0895-4356/90 $3.00 + 0.00 Copyright Q 1990 Pergamon Pm8 plc
J Cth E#&dol Vol. 43, No. 2. pp. 133-140, 1990 Printed in Great Britain. All righta rcsmd
AGE RELATED
CHANGES IN AGE OF STARTING SMOKE
TO
J. J. WEMKAMand T. D. STERLING School of Computing Science, Faculty of Applied Science, Simon Fraser University, Bumaby, B.C.. Canada VSA IS6 (Received in revised form 3 1 May 1989)
Average Age of Starting to Smoke (AASS) has been reported to decline for younger birth cohorts. That apparent decline has been used to support a conclusion of an increase in smoking among younger individuals. However, in some cases the apparent decline is an artifact of the method of computation which arises when the quantity being averaged is related to a quantity used to classify subjects for comparison. In one other case, a second type of error arises because the distribution of smoking initiation with age changed in such a way that the proportion of individuals taking up smoking at older ages declined more rapidly than the proportion starting at younger ages. In fact, comparison of the 1970 National Health Interview Survey (NHIS) to the 1979/80 NHIS shows a uniform decrease in starting to smoke among teens and preteens. Examplesare discussed which show that estimates of possible disease related factors actually experienced by a cohort are possible only if other suitable data are available for comparable representative sections of the population at different time periods and for different ages. Abstract-The
Age dependent errors
Average Age of Starting to Smoke
2. Extrapolation from the prevalence at one or several different ages at difirent
INTRODUCTION
is common practice to use the incidence and/or prevalence of factors thought to be related to a disease as a measure of a possible impact of that disease on the community. It is therefore to be expected that the incidence and prevalence of smoking, especially at younger ages, and their changes over time are of considerable interest. However, as the history of such efforts shows, especially in the case of tuberculosis [l], it is not an easy task to derive unbiased estimates.* For infectious and chronic diseases two methods are used: It
1. Extrapolation from the prevalence at one or several different ages at one time. lE-stimatesof infectious disease related factors are subject to almost identical problems as those of factors related to chronic disease.However, they may differ in what use is made of them. For instance, epidemiologists often are interested in the unn& risk of infection while such a concept may be meaningless for chronic disease related factors such as smoking or occupational exposures. c.e
43,2-S
Smoking patterns
times.
Of these two methods, the first (extrapolation at one or several different ages at one time) is subject to two errors. The first, an error of calculation, arises when a quantity being averaged (such as age of first infection or smoking) is closely related to a quantity (such as time of birth or current age) used to classify subjects for comparison. This error is due to age dependency. The second error arises because the distribution of the disease related factor may differ for different comparison groups. We shall label this type of error the distribution error. The first error is exemplified by an estimate of Average Age of Starting to Smoke (AASS) made in an analysis of data from the new American Cancer Society (ACS) prospective study of 1.2 million men and women [2]. The second error is demonstrated by the analysis of age of starting 133
134
J. J. WEINKAM and T. D. STERLING
to smoke data used in the 1989 Surgeon General’s Report [3]. A recent analysis by Stellman and Gatlinkel [2] computes AASS for successive birth cohorts. These averages become smaller for younger birth cohorts and the decline is more pronounced for females than for males. They infer from their analysis that, “The age at which smokers born at different times reported they began to smoke is seen to drift gradually downward for more recent birth cohorts. Many years ago, the few women who smoked cigarettes at all tended to take up the habit later in life. In recent times, teens and pre-teens, particularly girls, are experimenting at much younger ages than ever before.” [2, p. 1059, especially Fig. 31. This assertion appears to support a current belief that over time individuals have started to smoke at progressively younger ages [4-6]. However, is it really true that the decreasing AASS for successive birth cohorts means that proportionately more people in the younger cohort have taken up smoking at earlier ages? Or is this decline of AASS due to an artifact of the method of computing the AASS, namely that in computing AASS for a cohort of older individuals, persons are included who started smoking at ages not yet attained by members of a younger birth cohort? In the present instance, an error arises when the AASS is computed separately for successive birth cohorts (i.e. groups of subjects classified according to when they were born which in turn determines their current age). As a simple example, the AASS among high school students will be less than the AASS among college students simply because college students tend to be older than high school students. Among college students are individuals who started smoking after leaving high school, but no such persons are available among high school students. The AASS is to a considerable extent age dependent in this example. Moreover, averages are especially prone to the influence of a long tail of either very high or very low values. This is the case for the age of starting to smoke distribution. While most smokers start between the ages of 15 and 20, there are sizable numbers of individuals who start smoking at ages older then 25 but relatively few before the age of 12. This last factor enhances the bias due to age dependency. In fact, the true AASS for a cohort could only be determined by following the cohort for its entire lifespan. Any computation of AASS for a living cohort is necessarily a
truncated or censored estimate. Of course, it is possible, using lifetable techniques, to compute an estimate of AASS which is corrected for the future taking-up of smoking that will occur among individuals in a living cohort. However, to do so requires making some assumptions about the age-specific rates at which members of the cohort who have never smoked will start to smoke in the future. The possibility of being misled by the age dependency may have been discounted in the past because of a belief that few people start cigarette smoking at older ages. However this belief is not supported by available data. For instance, Kandel and Logan [7] report that while marijuana and alcohol usage declines beginning at age 20 and 21, cigarettes usage continues to climb until the end of their surveillance period, which was at age 25. Similarly, La Vecchia [8] reports for a 6&70 year old Italian birth cohort that 24% of males and 59% of females report having started smoking at age 30 or older. While such a large proportion of North Americans do not start smoking after age 30, 5 or 10% certainly do start late in life and this can pull the average age up quite a bit. Harris [9] also computes the AASS using data from the National Health Interview Survey (NHIS) for