1 A MODEL FOR ISCHAEMIC HEART DISEASE AND STROKE III: APPLICATIONS By T. Chatterjee, A. S. Macdonald and H. R. Waters abstract This is the third in a series of three papers. In the first paper we describe a comprehensive stochastic model of an individual s lifetime that includes diagnosis with ischaemic heart disease and stroke and also the development of the major risk factors for these conditions. The second paper discusses in some detail models for changes in body mass index (BMI) and also the effects of these changes, in particular the current trend towards increasing prevalence of obesity, on diabetes, cardiovascular diseases and expected future lifetime. This paper is devoted to the following applications of the model described in the first paper: (a) quantifying the effects of smoking and of changes in smoking habits, and, (b) quantifying the effects of treatment with statins (drugs designed to lower cholesterol). keywords Diabetes, Framingham Heart Study, hypercholesterolaemia, hypertension, ischaemic heart disease, Markov model, mortality, smoking, statins, stroke.
2 1. Introduction This paper is the third in a series of three papers. In the first paper, Chatterjee et al. (2007a), we describe the structure and parameterisation of a stochastic model for an individual s lifetime, incorporating the occurrence of ischaemic heart disease (IHD) and stroke and the development of the following major risk factors for these events: (a) Age, (b) Sex, (c) Smoking, (d) Body Mass Index (BMI), (e) Diabetes, (f) Hypertension, and, (g) Hypercholesterolaemia. The model is a continuous-time, finite-state-space Markov model. Age is the continuous variable which plays the rôle of time. Sex and Smoking are deterministic factors, so that we assume we know an individual s smoking status throughout his/her life. The remaining risk factors, (d) to (g), are discretised into a small number of categories between which our individual can move. In the second paper in the series, Chatterjee et al. (2007b), we discuss in detail three models for changes in an individual s BMI and the effects of these changes on the prevalence of diabetes and cardiovascular diseases and on life expectancy. These models, labelled Models I, II and III, can be summarised as follows: Model I: This is parameterised using data from the Framingham Heart Study, Offspring & Spouses Cohort (OS) data, with the parameters adjusted so that the model produces prevalence rates for BMI categories at adult ages which match those of the population of England in 2003 as given by Sproston & Primatesta (2004). Model I does not allow for changes in the prevalence of obesity over calendar time. Model II: This is an adjusted version of Model I which allows for the intensities of moving to higher categories of BMI to increase for 20 years starting from a given time point. The rate of increase is chosen to match the increase in obesity in England from 1994 to 2003. Model III: This is the same as Model II except that there is no time limit on increases in the transition intensities. The models predict future levels of obesity in increasing order, with Model III being the most extreme; starting with 20 year old males in 2003, Model III predicts that over 96% of those who survive to age 80 will be obese. The models predict, in the order I then II then III, increasing prevalence of diabetes and cardiovascular diseases and also decreasing future life expectancy. However, while the effects on the prevalence of diabetes are significant, the effects on cardiovascular diseases and future life expectancy are much less significant. See Chatterjee et al. (2007b) for details. In this paper we discuss applications of the model specified in the first paper, Chatterjee et al. (2007a) to: (a) quantifying the effects of smoking and of changes in smoking habits, and, (b) quantifying the effects of treatment with statins (drugs designed to lower cholesterol).
