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The Actuary The magazine of the Institute & Faculty of Actuaries
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New drugs, old drugs, and expected future lifetime

Newspaper headlines announcing a
new ‘wonder drug’ or previously
unimagined properties of last
year’s wonder drug are a regular
occurrence. If 2006 was the year of Herceptin,
with headlines such as ‘Cancer victim loses
court fight over Herceptin’(1), ‘Herceptin wins
UK licence’(2), and ‘Postcode lottery cure scandal’(
3), then every year seems to be the year of
statins: ‘A new pill for all ills’(4), ‘Wider use of
statins could save thousands of lives’(5), ‘Could
the heart disease “wonder drug” save your
life?’(6), and ‘Statins benefits revealed’(7).
Actuaries need to be aware of these advances
since, together with changes in lifestyle, new
drugs are a major underlying cause of increasing
life expectancy. A few years ago the Social Policy
Board set up the grandly named Actuaries’ Panel
on Medical Advances (APMA) to investigate
these developments. In this article we summarise
some of APMA’s work relating to Herceptin
and statins. This work will be presented at a
Faculty of Actuaries sessional meeting in Edinburgh
on 14 January 2008, and the paper for
that meeting will contain full details of the
models and calculations discussed in this article.
Herceptin
Herceptin is the brand name of Trastuzumab, a
drug designed to treat certain types of breast
cancer (BC). These types of BC are known as
HER2-positive and they account for about 25%
of all BC cases in the UK. Herceptin was initially
licensed to treat advanced cases of HER2-
positive BC, but following a high-profile campaign
it was licensed in 2006 for treatment of
early-stage HER2-positive BC. The model illustrated
in figure 1 can help us measure the effect
of Herceptin on expected future lifetime.
The model has four states, labelled 03, with
‘healthy’ representing ‘not (yet) diagnosed with
BC’. For simplicity we will assume the intensities
for transitions between the states, denoted
?ij
x, depend only on the woman’s current age, x,
and so this is a Markov model. To parameterise
this model we need functions for the ?ij
xs. This
requires a set of assumptions, some of which are
more heroic than others! Having made these assumptions we can do some calculations.
Table 1 shows the expected future lifetime for
a woman diagnosed with BC at different ages.
The values shown for those diagnosed with
HER2-positive BC assume treatment with Herceptin.
Without Herceptin, the expected future
lifetimes from a given age at diagnosis with
HER2-positive BC would be the same as those
shown in table 1 for HER2-negative BC, and so
the difference in expected future lifetime is one
measure of the benefit of Herceptin.
The benefits of Herceptin for women with
HER2-positive BC are clear from table 1
assuming our modelling assumptions are reasonable.
What about its effect on women in
general? One way of assessing this is to consider
level premium rates for term insurance from
ages 20, 30 and 40 up to age 65 for women who
have not (yet) been diagnosed with BC. We can
calculate these rates assuming Herceptin is not
available and then assuming it is available. The
difference will give an indication of the impact
of the availability of Herceptin over the corresponding
age range. The maximum difference in
these premium rates is of the order of just 1%.
A key assumption in our calculations is that
the effect of Herceptin is to reduce the force
of mortality by a factor 0.727, so that
?13
x = 0.727 × ?23
x. The factor 0.727 comes from
a study of survival rates for BC cases that has so
far lasted only three years, but we have assumed
it is valid at all ages indefinitely into the future.
We could do some sensitivity tests, assuming,
for example, that the beneficial effect of Herceptin
lasts for only five years, but any such
assumptions would be pure guesswork.
This illustrates one of the difficulties of trying
to assess the long-term effects of medical breakthroughs
by their very nature, reliable data for
the long-term effects do not exist.
A point to note is that Herceptin has a marked
effect on the life expectancy of a woman diagnosed
with breast cancer (table 1) but a much
smaller effect on the general population. This is
not surprising since most healthy women aged
20, 30 or 40 will never be diagnosed with breast
cancer and so the effect of Herceptin on their life
expectancy is much less dramatic than it is for
a woman diagnosed with HER2-positive BC.
Statins
Now let us turn our attention to statins. Statins
are a class of drug designed to lower cholesterol
levels. In particular, they lower the level of low
density lipoprotein (LDL), the so-called ‘bad
cholesterol’, which is a major risk factor for heart
disease. The first statins were licensed in the UK
in the late 1980s and they have been developing,
and hitting the headlines, ever since.