a sequence of birth cohorts without correcting for age dependency. He finds a decline in AASS similar to that reported by Stellman and Garfinkel [2]. Beginning with the oldest birth cohort and proceeding to the youngest, the AASS declines from 21 to 16 for males and from 3 1 to 17 for females. However, Harris does not offer the apparent decline of AASS as evidence that people are taking up smoking at earlier ages. Instead he uses AASS as the starting age for subjects with unknown age started in constructing age specific prevalence curves. While this particular use of the AASS (i.e. to replace missing data for cases in which the age of starting to smoke is unknown) avoids misinterpreting the age dependency, it introduces a more subtle artifact-it concentrates at a single age in each cohort the incidence of starting to smoke of all individuals who failed to report their actual age of starting. This has the effect of increasing the slope of the age specific smoking prevalence curve for each cohort in Harris’s Figs 1 and 2 and could possibly have introduced a spurious downward shift in the age of peak smoking prevalence in which Harris was interested. The error introduced by the age dependency in computing AASS can be avoided by fixing an
Age Related Changes in Age of Starting to Smoke
upper age for starting to smoke (the age of truncation) that remains the same for each birth cohort and by confining attention to birth cohorts for which all individuals have already attained the age of truncation. In this way the AASS for each successive birth cohort is computed for all individuals who started to smoke at ages younger than the age of truncation and all cohort members who could possibly start smoking before that age have already done so. The AASS computed in this manner is an underestimate of the true AASS, because it excludes all individuals in that birth cohort who have or will start to smoke at ages older than age of truncation. The AASS computed in this way does not depend on the current age of the birth cohort as long as the age of truncation is the same for all cohorts and there is no differential survival of smokers and nonsmokers (i.e. a survivor bias). The underestimate could be made smaller by raising the age of truncation, but only at the cost of excluding more of the younger individuals from the analysis. On the other hand, by lowering the age of truncation, more of the younger individuals can be included but at the cost of further underestimating the AASS. In the present instance, we shall compute the AASS for successive birth cohorts of individuals who started smoking at ages that were less than 25. We shall call ours the age in&pendent method. The 1989 Surgeon General’s Report [3] also bases its estimate of the average age of starting to smoke on data of reported age of starting to smoke obtained at one time. Making corrections for age dependency (similar to the ones we discuss) an apparent decline in the age of starting to smoke is observed for white females (but not for males or black females).* However, by comparing two different time periods at which data on initiation are available, it can be shown that the observation of a decrease in age of starting to smoke for white females in the Surgeon *Based on analyses in the report, the Surgeon General’s conclusion that the average age of starting to smoke has fallen over time is incorrect for white and black males and for black females. tThe basic tabulation was done using 5 year age groups for the entire range of ages covered by the NHIS so that subsequent calculations using the age independent method could be done using upper limits of 20, 25, or 30 years. Only the results for an upper limit of age 25 are presented here. There were too few subjects in the 90-94 and 95 + up categories, therefore in the results presented here we dropped the last two age categories entirely. SSince we used 1979 as the time of interview, age 20-24 corresponds to the 1955-1959 birth cohort, and so on.
135
General’s Report is an example of the distribution error. The error is due to the fact that a change in the distribution of smoking initiation with age occurred in which the proportion of individuals taking up smoking at older ages declined more rapidly than that at younger ages. We use the National Center for Health Statistics (NCHS) NHIS to compute the age dependent and age independent AASS for successive birth cohorts. The NHIS is ideal for the exploration we undertake here because it is a large probability sample of the U.S. population with well established reliability and validity [lo]. Since the ACS sample represents a different population, our results could differ from those Stellman and Garfinkel would have obtained had they used our method of computation. However, the relationship between the age dependent and the age independent methods would be similar for the two populations. Another advantage of using NHIS is that identical questions on age of starting to smoke were asked 10 years apart (1970 and 1979/80) so that proportions can be compared for a 10 year interval of individuals who started to smoke at various ages. In this way we can demonstrate the distribution error which the Surgeon General’s Report could have avoided if it had based its analysis on the initiation of smoking at different ages and at different time periods. METHOD
The 1970 and the combined 1979/80 NHIS public use data tapes were used for this analysis. The NHIS collects information on a nationwide sample of households as part of an ongoing activity of the NCHS. The 1970 NHIS data included useful information on smoking practice for 75,497 individuals and the 1979/80 NHIS on 34,800 individuals who were 17 years of age or older. The NHIS data sets include weighting factors which compensate for variations in sampling rate or in the population density within different sampling strata and adjust to the race/age/sex distribution of the U.S. population [I I]. Subjects in the NHIS file were cross classified as follows: Sex: male, female Race: white, black (other races were dropped) Tobacco (actually cigarette) use: Never, Former, Current (unknown status were dropped) Age (at time of interview): 20-24,25-29,. . . , 90-94, 95 + up.tt
136
J. J. W~NKAMand T. D.
Both the number of subjects and the sum of the weights were accumulated for each category. Let ZV,,0denote the number of subjects and W,,, denote the sum of the weights in each sex, race, tobacco, and age group. The subjects who had ever smoked were further classified according to age of starting to smoke by single years from age O-29, age 30+ up, and unknown who were dropped. Again both the number of subjects and the sum of the weights were accumulated. Let nsrrnb denote the number of subjects and w,,,, denote the sum of the weights in each sex, race, tobacco, age, and age begun smoking group. Finally, let P,,,Obe the set of subjects of sex, s, race, r, tobacco use t, and age a, who started at age 30 + up and let X wo = p;,*
wP*
Age independent method
To compute the age independent AASS for sex s, race r, age groups a,, . . . , a,, and a set of tobacco use groups T, for those who started smoking before age b0 where a, 2 b,,,* let
1
wsrub
rcT.mo,....o~
, b,, - 1. Then the age indepenforb=O,l,... dent AASS is given by: L.-I -y. bEb
0.5+*.