3 The effects in which we are interested are the prevalence of ischaemic heart disease (IHD) and stroke and future life expectancy. The model used in this paper incorporates Model I for changes in categories of BMI, rather than Models II or III. Since our main focus here is on IHD, stroke and future life expectancy, the choice of BMI model has little effect on our results and conclusions. In Section 2 we review the rôle of smoking in our model, calculate the prevalence of IHD and stroke for individuals with different smoking profiles and then calculate the effects on these quantities of smokers giving up smoking at given future ages. These last calculations are particularly relevant in view of recent bans on smoking in enclosed public places introduced in the Republic of Ireland (2004), Scotland (2006), England and Wales (2007) and in other territories. Hypercholesterolaemia is a major risk factor for IHD. See Stanner (2005). Statins are a class of drug designed to lower the level of cholesterol. They were first licenced in the UK in the late 1980s and increasingly prescribed through the 1990s into the present century. In Section 3 we describe the effect of statins on hypercholesterolaemia and hence on IHD. In Section 4 we discuss briefly current thresholds for recommending treatment for hypercholesterolaemia and in Section 5 we show results quantifying the effect of prescribing statins. Acknowledgements are given at the end of this paper. The full list of references for all three papers is included at the end of Chatterjee et al. (2007a). Further details of the research underlying this paper and its two companion papers can be found in Chatterjee (2007). 2. Smoking, IHD, stroke and future life expectancy 2.1 The effect of smoking on IHD, stroke and mortality Our model for an individual s future lifetime, as set out in Chatterjee et al (2007a), incorporates smoking in a number of different ways: (a) Smoking is a direct risk factor for myocardial infarction (MI). Current smokers have a relative risk of MI 3.436 times that of those who have never smoked. (b) Smoking is a direct risk factor for hard stroke (HS), but not for transient ischaemic attack (TIA). Current smokers have a relative risk of HS 2.158 times that of those who have never smoked. (c) Smoking is not a direct risk factor for diabetes, hypertension or hypercholesterolaemia. (d) Smoking does have a small effect on BMI: giving up smoking tends to increase BMI and resuming smoking tends to decrease BMI. (e) Independently of its effect on MI and HS, smoking is a direct risk factor for mortality. Current smokers have a relative risk of dying 1.766 times that of those who have never smoked. (f) The effects on MI, HS and mortality do not depend on sex, the number of cigarettes smoked or the number of years the individual smoked. See Chatterjee et al. (2007a) for details. The literature contains the following, not wholly consistent, points which, on balance, support our model in relation to the effect of smoking on IHD and stroke:
4 (i) The effects of smoking are both long and short term. Giving up smoking should, in principle, eliminate almost immediately the acute effects, but the atherosclerotic damage persists even after quitting. See Negri et al. (1994) and Lightwood and Glantz (1997). (ii) The odds ratio of acute MI for current smokers relative to non-smokers is 3.4. See Negri et al. (1994). (iii) The odds ratios for MI or coronary death among current smokers are 2.71 for men and 4.70 for women, compared to individuals who have never smoked. See Dobson et al. (1991). (iv) Cook et al. (1986) state that there is no trend in risk of IHD or stroke with the number of cigarettes smoked per day. This view is consistent with Lightwood and Glantz (1997), who modelled the effect of smoking, and of quitting, without taking account of the number of cigarettes smoked. However, Negri et al. (1994) found that the risk estimates for former smokers are higher at younger ages and directly related to the number of cigarettes smoked. (v) Men who have given up smoking in the last 5 years have a risk of IHD virtually identical to current smokers. The risk goes down to about twice that of never-smokers for men who have given up smoking for more than 5 years. But this risk does not go down further even after a 20-year follow-up. See Cook et al. (1986). (vi) The odds ratios of MI or coronary death among ex-smokers are similar to those of current smokers for the first year and then they decrease. After about 3 years the risk is not significantly elevated beyond that for never-smokers. See Dobson et al. (1991). (vii) The odds ratio of acute MI for ex-smokers relative to never-smokers is 1.4 for subjects who have given up smoking for one year, 1.5 for two to five years and 1.1 for six to ten years. The relative risk tends to decrease with the time since quitting and to become close to that of never-smokers after 10 years without smoking. See Negri et al. (1994). 2.2 The effect of giving up smoking The model set out in Chatterjee et al. (2007a) deals with individuals who never smoke and those who continue to smoke for the rest of their lives. We need to model the effects on IHD, stroke and mortality of giving up smoking. Our model for the relative risk of MI for current and ex smokers, relative to those who have never smoked, is as follows: and the model for the relative risk of HS is: RR(t) = (3.436 1.1)e t/1.592 + 1.1 (1) RR(t) = (2.158 1.1)e t/1.35 + 1.1 (2) where t is the time in years since giving up smoking. These models have exactly the same form as models proposed by Lightwood and Glantz (1997) in respect of acute MI and stroke, though some of our parameter values are different. Note that: (a) These models do not depend on sex, age, number of years as a smoker or the number of cigarettes smoked each day. This agrees with Lightwood and Glantz s model, except that their model for MI does depend on sex.
