- Email: [email protected]
Reply to Mr. Goldstein
Volume Number
Correspondence
114 4
births, the sensitivity of the statistical comparisons of death rates is equivalent to that in a sample of births only, of a size of 150,000. This is larger than all the other published studies put together! Another fact which Yerushalmy overlooks is that uZZ the major studies show similar reductions in average birth weight associated with smoking (150 to 200 grams). If this finding is taken seriously, we have to look for an explanation of why the studies show apparently inconsistent findings regarding mortality differences. There is, in fact, no “paradox” about this, and the explanation, I believe, is related to the observation that the large differences between smokers and nonsmokers tend to occur in the samples containing high proportions of low-birthweight babies. It is clear that a reduction of, say, 200 grams in birth weight will have a much greater effect on the mortality risk of a baby who would have a low birth weight anyway than on a baby of normal birth weight. One would, therefore, expect that those studies with larger proportions of low-birth-weight babies would also show greater differences in mortality rates between smokers and nonsmokers. This point and other related ones are taken up in more detail elsewhere.3 My final comment concerns the higher mortality rate among low-birth-weight babies of nonsmokers compared to the low-birth-weight babies of smokers. Yerushalmy finds this interesting but can find no reasonable explanation for it. It is, on the contrary, perfectly reasonable and a simple consequence of the fact that the smokers’ babies who weigh less than 2,500 grams have a higher mean birth weight than the nonsmokers’ babies under 2,500 grams. The reason for this is that the birth-weight distribution for babies of smokers is shifted down from that of babies of nonsmokers by about 200 grams, and the shape of this distribution is, therefore, the same as the shape of that for nonsmokers’ babies under about 2,700 grams. This can clearly be seen in Fig. 3 of Yerushalmy’s paper. I have tried to show that the available evidence does not support either Yerushalmy’s claim that maternal smoking is unrelated to perinatal death or his claim that it is the smoker rather than the smoking which is causative. In the present state of knowledge, we have little alternative but to work on the assumption that smoking C harmful, and it would be a pity if his paper
571
were to cause any reduction in efforts to persuade mothers to give up smoking during pregnancy. H. National Children’s Adam Howe 1 Fitzroy Square London WlP, 5AH,
Goldstein
Bureau
England
REFERENCES
Yerushalmy, J.: AM. J. OBSTET. GYNECOL. 112: 277, 1972. Butler, N. R., and Alberman, E. D.: Perinatal Mortality, Edinburgh, 1969, E. & S. Livingstone, Ltd. Butler, N. R., Goldstein, H,, and Ross, E.: Br. Med. J. April 15, p. 127, 1972. Reply To
the
to
Mr.
Goldstein
Editors:
First, it is important to ascertain whether infants of smoking mothers suffer higher neonatal mortality rates than those of nonsmokers. In the paper, I gave a very definite negative answer to this question. This was based on a comprehensive review of the literature. Mr. Goldstein bases his affirmative answer basically on a single study in which he participated, namely, the British study of Butler and Alberman (see Reference 2 in the above letter). There are 14 relatively small studies and 4 studies based on large samples in which the question of the perinatal mortality rate is discussed in connection with smoking during pregnancy. As to the smaller studies, I stated as follows: “ . . . the probability that 7 of 14 studies, each of which was based on some 2,000 pregnancies, would miss a 35 per cent increase in mortality rate, if such an increase really existed, is very small. . . .” I thought at the time that the proof of this statement was not very complicated and, therefore, did not provide it in the text. However, since Mr. Goldstein states that, “. . . there seems to be an error in the calculation of the probability. . . .,” I am providing the familiar textbook solution. I obtained an estimate of the increase in the proportion of low birth weight among infants of smokers from the data in the studies based on large samples. The weighted averages for the incidence of low birth weight yielded by these studies are 4.99 per cent for nonsmokers and 8.60 per cent for smokers. (Incidentally, these figures are very close to the 5.4 and 9.3 per cent, respectively, of the studies of Butler and associates in which Mr. Goldstein participated.)