Eb=
1
for b = 0, . . . ,30. AASS is given by
Then
Wsr,czb
the age dependent
r‘T.ato,....q
0.5 + b-o
3-l
26 b=O Comparison of distribution of age of starting to smoke at d@erent times
The percentage of white and black, males and females who have started to smoke before 12, between 12 and 15, 16 and 18, 19 and 20, and 20 and 24 years of age were compared for 1970 and 1979/80. The results of this comparison are given in Table 4.
bP
where wp is the NHIS weight for person p and bp is the age at which person p began to smoke.
Eb=
SlERLINCi
;xo Eb 5
(The 0.5 accounts for the fact that the recorded age is age at last birthday, and on the average subjects have lived 0.5 years since their last birthday.)
RESULTS
Table 1 shows the males and females in birth cohorts 1915-24, 1905-14, and 1895-1904 (i.e. age groups 554, 65-74, and 75-84) who started to smoke after the age of 25 (expressed a percent of all individuals and of all smokers in these birth cohorts). The percent of all individuals indicates the relative proportion in the birth cohorts who take up the habit relatively late in life. The percent of all smokers indicates the extent to which individuals who started smoking after age 25 will produce an upward trend in AASS in these cohorts. (Table 1 does not show how many of these individuals quit smoking.) Table 2 gives the age independent AASS (and their standard errors) for individuals over 25 years of age who started to smoke before the age of 25, broken down by successive 10 year birth cohorts. Table I. Males and females in 1915-24. 1905-14, and 1895-1904* birth cohorts who started to smoke after the age of 25 as percent of all individuals and of all smokers in these birth cohorts (from 197911980NHIS data) White
Age dependent method
To compute the age dependent AASS for sex s, race r, age groups a,, . . . , a,, and a set of tobacco use groups T, let *For example, suppose the age of truncation is 25, and we wish to compute the AASS for white female ever smokers in the 2544 age range. In that case, b, = 25; s = female; r = white; T = {current, former} so that r takes on the values I = current and t = former; and u, = 25-29, cr = 40-44, so that a takes on the values 25-29, 30-34, 35-39, 4044.
Birth cohort
Percent all
Black
Percent smokers
Percent all
Percent smokers
9.18 4.12 5.67
13.57 7.56 10.53
15.20 9.85 8.24
34.76 43.92 49.35
Males
1915-24 1905-14 18954
4.74 7.26 7.80
3915-24 1905-14 18954
II.09 14.37 12.21
6.40 10.54 14.18 Females
*Corresponding and 7584.
25.06 39.97 69.61
to age groups in 1979 of 55-64. 65-74,
Age Related Changes in Age of Starting lo Smoke
137
Table 2. AASS for individuals over 25 years of age who started to smoke beforr age 25 (from 1979/1980NHIS data) White Birth cohort
Current
Black
Former
Ever
Current
Former
Ever
Males 1945-54
Avg. age SE
17.36 0.08
17.32 0.12
17.35 0.07
17.93 0.21
16.81 0.56
17.71 0.20
1935-44 Avg. age SE
17.02 0.11
17.38 0.12
17.16 0.08
17.65 0.31
18.37 0.57
17.85 0.27
17.06 0.12
17.42 0.11
17.23 0.08
17.73 0.39
17.08 0.54
17.52 0.32
1915-24 Avg. age SE
16.66 0.14
17.24 0.14
16.96
0.10
17.45 0.46
17.22 0.42
17.38 0.34
1905-14 Avg. age SE
16.87 0.22
17.40 0.14
17.23 0.12
16.76 0.66
18.10 0.65
17.34 0.47
1895-1904 Avg. age SE
16.70 0.40
17.05 0.26
16.98 0.22
16.50 0.93
18.14 0.75
17.56 0.60
1895-1954 Avg. age SE
17.07 0.05
17.33 0.06
17.19 0.04
17.66 0.15
17.48 0.24
17.61 0.13
1925-34 Avg. age
SE
Females 1945-54 Avg. age SE
17.90 0.08
17.89
0.11
17.90 0.07
18.65 0.22
18.38 0.39
18.59 0.19
193s44 Avg. age SE
18.17 0.09
18.25
18.19
0.13
0.08
18.08 0.33
18.48 0.48
18.17 0.27
1925-34 Avg. age SE
18.79 0.11
18.68 0.14
18.76 0.08
18.02 0.44
17.82 0.71
17.97 0.37
1915-24 Avg. age SE
19.06 0.13
18.75 0.16
18.94
0.10
18.09 0.62
17.83 0.81
18.00 0.49
1905-14 Avg. age SE
18.71 0.22
18.99 0.21
18.84 0.15
16.90 1.42
19.19 0.61
18.20 0.69
1895-1904 Avg. age SE
18.85 0.97
19.12 0.50
19.01 0.49
16.17 2.59
20.50 -
17.73 1.80
1895-1954 Avg. age SE
18.37 0.05
18.40 0.06
18.38 0.04
18.24 0.17
18.31 0.26
18.26 0.14
There is no consistent the age independent
or significant
change in
AASS from older to younger birth cohorts. Computations of the age independent AASS using 20 and 30 years of age as the upper limit exhibit the same trends as are seen in Table 2. (They are not shown here but are available on request.) Table 3 shows the age dependent AASS for the same birth cohorts. The age dependent AASS decreases steadily for males and very sharply and significantly for females. In
fact, the shape of the falling trend is almost identical for white males and females to that observed by Stellman and Garfinkel [2] for the ACS data and shown in their Fig. 3. (Stellman and Garfinkel’s graphs show males and females for all races combined, while our results are presented separately for whites and blacks. However the proportion of nonwhites in their sample is only a fraction of the proportion of nonwhites in the U.S. population.)
