Cohort bias in the analysis of Californian passive smoking
In Enstrom and Kabat’s paper on passive smoking in California (1)
there is a striking and perverse relationship between the level of spousal
smoking in 1959 and the risk of death from Coronary Heart Disease (CHD) in
the ‘passive smoker’ as defined by the study – the greater had been a
man’s cigarette consumption in 1959 the less likely, it seems, was the
death of his wife from CHD.
I would suggest that there is a clear reason for this anomaly that
illustrates a profound flaw in the paper’s method and throws into question
its findings.
Selection bias
If we consider the group of never-smoking women married to smokers in the
Californian paper, it is clear that there was a bias in their age
distribution at the outset of the study. The 1959 mean age of women
married to smokers decreased with the level of smoking in their spouses.
Thus the wives of 40-a-day smokers had a mean age 4 years younger than the
wives of 1 to 19-a-day smokers.
The emergence of this pattern is not surprising. Smokers are likely
to die prematurely and this tendency increases with the heaviness of the
habit. As a result, random selection from the general population will
produce the observed bias in age of couples (assuming, reasonably, that
there is an association between the age of spouses).
Never-smoking husbands of smoking women did not have the same age
gradient, perhaps because of the small numbers (45) in the 40-a-day group.
However, they had an average age in 1959 some 4-5 years lower than never-
smoking husbands of never-smoking wives.
Taking the example of the wives of 40-a-day smokers, by virtue of
being nearly 4 years younger on average than the control group, their age
specific mortality rates, were one to calculate them, would be drawn from
observations made on average 4 years later than the controls.
Cohort effect
Against a background of stable mortality this might not matter. However,
during the period of study, the CHD mortality rate in the USA, as in other
western nations, was falling very rapidly (2)
(http://www.cdc.gov/nchs/hus.htm). Between the mid-1960s and mid-1990s it
fell by as much as two thirds in the 45-74 age group. On average this
means that mortality rates for these age groups were falling by about 15%
in every four year period.
Some of this change, perhaps as much as a third, may be attributed to
changes in smoking behaviour (3) . The majority is attributable to other
factors.
For any given age the ‘passive smokers’ were, thus, predominantly
from a population whose overall CHD mortality had fallen significantly in
relation to the controls of the same age.
In their analysis, Enstrom and Kabat used the Cox proportional hazard
model. This approach, being a form of survival analysis, maps survival
curves for compared groups from entry to the study and tests for a
difference between these curves.
Given the trend of rapidly changing societal CHD mortality, the
mortality profile of a risk group is characteristic of an interaction
between age and the time at which the observations were made, and is not
simply a function of the age of the subjects within that risk group.
Adjusting for age alone will not remove the interaction of age and
time of observation from the analysis. As a result, this cohort effect has
not been controlled out of the calculations through age-adjustment.
Indeed, no mention is made of it as a potential issue.
This cohort effect means that even if no difference in risk existed
between female partners of 40-a-day smokers and controls, the partners of
smokers should, in the absence of correction, exhibit a marked reduction
in CHD mortality risk.
It is likely that this is the origin of the trend in relative risk
seen in never-smoking women married to smoking men.
The spouses of smoking wives, on the other hand, are described in the
results as having relative risks which, although non-significant, are
below 1 for those married to smokers consuming 0-20 cigarettes and higher
than 1 in the >21-a-day group. In this instance there is an apparent
upward gradient with increased spousal smoking.
I would suggest in this instance that the lack of an age gradient at
entry to the study may have allowed the emergence of a genuine gradient in
association of CHD risk with passive smoking. The numbers are much
smaller, but again it is likely that the relative risks have been
diminished by a cohort effect. A real association may have been reduced in
scale and rendered non-significant.
Other factors
Davey Smith (4) has drawn attention to potential problems of confounding
in Enstrom and Kabat’s study. He and others have argued that being married
to a smoker was a very poor indicator of passive smoking exposure for much
of the period of this study, given the high degree of environmental
exposure that obtained outside the home in past decades.
If the risk arising from passive smoking were an increase in CHD
mortality of 30%, the latter factor alone would be likely to render
smaller the observed difference. This issue has been explored elsewhere
and I wouldn’t wish to dwell on it further.
Further comment, however, should be made on use of the Cox
proportional hazard model. This method is critically dependent upon
proportionality between the two curves at all points following entry to
the study (5).
It is not impossible to test for proportionality of hazard but it is
difficult and is frequently not done. We are not told if such a test was
performed by Enstrom & Kabat, but as it is not mentioned in their
method, or in the statistical referees comments it seems likely that
proportionality has been assumed.
