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Z i: ,;~::•: • [ Z:¸, BRITISH AMERICAN TOBACCO Copy Request Form Request Number: Organization: Physicians for a smoke free Canada 26 I Request Details Request Date: ......... [..~....~...~ ........................... . . • oJ • • File Number: ........ ~. ........... Box Number: .... .~.....~....~..2. Page Range: First Page ~ 1 C 0 ~ "~ ~ ~ t LastVage [ / C.~ (~)(0 "~ 8 0 ~:~ Requested By: (Print Name) .... .~~.. ~~. ................... Details below will be filled in by Depository. Staff Only II Copy Details Copied By: ...~~..."2 ................. ~.....~ .......... Date: .... ~.~./¢~. ,.~./~..~. ............Time:..../. Z'.~,~, A~'. ......... Copy Checked By: ...................................................... .. .. Date: .......................... ......... . Time: ............................. .. III Delivery Details Checked By: .................................... Date: ............... ..... Sent By: ........................ Date: • eB~oul.nooeDioe o• ~eooolgoliooooaoo,oeo BATCo document for PFSFC 1 March 1999

CONFIDENTIAL Estimation of loss of llfe in relation to a disease or to a factor causln~ it; with particular reference to smoking Author : P.N. Lee Date : 1.2.78 Introduction Following the publication of the latest Royal College of Physicians Report on Smoking and Health (R.C.P., 1977), considerable attention was given i~ the press, both in the United Kingdom end abroad, to the claim contained in it that '"on average the time by which a habitual cigarette smoker's life is shortened is about 53 minutes for each cigarette smoked - which is not much less than the time he spends smoking it." This claim was first made by Diehl (1969), who based his calculations on tables provided by Hammond (1969) giving the loss of life expeotsncy of U.S. men of various ages smoking different numbers of cigarettes. Such a claim is only one among a number of ways in which the loss of life due to smoking can be quantified. The aim of this paper is to look at a number of methods of general application in estimating loss of life in relation to a disease or to a factor causing it, and to apply the ones thought most useful to obtain estimates relevant to the population of England and Wales of the loss of life due to smoking and to diseases associated with it. This paper starts, in Section 2, by looking at the theory behind estimation of loss of life in the experimental situation. The concept of the life table is introduced and the advantages and disadvantages of a number of alternative statistics describing differences in survival between exposed and non-exposed groups are discussed. In practice, human data on the relationship between smoking and mortality is collected observationally rather than experimentally. The problems involved in collecting relevant data are discussed in Section 3 along with the assumptions required in extrapolating results obtained to the current • smoker in England and Wales. Following discussion of what data actually are available (Section 4), calculations of the loss of life due to smoking and some smoklng-~ssociated diseases are made in Section 5. The conclusions of the paper are then discussed in Section 6 and summarized in Section 7. C~ C~ ~j BATCo document for PFSFC 1 March 1999

2= -2- Est~nation of loss of life in the experimental situation 2.1 The two.~r0uP experiment In an ideal world, to determine the loss of life related to a particular factor, one would take a population and randomly allocate it into two groups. One group would then be exposed to the factor of interest while the other group would not. The mortality of each grotrp would then be monitored for the rest of its life by noting the time at which each member died. Statistics describing the difference between the mortality experience of the ~wo groups would then be computed and could be taken to be relevant to the effect the factor would have on the loss of life of other people typical of the original population. In the real world, such an experimentaZ approach is only usually possible with animals and inferences have to be made about the effects of a factor from other types of data. The problems involved and assumptions required to make such inferences are discussed later (Section 3); for the moment our interest is centred on what are, and are not, useful statistics to describe the effect of a factor on mortality and for this it is convenient to stay with our ideal situation. To further simplify discussion of method we assume, firstly, that exposure to the factor of interest is at a regular rate throughout lifetime, and, secondly, that the original population are all of the same age at the beginning of the experiment. 2.2 Functions deecrtbin~ survival Survival data are data of times to death. The distribution of survival times can be characterized by three equivalent functions (Gross and Clark, 1975): a) Death Density Function f(t) f(t)dt is the probability that a person will dle in the time interval (t, t + dr). If we assume that the experiment starts at time zero it follows that f(t) is non-negative. BATCo document for PFSFC 1 March 1999

