What is the optimal age for starting lipid lowering treatment? A mathematical modelBMJ 2000; 320 doi: https://doi.org/10.1136/bmj.320.7242.1134 (Published 22 April 2000) Cite this as: BMJ 2000;320:1134
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EDITOR - We find the important article by Ulrich et al(1) erroneous on a particular point. In short, the error is using average instead of incremental cost-effectiveness as a criterion.
One sums up the resources spent on producing any medical treatment with one variable, the money spent on that treatment. Suppose that one could also sum up the health effects of any treatment with just one variable, "the health effect" (HE). To maximize the health effect given the money spent on medical treatment, the government should use the following principle. The first penny should go to the treatment that gives the highest HE for that penny. The next penny should go to the treatment among the remaining treatment possibilities that gives the highest HE for that penny. And so on. In this way the last penny spent would give a lower HE than any of the other pennies. We can call this lowest HE-value HE0.
The more money the government spends on medical treatment, the lower the value of HE0 will be. How much the government should spend is a political, not a scientific question. But to maximize the health effect, given the money spent, doctors must treat patients according to the principle above. This means that they should increase the amount of money spent on a given patient until one more penny would give a health effect lower than HE0.
The topic of Ulrich et al is lipid lowering drugs. Which patients should use these drugs, and at what age should they start using them? The table sums up an example from Ulrich et al. Ulrich et al measures health effects and costs as defined in the table. We can symbolize the "incremental effect per cost" in the table with I. Thus I is an example of the variable "the incremental health effect per penny" described above.
_________________________________________________________ Effects (years without coronary heart disease events gained per patient) and costs (years on lipid lowering drugs per patient) for various starting ages of lipid lowering drug therapy _____________________________________________________________________ Starting Effect Cost Effect Incr. Incr. A age (years)1(years)2 per cost3 effect cost (years)2 (years)2 _____________________________________________________________________ None 0 0 - - - 60 years 0.86 15.4 5.58/100 0.86 15.4 5.58/100 40 years 2.67 35.2 7.58/100 1.81 19.8 9.14/100 35 years 2.93 39.9 7.34/100 0.26 4.7 5.53/100 ______________________________________________________________________ A=Incremental effect per cost2 1 Values estimated from Ulrich et al (1) fig.3a 2 Calculated values 3 Values estimated from Ulrich et al (1) fig.3c
Suppose that the value analogous to HE0, I0, is I0 = 5%. The value I = 5.58% for start at age 60 compared to no treatment shows that age 60 is better than no treatment, since I > I0. Analogously, age 40 is better than age 60, and age 35 is better than age 40. So, given I0 = 5%, the patient should start treatment at age 35.
Suppose I0 = 6%. Then no treatment is better than age 60, and age 40 is better than age 35. The value of I for age 40 compared to no treatment is the same as the (average) effect per cost for age 40, I = 7.58%. So, given I0 = 6%, the patient should start treatment at age 40. In the same example, Ulrich et al chooses age 40 because this has the highest (average) effect per cost, 7.58%. Although arriving at a similar result, the above shows that their argumentation is erroneous. And, if I0 = 5% or 8%, the best alternatives are age 35 and no treatment, respectively.
We believe the model of Ulrich et al is an important improvement compared to current guidelines for the prescribing of lipid lowering drugs. If one wants to maximize the health effect as measured by the model, given the money spent, one should try to come to some consensus on how high I0 should be and use the model accordingly.
Another discussion of this can be found at
professor of clinical pharmacology
Department of Pharmacotherapeutics, University of Oslo, 1065 Blindern, N-0316 Oslo, Norway
Competing interests: None
1 Ulrich S, Hingorani AD, Martin J, Vallance P. What is the optimal age for starting lipid lowering treatment? A mathematical model. BMJ 2000;320:1134-40.