Age-specific mortality from CHD increases exponentially in adult life
other than at extremes of old age. In comparing two CHD survival curves
for different risk groups, one is almost certainly comparing two
exponential curves which differ not only in scale but also in doubling
time. As such they cannot be proportional.
How much this non-proportionality matters is hard to say, but one
would have to question the effectiveness of age-adjustment for two such
curves under the Cox proportional hazard model. The curves are likely to
differ in shape, both as a result of the cohort from which they are drawn
and arising from any genuine difference in risk.
Conclusion
The cohort effect described in this letter is potentially as large or
larger than any of these factors. Although we cannot know with precision,
its scale is plausibly sufficient to obliterate a genuine effect of
passive smoking.
In its support: the effect can be seen to arise systematically
through a random process; there is clear evidence of its existence in the
presented data; the outcomes of analysis are consistent with its effects
and their biologically implausible anomalies become explicable; allowance
was not made for it in the method (nor identified as a problem in the
referees’ comments); and it would reconcile observations from this study
with others.
Against this hypothesis: my assumptions are based on trends whose
significance has not been statistically tested; and I have interpolated
broad population trends to a specific population.
On balance, and taken together with the other flaws in the design, I
would suggest that a cohort bias is a central flaw of the study of ETS and
tobacco related mortality.
Importantly, the strength of this cohort effect is likely to be
sufficient that the risk of passive smoking could quite plausibly be as
high as previous studies have suggested, and yet still not be apparent
under Enstrom and Kabat’s method.
References
1. Enstrom JE, Kabat GC. Environmental tobacco smoke and tobacco related
mortality in a prospective study of Californians, 1960-98. BMJ
2003;326(7398):1057-0.
2. National Center for Health Statistics. Health, United States,
2002. Hyattsville, Maryland: NCHS; 2002.
3. Capewell S, Morrison CE, McMurray JJ. Contribution of modern
cardiovascular treatment and risk factor changes to the decline in
coronary heart disease mortality in Scotland between 1975 and 1994. Heart
1999;81(4):380-6.
4. Davey Smith G. Effect of passive smoking on health. BMJ
2003;326(7398):1048-1049.
5. Altman DG, Machin D, Bryant TN, Gardner MJ. Statistics with
confidence. Second edition ed. London: BMJ Books; 2000.
Competing interests:
None declared
Competing interests:
No competing interests
29 May 2003
Eugene Milne
Deputy Medical Director
Northumberland, Tyne & Wear Strategic Health Authority, Newcastle upon Tyne, NE4 6BE
Rapid Response:
Cohort bias in the analysis of Californian passive smoking
In Enstrom and Kabat’s paper on passive smoking in California (1)
there is a striking and perverse relationship between the level of spousal
smoking in 1959 and the risk of death from Coronary Heart Disease (CHD) in
the ‘passive smoker’ as defined by the study – the greater had been a
man’s cigarette consumption in 1959 the less likely, it seems, was the
death of his wife from CHD.
I would suggest that there is a clear reason for this anomaly that
illustrates a profound flaw in the paper’s method and throws into question
its findings.
Selection bias
If we consider the group of never-smoking women married to smokers in the
Californian paper, it is clear that there was a bias in their age
distribution at the outset of the study. The 1959 mean age of women
married to smokers decreased with the level of smoking in their spouses.
Thus the wives of 40-a-day smokers had a mean age 4 years younger than the
wives of 1 to 19-a-day smokers.
The emergence of this pattern is not surprising. Smokers are likely
to die prematurely and this tendency increases with the heaviness of the
habit. As a result, random selection from the general population will
produce the observed bias in age of couples (assuming, reasonably, that
there is an association between the age of spouses).
Never-smoking husbands of smoking women did not have the same age
gradient, perhaps because of the small numbers (45) in the 40-a-day group.
However, they had an average age in 1959 some 4-5 years lower than never-
smoking husbands of never-smoking wives.
Taking the example of the wives of 40-a-day smokers, by virtue of
being nearly 4 years younger on average than the control group, their age
specific mortality rates, were one to calculate them, would be drawn from
observations made on average 4 years later than the controls.
Cohort effect
Against a background of stable mortality this might not matter. However,
during the period of study, the CHD mortality rate in the USA, as in other
western nations, was falling very rapidly (2)
(http://www.cdc.gov/nchs/hus.htm). Between the mid-1960s and mid-1990s it
fell by as much as two thirds in the 45-74 age group. On average this
means that mortality rates for these age groups were falling by about 15%
in every four year period.
Some of this change, perhaps as much as a third, may be attributed to
changes in smoking behaviour (3) . The majority is attributable to other
factors.
For any given age the ‘passive smokers’ were, thus, predominantly
from a population whose overall CHD mortality had fallen significantly in
relation to the controls of the same age.