I38
J. J. WEINKAM and T. D. STERLING Table 3. AASS for individuals over 25 years of age, computed using the age dependent method (from 19790980 NHIS data) White Birth cohort
Current
-_ Ever
Former
Black Current
Former
Ever
Males 1945-54 Avg. age SE
17.54 0.09
17.41 0.13
17.50 0.07
18.28 0.26
17.34 0.63
18.09 0.24
193544 Avg. age SE
17.54 0.14
17.66 0.14
17.59 0.10
18.63 0.48
19.00 0.63
18.73 0.39
1925-34 Avg. age SE
17.77 0.16
18.02 0.17
17.89 0.12
18.56 0.46
17.98 0.68
18.37 0.38
1915-24 Avg. age SE
17.61 0.21
18.00 0.17
17.81 0.14
19.06 0.71
19.10 0.77
19.08 0.54
1905-14 Avg. age SE
18.75 0.40
18.72 0.22
18.73 0.20
17.55 0.82
19.96 1.26
18.63 0.73
189551904 Avg. age SE
17.79 0.65
19.48 0.47
19.18 0.40
16.50 0.93
24.27 4.28
21.82 3.03
189551954 Avg. age SE
17.69 0.07
18.06 0.08
17.86 0.05
18.47 0.21
18.76 0.40
18.56 0.19
Females 1945-54 Avg. age SE
18.52 0.10
18.19 0.13
18.42 0.08
19.31 0.27
19.16 0.50
19.28 0.24
193544 Avg. age SE
19.34 0.15
19.04 0.19
19.24 0.12
20.03 0.50
18.48 0.48
19.72 0.42
1925-34 Avg. age SE
21.19 0.23
26.63 0.28
21.02 0.18
20.53 0.71
21.09 1.19
20.68 0.61
1915-24 Avg. age SE
22.51 0.28
21.79 0.35
22.24 0.22
23.98 1.13
21.70 1.75
23.29 0.95
1905-14 Avg. age SE
25.74 0.58
24.35 0.50
25.12 0.39
26.51 3.62
25.85 2.51
26.14 2.08
1895-1904 Avg. age SE
34.72 1.73
28.29 1.06
31.66 1.06
24.20 11.54
31.41 3.66
28.68 4.77
1895-1954 Avg. age SE
20.89 0.11
20.71 0.14
20.83 0.09
20.76 0.33
21.27 0.60
20.90 0.29
The relationships between the age dependent and age independent methods of computation are also shown graphically in Figs 1 and 2. The age independent AASS does not change appreciably with increasing or decreasing age of birth cohorts. A conclusion that younger individuals are taking up smoking in increasing numbers is not justified. Even if the age independent AASS did decrease for younger birth cohorts, this would not necessarily imply that proportionately more individuals were taking up smoking at younger ages. It could just as well
be true that proportionately fewer individuals were taking up smoking at older ages. To answer the question of whether or not more individuals are taking up smoking at younger ages requires comparing the distributions of age of starting to smoke for successive time periods. Differences in a summary statistic such as AASS can be misleading. The fact that 1970 and 1979/80 NHIS asked identical questions concerning age of starting to smoke makes it possible to compare the distribution of age started to smoke for two
Age Related Changes in Age of Starting to Smoke
1 ,,I
1945-!M
la3544
lsa-34
tsm-24
lsos-14
le9!m4
l945-54
l9xv44
l925-34
t9rr24
190544 !a9504
Birth cohwt
Birth cohort
Fig. 1. Graphic presentation of trends in male eversmoker’s age of starting to smoke for age dependent and age independent methods of computation.
Fig. 2. Graphic presentation of trends in female eversmoker’s age of starting to smoke for age dependent and age independent methods of computation.
comparable samples surveyed 10 years apart, and based on probability samples of the U.S. population. Table 4 compares for the 1970 and 1979/80 U.S. population, the percent of black and white males and females between the ages of 25 and 34 who started to smoke at different ages. This is the youngest group for which such a comparison is possible if ages of starting up to 25 are to be considered. Percentages are expressed as percent of all black and white males and females in the respective 25-34 age groups. There is a significant decrease in the proportion of individuals starting to smoke before age 25 in each race and sex group from 1970 to 1979/80 (except for a very small and not significant increase for black males 12-15 and white females below 15). For instance, the percentage of white females in the 25-34 age group who started to smoke before age 25 decreased from 49.72% in 1970 to 45.00% in 1979/80, a decrease of almost 10%. For white males the drop was from 66.64 to 60.60%, again a decrease of almost 10%. It is
of interest that the decreases for white males and females were quite similar. Decreases in individuals starting to smoke are more pronounced among blacks, especially black males. (Again, Table 4 does not indicate the number of individuals within the 25-34 age range who both started and ceased smoking. Readers may refer to our paper in the American Journal of Industrial Medicine [12] that gives some breakdowns for smoking cessation in the same population.) DISCU!WON
Errors due to age dependencies have a long and distinguished history in epidemiology and statistics. For instance, Warren [13] claimed in 1956 that radiologists died at an average age that was younger than that of other medical specialties because of their exposure to radiation. However, as Seltser and Sartwell [14] showed in 1958, the difference in average age at death was due to differences in the age distributions as radiology still was a new profession
Table 4. Percent of black and white males and females who started to smoke in different age ranges in 1970 and 1979/80 White
Age
Black
Started
smoking
1970
1979180 change
1979180
change
1970 3.77 13.56 31.02 12.17 10.35 70.87
1.35 14.04 25.73 8.98 8.33 58.43
-2.42 +0.48 -5.29 -2.02 -2.02 -12.44
0.80 7.69 17.56 9.11 9.29 44.45
0.14 6.72 17.04 7.95 6.94 38.79
-0.66 -0.97 -0.52 -1.16 -2.25 -7.70
J Cth E#&dol Vol. 43, No. 2. pp. 133-140, 1990 Printed in Great Britain. All righta rcsmd
AGE RELATED
CHANGES IN AGE OF STARTING SMOKE
TO
J. J. WEMKAMand T. D. STERLING School of Computing Science, Faculty of Applied Science, Simon Fraser University, Bumaby, B.C.. Canada VSA IS6 (Received in revised form 3 1 May 1989)
Average Age of Starting to Smoke (AASS) has been reported to decline for younger birth cohorts. That apparent decline has been used to support a conclusion of an increase in smoking among younger individuals. However, in some cases the apparent decline is an artifact of the method of computation which arises when the quantity being averaged is related to a quantity used to classify subjects for comparison. In one other case, a second type of error arises because the distribution of smoking initiation with age changed in such a way that the proportion of individuals taking up smoking at older ages declined more rapidly than the proportion starting at younger ages. In fact, comparison of the 1970 National Health Interview Survey (NHIS) to the 1979/80 NHIS shows a uniform decrease in starting to smoke among teens and preteens. Examplesare discussed which show that estimates of possible disease related factors actually experienced by a cohort are possible only if other suitable data are available for comparable representative sections of the population at different time periods and for different ages. Abstract-The