572
Correspondence
For the best estimate of the neonatal mortality rate of low-birth-weight infants and of the heavier infants, I used the largest available study on this subject based on some 750,000 births.r These rates are 174 per thousand for low-birth-weight infants and 7.8 per thousand for infants weighing more than 2,500 grams. I introduce the following conditional probabilities : P(D/S)
=
Pr
(an infant of a smoking mother will die during the neonatal period) ;
P(L/S)
=
Pr
(a smoking mother to a low-birth-weight
P(D/L)
=
Pp
(a low-birth-weight in the neonatal
The symbols defined for P(D/z) of more
P( D/s) nonsmoking
and
will
give birth infant) ;
infant period).
will
P( L/s) mothers’
is defined for infants than 2,500 grams.
die
are similarly infants, and
with birth weights The problem is to
prove that P(D/S) is no greater than P(D/g). These two probabilities may be estimated from the available information with the use of the familiar formulas : P(D/S) P(D/s) P(D/L)
= =
P(L/S)P(D/L) P(L,‘s)P(D/L)
=
0.174; P(D/r) and P(L/3)
0.0860;
+ P(x/S)P(D/x); + P(x/s)P(D/x). =
= 0.0078; 0.0499.
P(L/S)
=
Substituting these values in the above formulas provides the following estimates: (PD/S) = 0.0221, and P(D/$) = 0.0161 (an expected increase in the mortality rate of infants of smokers of 37 per cent). Based on these estimates, we can compute the desired probabilities. For a study of 2,000 infants (1,000 infants each of smoking mothers and of nonsmoking mothers), normal approximation shows that the probability that the death rate of infants of smoking mothers will be no greater than the death rate of infants of nonsmoking mothers is r = 0.163. NOW suppose there are 14 such studies and let X be the number of studies where the death rate of infants of smoking mothers will be no greater than that of nonsmoking mothers. Clearly, X is a binomial random variable with the parameter r = 0.163 and the probability distribution : (0.163)'(
k =
(1 - 0.163)1*-k 0, I, . ., 14:
Direct ability:
computation
Pr(X
yields
2
7)
the
=
cumulative
prob-
0.00366.
This means that the probability is 0.00366 (or 3.7 in 1,000) that, among 14 studies, 7 or more will show infant death rates of smoking mothers no greater than those of nonsmoking mothers. Since this probability is very small, the hypothesis that an increase in neonatal death in infants of smokers exists is rejected. As to the larger studies, Mr. Goldstein uses the results of our studies among the blacks as support for the findings of the studies in which he participated. He states, “. two studies (Yerushalmy’s of blacks and Butler and Alberman’s) show large and significunt differences between smokers and nonsmokers. . . .” (the underscoring of the word significant is mine). I don’t know what test of significance Mr. Goldstein used on our data, but in this case it is not necessary for me to go into great detail. The total number of blacks in our study was some 3,300. In a previous paper,z with which Mr. Goldstein is familiar since he wrote a letter about it to the editor of the American Journal of Efidemiology, the breakdown is given as 2,219 nonsmokers and 1,071 smokers. The respective neonatal mortality rates were 17.1 and 21.5 per thousand. A simple test would show that the probability that a difference as large as or larger than this could have occurred by chance is very great ($ = 0.75; P > 0.30). We are, therefore, left with only a single large study showing an increase in the perinatal mortality rate of infants of smokers and 3 large studies which found no such difference. These are in addition to the 7 relatively smaller studies which found no difference. Mr. Goldstein did not mention that the only study which found the difference, namely, the one in which he was retrospective, All the other participated, three were prospective. As to the 6,500 deaths (the so-called 3 month deaths), the less said about these, the better. The control subjects for these were not from the cohort of births in the 3 months but from those of a single week. In fact, the main report of Butler and Alberman on smoking utilized only the data from the so-called “control week” and did not leave themselves open to serious methodologic criticism by including the “3 month deaths.”
