article is assignment of its
proper code number, with a unique identifier.
This is a continuation of the complete coding
of 1,219 mortality or morbidity entries for A
Descriptive Index of Mortality Studies from Selected Sources, 1951-1995, a reference volume
sponsored by AAIM, SOA, HOLUA, IHOU
and the MIB, due for publication in 1998. An
earlier abridged coding list may be found in
Chapter 5 of the 1994 Medical Risks volume?
With publication of the Descriptive Index book,
the Editor of the Journal of Insurance Medicine will assume responsibility for the coding
and code repository needed for assignment of
the unique identifier. The author of the mortality abstract or article will also be able to
assign the subject code and a source code M
(up to the year 2000), but not the unique identifier. In any case the Editor will be the final
coding arbiter.
Conclusion of Article
It is hoped that this article will encourage
some medical directors and underwriters to
try their hand at the (to me) fascinating task of
transforming the results of a good follow-up
study into a mortality abstract that will help
all whose daily work is medical underwriting
or risk selection. Some authors may feel burdened by the constraints of the abstract format, and I would urge these to employ the
article format they prefer, as long as it is clear
to the reader and acceptable to the editor. Most
of the details of table design and selection of
data to include in tables and text are applicable to the more conventional medical article.
There is nothing sacrosanct about the abstract
design, which was intended to provide a compact format that would include most of the
essential comparative mortality data needed
by the interested reader. It has proved to be a
VOLUME 30 NUMBER 1 1998
JOURNAL OF INSURANCE MEDICINE
useful device for presenting data on comparative mortality derived from published followup studies, but the format is not crucial.
References
1. Singer RB, Kita MW and Avery JR, editors, Medical Risks 1991 Compend of Mortality and Morbidity. Westport, Conn.,
Praeger Publishers (1994). See Chapter 4, "Guidelines for evaluation of follow-up articles and preparation of mortality
abstracts," pp 89-99.
2. Ibid. See Chapter 2, Pokorski RJ, "Mortality methodology," pp
4-36.
3. Brackenridge RDC and Elder WJ, Medical Selection of Life
Risks, 3rd edition. New York, Stockton Press (1996). See Chapter 4, Singer RB, "The application of life table methodology to
risk appraisal," pp 57-78.
4. Singer RB, Secular Change, 1972-1995 in the Comparative
Mortality of Patients Observed in the Registry of the Cystic
Fibrosis Foundation. J Ins Med 1997;29:233-239.
5. Fitzsimmons SC, Cystic Fibrosis Foundation Patient Registry,
1995 Annual Data Report. Bethesda, Md. (1996). See also 1994
Annual Report, published in 1995.
6. Fitzsimmons SC, What’s new? [Cystic Fibrosis]. J Ins Med
1995;27:124-130. (Part of the Transactions of the 103rd annual
meeting of AAIM.)
7. Singer RB and Levinson L, editors, Medical Risks - Patterns of
Mortality and Survival. Lexington, Mass., Lexington Books
(1976). See abstract 785.
8. Lew EA and Gajewski J, editors, Medical Risks - Mortality by
Age and Time Elapsed. Westport, Conn., Praeger Publishers
(1990).
Singer RB and Balakrishna S, Mortality in Medicare patients on
dialysis for end-stage renal disease (ESRD). J Ins Med
1995;27:28-32.
35
JOURNAL OF INSURANCE MEDICINE
VOLUME 30 NUMBER 1 1998
Table I
CYSTIC FIBROSIS PATIENT REGISTRY LIFE TABLE ANALYSIS - ALL PATIENTS
U.S. Afl’diated Centers - Patients Under Care in 1995
~
Years of
Number of
~
Dea~s
Mortality
00-01
01-02
02-03
03-04
04-05
05-06
06-07
07-08
08-09
09-10
10-11
11-1212-13
13-14
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22
22-23
23-24
24-25
25-26
26-27
27 -28
28-29
380.033
607.612
674.885
767.973
794.342
805.012
787.218
810.639
818.002
839.062
814.457
765.142
753.978
747.263
713.118
662.856
586.027
577.947
512.572
507.256
462.932
391.773
361.000
373.235
363.371
349.342
311.552
261.561
247.359
4
2
2
2
1
4
3
5
5
3
5
9
6
7
13
17
8
15
9
24
27
14
12
14
15
7
1$
1i
9
0.010525
0.003292
0.002963
0.002604
0.001259
0.004969
0.003811
0.006168
0.006112
0.003575
0.006139
0.011763
0.007958
0.009368
0.018230
0.025647
0.013651
0.025954
0.017559
0.047313
0.058324
0.035735
0.03324 !