Age dependent errors
Average Age of Starting to Smoke
2. Extrapolation from the prevalence at one or several different ages at difirent
INTRODUCTION
is common practice to use the incidence and/or prevalence of factors thought to be related to a disease as a measure of a possible impact of that disease on the community. It is therefore to be expected that the incidence and prevalence of smoking, especially at younger ages, and their changes over time are of considerable interest. However, as the history of such efforts shows, especially in the case of tuberculosis [l], it is not an easy task to derive unbiased estimates.* For infectious and chronic diseases two methods are used: It
1. Extrapolation from the prevalence at one or several different ages at one time. lE-stimatesof infectious disease related factors are subject to almost identical problems as those of factors related to chronic disease.However, they may differ in what use is made of them. For instance, epidemiologists often are interested in the unn& risk of infection while such a concept may be meaningless for chronic disease related factors such as smoking or occupational exposures. c.e
43,2-S
Smoking patterns
times.
Of these two methods, the first (extrapolation at one or several different ages at one time) is subject to two errors. The first, an error of calculation, arises when a quantity being averaged (such as age of first infection or smoking) is closely related to a quantity (such as time of birth or current age) used to classify subjects for comparison. This error is due to age dependency. The second error arises because the distribution of the disease related factor may differ for different comparison groups. We shall label this type of error the distribution error. The first error is exemplified by an estimate of Average Age of Starting to Smoke (AASS) made in an analysis of data from the new American Cancer Society (ACS) prospective study of 1.2 million men and women [2]. The second error is demonstrated by the analysis of age of starting 133
134
J. J. WEINKAM and T. D. STERLING
to smoke data used in the 1989 Surgeon General’s Report [3]. A recent analysis by Stellman and Gatlinkel [2] computes AASS for successive birth cohorts. These averages become smaller for younger birth cohorts and the decline is more pronounced for females than for males. They infer from their analysis that, “The age at which smokers born at different times reported they began to smoke is seen to drift gradually downward for more recent birth cohorts. Many years ago, the few women who smoked cigarettes at all tended to take up the habit later in life. In recent times, teens and pre-teens, particularly girls, are experimenting at much younger ages than ever before.” [2, p. 1059, especially Fig. 31. This assertion appears to support a current belief that over time individuals have started to smoke at progressively younger ages [4-6]. However, is it really true that the decreasing AASS for successive birth cohorts means that proportionately more people in the younger cohort have taken up smoking at earlier ages? Or is this decline of AASS due to an artifact of the method of computing the AASS, namely that in computing AASS for a cohort of older individuals, persons are included who started smoking at ages not yet attained by members of a younger birth cohort? In the present instance, an error arises when the AASS is computed separately for successive birth cohorts (i.e. groups of subjects classified according to when they were born which in turn determines their current age). As a simple example, the AASS among high school students will be less than the AASS among college students simply because college students tend to be older than high school students. Among college students are individuals who started smoking after leaving high school, but no such persons are available among high school students. The AASS is to a considerable extent age dependent in this example. Moreover, averages are especially prone to the influence of a long tail of either very high or very low values. This is the case for the age of starting to smoke distribution. While most smokers start between the ages of 15 and 20, there are sizable numbers of individuals who start smoking at ages older then 25 but relatively few before the age of 12. This last factor enhances the bias due to age dependency. In fact, the true AASS for a cohort could only be determined by following the cohort for its entire lifespan. Any computation of AASS for a living cohort is necessarily a
truncated or censored estimate. Of course, it is possible, using lifetable techniques, to compute an estimate of AASS which is corrected for the future taking-up of smoking that will occur among individuals in a living cohort. However, to do so requires making some assumptions about the age-specific rates at which members of the cohort who have never smoked will start to smoke in the future. The possibility of being misled by the age dependency may have been discounted in the past because of a belief that few people start cigarette smoking at older ages. However this belief is not supported by available data. For instance, Kandel and Logan [7] report that while marijuana and alcohol usage declines beginning at age 20 and 21, cigarettes usage continues to climb until the end of their surveillance period, which was at age 25. Similarly, La Vecchia [8] reports for a 6&70 year old Italian birth cohort that 24% of males and 59% of females report having started smoking at age 30 or older. While such a large proportion of North Americans do not start smoking after age 30, 5 or 10% certainly do start late in life and this can pull the average age up quite a bit. Harris [9] also computes the AASS using data from the National Health Interview Survey (NHIS) for a sequence of birth cohorts without correcting for age dependency. He finds a decline in AASS similar to that reported by Stellman and Garfinkel [2]. Beginning with the oldest birth cohort and proceeding to the youngest, the AASS declines from 21 to 16 for males and from 3 1 to 17 for females. However, Harris does not offer the apparent decline of AASS as evidence that people are taking up smoking at earlier ages. Instead he uses AASS as the starting age for subjects with unknown age started in constructing age specific prevalence curves. While this particular use of the AASS (i.e. to replace missing data for cases in which the age of starting to smoke is unknown) avoids misinterpreting the age dependency, it introduces a more subtle artifact-it concentrates at a single age in each cohort the incidence of starting to smoke of all individuals who failed to report their actual age of starting. This has the effect of increasing the slope of the age specific smoking prevalence curve for each cohort in Harris’s Figs 1 and 2 and could possibly have introduced a spurious downward shift in the age of peak smoking prevalence in which Harris was interested. The error introduced by the age dependency in computing AASS can be avoided by fixing an
