|
|
 |
 |
 |
 |
 |
|
|
Expertise > Actuarial > Critical Illness Address
by Phillip. G.
Alistair CAMMIDGE FIA Director Lotter
Actuarial Partners Inc. for: Delivered
at the September 14, 1999 Annual Meeting of the Actuarial Society of
Greater New York:
ACTUARIAL
ASPECTS of CRITICAL ILLNESS INSURANCE 1.
Introduction Critical
illness is nature’s most unkind and forceful way of telling you to
slow down, demanding you change your lifestyle, take some time off,
even think about early retirement. How
then will you cope with the enormous negative influence on your
personal cash flows that are certain to follow when you are
diagnosed with a critical illness? How will you pay the mortgage,
put your children through university and cope with a multitude of
other unfavorable influences on your personal cash flow? Think also
about such issues as reduction in your earning ability as well as
heroic efforts to save your life, special treatments and equipment,
all of it unfunded by your medical insurance? The
answer is surely Critical Illness insurance! 2.
Actuarial Health Insurance Conference: University of Warwick. During
early September 1999, I attended an actuarial conference at the
University of Warwick (England). This annual conference brings
together British actuaries practicing in critical illness insurance
(CII) and other health products – such as disability insurance and
major medical insurance. The conference is very well attended. So
many would-be attendees had to be turned away that next year the
conference is moving to a larger venue. At
the Warwick conference, erudite papers were presented dealing with
CII reserving, the cost of rate guarantees and stochastic modelling
of fluctuations in disease incidence. At
the University of Warwick Conference, I overheard the following
remarks: “Critical
illness insurance is the product of the future – and I have seen
the future!” “My
father died of cancer; he had it before it became so popular.” 3.
Product History. CII
was first developed in South Africa and thereafter transitioned to
the UK; the first policies being issued there in 1986. In
the British Isles and South Africa, CII is regarded as a mature,
mainstream insurance product. While I was in the UK, I saw two
surveys in the papers’ financial pages of CII policies like those
seen in the US covering term products i.e. monthly costs of
100,000 at age 50. In the UK, CII is now almost a commodity product. The
transition from South Africa to the UK was followed by exportations
to the Far East, Australia and Europe. I am told that, in Australia,
Critical Illness rider benefits are now almost a prerequisite for a
life insurance sale. Similar remarks apply to certain other markets. 4.
Technical Information. The
best-known actuarial paper relating to CII is titled ‘Dread
Disease Cover – An Actuarial Perspective’. The authors are
Alison DASH, MA, FIA and David GRIMSHAW, MA, FIA. It was presented
to the Staple Inn Actuarial Society in London in January 1990. At
the Warwick Conference, a committee report was presented on current
progress with the analysis of 1996 and 1997 CI incidence data
furnished by UK and Irish insurance companies. To date, data
relating to this period has been received from offices that have
experienced 4,221 CI claims. The committee is currently badgering
tardy offices to speed up data submission. Results will be
published by the committee and contrasted with those pertaining to
the period 1991-95, published earlier. The
standard British CI incidence rate table, IC94 was published in the
paper ‘Reserving for Critical Illness Guarantees’ a Report by
the Society of Actuaries in Ireland Working Party. Work is under way
to develop a new standard table. The
ongoing actuarial experience studies in the UK are very valuable. We
can expect that active critical illness insurers and new UK entrants
to this marketplace will be able to operate more competitively on
the basis of these tables. Note, however that there has been a time
lag of almost two decades from UK product introduction to the
emergence of credible useful UK industry experience. Here
in the USA we have no standard table of CI incidence and there is no
arrangement for insurance companies to submit data to a central
collecting agency, as is the case with mortality experience. The UK
experience is not applicable to coverage provided in the US. In the
US, substantive product introductions are only now commencing. Here
we face a decade or two of statistical scarcity until a credible
insured lives experience emerges: in the USA, meanwhile, we have to
employ eclectic methods of determining what insured Critical Illness
incidence rates are to be costed into our premiums. These eclectic
methods are the primary subject of today’s presentation entitled
‘Rate-making Secrets of Critical Illness’ insurance. The
US actuary who wishes to launch a new Critical Illness product,
nonetheless, suffers not from a lack of information, but from
an excess of it. More data is available than ever before – on the
web and elsewhere. However, the web surfer is wading through
treacle. Much of the material is repetitive and of doubtful
scientific validity.