5 (b) The parameters 3.436 and 2.158 are taken from Chatterjee et al. (2007a, Table 9); they are the relative risks for current smokers estimated from the Framingham data and appropriate to the OS cohort. Lightwood and Glantz s values are 2.88 (MI, males), 3.85 (MI females) and 2.80 (stroke). (c) The parameter 1.1 for the residual effect on the relative risk of MI and HS of having smoked has been chosen taking account of Lightwood and Glantz s own values, (1.17 (MI, males), 1.40 (MI, females) and 1.42 (stroke)), the values reported in points (v), (vi) and (vii) above, and our own values for the relative risk for ex smokers estimated from the Framingham data. These last values, which do not take account of time since giving up smoking, are 1.054 (MI) and 1.227 (HS). (d) The parameters 1.592 and 1.35, which control the rate of decay of the relative risk, are taken directly from Lightwood and Glantz s model. Numerically, formulae (1) and (2) tell us that the relative risks of MI and HS for current and ex-smokers are: 1. independent of age, sex and all other explanatory variables, 2. higher by a factor 3.436 (resp. 2.158) for current smokers in respect of MI (resp. HS), 3. ultimately higher by a factor 1.1 for ex-smokers who stopped smoking a long time ago, 4. higher by factors 2.346, 1.765 and 1.455 in respect of MI (resp. 1.604, 1.340 and 1.215 for HS) for someone who stopped smoking 1, 2 or 3 years ago. Our model for the relative risk of mortality for current and ex-smokers is as follows: RR(t) = (exp(0.5689) 1.09)e 0.000322t4 + 1.09 (3) Apart from the parameter exp(0.5689) (= 1.7663), which is the relative risk of mortality for current smokers and is taken from Chatterjee et al. (2007a, Table 11), this formula has been chosen by fitting a curve to data in Kawachi et al. (1993). Details can be found in Chatterjee (2007). 2.3 Trends in the prevalence of smoking Table 1 shows the prevalence of smoking in the UK for selected years, split by sex and age band. The prevalence of smoking in the UK has declined slowly from 1974 to 2003. Table 2 shows the prevalence of current and ex-smokers in the UK in 2003 split by sex and the age at which they started smoking. A feature of Table 2 is that it indicates that almost all smokers start smoking before age 25. Many countries have imposed a ban on smoking in enclosed public places, among them the Republic of Ireland (2004), Scotland (2006), Wales (2007) and England (2007). The effect of the ban on the prevalence of smoking in the Republic of Ireland, introduced on 29 March 2004, can be seen in figures produced by The Office for Tobacco Control, OTC (2007). These figures, 12 month moving averages, show that the overall prevalence of smoking fell from around 25.5% when the ban was introduced, to a low point of just over 23% in February 2005, from where it has risen and stabilised at about 24.4% in June 2007. The effects on some age groups are very different from the overall pattern. The prevalence of smoking among those aged 15 to 18 rose sharply from February 2006 to 21.5% in June 2007 it had been a little over 18% in April 2004. For those aged 71+ the prevalence of smoking has dropped from around 13% when the ban was introduced to less than 10% in June 2007.
6 Table 1: Prevalence of smoking (%) in the UK. Source: Rickards (2003). Age 1974 1982 1992 1998 2000 2001 2002 2003 Male 16-19 42 31 29 30 30 25 22 27 20-24 52 41 39 41 35 40 37 38 25-34 56 40 34 38 39 38 36 38 35-49 55 40 32 33 31 31 29 32 50-59 53 42 28 28 27 26 27 26 60 and over 33 21 29 16 16 16 17 16 All aged 16 and over 51 38 29 30 29 28 27 28 Female 16-19 38 30 25 32 28 31 29 25 20-24 44 40 37 39 35 35 38 34 25-34 46 37 34 33 32 31 33 31 35-49 49 38 30 29 27 28 27 28 50-59 48 40 29 27 28 25 24 23 60 and over 26 23 19 16 15 17 14 14 All aged 16 and over 41 33 28 26 25 26 25 24 Table 2: Percentages of smokers and ex-smokers in 2003 in the UK, classified by age at which they started smoking regularly. Source: Rickards (2003). Age Current Smoker Ex Smoker Male Under 16 45 38 16-17 25 28 18-19 14 18 20-24 11 12 25 and over 5 4 Female Under 16 39 29 16-17 25 27 18-19 17 21 20-24 12 15 25 and over 7 8 It is clearly of interest to use our model to investigate the effect of smoking, particularly giving up smoking, on expected future lifetime and on the prevalence of IHD and stroke.