0.037510
0.041280
0.020038
0.057775
0.042055
0.036384
29-30
30-31
241.411
237.190
13
10
0.053550
0.042~60
31-32
32-33
33-34
34-35
35-36
36-37
37-38
38-39
39-40
40-41
41-42
42-43
43 +
225.249
186.511
174.858
171.765
150.043
142.891
105.952
105.377
90.423
79.691
66.067
62.157
293.64 1
13
8
5
6
7
6
6
6
2
3
0
2
27
0.057714
0.042893
0.028595
0.034932
0.046653
0.041990
0.056629
0.056938
0.022118
0.037646
0.000(300
0.032176
0.091949
TOTAL DEATHS
Cumulative
Ra~
Survi~
0.98J~53
0.98628
0.98336
0.98080
0.97957
0.97471
0.97101
0.96503
0.95915
0.95573
0.94988
0.93877
0.93133
0.92265
0.90598
0.88304
0.87107
0.84875
0.83398
0.79544
0.75037
0.72403
0.70036
0.67458
0.64730
0.63446
0.59884
0.57418
0.55366
0.52464
0.~0295 .
0.47477
0.45484
0.44201
0.42684
0.40738
0.39063
0.36913
0.34870
0.34107
0.32847
0.32847
O. 31807
( 0.29012 )~ .
385
Median for cumulative survival:
lower 95% confidence:
upper 95% confide~nce:
30..1 years
28.4 years
,31.8 years
Cystic Fibrosis Pmtimt lP~egistry, I99~; Ammal D~t Report
(AUGUST - 1996)
36
31.1
29.3
35.2
28.3
26.2
31.5
VOLUME 30 NUMBER 1 1998
JOURNAL OF INSURANCE MEDICINE
Table II
ComparativeMortality by Age m Patients Observed in the Registry of
the Cystic Fibrosis Foundation, 1994-1995
Age
Exposure
No. of Deaths
Mortality
Mean Annual Mortality Rate per 1,000
(Years)
Pt.-Yrs. Distrib.
Observed Expected*
Ratio
Observed Expected Excess
x
E %Total
d
d’
lOOd/d’
0- 1
1-5
5 - 10
10 - 15
790
5,743
8,061
7,452
2.1
15.0
21.1
19.5
7
21
38
89
6.00
1.72
1.61
1.49
117%
1,220
2,400
6,000
15 - 20
20 - 25
25 - 30
30- 35
35 - 40
40 up
5,545
3,842
2,728
1,953
1,134
932
14.5
10.1
7.1
5.1
3.0
2.5
143
156
113
92
57
52
4.44
3.84
3.00
2.54
1.93
3.17
3,200
4,100
3,800
3,600
3,000
1,600
q
q’
(q-q’)
8.9
3.5
4.7
11.9
7.6
0.3
0.2
0.2
1.3
3.2
4.5
! !.7
26
41
41
47
50
56
0.8
1.0
1.1
1.3
1.7
3.4
25
40
40
46
48
53
*Basis of expected mortality: 1990 Abridged U.S. Life Table for the white population.
Table III
Expected Mortality Rates per 1,000 from 1990
Abridged U.S. Life Table for the White Population
Age
Group
x to x+Ax
0-1
1-5
5 - 10
10- 15
15 - 20
Central
Age
Annual Mortality Rate per 1,000
Male
Female Both*
Age
Group
Central
Age
Annual Mortality Rate per 1,000
Male
Female Both*
xc
q’
q’
q’
x to x+x
Xc
q’
q’
0-1
2.5
7
12
17
8.35
0.42
0.24
0.21
1.21
6.59
0.34
0.17
0.16
0.49
7.6
0.3
0.2
0.2
0.8
20- 25
25 - 30
30-35
35-40
40 up
22
27
32
37
(47)#
1.46
1.54
1.91
2.43
---
0.46
0.55
0.68
0.95
q’
1.0
1.1
1.3
1.7
3.4#
*Mean for M and F q’ used as sufficiently accurate. See text.
#See Table IV for accurate calculation of mean q’, based on age distribution, 40 years and up.
37
JOURNAL OF INSURANCE MEDICINE
VOLUME 30 NUMBER 1 1998
Table IV
Derivation of Mean Expected Mortality Rate (q’), Based on
Age Distribution on December 31, Ages 40 - 71 Years,
1994 and 1995 Annual Reports of the Cystic Fibrosis Foundation
Age Group
Years
No. Alive, December 31
1994
1995
Total No.
Alive
Expected Annual
Mortality Rate*
Expected
Deaths
s
s
s
q’
d’
40-45
45-50
50-55
55-60
60-65
65-70
70-71
300
127
37
18
5
2
0
330
157
36
29
8
0
2
630
284
73
47
13
2
2
0.0024
0.0033
0.0053
0.0086
0.0140
0.021
0.029
1.56
0.94
0.39
0.41
0.18
0.04
0.06
40-71
489
562
1,051
0.0034#
3.53
x to x+Ax
*Basis of expected mortality: 1990 Abridged U.S. Life Table for the white population.
#Mean q’ (age 40-71 years) = ~d~s. The actual mean age for this distribution is 45.0 years, but the
tabular age corresponding to the mean q’ is 47 years. See text.
38