Age Related Changes in Age of Starting to Smoke
upper age for starting to smoke (the age of truncation) that remains the same for each birth cohort and by confining attention to birth cohorts for which all individuals have already attained the age of truncation. In this way the AASS for each successive birth cohort is computed for all individuals who started to smoke at ages younger than the age of truncation and all cohort members who could possibly start smoking before that age have already done so. The AASS computed in this manner is an underestimate of the true AASS, because it excludes all individuals in that birth cohort who have or will start to smoke at ages older than age of truncation. The AASS computed in this way does not depend on the current age of the birth cohort as long as the age of truncation is the same for all cohorts and there is no differential survival of smokers and nonsmokers (i.e. a survivor bias). The underestimate could be made smaller by raising the age of truncation, but only at the cost of excluding more of the younger individuals from the analysis. On the other hand, by lowering the age of truncation, more of the younger individuals can be included but at the cost of further underestimating the AASS. In the present instance, we shall compute the AASS for successive birth cohorts of individuals who started smoking at ages that were less than 25. We shall call ours the age in&pendent method. The 1989 Surgeon General’s Report [3] also bases its estimate of the average age of starting to smoke on data of reported age of starting to smoke obtained at one time. Making corrections for age dependency (similar to the ones we discuss) an apparent decline in the age of starting to smoke is observed for white females (but not for males or black females).* However, by comparing two different time periods at which data on initiation are available, it can be shown that the observation of a decrease in age of starting to smoke for white females in the Surgeon *Based on analyses in the report, the Surgeon General’s conclusion that the average age of starting to smoke has fallen over time is incorrect for white and black males and for black females. tThe basic tabulation was done using 5 year age groups for the entire range of ages covered by the NHIS so that subsequent calculations using the age independent method could be done using upper limits of 20, 25, or 30 years. Only the results for an upper limit of age 25 are presented here. There were too few subjects in the 90-94 and 95 + up categories, therefore in the results presented here we dropped the last two age categories entirely. SSince we used 1979 as the time of interview, age 20-24 corresponds to the 1955-1959 birth cohort, and so on.
135
General’s Report is an example of the distribution error. The error is due to the fact that a change in the distribution of smoking initiation with age occurred in which the proportion of individuals taking up smoking at older ages declined more rapidly than that at younger ages. We use the National Center for Health Statistics (NCHS) NHIS to compute the age dependent and age independent AASS for successive birth cohorts. The NHIS is ideal for the exploration we undertake here because it is a large probability sample of the U.S. population with well established reliability and validity [lo]. Since the ACS sample represents a different population, our results could differ from those Stellman and Garfinkel would have obtained had they used our method of computation. However, the relationship between the age dependent and the age independent methods would be similar for the two populations. Another advantage of using NHIS is that identical questions on age of starting to smoke were asked 10 years apart (1970 and 1979/80) so that proportions can be compared for a 10 year interval of individuals who started to smoke at various ages. In this way we can demonstrate the distribution error which the Surgeon General’s Report could have avoided if it had based its analysis on the initiation of smoking at different ages and at different time periods. METHOD
The 1970 and the combined 1979/80 NHIS public use data tapes were used for this analysis. The NHIS collects information on a nationwide sample of households as part of an ongoing activity of the NCHS. The 1970 NHIS data included useful information on smoking practice for 75,497 individuals and the 1979/80 NHIS on 34,800 individuals who were 17 years of age or older. The NHIS data sets include weighting factors which compensate for variations in sampling rate or in the population density within different sampling strata and adjust to the race/age/sex distribution of the U.S. population [I I]. Subjects in the NHIS file were cross classified as follows: Sex: male, female Race: white, black (other races were dropped) Tobacco (actually cigarette) use: Never, Former, Current (unknown status were dropped) Age (at time of interview): 20-24,25-29,. . . , 90-94, 95 + up.tt
136
J. J. W~NKAMand T. D.
Both the number of subjects and the sum of the weights were accumulated for each category. Let ZV,,0denote the number of subjects and W,,, denote the sum of the weights in each sex, race, tobacco, and age group. The subjects who had ever smoked were further classified according to age of starting to smoke by single years from age O-29, age 30+ up, and unknown who were dropped. Again both the number of subjects and the sum of the weights were accumulated. Let nsrrnb denote the number of subjects and w,,,, denote the sum of the weights in each sex, race, tobacco, age, and age begun smoking group. Finally, let P,,,Obe the set of subjects of sex, s, race, r, tobacco use t, and age a, who started at age 30 + up and let X wo = p;,*
wP*
Age independent method
To compute the age independent AASS for sex s, race r, age groups a,, . . . , a,, and a set of tobacco use groups T, for those who started smoking before age b0 where a, 2 b,,,* let
1
wsrub
rcT.mo,....o~
, b,, - 1. Then the age indepenforb=O,l,... dent AASS is given by: L.-I -y. bEb
0.5+*.