Volume
114
Number
4
Pride of authorship is an understandable human frailty. But in this case it is stretched a bit. Any objective evaluation of ull the evidence must come to the definite conclusion that infants of smokers do not suffer higher neonatal mortality rates than infants of nonsmokers. Mr. Goldstein finds easy explanations for other puzzling findings without bothering to test them. Thus, when referring to the finding, in all 3 large studies, that the mortality rate among low-birthweight infants of nonsmokers is much higher than that of low-birth-weight infants of smokers, he states that, “It is . . . perfectly reasonable and a simple consequence of the fact that the smokers’ babies who weigh less than 2,500 grams have a higher mean birth weight than the nonsmokers’ babies under 2,500 grams.” In the paper which was published in the American Journal of Eflidemiology,z with which Mr. Goldstein is familiar, Table 5, page 448, I compared the neonatal mortality rates of babies of nonsmokers and smokers not only in the group weighing 2,500 grams or less as a whole but in each subdivision. For example, in those babies weighing 1,5GO grams or less, the neonatal mortality rates for nonsmokers and smokers were 791.7 and 565.2, respectively. In the group with birth weights of 1,5Gl to 2,GGG grams, the corresponding rates were 406.3 and 346.2, respectively, and, in the group with birth weights of 2,OGl to 2,5GO grams, the corresponding rates were 78.G and 26.6, respectively. Mr. Goldstein also has a very simple explanation for the new finding in the paper published in this ~ouaXAI~-that women who subsequently became smokers had a high incidence of lowbirth-weight infants also during the period before they started to smoke. He states: “. . . in the group of mothers who began smoking before they were 25 years of age, the babies who were born before smoking started will belong to mothers younger than those who never smoked at all.” Anyone who is familiar with the problem of reproduction in human beings knows that within the limited range of ages under 25 years the variation in the proportion of low-birth-weight infants is very small and could not account for the large differences found. Mr. Goldstein apparently was not aware of this, but he could have easily tested it on his own material. In any case, Table
Correspondence
573
Table I. Proportion
of low-birth-weight by age of mother (white) I I 5 2,500 grams
infants
Total live births
15 16 17 18 19 20 21 22 23 24 25 Total
Per cent
No.
20 69 170 347 535 732 766 751 783 719 653
1 5 14 22 37 42 43 45 38 44 37
5.0 7.2 8.2 6.3 6.9 5.7 5.6 6.0 4.9 6.1 5.7
5,543
328
5.9
1 which is based on all our data from women 25 years and younger shows definitely that the differences age by age are small and irregular. Mr. Goldstein closes his letter with the pious statement that, “. it would be a pity if his paper were to cause any reduction in efforts to persuade mothers to give up smoking during pregnancy.” May 1 say that, on the contrary, it would be a pity to recommend a course of action based on conjectures, subjective notions, and easy explanations not supported by available data. The hard scientific data show conclusively that it is not reasonable to expect that giving up smoking will cause a rise in birth weight. It is important to consider also the possibility that “efforts to persuade mothers to give up smoking during pregnancy” may result in emotional stress and feelings of guilt among mothers who may have tried to quit smoking and did not succeed. Professor Child Health and Deuelopment School of Public Health University of California Berkeley, California 94720
1. Yerushalmy of Biostatistics Studies
REFERENCES
Shapiro, S,, Schlesinger, E., and Nesbitt, R. E, L.: Infant, Perinatal, Maternal and Childhood Mortality in the United States, Boston, 1968, Harvard University Press, p. 51. 2. Yerushalmy, J.: Am. J, Epidemiol. 93: 443, 1971. I.
Correspondence
114 4
births, the sensitivity of the statistical comparisons of death rates is equivalent to that in a sample of births only, of a size of 150,000. This is larger than all the other published studies put together! Another fact which Yerushalmy overlooks is that uZZ the major studies show similar reductions in average birth weight associated with smoking (150 to 200 grams). If this finding is taken seriously, we have to look for an explanation of why the studies show apparently inconsistent findings regarding mortality differences. There is, in fact, no “paradox” about this, and the explanation, I believe, is related to the observation that the large differences between smokers and nonsmokers tend to occur in the samples containing high proportions of low-birthweight babies. It is clear that a reduction of, say, 200 grams in birth weight will have a much greater effect on the mortality risk of a baby who would have a low birth weight anyway than on a baby of normal birth weight. One would, therefore, expect that those studies with larger proportions of low-birth-weight babies would also show greater differences in mortality rates between smokers and nonsmokers. This point and other related ones are taken up in more detail elsewhere.3 My final comment concerns the higher mortality rate among low-birth-weight babies of nonsmokers compared to the low-birth-weight babies of smokers. Yerushalmy finds this interesting but can find no reasonable explanation for it. It is, on the contrary, perfectly reasonable and a simple consequence of the fact that the smokers’ babies who weigh less than 2,500 grams have a higher mean birth weight than the nonsmokers’ babies under 2,500 grams. The reason for this is that the birth-weight distribution for babies of smokers is shifted down from that of babies of nonsmokers by about 200 grams, and the shape of this distribution is, therefore, the same as the shape of that for nonsmokers’ babies under about 2,700 grams. This can clearly be seen in Fig. 3 of Yerushalmy’s paper. I have tried to show that the available evidence does not support either Yerushalmy’s claim that maternal smoking is unrelated to perinatal death or his claim that it is the smoker rather than the smoking which is causative. In the present state of knowledge, we have little alternative but to work on the assumption that smoking C harmful, and it would be a pity if his paper
571
were to cause any reduction in efforts to persuade mothers to give up smoking during pregnancy. H. National Children’s Adam Howe 1 Fitzroy Square London WlP, 5AH,
Goldstein
Bureau
England
REFERENCES
Yerushalmy, J.: AM. J. OBSTET. GYNECOL. 112: 277, 1972. Butler, N. R., and Alberman, E. D.: Perinatal Mortality, Edinburgh, 1969, E. & S. Livingstone, Ltd. Butler, N. R., Goldstein, H,, and Ross, E.: Br. Med. J. April 15, p. 127, 1972. Reply To
the
to
Mr.