7 2.4 Numerical results Table 3 shows values for the expected future lifetime and the expected future Event free lifetime for males and females, starting from ages 20 and 40 for different smoking profiles. These profiles are Non-smokers (people who never smoke at any time), Current smokers (people who smoke from before age 20 and continue as smokers for their remaining lifetime) and Given up smoking (people who smoke from before age 20, give up smoking at the age indicated and then never smoke again). Event free future lifetime is the time until the diagnosis of IHD or HS or death, whichever occurs first. Table 4 shows the prevalence of IHD, HS and IHD or HS at ages 60 and 80 for starting ages 20 and 40 and for different smoking profiles. For both Tables 3 and 4 the starting population has an HSE 2003 profile (see Chatterjee et al. (2007a, Section 12.2) with the extra condition that for the Event free calculations in Table 3 and all the calculations in Table 4, they have not been diagnosed with either IHD or HS before the starting age of 20 or 40. Tables 3 and 4 show that: (a) Smoking reduces expected future lifetime (EFL) and expected future Event free lifetime considerably. For a male aged 20 the difference in EFL is 7.1 years and for a female aged 20 it is 6.3 years. (b) The prevalence of IHD and stroke at ages 60 and 80 is considerably greater for smokers than for those who never smoke. These facts are well known. What is perhaps more interesting is that giving up smoking, no matter how late in life, can significantly implove EFL and reduce the probability of IHD and/or stroke. For example, for females age 80 who smoked from before age 20 until they were 60 and then gave up, the percentage with IHD and/or stroke is 21.1, but among those still alive at age 80 who continued smoking until at least age 80, the percentage is 29.3.
8 Table 3: Effect of giving up smoking at different ages. Expected future lifetime from Expected future Event free lifetime Age 20 Age 40 Age 20 Age 40 Smoking profile Male Female Male Female Male Female Male Female Non smoker 58.58 62.42 39.32 43.03 53.23 58.19 34.01 38.97 Given up smoking at age 20 57.5 61.5 38.5 42.3 52.3 57.3 33.3 38.3 30 57.2 61.2 38.5 42.3 51.8 56.9 33.3 38.2 40 56.6 60.8 38.2 42.0 51.1 56.5 33.0 38.0 50 55.8 60.2 37.3 41.4 50.0 55.7 31.8 37.2 60 54.4 59.2 35.9 40.4 48.4 54.5 30.1 35.9 70 52.7 57.8 34.1 38.9 46.8 53.0 28.4 34.5 80 51.7 56.5 33.1 37.6 46.0 51.8 27.5 33.1 Current smoker 51.5 56.1 32.9 37.2 45.8 51.4 27.4 32.8
9 Table 4: Effect on prevalence of giving up smoking at different ages. Age 20 Age 40 Age 20 Age 40 Smoking profile Male Female Male Female Male Female Male Female Prevalence of IHD at age 60 Prevalence of IHD at age 80 Non smoker 8.7 4.6 8.7 4.5 22.4 13.8 22.5 13.9 Given up smoking at age 30 9.2 4.8 8.9 4.6 22.9 14.1 22.9 14.2 60 14.1 6.7 13.7 6.5 25.1 15.2 25.0 15.3 Current smoker 14.1 6.7 13.7 6.5 32.7 21.0 32.7 21.2 Prevalence of stroke at age 60 Prevalence of stroke at age 80 Non smoker 1.7 1.8 1.8 1.8 8.3 5.8 8.5 5.8 Given up smoking at age 30 1.9 2.1 1.9 1.9 8.9 6.1 9.0 6.1 60 3.1 3.3 3.0 3.1 9.3 6.7 9.3 6.7 Current smoker 3.1 3.3 3.0 3.1 14.6 9.7 14.7 9.7 Prevalence of IHD/stroke at age 60 Prevalence of IHD/stroke at age 80 Non smoker 10.2 6.2 10.2 6.1 29.8 18.9 29.9 19.0 Given up smoking at age 30 10.8 6.6 10.5 6.3 30.8 19.6 30.8 19.6 60 16.7 9.6 16.3 9.3 33.1 21.1 33.1 21.2 Current smoker 16.7 9.6 16.3 9.3 44.1 29.3 44.1 29.6
10 3. Statins Statins are drugs designed to lower cholesterol, in particular low density lipoprotein (LDL). They were first licenced for use in the UK in 1987 and have been developed at intervals since then, with one of the most recent, rosuvastatin, being licenced in the UK in 2003. They have attracted considerable attention in recent years in both the popular press and the medical literature. For example: A new pill for all ills. The Independent 26 April 2004. Wider use of statins could save thousands of lives. The Independent 27 September 2005. Could the heart disease wonder drug save your life? The Mirror 26 January 2006. A statin is one of the components of the Polypill proposed by Wald and Law (2003) in an article entitled A strategy to reduce cardiovascular disease by more than 80% published in the British Medical Journal. This article was the basis for an Editorial in the same issue of BMJ entitled The most important BMJ for 50 years? (Smith (2003)). The dose of the statin proposed for the Polypill would reduce LDL by 1.8 mmol/l (Wald and Law (2003)). While this reduction in LDL takes place