Competing interests: _________________________________________________________Effects (years without coronary heart disease events gainedper patient) and costs (years on lipid lowering drugsper patient) for various starting ages of lipid loweringdrug therapy _____________________________________________________________________ Starting Effect Cost Effect Incr. Incr. A age (years)1(years)2 per cost3 effect cost (years)2 (years)2 _____________________________________________________________________ None 0 0 - - -60 years 0.86 15.4 5.58/100 0.86 15.4 5.58/10040 years 2.67 35.2 7.58/100 1.81 19.8 9.14/10035 years 2.93 39.9 7.34/100 0.26 4.7 5.53/100______________________________________________________________________A=Incremental effect per cost21 Values estimated from Ulrich et al (1) fig.3a2 Calculated values3 Values estimated from Ulrich et al (1) fig.3c
Editor- Ulrich et al(1) have bravely attempted to tackle a problem
which has been quietly side-stepped for some time; namely that lipid
lowering does not (as far as we are aware) prevent coronary heart disease,
it merely postpones it. The concept of assessing the value of treatment
in terms of 'event free life years' is a useful one, but using a risk
calculator to estimate potential benefit is fraught with difficulty.
The authors base their calculation on the Framingham equation, in
common with most coronary risk calculators, and have made one particularly
common, but incorrect, assumption regarding age. With the publication of
the Framingham equation, Anderson et al(2) stated that the equation 'may
be used for estimating outcome probabilities over a range of 4 to 12 years
for persons aged 30 to 74 years'. Quoting calculated risks for ages 15 to
94 years is therefore clearly inappropriate. To attempt to recalculate
such risks using a pharmacologically lowered cholesterol is even less
Anderson's statement is also relevant to the notion of a '3% annual
risk' which cannot be reliably predicted by the Framingham equation
directly. The Joint British Guidelines(3) circumvent this by referring to
a '30% 10 year risk', which will in fact identify subjects whose initial
risk is less than 3% p.a. because the risk is higher in the later years.
Finally, it should be remembered that the equation is less reliable
at the extremes of any of the variables included, hence a very high
cholesterol in a young person should stimulate further clinical thought.
Ulrich et al illustrate calculated benefits of treatment for cholesterol
levels of 9 mmol/l and greater. Such individuals require proper
investigation of their dyslipidaema rather than a keyboard exercise to
(badly) estimate cardiovascular risk.
1. Ulrich S, Hingorani A D, Martin J, Vallance P. What is the
optimal age for starting lipid lowering treatment? A mathematical model.
2. Anderson K M, Odell P M, Wilson P W F, and Kannel W B. Cardiovascular
disease risk profiles. Am Heart J 1991;121:293-8.
3. Wood D et al. Joint British guidelines on prevention of coronary heart
disease in clinical practice. Heart 1998;80(Suppl 2):S1-S29.
Competing interests: No competing interests
Ulrich1 and colleagues’ mathematical model adds an extra dimension to the
current debate on assessing and managing coronary risk. Unfortunately, in
order to make their point, they stretch the Framingham risk equation2
beyond its age limits (35 - 70) and this is reflected in their unexpected
projection that a 15 year old with a moderately high risk factor profile
(for someone in middle age) has a 14% cumulative risk of CHD by the age of
45. They also fail to allow for the differences between smokers and non-
smokers in non-coronary mortality which would reduce the apparent benefit
of lipid lowering in smokers.
Using their model, but based on a starting age of 35 and using CHD-
free survival to age 65 rather than the end of life as an endpoint, I have
written a java applet to run over the internet at
http://medicine21.com/heartGP/ccrc.htm which allows users to explore the
model interactively. Changing the start and end points of the calculation
has the effect of shifting the “optimal age for starting treatment” to
around 45 from Ulrich’s 40 but the overall pattern is unchanged.
The idea of CHD-free life-years gained per year of treatment can be
converted into a simple measure of potential benefit to the individual of
CHD-free days gained per year of treatment. For instance for a 40 year old
female with systolic BP of 160 and total cholesterol:HDL cholesterol ratio
of 6, statin treatment to the age of 65 (assuming a 30% reduction in CHD
events3 would gain an average of 12 CHD-free days per year of treatment).
If she was a diabetic smoker the average gain would be around 38 days per
year. This simple representation of benefit may be useful in informing
both individual patients and the wider debate on who should receive
Sanquhar Health Centre, Dumfriesshire DG4 6BT
1.Ulrich S, Hingorani A, Martin J, Vallance P. What is the optimal
age for starting lipid lowering tratment? A mathematical model. BMJ
2. Anderson KM, Wilson WF, Odell PM, Kannel WB. An updated coronnary risk
profile. A statement for health professionals. Circulation 1991;83:356-62
3. Shepherd J, Cobbe SM, Ford I, et al for the West of Scotland Coronary
Prevention Group. Prevention of coronary heart disease with pravastatin in
men with hypercholesterolaemia. N Eng J Med 1995;333:1301-7
Competing interest: I am the author of FramPlus a shareware coronary
risk prediction programme.