Goldstein
Editors:
First, it is important to ascertain whether infants of smoking mothers suffer higher neonatal mortality rates than those of nonsmokers. In the paper, I gave a very definite negative answer to this question. This was based on a comprehensive review of the literature. Mr. Goldstein bases his affirmative answer basically on a single study in which he participated, namely, the British study of Butler and Alberman (see Reference 2 in the above letter). There are 14 relatively small studies and 4 studies based on large samples in which the question of the perinatal mortality rate is discussed in connection with smoking during pregnancy. As to the smaller studies, I stated as follows: “ . . . the probability that 7 of 14 studies, each of which was based on some 2,000 pregnancies, would miss a 35 per cent increase in mortality rate, if such an increase really existed, is very small. . . .” I thought at the time that the proof of this statement was not very complicated and, therefore, did not provide it in the text. However, since Mr. Goldstein states that, “. . . there seems to be an error in the calculation of the probability. . . .,” I am providing the familiar textbook solution. I obtained an estimate of the increase in the proportion of low birth weight among infants of smokers from the data in the studies based on large samples. The weighted averages for the incidence of low birth weight yielded by these studies are 4.99 per cent for nonsmokers and 8.60 per cent for smokers. (Incidentally, these figures are very close to the 5.4 and 9.3 per cent, respectively, of the studies of Butler and associates in which Mr. Goldstein participated.)
572
Correspondence
For the best estimate of the neonatal mortality rate of low-birth-weight infants and of the heavier infants, I used the largest available study on this subject based on some 750,000 births.r These rates are 174 per thousand for low-birth-weight infants and 7.8 per thousand for infants weighing more than 2,500 grams. I introduce the following conditional probabilities : P(D/S)
=
Pr
(an infant of a smoking mother will die during the neonatal period) ;
P(L/S)
=
Pr
(a smoking mother to a low-birth-weight
P(D/L)
=
Pp
(a low-birth-weight in the neonatal
The symbols defined for P(D/z) of more
P( D/s) nonsmoking
and
will
give birth infant) ;
infant period).
will
P( L/s) mothers’
is defined for infants than 2,500 grams.
die
are similarly infants, and
with birth weights The problem is to
prove that P(D/S) is no greater than P(D/g). These two probabilities may be estimated from the available information with the use of the familiar formulas : P(D/S) P(D/s) P(D/L)
= =
P(L/S)P(D/L) P(L,‘s)P(D/L)
=
0.174; P(D/r) and P(L/3)
0.0860;
+ P(x/S)P(D/x); + P(x/s)P(D/x). =
= 0.0078; 0.0499.
P(L/S)
=
Substituting these values in the above formulas provides the following estimates: (PD/S) = 0.0221, and P(D/$) = 0.0161 (an expected increase in the mortality rate of infants of smokers of 37 per cent). Based on these estimates, we can compute the desired probabilities. For a study of 2,000 infants (1,000 infants each of smoking mothers and of nonsmoking mothers), normal approximation shows that the probability that the death rate of infants of smoking mothers will be no greater than the death rate of infants of nonsmoking mothers is r = 0.163. NOW suppose there are 14 such studies and let X be the number of studies where the death rate of infants of smoking mothers will be no greater than that of nonsmoking mothers. Clearly, X is a binomial random variable with the parameter r = 0.163 and the probability distribution : (0.163)'(
k =
(1 - 0.163)1*-k 0, I, . ., 14:
Direct ability:
computation
Pr(X
yields
2
7)
the
=
cumulative
prob-
0.00366.