Critical
illness refers to (diagnosis of) various severe medical conditions
of which the most commonly referenced are cancer, heart attack and
stroke. Numerous other conditions such as renal failure, organ
transplant or heart surgery may be included. Critical
illness (dread disease) insurance products may be free-standing (
i.e. the benefit is payable on dread disease diagnosis only) or
combined with life and/or savings products. In combined form, the
benefit is payable on the first of dread disease diagnosis,
attainment of a specified age or death. This form of benefit is
referred to as an ‘acceleration benefit’.
6. Less Generally Known Ratemaking Ideas. The
actuary deriving rates for critical illness insurance products will
consider both stand-alone benefits and CII (acceleration) riders to
existing life policies. For the latter, he (or she) must have regard
not only to incidence rates but also CI death rates (to avoid double
counting this risk). The
annual cash flow cost of a life insurance accelerated on critical
illness is represented by the formula:
where
x references the year of age x to x+1, the term on the left hand
side is the unit cash flow cost, the first term on the right hand
side is the critical incidence rate at age x and the second term on
the right hand side represents the product of the familiar mortality
rate and 1 minus the proportion of deaths that are expected to occur
in the year following age x that will be diagnosed as being caused
by critical illness. 7.
Calculational and Programming Problems. Critical
illness calculations will involve handling multi-dimensional
matrices. So it is important to select a language - such as APL–
that handles such objects easily. It is necessary to calculate many
values by iteration, resulting in lengthy run times. As a guide to
your computing requirements, even if you use a (symbolically)
concise language such as APL, a suitable critical illness incidence
and premium calculational system will require at least 18,000 lines
of code. Windows 95 is liable to crash during lengthy runs through
such program suites – Windows NT and Windows 98 are to be
preferred, being more stable operating environments. You should be
aware that, as far as we can tell, no currently available robust
commercial software exists that will cope with the multi-state model
underlying Critical Illness experience and modeling. Care
should be taken in using life insurance pricing software for pricing
Critical Illness, since rough and ready approximations can only be
used for very simple CI products. 8. Practical
Considerations in Obtaining Critical Illness Incidence Rates. There
are many clinical studies of a large variety of diseases and disease
conditions. However clinical studies generally focus on
experience following diagnosis of a particular disease condition,
primarily for the purpose of evaluating treatment. Not many
studies focus on the incidence of critical illnesses. A
registry program of some sort is necessary to gather meaningful
information on incidence rates. Both in the United States and
worldwide there are excellent registry programs for cancer.
The National Cancer Institute administers its SEER registry program
on a nationwide basis in the United States and provides statistics
on a regular basis. With the exception of the Framingham Study
(of heart attack and stroke incidence), this is not the case for
other disease categories that would normally be insured for critical
illness.