Eb=
1
for b = 0, . . . ,30. AASS is given by
Then
Wsr,czb
the age dependent
r‘T.ato,....q
0.5 + b-o
3-l
26 b=O Comparison of distribution of age of starting to smoke at d@erent times
The percentage of white and black, males and females who have started to smoke before 12, between 12 and 15, 16 and 18, 19 and 20, and 20 and 24 years of age were compared for 1970 and 1979/80. The results of this comparison are given in Table 4.
bP
where wp is the NHIS weight for person p and bp is the age at which person p began to smoke.
Eb=
SlERLINCi
;xo Eb 5
(The 0.5 accounts for the fact that the recorded age is age at last birthday, and on the average subjects have lived 0.5 years since their last birthday.)
RESULTS
Table 1 shows the males and females in birth cohorts 1915-24, 1905-14, and 1895-1904 (i.e. age groups 554, 65-74, and 75-84) who started to smoke after the age of 25 (expressed a percent of all individuals and of all smokers in these birth cohorts). The percent of all individuals indicates the relative proportion in the birth cohorts who take up the habit relatively late in life. The percent of all smokers indicates the extent to which individuals who started smoking after age 25 will produce an upward trend in AASS in these cohorts. (Table 1 does not show how many of these individuals quit smoking.) Table 2 gives the age independent AASS (and their standard errors) for individuals over 25 years of age who started to smoke before the age of 25, broken down by successive 10 year birth cohorts. Table I. Males and females in 1915-24. 1905-14, and 1895-1904* birth cohorts who started to smoke after the age of 25 as percent of all individuals and of all smokers in these birth cohorts (from 197911980NHIS data) White
Age dependent method
To compute the age dependent AASS for sex s, race r, age groups a,, . . . , a,, and a set of tobacco use groups T, let *For example, suppose the age of truncation is 25, and we wish to compute the AASS for white female ever smokers in the 2544 age range. In that case, b, = 25; s = female; r = white; T = {current, former} so that r takes on the values I = current and t = former; and u, = 25-29, cr = 40-44, so that a takes on the values 25-29, 30-34, 35-39, 4044.
Birth cohort
Percent all
Black
Percent smokers
Percent all
Percent smokers
9.18 4.12 5.67
13.57 7.56 10.53
15.20 9.85 8.24
34.76 43.92 49.35
Males
1915-24 1905-14 18954
4.74 7.26 7.80
3915-24 1905-14 18954
II.09 14.37 12.21
6.40 10.54 14.18 Females
*Corresponding and 7584.
25.06 39.97 69.61
to age groups in 1979 of 55-64. 65-74,
Age Related Changes in Age of Starting lo Smoke
137
Table 2. AASS for individuals over 25 years of age who started to smoke beforr age 25 (from 1979/1980NHIS data) White Birth cohort
Current
Black
Former
Ever
Current
Former
Ever
Males 1945-54
Avg. age SE
17.36 0.08
17.32 0.12
17.35 0.07
17.93 0.21
16.81 0.56
17.71 0.20
1935-44 Avg. age SE
17.02 0.11
17.38 0.12
17.16 0.08
17.65 0.31
18.37 0.57
17.85 0.27
17.06 0.12
17.42 0.11
17.23 0.08
17.73 0.39
17.08 0.54
17.52 0.32
1915-24 Avg. age SE
16.66 0.14
17.24 0.14
16.96
0.10
17.45 0.46
17.22 0.42
17.38 0.34
1905-14 Avg. age SE
16.87 0.22
17.40 0.14
17.23 0.12
16.76 0.66
18.10 0.65
17.34 0.47
1895-1904 Avg. age SE
16.70 0.40
17.05 0.26
16.98 0.22
16.50 0.93
18.14 0.75
17.56 0.60
1895-1954 Avg. age SE
17.07 0.05
17.33 0.06
17.19 0.04
17.66 0.15
17.48 0.24
17.61 0.13
1925-34 Avg. age
SE
Females 1945-54 Avg. age SE
17.90 0.08
17.89
0.11
17.90 0.07
18.65 0.22
18.38 0.39
18.59 0.19
193s44 Avg. age SE
18.17 0.09
18.25
18.19
0.13
0.08
18.08 0.33
18.48 0.48
18.17 0.27
1925-34 Avg. age SE
18.79 0.11
18.68 0.14
18.76 0.08
18.02 0.44
17.82 0.71
17.97 0.37
1915-24 Avg. age SE
19.06 0.13
18.75 0.16
18.94
0.10
18.09 0.62
17.83 0.81
18.00 0.49
1905-14 Avg. age SE
18.71 0.22
18.99 0.21
18.84 0.15
16.90 1.42
19.19 0.61
18.20 0.69
1895-1904 Avg. age SE
18.85 0.97
19.12 0.50
19.01 0.49
16.17 2.59
20.50 -
17.73 1.80
1895-1954 Avg. age SE
18.37 0.05
18.40 0.06
18.38 0.04
18.24 0.17
18.31 0.26
18.26 0.14
There is no consistent the age independent
or significant
change in
AASS from older to younger birth cohorts. Computations of the age independent AASS using 20 and 30 years of age as the upper limit exhibit the same trends as are seen in Table 2. (They are not shown here but are available on request.) Table 3 shows the age dependent AASS for the same birth cohorts. The age dependent AASS decreases steadily for males and very sharply and significantly for females. In
fact, the shape of the falling trend is almost identical for white males and females to that observed by Stellman and Garfinkel [2] for the ACS data and shown in their Fig. 3. (Stellman and Garfinkel’s graphs show males and females for all races combined, while our results are presented separately for whites and blacks. However the proportion of nonwhites in their sample is only a fraction of the proportion of nonwhites in the U.S. population.)