-3- b) Survivorship Function S(t) S(t) is the probability that a person will survive to at least time t (t>O). It follows that S' S(t) = f (T)dT t and that f(t) = -S~(t) S(t) is a non-negative decreasing function starting from 1 at time zero. C) Hazard Function k(t) A(t)dt is the probability that a person will die in the time interval (t, t + dr) iv~_v_e~he has survived to time t. This the L~ll'~'=~ function, whlch.!s also known as failure rate~r the A incidence rate, satisfies the condition ACt) = f(t)/S(t) A(t) is non-negative but may be increasing (such as in the Weibull distribution k(t) = btk where b and k are constants), constant (such as in the exponential distribution A(t) = a) or have other more erratic shapes. 2.3 Cohort life-table For absolute precision one observes, as mentioned above, the actual time at which deaths occur. In practice, especially for human popu- lations, it is usually convenient to group the data into certain defined time intervals rather than actual points of time. We shall assume, for our purposes that ~he data we have for each group conslsts of information relevant to n time intervals (t : 1, .... n) as follows: ti Age of population at beginning of interval i Ai "Number alive at beginning of interval i Di Number dying from all causes in interval i Li Number dying from a particular cause of interest in interval i Yi "Midpoint" of intervali. c~ c~ BATCo document for PFSFC 1 March 1999

-4- Such information is known as a life-table. According to the nomenclature of Gross and Clark (1975), the particular type of life- table we are dealing with here is a cohort life-table, a "cohort" being a group of individuals born at about the same time. Later on (Section 3.5), we consider other forms of life table. We note that, because we have assumed all people are followed until death, Ai - Di -- Ai + 1 for all i and that t1 = 0 and An = Dn. Yi' the "midpoint" of interval i, can usually, if the interval is sufficiently small, be taken as the actual midpoint of the age-interval considered. If more accurate answers are required the actual average age at which deaths in the interval occur should be substituted. Pi = Ai/A1 estimates S(ti) the survivorship function at age ti. Description of the mortality of a population by life-tables has a long history dating back to the pioneer work of Halley (1693 - sic). Mortality indicators in general have been reviewed in the literature on a number of occasions (e.g. Woolsey (1943), Haenszel (1950), Logan and Benjamin (1953), Kitagawa (1966), Benjamin and Haycocks (1970), Romeder and McWhinnie (1977)). In this, and the sections that follow, we discuss the merits of a number of statistics that have been suggested to summarize the main features both of the information contained in a life-table and of the differences between the two life-tables being compared. We start by looking at some of the more simple statistics that have been employed in the past. 2.4 Measures of the number d~ing One obvious type of statistic to look at is the proportion dying. Clearly if one is lookinE at total mortality then the proportion dying over the whole experiment will be 100% and will offer no dis- crimination between the groups. However it can be useful to compare the proportion dying between two particular time points tj and tk, especially if the time period represent, in some sense, "premature" deaths. This statistic, Ql' is defined by S~k) A~ - Ak Q1 = I = S(tj) Aj If one is interested in mortality from a particular cause then the total proportion dying from this cause BATCo document for PFSFC 1 March 1999