The
SEER Cancer Program provides a wealth of information on incidence
rates, mortality rates and survival rates for all types of cancer. SEER
is the Surveillance, Epidemiology, and End Results Program that is
based within the Cancer Control Research Program at the National
Cancer Institute (NCI). The National Cancer Act of 1971
mandated the collection, analysis and dissemination of data useful
in the prevention, diagnosis and treatment of cancer. This
mandate led to the establishment of the SEER Program. A
continuing project of the NCI, the SEER Program collects cancer data
on a routine basis from designated population-based cancer
registries in various areas of the country. Trends in cancer
incidence, mortality and patient survival in the United States are
derived from this database. Data from the eleven SEER geographic
areas used in the SEER study reports represent an estimated 13.9
percent of the United States population. The said eleven areas
were selected primarily for their ability to reliably operate and
maintain a population-based cancer reporting system and for their
epidemiologically significant population subgroups. With
respect to selected demographic and epidemiological factors, they
are reasonably representative subsets of the United States
population. The
SEER Cancer Statistics Review (CSR), containing the most recent
cancer incidence, mortality and survival statistics, is made
available by NCI annually. Data are presented for a wide spectrum of
cancers. All incidence and mortality rates are age-adjusted to
minimize the effect of a difference in age distributions when making
comparisons. Data relating to In Situ cancers is also provided. The
SEER Program is conducted under contract with non-profit, medically
oriented organizations having statutory responsibility for
registering diagnosis of cancer among residents of their respective
geographic coverage areas. These contractors submit a computer
tape to NCI twice each year containing data on all reportable
diagnoses of cancer. The
SEER reports identify 41 separate cancer sites plus an "all
other" sites category. Data on incidence, mortality and
survival rates for invasive cancers is provided individually for 23
separate sites, or site groupings. The report includes data for
invasive cancers for all sites combined as well. The
most recent SEER data incorporates the year 1996 and is available on
CD-ROM. The
actuary practicing in the CI field must have regard to the
definition of CI his client is employing when analyzing cancer
statistics. For example, only ‘life-threatening’ cancers may be
covered by the chosen definition. If the derived incidence rate is
not in close correspondence with the insured definition of cancer,
the derived rates will not be usable for pricing or reserving. 10.
Specifics of Heart and Stroke Incidence Rates. Whereas
the SEER cancer program is comprehensive and data rich, no
comparable system exists in the US for the surveillance of the
epidemiology of heart attacks and strokes. The information furnished
by the American Heart Association (AHA) is too sketchy to be of use
in determining incidence rates. The
Framingham Study was organized under the auspices of the National
Heart Institute 1949. An objective of the study was to determine the
incidence of coronary heart disease by age and sex with sufficient
reliability so these figures might be applicable to other areas of
the US. The most authoritative published work on the Framingham
Study is The Framingham Study - The Epidemiology of Atherosclerotic
Disease, by Thomas Royle DAWBER, Harvard University Press 1980. The
general plan of the study was to select a reasonably stable
population of adults who would vary in the characteristics believed
to be related to heart disease. It was the documented intention of
the study that “An initial examination would be carried out to
determine the presence of any stigmata of existing disease."
Subjects free of such stigmata would be followed for a (then
proposed) period of 20 years, to determine which of them would
"…eventually develop coronary heart disease. During the study
period an effort would be made to characterize each of the subjects
with regard to a number of bodily traits, life habits or other
factors believed to relate in any way to the eventual development of
this disease." Among
numerous other details, the study furnishes numerical data relating
to myocardial infarction and CVA obtained from the study cohort
experience years1949 to 1974. The
numbers provided by the study indicate a steady progression of
cardiovascular disease incidence rates with age in respect of males.
The study reported that a cohort of lives was examined over a
24-year period (at two-yearly intervals). The number of the starting
male and female lives in the cohort as tabulated is 5,172. The
Framingham statisticians define the "crude rate" as
"the number of cases developing from the number of subjects
studied" and describes the "corrected rate" as the
crude rate, adjusted for persons who are removed from risk during
the observation period. This concept corresponds to the concept of
Pollardization, discussed later. 11.
Some specifics of Organ Transplants. Bone
marrow transplants, in the vast majority of cases, follow incidences
of cancer. Thus, if you cover cancer, as the policies almost
invariably do, addition of a charge for bone-marrow transplants is
considered inappropriate, since the cost of cancer incidence is
included in the rates before addition of the transplant claim costs.