In their analysis, Enstrom and Kabat used the Cox proportional hazard
model. This approach, being a form of survival analysis, maps survival
curves for compared groups from entry to the study and tests for a
difference between these curves.
Given the trend of rapidly changing societal CHD mortality, the
mortality profile of a risk group is characteristic of an interaction
between age and the time at which the observations were made, and is not
simply a function of the age of the subjects within that risk group.
Adjusting for age alone will not remove the interaction of age and
time of observation from the analysis. As a result, this cohort effect has
not been controlled out of the calculations through age-adjustment.
Indeed, no mention is made of it as a potential issue.
This cohort effect means that even if no difference in risk existed
between female partners of 40-a-day smokers and controls, the partners of
smokers should, in the absence of correction, exhibit a marked reduction
in CHD mortality risk.
It is likely that this is the origin of the trend in relative risk
seen in never-smoking women married to smoking men.
The spouses of smoking wives, on the other hand, are described in the
results as having relative risks which, although non-significant, are
below 1 for those married to smokers consuming 0-20 cigarettes and higher
than 1 in the >21-a-day group. In this instance there is an apparent
upward gradient with increased spousal smoking.
I would suggest in this instance that the lack of an age gradient at
entry to the study may have allowed the emergence of a genuine gradient in
association of CHD risk with passive smoking. The numbers are much
smaller, but again it is likely that the relative risks have been
diminished by a cohort effect. A real association may have been reduced in
scale and rendered non-significant.
Other factors
Davey Smith (4) has drawn attention to potential problems of confounding
in Enstrom and Kabat’s study. He and others have argued that being married
to a smoker was a very poor indicator of passive smoking exposure for much
of the period of this study, given the high degree of environmental
exposure that obtained outside the home in past decades.
If the risk arising from passive smoking were an increase in CHD
mortality of 30%, the latter factor alone would be likely to render
smaller the observed difference. This issue has been explored elsewhere
and I wouldn’t wish to dwell on it further.
Further comment, however, should be made on use of the Cox
proportional hazard model. This method is critically dependent upon
proportionality between the two curves at all points following entry to
the study (5).
It is not impossible to test for proportionality of hazard but it is
difficult and is frequently not done. We are not told if such a test was
performed by Enstrom & Kabat, but as it is not mentioned in their
method, or in the statistical referees comments it seems likely that
proportionality has been assumed.
Age-specific mortality from CHD increases exponentially in adult life
other than at extremes of old age. In comparing two CHD survival curves
for different risk groups, one is almost certainly comparing two
exponential curves which differ not only in scale but also in doubling
time. As such they cannot be proportional.
How much this non-proportionality matters is hard to say, but one
would have to question the effectiveness of age-adjustment for two such
curves under the Cox proportional hazard model. The curves are likely to
differ in shape, both as a result of the cohort from which they are drawn
and arising from any genuine difference in risk.
Conclusion
The cohort effect described in this letter is potentially as large or
larger than any of these factors. Although we cannot know with precision,
its scale is plausibly sufficient to obliterate a genuine effect of
passive smoking.
In its support: the effect can be seen to arise systematically
through a random process; there is clear evidence of its existence in the
presented data; the outcomes of analysis are consistent with its effects
and their biologically implausible anomalies become explicable; allowance
was not made for it in the method (nor identified as a problem in the
referees’ comments); and it would reconcile observations from this study
with others.
Against this hypothesis: my assumptions are based on trends whose
significance has not been statistically tested; and I have interpolated
broad population trends to a specific population.
On balance, and taken together with the other flaws in the design, I
would suggest that a cohort bias is a central flaw of the study of ETS and
tobacco related mortality.
Importantly, the strength of this cohort effect is likely to be
sufficient that the risk of passive smoking could quite plausibly be as
high as previous studies have suggested, and yet still not be apparent
under Enstrom and Kabat’s method.
References
1. Enstrom JE, Kabat GC. Environmental tobacco smoke and tobacco related
mortality in a prospective study of Californians, 1960-98. BMJ
2003;326(7398):1057-0.
2. National Center for Health Statistics. Health, United States,
2002. Hyattsville, Maryland: NCHS; 2002.
3. Capewell S, Morrison CE, McMurray JJ. Contribution of modern
cardiovascular treatment and risk factor changes to the decline in
coronary heart disease mortality in Scotland between 1975 and 1994. Heart
1999;81(4):380-6.
4. Davey Smith G. Effect of passive smoking on health. BMJ
2003;326(7398):1048-1049.
5. Altman DG, Machin D, Bryant TN, Gardner MJ. Statistics with
confidence. Second edition ed. London: BMJ Books; 2000.
Competing interests:
None declared
Competing interests: No competing interests