Competing interests: No competing interests
EDITOR – The mathematical model for the optimal age to start lipid
lowering (read: statin) treatment by Ulrich et al (BMJ April 24 2000)
makes assumptions such as "Reducing cholesterol concentrations decreases
the risk of heart attacks and strokes ..." while it is implied that
statins are the drugs of choice –and that their use during many decades
can be economical, acceptable and safe.
The model ignores the fact there are societies (ex.: Sweden vs.
Lithuania) where 10% lower total and LDL cholesterol is correlated with
four times more coronary heart disease (CHD)(1), which points to the
existence of major confounders like antioxidants(1).
Another confounder is the amount of omega-3 fatty acid in the diet.
Increased omega-3 is linked to an about 70% reduction in CHD deaths in the
Lyon Diet Heart Study --and quoting from Dr. Leaf's editorial regarding
this study(2): "... relatively simple dietary changes achieved greater
reductions in risk of all-cause and coronary heart disease mortality ...
than any of the cholesterol - lowering studies to date. This is
emphasized by the finding that the unprecedented reduction in CHD was not
associated with differences in total cholesterol levels...". In this
case, the main treatment difference was an increase in omega-3's from a
margarine containing the equivalent of two table spoons of canola oil per
The presence of such confounders and of others like homocysteine and
inflammation that are outside the cholesterol lowering paradigm may well
invalidate the mathematical model presented.
The article finally ignores the existence of niacin as an economical
blood lipid altering drug with a proven mortality lowering track record
(3). Generic niacin is about 10 times cheaper than a statin while the
slightly more expensive no-flush inositol hexaniacinate is as easy to take
as any statin.
Cholesterol-level based models are further complicated by the fact
that statins and niacin have roles other than in lowering lipids. These
roles may well have important short and long term effects on heart disease
The mathematical model presented is interesting but there are many
less "invasive" and less expensive alternatives that should be explored
before a substantial part the population is placed on statins, a strategy
that threatens to deplete the financial resources of patients and health
(1) Kristenson M et al, Antioxidant state and mortality from coronary
heart disease in Lithuanian and Swedish men: concomitant cross sectional
study of men aged 50. BMJ 1997; (314): 629-33.
(2) Leaf A, Dietary Prevention of Coronary Heart Disease. Circ;
1999; 99: 733-5.
(3) Canner PL et al, Fifteen year mortality in Coronary Drug Project
patients: long-term benefit with niacin. J Am Coll Cardiol 1986; (6):1245
Competing interests: No competing interests
I read with great interest Ulrich and colleagues’ mathematical
modelling to decide on the optimal age to start lipid lowering treatment.
This report was based inevitably on data obtained from population studies,
and hence it is difficult to know how applicable the suggestions are to
the individual. In other words, when faced with a patient in the clinic,
it is difficult to answer a question such as this, “How do you know this
treatment will benefit me as an individual?” Also, it was not evident that
adverse drug effects were considered in the model.
It is common practice that risk factors are considered detached from
“actual” pathophysiology, when it is the disease process that we are
trying to alter at least in the context of primary prevention. Since
myocardial infarction is essentially a vascular disease, it makes sense to
decide treatment on the vascular state. There is mounting research
evidence suggesting that endothelial dysfunction is the precursor to
vascular diseases. Individuals with endothelial dysfunction regardless of
risk factors should therefore be identified for preventative measures,
including drug treatment. Of course, it follows that the more risk factors
one have the more likely that endothelial dysfunction is present. At least
this approach will spare individuals with borderline risk profile but with
normal vascular state from unnecessary treatment. What is urgently needed
is a way of assessing the vascular state quantitatively and non-
invasively, allowing repeat measures to be taken to judge progress.
Currently, we are debating when to start treatment, and once started, we
hope that we have done the right thing for our patients, but for them,
they can only find out after they have lived their life on a pill. In a
way, taking a statin for primary prevention is analogous to buying an
Competing interests: No competing interests