-5- I=1 'J can give some indication of the magnitude of the problem caused by the disease. It is, however, limited in its usefulness by the fact that it gives no information as to .when the deaths occur. There are two other types of indicator which have the same objection that they concentrate on numbers of deaths and ignore when deaths occur. The first of these are standardised death rates. They can be calculated by two methods, the direct and the indirect method. In the direct method, the rate, Q3' is a weighted sum of the individual crude death rates (Ri) , with the weights representing the populations in each age-group in some standard population. Thus, if wi are the weights, Q3 is defined by n Q3 = E wiRI i=l In the indirect method, the number of deaths from the cause of interest observed (0i) in an interval is compared with that expected (El) if some standard death rates (Ri ) from the cause had existed. The sum of deaths observed from all intervals is divided by the total expected to give a 'Standardized Mortality Ratio', Q4" Q4 is defined by n n Z 0i q4 = n n E1 g AIRi i=l i=l A problem with both these indicators, as was pointed out by Yerushalmy (1951), is that they are markedly affected by relatively small differences in mortality in older ages when deaths are frequent and little affected by large proportional differences in early years which cause great loss of life. The final type of statistic, quite popular in quantifying the effect of smoking (e.g.R.C.P. (1971)) is the number of deaths associated with the factor. To calculate this statistic, QS' the number of deaths "that ~-, actually occur in as interval in the exposed group are compared with the ~-~ number that would have occurred had the exposed'group had the same number at risk in the interval but the death rates of the non-exposed group. In-.,j o~her words BATCo document for PFSFC 1 March 1999

-6- 1 where the first subscript refers to the group (1 = non-exposed, 2 = exposed) and the second to the time interval. Apses from the fact that Q5 gives no Indication at all of life-shortening, the main defect- with this Statistic is that i¢ carries with it the implication that, had the factor not existed, this number of deaths would, in some sense, have been avoided. Clearly everyone dies once, so what is Che real implication? As normally used, the number of deaths associated with a factor Is attached to a time scale, e.g. "50,000 deaths a year are asso- ciated with smoking" but what does this mean? As calculated, if the time intervals were years, and if in fact this calculation was carried out on population data rather than our idealized cohort data, the statistic would a reasonable estimate of the numbers of deaths that would not have occurred in the year following a universal giving up of smoking, assumin~ (and there Is evidence to show that for some diseases, e.g. lung cancer (Doll (1971)), this is not the case) that on giving up smokers age-specific death rates reverted at once to those of never smokers. However, it would be accurate for the first year and would be ~ecreasingly inaccurate only for subsequent years. The reason being, of course, that in later years, due to the lower mortality immediately following mass giving-up (on the assumption quoted), there would be more survivors at higher ages and consequently more deaths than the current age-distribution would suggest. As shown in Appendix A, it can be estimated (under certain further assumptions) that, on mass giving up of smoking at the end of 1975, 80,000 less male deaths in England and Wales would have occurred the first year afterwards than had no giving-up occurred. However this number would be half as much by 1988 and down to 12,000 by the year 2,000. 2.5 Life expectation and average a6e at death Another simple statistic that has been used to assess mortality is average age at death. Average age at death of the whole population from all causes is identical ¢o expectation of life at birth; expectation of life at age t, Q6' being defined by the expression c° Qs Jt and measurinj the aversga number o! additional years people slave at age t live on average. C~ C~ BATCo document for PFSFC 1 March 1999

-7- Average age at death of those people dying only of the cause of interest, QT' is an alternative statistic which has been used by some workers. It is defined by n n Q7--i~l (LiYi)/t--Z1Li ~hough it can be of value in some circumstances to compare such an average for one cause of death with a similarly computed average for another cause, it only measures when the disease occurs and not how many people die of it. Furthermore it is not a very useful statistic to measure life shortening. It night be thought that, a cause of death resulting in an average age of death x years less than the average age of death from all causes is in some sense an indication that the cause takes x years off life. That this reasoning is incorrect can be seen if one considers a cause of death with an average age greater than the expectation of life at birth. On the implied line of reasoning this cause adds years onto life, which is, of course, nonsense. Average age at death can also be a very misleading statistic to use when comparing groups exposed to different levels of a ~actor of interest. If, for example, the cause of death of interest is the only one affected by a factor and is relatively rare, and if the effect of the factor is simply to multiply the age-specific incidence rate ~rom the cause by an age-independent constant, it can be easily seen that, though the pro-~ portion of cases of the cause of death in the group more exposed to the factor will be greater than in the group less exposed, the distribution of times of death from the cause, and hence the average age at death from the cause, will be virtually identical in the two groups. If, further- more, the average ages at death from the cause are compared in cross- sectional data, where the age distribution of the more and less exposed groups are different, it is not surprising that fairly meaningless results can be obtained. Yor example, Passey (1962) studied successive hospital lung cancer patients and observed that the average age of death of the heavy smokers did not differ from that of the light smokers. He concluded that there was an anomaly to be explained, but as Pike and Doll (1965) pointed out, following out general line of argument above, if was only the poor choice of statistic that had led to the apparent anomaly. 0 0 BATCo document for PFSFC 1 March 1999