I38
J. J. WEINKAM and T. D. STERLING Table 3. AASS for individuals over 25 years of age, computed using the age dependent method (from 19790980 NHIS data) White Birth cohort
Current
-_ Ever
Former
Black Current
Former
Ever
Males 1945-54 Avg. age SE
17.54 0.09
17.41 0.13
17.50 0.07
18.28 0.26
17.34 0.63
18.09 0.24
193544 Avg. age SE
17.54 0.14
17.66 0.14
17.59 0.10
18.63 0.48
19.00 0.63
18.73 0.39
1925-34 Avg. age SE
17.77 0.16
18.02 0.17
17.89 0.12
18.56 0.46
17.98 0.68
18.37 0.38
1915-24 Avg. age SE
17.61 0.21
18.00 0.17
17.81 0.14
19.06 0.71
19.10 0.77
19.08 0.54
1905-14 Avg. age SE
18.75 0.40
18.72 0.22
18.73 0.20
17.55 0.82
19.96 1.26
18.63 0.73
189551904 Avg. age SE
17.79 0.65
19.48 0.47
19.18 0.40
16.50 0.93
24.27 4.28
21.82 3.03
189551954 Avg. age SE
17.69 0.07
18.06 0.08
17.86 0.05
18.47 0.21
18.76 0.40
18.56 0.19
Females 1945-54 Avg. age SE
18.52 0.10
18.19 0.13
18.42 0.08
19.31 0.27
19.16 0.50
19.28 0.24
193544 Avg. age SE
19.34 0.15
19.04 0.19
19.24 0.12
20.03 0.50
18.48 0.48
19.72 0.42
1925-34 Avg. age SE
21.19 0.23
26.63 0.28
21.02 0.18
20.53 0.71
21.09 1.19
20.68 0.61
1915-24 Avg. age SE
22.51 0.28
21.79 0.35
22.24 0.22
23.98 1.13
21.70 1.75
23.29 0.95
1905-14 Avg. age SE
25.74 0.58
24.35 0.50
25.12 0.39
26.51 3.62
25.85 2.51
26.14 2.08
1895-1904 Avg. age SE
34.72 1.73
28.29 1.06
31.66 1.06
24.20 11.54
31.41 3.66
28.68 4.77
1895-1954 Avg. age SE
20.89 0.11
20.71 0.14
20.83 0.09
20.76 0.33
21.27 0.60
20.90 0.29
The relationships between the age dependent and age independent methods of computation are also shown graphically in Figs 1 and 2. The age independent AASS does not change appreciably with increasing or decreasing age of birth cohorts. A conclusion that younger individuals are taking up smoking in increasing numbers is not justified. Even if the age independent AASS did decrease for younger birth cohorts, this would not necessarily imply that proportionately more individuals were taking up smoking at younger ages. It could just as well
be true that proportionately fewer individuals were taking up smoking at older ages. To answer the question of whether or not more individuals are taking up smoking at younger ages requires comparing the distributions of age of starting to smoke for successive time periods. Differences in a summary statistic such as AASS can be misleading. The fact that 1970 and 1979/80 NHIS asked identical questions concerning age of starting to smoke makes it possible to compare the distribution of age started to smoke for two
Age Related Changes in Age of Starting to Smoke
1 ,,I
1945-!M
la3544
lsa-34
tsm-24
lsos-14
le9!m4
l945-54
l9xv44
l925-34
t9rr24
190544 !a9504
Birth cohwt
Birth cohort
Fig. 1. Graphic presentation of trends in male eversmoker’s age of starting to smoke for age dependent and age independent methods of computation.
Fig. 2. Graphic presentation of trends in female eversmoker’s age of starting to smoke for age dependent and age independent methods of computation.
comparable samples surveyed 10 years apart, and based on probability samples of the U.S. population. Table 4 compares for the 1970 and 1979/80 U.S. population, the percent of black and white males and females between the ages of 25 and 34 who started to smoke at different ages. This is the youngest group for which such a comparison is possible if ages of starting up to 25 are to be considered. Percentages are expressed as percent of all black and white males and females in the respective 25-34 age groups. There is a significant decrease in the proportion of individuals starting to smoke before age 25 in each race and sex group from 1970 to 1979/80 (except for a very small and not significant increase for black males 12-15 and white females below 15). For instance, the percentage of white females in the 25-34 age group who started to smoke before age 25 decreased from 49.72% in 1970 to 45.00% in 1979/80, a decrease of almost 10%. For white males the drop was from 66.64 to 60.60%, again a decrease of almost 10%. It is
of interest that the decreases for white males and females were quite similar. Decreases in individuals starting to smoke are more pronounced among blacks, especially black males. (Again, Table 4 does not indicate the number of individuals within the 25-34 age range who both started and ceased smoking. Readers may refer to our paper in the American Journal of Industrial Medicine [12] that gives some breakdowns for smoking cessation in the same population.) DISCU!WON
Errors due to age dependencies have a long and distinguished history in epidemiology and statistics. For instance, Warren [13] claimed in 1956 that radiologists died at an average age that was younger than that of other medical specialties because of their exposure to radiation. However, as Seltser and Sartwell [14] showed in 1958, the difference in average age at death was due to differences in the age distributions as radiology still was a new profession
Table 4. Percent of black and white males and females who started to smoke in different age ranges in 1970 and 1979/80 White
Age
Black
Started
smoking
1970
1979180 change
1979180
change
1970 3.77 13.56 31.02 12.17 10.35 70.87
1.35 14.04 25.73 8.98 8.33 58.43
-2.42 +0.48 -5.29 -2.02 -2.02 -12.44
0.80 7.69 17.56 9.11 9.29 44.45
0.14 6.72 17.04 7.95 6.94 38.79
-0.66 -0.97 -0.52 -1.16 -2.25 -7.70