Premiums
appropriate for organ transplants should, therefore be based on
discernable Hard Organ Transplant incidences. Hard
Organ Transplant rates can be derived on the basis of statistics
available from UNOS, the United Network for Organ Sharing, in
Richmond, Virginia. UNOS administers the national Organ Procurement
and Transplantation Network (OPTN) and the U.S. Scientific Registry
on Organ Transplantation under contracts with the U.S. Department of
Health and Human Services. The U.S. Scientific Registry is the most
complete medical database in the world. If
you cover kidney transplants, they may be costed under End Stage
Renal Disease (ESRD), hence they should not be included in hard
organ transplant costs. Since
Hard Organ Transplant rates are much higher for men, it is suggested
that you test your final population incidence rates against other
demographic parameters before you obtain rates suitable for your
insured portfolio. 12.
Some specifics of End Stage Renal (kidney) Disease (ESRD) Medicare
statistics relating to ESRD provide a fruitful first step in
deriving ESRD rates. ESRD
experience is sensitive to demographic parameters such as sex and
ethnicity. Translation of these types of rates to insured portfolios
poses a modeling challenge. 13.
Some specifics of Heart Surgery. Heart
Surgery generally means Coronary Bypass, Heart Valve and Aorta Graft
Surgery, but your company’s specific definitions will govern. The
use of coronary bypass surgery as a prophylactic measure against
first heart attacks differs widely from continent to continent. It
should be noted that Dash & Grimshaw, in their development of UK
CI incidence rates, make no charge for coronary artery surgery.
The authors simply accept that all coronary artery surgery will
follow a heart attack. Such reasoning may be correct when
applied to UK risks; however, in the US, coronary bypass surgery is
commonly performed before first infarction to prevent a
life-threatening incidence. Thus the Dash & Grimshaw approach is
likely to underestimate US costs. There
is insufficient US information relating to the cost of the benefit
when incorporated in a US critical illness insurance policy. A
reasonable method of deriving age specific heart surgery rates would
be to relate such statistics as are available statistics to the much
more reliable population heart attack incidence rates and then to
true up overall population incidences in accordance with demographic
data, finally comparing overall incidence with foreign norms. The
reasoning is that the relationship between overall MI experience and
heart surgery experience should be similar between countries with
similar medical funding facilities. On useful norm is provided by
South African insured lives, who enjoy approximately the same levels
of medical care as US lives, under privately funded medical care. 14.
Some specifics of Loss of Sight. Hearing, Speech, Limbs and
Paralysis. There
are almost no useful statistics available relating to these
conditions taken individually. Taken together, however, the
conditions are a good part of the experience one would have if one
were to sell a lump sum disability benefit. Lump
sum disability insurance generally pays a face amount on the
occurrence of total and permanent disability. In the USA, lump sum
disability insurance is nowadays less popular because of the
conflict between the restrictive definitions needed to underwrite
this business profitably and the liberal conditions demanded by the
market place. Nevertheless, reasonably reliable lump sum statistics
pertaining to the US are available. Lump
Sum Table disability incidence rates contain a component for causes
of disability that are not attributable to blindness, deafness, loss
of speech or loss of use of limbs (including any type of paralysis).
Such causes would include Multiple Sclerosis, brain damage,
orthopedic and arthritic ailments including rheumatoid arthritis and
osteoarthritis, connective tissue disorders such as Lupus
Erythematosus, non-paralyzing spinal disorders, severe asthma and
other pulmonary disorders, many nervous conditions and mental
disorders as well as circulatory
maladies not attributable to heart attack or stroke. Lump
Sum Table experience includes an embedded measure of malingering and
dishonesty among insureds. As mentioned before, however, the
considered conditions are precisely those that cannot readily be
fraudulently presented as claim events! Nevertheless,
Lump sum Table experience offers an excellent starting point for the
derivation of the required incidence rates. Judicious elimination of
double counting and sensible graduation and adjustment should enable
practitioners to derive useful estimates on this basis. 15. Some Specifics
on Critical Illness Death Rates. Data
in respect of insured lives is to be found in the SOA 1983-87 Study.