-8- R.8 Measures of loss of life expectation In the preceding sections it should have become clear that any statistic not taking into account both the frequency an__~d the time of occurrence of death is not an adequate description of the effect a factor has on loss of life. A better approach, and one that has been tried by various workers over the last 30 years, is to quantify the effect in terms of numbers of years lost. Some of these attempts have tried to take into account to at least some extent the fact that the loss of years of life at young ages may be of more importance to an individual, or to a society, than the loss of a similar number of years in old age. Thus, a number of workers, e.g. Murray and Axtell (1974), Romeder and McWhinnie (1977), have estimated the number of years of "active life" lost. Though the critical age differs (usually between 60 and 70), the same essential method of calculation has been used; it has been assumed that any person dying before the critical age has lost a number of active years equal to the difference between the critical age and the year of death. Other workers have used deaths occurring at all ages and have counted years lost to life expectancy, e.g. Dempsey (1947) who used life expectancy at birth and Dickinson and Welker (1948) who used life expectancy at age of death. Both these types of measure have objections. The years of "active life" lost measures, as described above, are over-estimates as it is clear that some of those dying early would still not have reached the critical age had they not died when they did. Hakulinen and Teppo (1978) got round this objection by using adjusted life-table procedures (see Section 2.10) to estimate the subsequent survival pattern of the "reincarnated" population, i.e. the survival of those who would not have died had the cause of death of interest been removed. An alternative method would be to compare the years of "active life" lost in the exposed and non-exposed groups. However these measures all have the disadvantage that an essentially arbitrary choice of critical age has to be made and that information on people of age greater than this is i Eric red. The loss of years to life expectancy measures mentioned above have the disadvan~ale that they do not take account Of the fact that, had the cause of death been removed, the life expectancy itself would have -..j BATCo document for PFSFC 1 March 1999

been altered. Furthermore~ the resulting statistic can be rather difficult to interpret especially i~ it is calculated on a per decedents rather than a per head of population at risk of basis. Thus, as we shall show later, the average years lost to life expectancy of lung cancer decedents for some populations is in fact less than the averag~ years lost for all decedents. Is lung cancer a good thing . therefore? It can also be shown that (considering cross-sectional data rather than life-table type data), even had smoking no effect on mortality at all, the average loss of life expectancy of smokers who die in a given t~ne period would be greater than that of non-smokers who die in the same periodp simply because smokers are younger than non-smokers. It is clear that such statistics are liable to misuse by the uninitiated. 2.7 Recommended methods for comparison of two life-tables Probably the most infor~ative method of quantifying the loss of life due to a factor is to compute the difference in li~e expectation o~ the exposed and non-exposed groups from the st~t of the experiment. Xf it is desired to place a different value, V(t), on life at different ages then one ~could calculate the difference between the two groups in their "expected value of life", QSp where Q8 is defined by Q8 = ~T f(T, Z(T)dT where Z(T) the total value of life up to time T is given by Z(T) = ~2V(UIdU. An alternative good method is to compare the proportions dying over some special age range of interest (Q1). ~his method has, for example, been used by the R.C.P. (1977) to quantify the effect o~ smoking. They pointed out that, in the study of British Doctors (see .Section 4.2) a male smoker of 25 cigarettes or more daily aged 35 had a 40% chance of dying by age 65 whereas~ over the same period a non- smoker only had a 15% chance. In particular circumstances, other comparisons of life-tables can be extremely informative. For example, if the effect of the factor is simply to transform the death density function so that either or c-~ Cr~ BATCo document for PFSFC 1 March 1999