very quickly within about 6 months the effect on IHD takes longer. Based on a meta analysis, Law et al. (2003) claim that the effect on fatal and non fatal MI of this reduction in LDL is a reduction in the relative risk of MI, as shown in Table 5, and that this relative reduction does not depend on the starting concentration of LDL. It should be noted that most of the studies included in this meta analysis lasted less than 5 years. Reliable data on the long term effects of statins, in particular for the most recently developed statins, are not yet available. Table 5: Percentage reduction in risk of fatal and non-fatal MI by duration of treatment. % Reduction in risk for Duration of treatment a reduction in LDL of 1.8 mmol/l 1st year 19 2nd year 39 3rd-5th years 51 6th and subsequent years 55 Law et al. (2003) also claim that statins have beneficial effects on stroke, with an immediate and lasting reduction of 17% in the relative risk of stroke for a 1.8 mmol/l reduction in LDL. This is interesting because hypercholesterolaemia is not a direct risk factor for stroke, see Chatterjee et al. (2007a, Section 9), though there is evidence in the literature that statins have benefits beyond lowering LDL. See Vaughan et al. (1996), Palinski (2001) and Wannamethee et al. (2000).
11 4. Treatment thresholds for hypercholesterolaemia Various thresholds have been proposed, and are used, to determine when to prescribe statins. These treatment thresholds are typically based on the concentration of LDL, the presence of other risk factors, for example smoking and diabetes, and the calculated risk of IHD over a given time period. See McElduff et al. (2006) for a survey of these protocols. McElduff et al. (2006) surveyed 1653 men aged between 49 and 65 to determine what percentage would be eligible for treatment with statins given each of five protocols. The answers ranged from 14% to 77%, with all but one protocol covering 58% or more of the surveyed population. Wald and Law (2003) propose that the Polypill should be taken by everyone over age 55. This has some justification since age is a major risk factor for IHD and stroke and since there are beneficial effects from taking statins whatever the initial concentration of LDL. A UK Government adviser, Professor Roger Boyle, has been reported as saying there are benefits in giving statins to all men over age 50 and all women over age 60 (Times (2007)), although he is also reported as saying that people are not yet ready for mass medication. 5. The effects of treatment with statins 5.1 Numerical results In this section we use the model described in the first paper in this series, Chatterjee et al. (2007a), to quantify the effect of statins on future expected lifetime and future expected event free lifetime, i.e. expected time until the first of IHD, stroke or death. To simplify the presentation, we use age as the threshold for treatment with statins. Calculations based on other thresholds can be found in Chatterjee (2007). We will assume initially that the effect of treatment with statins from any age is a reduction in the intensity of MI as shown in Table 5 and a reduction of 17% in the intensity of HS. The figures in Table 6 show the future expected lifetimes and future expected event free lifetimes from age 20 for males/females, non smokers/smokers assuming statins are not available ( Untreated ) and then assuming statins are taken by everyone reaching the different ages indicated ( Treated at age... ). The difference between the Treated at age... and Untreated figures measures the beneficial effect of statins. The starting point for these calculations is an HSE 2003 profile (assuming no prior IHD or stroke in the case of the event free calculations). The figures in Table 6 show that the benefits from taking statins are greater for men than for women and greater for smokers than for non smokers, i.e. greater for those at greater risk of IHD and stroke. The figures in Table 7 show the effects from age 50 of treatment with statins on future expected lifetime and future expected event free lifetime for different starting profiles relating to diabetes, hypercholesterolaemia and hypertension. In each case Low refers to the lowest and High to the highest category of the risk factor, as defined in Chatterjee et al. (2007a, Section 2). The starting point is an HSE 2003 profile in all respects except for the three risk factors and for the smoking pattern, as shown. These figures show in general terms that the benefits of statins are greater if the risk of IHD or stroke is higher.