This gives figures for only a limited range of causes. Population
data is available from the National Center for Health Statistics (NCHS)
presents the Report of Final Mortality Statistics for each calendar
year Data shown in this report are based on information from
all death certificates filed in the 50 States and the District of
Columbia. It is believed that more than 99 percent of deaths
occurring in this country are registered. Causes of death
presented in this report are classified in accordance with the Ninth
Revision of the International Classification of Diseases (ICD-9).
From this information we may derive age specific population
proportions of deaths by cause. A
note of caution must be inserted when interpreting mortality
statistics by cause of death. Clearly, CI weakens a body, leaving it
more vulnerable to further CI assaults and to attacks by
opportunistic infections. Thus the sufferer may be recorded as dying
from another cause when the underlying reason was CI. Further,
doctors are frequently influenced not to note certain conditions –
including cancer – as the cause of death. 16. Some
Specifics on graduation of raw cancer, heart attack and stroke
rates. Once
derived, US population cancer incidence rates must be adjusted to an
insured lives basis (i.e. applicable to assureds free of prior
cancer incidence). To re-base the figures to apply to a population
free of prior cancer, we employ the method pioneered by the
Australian actuary, A.H. Pollard FIA. (See paper ‘The Interaction
between Morbidity and Mortality’ by A.H. Pollard PhD FIA detailed
in the bibliography.) ‘Pollardization’ describes the removal
from the data of critical illness victims to obtain figures
pertaining to a population free of prior critical illness. This
process is simple at low incidence rates but prone to error as
incidence rates mount towards 10% per annum at the old ages.
Problems arise due to second and subsequent incidences incorporated
in the population data – regarding which few reliable statistics
are available. Raw cancer rates from SEER require Pollardization.
The denominator in SEER rate fractions is the entire population (of
relevant age, sex etc) including those already suffering from
cancer. The numerator must be replaced with the corresponding
population free of cancer. Pollardization
is performed by establishing a model population divided into two
components; healthy and sick; those free of e.g. cancer and those
who have been afflicted by it. The population at some young age is
assumed to be free of cancer and the raw (age and sex-specific)
population cancer rate may be applied to it to derive the youngest
sick and hence the surviving healthy. For each subsequent age, the
healthy are depleted by death and sickness, the sick are depleted by
death but incremented by the healthy who have fallen sick. When
populations of healthy and numbers falling sick have been
calculated, division yields Pollardized sickness incidence rates.
Critical to the process is the ability to apply differential death
rates to the sick and the population as a whole. The sick are
regarded as suffering all deaths from cancer plus the same rate of
mortality from other causes as the population as a whole. Framingham
population heart and stroke rates have already been Pollardized. The
shape of the Framingham data relating to males confirms that
atherosclerotic disease in males increases steadily with age.
The data suggests that atherosclerotic disease in males exhibits the
same type of progression with age as mortality. On the basis
of studies such as the Framingham study and on the basis of
plausible models of disease, scientific workers have come to believe
that chronic diseases such as cancer, diabetes and cardiovascular
diseases are associated with aging. The
Framingham data must be graduated to produce annual incidence rates
for all relevant ages. The
male heart attack and stroke figures may be graduated with a variant
of Makeham’s formula. Several sophisticated versions of
Makeham’s formula are available. While
the shape of the Framingham data relating to males could be readily
reconciled with a Makeham - type curve, a similar exercise working
with the female data was not possible. We believe that
the incompatibility of the female Framingham data with a Gompertz or
Makeham curve may be due to sparseness of the data (fewer women were
affected by atherosclerotic disease), and, possibly, a different
secular progression of atherosclerotic disease in women. A feasible
way of graduating the female Framingham experience is to use a
standard table. The only standard tables currently available are
obtainable from the Dash & Grimshaw paper or the IC94 table. 17.
An Alternative Approach: Lotter-Bayes. The
Lotter/Bayes method is an application by J.L. Lotter FIA of Bayes
Theorem to the derivation of critical illness incidence rates. This
note draws upon unpublished work by J.L. Lotter. Similar ideas are
implicit but not stated or developed in ‘Notes on Living Assurance
in South Africa’ by P.J. Davies FIA. (See bibliography.) Bayes
Theorem is derived in many actuarial and probability text books, in
particular: ‘Probability - An Intermediate Text-Book’ by M.T.L.