To model the effect of statins on life expectancy
we need a model for ischaemic heart disease
(IHD) that incorporates the development of
risk factors for IHD, particularly high cholesterol.
The model is shown in figure 2. It is a Markov
model so that the probability of any future transition depends only on the current state
and the individual’s current age. The model
includes stroke as well as IHD since not only do
IHD and stroke have many risk factors in common,
such as obesity and smoking, but also,
curiously, statins have the effect of lowering the
incidence rates for stroke even though high
cholesterol is not a major risk factor for stroke.
Figure 2 is deceptively simple. The ‘no IHD or
stroke’ state actually consists of 160 separate
states, one for each combination of categories
for diabetes (two), body mass index (five), LDL
(four), and hypertension (four); and for each of
these 160 combinations the ‘IHD and/or stroke’
state consists of 10 separate states: myocardial
infarction, transient ischaemic attack, hard
stroke and so on. In total the model has 1,761
states, 160 × (1 + 10) + 1, where the final state
is ‘dead’. The model is parameterised separately
for the two sexes, and allows deterministically
for different smoking patterns throughout life.
Decisions on when drugs should be prescribed
are taken on the basis of their medical benefits,
any possible side effects and costs. Such decisions
can be controversial, as was the case for Herceptin.
Prescription protocols for statins are based
on the individual’s level of LDL and the risk of
heart disease. It has been suggested that statins
should be prescribed for all men over age 50 and
all women over age 60 (8). This may smack of
‘mass medication’ but it has some merits given
that age is itself one of the major risk factors for
heart disease, and given that statins lower LDL
and the risk of heart disease and stroke whether
or not the initial level of LDL is high.
In table 2 we show the expected future lifetime
from age 20 assuming statins are not available,
and then assuming statins are taken by all
men from age 50 and by all women from age
60. Figures are shown for males and females,
both for individuals who have never and will
never smoke, and for individuals who will
smoke from age 20 for the rest of their lives.
Obesity and smoking
The model for heart disease and stroke allows
for the development of the important risk factors
obesity, diabetes and hypertension, as
well as high LDL and includes smoking habits.
We can therefore use it to assess the impact of
changing patterns of these risk factors on
expected future lifetime and on the future
prevalence of heart disease and stroke. Increasing
prevalence of obesity has received considerable
public attention in recent years, and
APMA has focused part of its efforts on quantifying
the likely effects of these changes. This
part of APMA’s work will be presented at the
sessional meeting on 14 January. Change in smoking habits is also a topical
issue given the bans on smoking in enclosed
public places introduced in the Republic of Ireland
(2004), Scotland (2006), and England and
Wales (2007). The figures in table 2 confirm
what is already well known: smoking reduces
your expected future lifetime. There is some
good news for smokers: no matter how long
you have smoked, it’s never too late to give up.
Table 3 shows values for the expected future lifetime
from age 20 for someone who is a current
smoker at age 20 and who either stops smoking
immediately or who stops at age 40, 60 or 80,
if they survive to that age, and then never
smokes again. These figures are all less than the
expected future lifetime for a 20-year old who
never smokes 58.6 and 62.4 years for males
and females, respectively but they are all
greater than the values for someone who never
gives up 51.6 and 56.1 years for males and
females, respectively.
It’s an interesting observation that giving up
an old drug, tobacco, at any age has a greater
impact on expected future lifetime than either
of the new drugs, Herceptin and statins. References (1) The Independent 15 February 2006
(http://news.independent.co.uk/uk/legal
/article345591.ece)
(2) The Sun 24 May 2006 (www.thesun.co.uk
/sol/homepage/news/article49405.ece)
(3) The Sun 28 September 2007
(www.thesun.co.uk/sol/homepage/woman
/health/health/article65048.ece)
(4) The Independent 26 April 2004 (http://news
.independent.co.uk/health/article57682.ece)
(5) The Independent 27 September 2005 (http://news
.independent.co.uk/health/article315325.ece)
(6) The Mirror 26 January 2006 (www.mirror
.co.uk/archive/2006/01/26/could-the-heart
-disease-wonder-drug-save-your-life-89520
-16629124)
(7) The Guardian 11 October 2007 (www.guardian
.co.uk/uklatest/story/0,,-6987763,00.html)
(8) The Times 28 July 2007 (www.timesonline
.co.uk/tol/news/uk/health/article2155500.ece)

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