12 Table 6: Effect of treatment with statins on expected future lifetime and expected future Event free lifetime from age 20 by age of treatment. Future Expected future lifetime from age 20 Male Female Never Smoked Current Smoker Never Smoked Current Smoker Treated from age 20 59.3 53.0 62.9 57.0 Treated from age 30 59.3 52.9 62.9 57.0 Treated from age 40 59.2 52.8 62.9 56.9 Treated from age 50 59.2 52.5 62.8 56.8 Treated from age 60 59.0 52.2 62.7 56.7 Untreated 58.6 51.6 62.4 56.1 Expected future event free lifetime from age 20 Male Female Never Smoked Current Smoker Never Smoked Current Smoker Treated from age 20 54.6 48.3 59.2 53.2 Treated from age 30 54.6 48.2 59.1 53.1 Treated from age 40 54.5 47.9 59.1 53.0 Treated from age 50 54.3 47.5 59.0 52.8 Treated from age 60 54.0 46.8 58.8 52.4 Untreated 53.2 45.8 58.2 51.4
13 Table 7: Effect of treatment with statins on expected future lifetime and expected future event free lifetime for individuals with different risk profiles from age 50. Expected future lifetime from age 50 Expected future event free lifetime from age 50 Male Female Male Female Never Current Never Current Never Current Never Current Diab. H Chol. H tens. Smoked Smoker Smoked Smoker Smoked Smoker Smoked Smoker Treated 31.3 26.2 34.5 29.6 28.1 23.1 31.9 26.9 Low Low Low Untreated 30.8 25.3 34.1 28.9 27.1 21.4 31.1 25.6 Difference 0.5 0.9 0.4 0.7 1.0 1.7 0.8 1.3 Treated 30.0 24.2 33.4 27.9 26.0 20.5 30.2 24.6 Low Low High Untreated 29.4 23.2 32.9 27.1 24.9 18.8 29.3 23.2 Difference 0.6 1.0 0.5 0.8 1.1 1.7 0.9 1.4 Treated 31.3 26.1 34.4 29.5 27.8 22.6 31.7 26.6 Low High Low Untreated 30.7 25.0 34.0 28.7 26.6 20.6 30.8 25.1 Difference 0.6 1.1 0.4 0.8 1.2 2.0 0.9 1.5 Treated 30.3 25.0 33.6 28.5 27.1 21.8 30.9 25.8 High Low Low Untreated 29.8 24.0 33.2 27.7 25.9 20.0 30.1 24.3 Difference 0.5 1.0 0.4 0.8 1.2 1.8 0.8 1.5 Treated 29.9 24.0 33.3 27.8 25.7 19.9 29.9 24.3 Low High High Untreated 29.2 22.7 32.9 26.9 24.3 17.8 28.9 22.6 Difference 0.7 1.3 0.4 0.9 1.4 2.1 1.0 1.7 Treated 28.8 22.7 32.3 26.5 24.8 19.1 29.1 23.3 High Low High Untreated 28.1 21.5 31.8 25.6 23.6 17.1 28.1 21.7 Difference 0.7 1.2 0.5 0.9 1.2 2.0 1.0 1.6 Treated 30.3 24.8 33.5 28.3 26.6 21.1 30.6 25.3 High High Low Untreated 29.6 23.6 33.1 27.5 25.2 18.9 29.7 23.6 Difference 0.7 1.2 0.4 0.8 1.4 2.2 0.9 1.7 Treated 28.7 22.4 32.2 26.3 24.3 18.2 28.7 22.8 High High High Untreated 27.9 21.0 31.7 25.3 22.8 15.8 27.6 20.9 Difference 0.8 1.4 0.5 1.0 1.5 2.4 1.1 1.9
14 5.2 Sensitivity testing In the first paper in this series, Chatterjee et al. (2007a, Section 13), we discussed the uncertainty of values for expected future lifetime, where this uncertainty arises from the variability of the estimates of the many parameters in the model described in that paper. For example, the standard deviation associated with the value of 58.6 in Table 6 for the Untreated expected future lifetime from age 20 for a male who never smokes is 0.6. See Chatterjee et al. (2007a, Table 15). The estimated expected future lifetime from age 20 for males treated with statins from age 50, 59.2 (Table 6), is thus within one standard error of the estimated Untreated expected future lifetime. This prompts questions about the statistical significance of this increase in expected future lifetime. However, by using the same sets of simulated parameters to calculate the Untreated and Treated from age 50 