Bizley FIA. (See bibliography) The
overhead projection furnishes a concise statement of the Lotter-Bayes
formulae. Convergence
from the initial set of Bayesian priors to the final calculated
values will be rapid if the initial Bayesian priors are well-chosen.
If the priors are very different from the actual incidence rates,
convergence may not take place at all! Thus,
as with the Pollard methodology, it is necessary to make an
assumption as to the mortality of these lives from other causes. 18.
Critical Illness Trends. Morbidity
(by cause) changes more rapidly over time than mortality; the
relationship between the two is complex. For example, the
encouraging decline in coronary heart disease witnessed in the US
over the last 30 years is due in great part to the improved survival
of sufferers. Different
critical causes change at different rates and in different
directions. Impact
of new medical technology and patient management practice differs by
critical cause. Public
health measures and media discussion impact trends. Consider the
publicity about the links between smoking and lung cancer and
between lifestyle and heart disease. Critical
illness insurance began, in the US as elsewhere, as insurance
against the ‘big three’; cancer, heart attack and stroke.
Competition breeds product differentiation which leads to escalating
numbers of conditions – up to 41 in the UK – being covered and a
weakening of claim definitions. 19.
International Comparisons. It
is unwise to use foreign critical illness data unless possessed of
extensive knowledge of the country. For example, the extensive UK
CII experience pertains to a population enjoying (basic!) public
medical provision. In some other countries, CII can be taken out as
a form of catastrophic medical expense insurance. South African
heart attack experience is notoriously higher than elsewhere. Though
death is the same around the world, yet even so we hear of people
living to unlikely ages in remote areas. Variations in morbidity
patterns are far greater than variations in mortality. Climate,
diet, public hygiene and general lifestyles have their impact. Legislation
and public health measures have differential impact. While in the US
we stress heroic treatment of sufferers after dread disease
incidence, other countries concentrate on public health measures to
reduce disease incidence. Impact
of public and private medical expense and disability insurance plans
affect the statistics. Are doctors paid per patient or paid
for work done? The
US rations medical care by ability to pay; other countries ration by
queuing. Nonetheless,
in the young US CII marketplace, it is instructive to compare US CI
incidence rates with foreign tables. The best known is that in the
paper ‘Dread Disease Cover – An Actuarial Perspective’ by
Alison DASH MA FIA and David GRIMSHAW MA FIA presented to the
Staple Inn Actuarial Society in January 1990. This table illustrates
the need to treat foreign data with care, rates at the higher ages
being substantially lower than many would think prudent for the USA. The
reserving table styled IC94 is frequently used in the UK; it may be
found in the paper ‘Reserving for Critical Illness Guarantees’
being a Report by the Society of Actuaries in Ireland Working Party
presented to the Society on 30th November 1994. The
Actuarial Society of South Africa Continuous Statistical
Investigations Committee Dread Disease Investigation 1991-1994
(published December 1997) merits study not only as the most
exhaustively-analyzed CII experience but also because it is derived
from insureds similarly placed in respect of medical services to our
customers in the US. (The UK system of public medical provision
significantly impacts sickness statistics there, as a perusal of the
Dash and Grimshaw paper will reveal.) 20.
Conclusion. Since
the invention of life assurance, the greatest innovation has been
policies which pay benefits while the insured is still alive. Human
nature being what it is, these are easier to sell! If
media are to be believed, we will soon have the technology to make
all children tall, lean, muscular and with 20/20 vision. Our
descendants will look like the cast of ‘Baywatch’. Meanwhile,
for those of us who are horizontally challenged, lazy and stressed,
critical illness insurance is the wave of the future – and
there is no fighting it. “Critical
illness is like a bill you cannot pay – without insurance.” Remark
during an actuarial conference at the University of Warwick.
|