expected future lifetimes, we can estimate the standard error of the estimated difference, 0.6 years, directly. The standard error of this difference is 0.08 years. Further details can be found in Chatterjee (2007). The standard deviation of the difference between the Treated from age... and Untreated future lifetimes discussed in the previous paragraph takes account only of the variability of the parameters of our model set out in Chatterjee et al. (2007a). In particular, it does not take account of any uncertainty relating to the reduction in the intensity of MI as set out in Table 5 or the figure of 17% for the reduction in the intensity of stroke resulting from treatment with statins. These estimates of the reduction in intensities are key parameters in assessing the effects of statins and we can assess their numerical significance by scenario testing arbitrarily assuming the reductions will be 30% higher (High scenario) or 30% lower (Low scenario) than the values shown in Table 5. These revised estimates are shown in Table 8, with the values for MI from Table 5 shown as the Standard scenario. Table 8: Percentage reduction in risk by duration of treatment High and Low scenarios. % Reduction in risk Event Duration of treatment High scenario Standard Low scenario Myocardial 1st year 25 19 13 Infarction 2nd year 51 39 27 3rd-5th years 66 51 36 6th and 72 55 39 subsequent years Stroke All durations 22 17 12 Figures for expected future lifetime and expected future event free lifetime from age 50 using these three different scenarios for the effect of statins are shown in Table 9. The Treated figures assume everyone is treated with statins from age 50. It can be seen from Table 9 that moving from the Low to the High scenario approximately doubles the increase in expected future ( Event free ) lifetime from age 50 in every case.
15 Table 9: Sensitivity testing for the effect of treatment with statins on expected future lifetime and expected future event free lifetime from age 50. Expected future lifetime from age 50 Expected future Event free lifetime from age 50 Male Female Male Female Never Current Never Current Never Current Never Current Smoked Smoker Smoked Smoker Smoked Smoker Smoked Smoker Treated 29.0 23.0 32.4 26.7 24.8 19.2 29.1 23.5 High scenario Untreated 27.9 21.0 31.7 25.3 22.8 15.8 27.6 20.9 Difference 1.1 2.0 0.7 1.4 2.0 3.4 1.5 2.6 Treated 28.7 22.4 32.2 26.3 24.3 18.2 28.7 22.8 Standard scenario Untreated 27.9 21.0 31.7 25.3 22.8 15.8 27.6 20.9 Difference 0.8 1.4 0.5 1.0 1.5 2.4 1.1 1.9 Treated 28.5 22.0 32.1 26.0 23.8 17.5 28.4 22.2 Low scenario Untreated 27.9 21.0 31.7 25.3 22.8 15.8 27.6 20.9 Difference 0.6 1.0 0.4 0.7 1.0 1.7 0.8 1.3
16 6. Conclusions Since reliable data on the long term benefits of statins are not yet available, figures coming from models such as ours which incorporate assumptions about these long term effects will necessarily be revised in the future when more reliable data do become available. Nevertheless, it seems clear from the figures presented in Section 5 that statins will have a significant impact on future life expectancy for some time to come. It is a sobering observation that even with our more optimistic assumption about the effect of statins, their effect on future life expectancy is considerably less than the effect for smokers of giving up smoking, cf Table 9 ( High scenario ) and Table 3.