This means that the probability is 0.00366 (or 3.7 in 1,000) that, among 14 studies, 7 or more will show infant death rates of smoking mothers no greater than those of nonsmoking mothers. Since this probability is very small, the hypothesis that an increase in neonatal death in infants of smokers exists is rejected. As to the larger studies, Mr. Goldstein uses the results of our studies among the blacks as support for the findings of the studies in which he participated. He states, “. two studies (Yerushalmy’s of blacks and Butler and Alberman’s) show large and significunt differences between smokers and nonsmokers. . . .” (the underscoring of the word significant is mine). I don’t know what test of significance Mr. Goldstein used on our data, but in this case it is not necessary for me to go into great detail. The total number of blacks in our study was some 3,300. In a previous paper,z with which Mr. Goldstein is familiar since he wrote a letter about it to the editor of the American Journal of Efidemiology, the breakdown is given as 2,219 nonsmokers and 1,071 smokers. The respective neonatal mortality rates were 17.1 and 21.5 per thousand. A simple test would show that the probability that a difference as large as or larger than this could have occurred by chance is very great ($ = 0.75; P > 0.30). We are, therefore, left with only a single large study showing an increase in the perinatal mortality rate of infants of smokers and 3 large studies which found no such difference. These are in addition to the 7 relatively smaller studies which found no difference. Mr. Goldstein did not mention that the only study which found the difference, namely, the one in which he was retrospective, All the other participated, three were prospective. As to the 6,500 deaths (the so-called 3 month deaths), the less said about these, the better. The control subjects for these were not from the cohort of births in the 3 months but from those of a single week. In fact, the main report of Butler and Alberman on smoking utilized only the data from the so-called “control week” and did not leave themselves open to serious methodologic criticism by including the “3 month deaths.”
Volume
114
Number
4
Pride of authorship is an understandable human frailty. But in this case it is stretched a bit. Any objective evaluation of ull the evidence must come to the definite conclusion that infants of smokers do not suffer higher neonatal mortality rates than infants of nonsmokers. Mr. Goldstein finds easy explanations for other puzzling findings without bothering to test them. Thus, when referring to the finding, in all 3 large studies, that the mortality rate among low-birthweight infants of nonsmokers is much higher than that of low-birth-weight infants of smokers, he states that, “It is . . . perfectly reasonable and a simple consequence of the fact that the smokers’ babies who weigh less than 2,500 grams have a higher mean birth weight than the nonsmokers’ babies under 2,500 grams.” In the paper which was published in the American Journal of Eflidemiology,z with which Mr. Goldstein is familiar, Table 5, page 448, I compared the neonatal mortality rates of babies of nonsmokers and smokers not only in the group weighing 2,500 grams or less as a whole but in each subdivision. For example, in those babies weighing 1,5GO grams or less, the neonatal mortality rates for nonsmokers and smokers were 791.7 and 565.2, respectively. In the group with birth weights of 1,5Gl to 2,GGG grams, the corresponding rates were 406.3 and 346.2, respectively, and, in the group with birth weights of 2,OGl to 2,5GO grams, the corresponding rates were 78.G and 26.6, respectively. Mr. Goldstein also has a very simple explanation for the new finding in the paper published in this ~ouaXAI~-that women who subsequently became smokers had a high incidence of lowbirth-weight infants also during the period before they started to smoke. He states: “. . . in the group of mothers who began smoking before they were 25 years of age, the babies who were born before smoking started will belong to mothers younger than those who never smoked at all.” Anyone who is familiar with the problem of reproduction in human beings knows that within the limited range of ages under 25 years the variation in the proportion of low-birth-weight infants is very small and could not account for the large differences found. Mr. Goldstein apparently was not aware of this, but he could have easily tested it on his own material. In any case, Table
Correspondence
573
Table I. Proportion
of low-birth-weight by age of mother (white) I I 5 2,500 grams
infants
Total live births
15 16 17 18 19 20 21 22 23 24 25 Total
Per cent
No.
20 69 170 347 535 732 766 751 783 719 653
1 5 14 22 37 42 43 45 38 44 37
5.0 7.2 8.2 6.3 6.9 5.7 5.6 6.0 4.9 6.1 5.7
5,543
328
5.9
1 which is based on all our data from women 25 years and younger shows definitely that the differences age by age are small and irregular. Mr. Goldstein closes his letter with the pious statement that, “. it would be a pity if his paper were to cause any reduction in efforts to persuade mothers to give up smoking during pregnancy.” May 1 say that, on the contrary, it would be a pity to recommend a course of action based on conjectures, subjective notions, and easy explanations not supported by available data. The hard scientific data show conclusively that it is not reasonable to expect that giving up smoking will cause a rise in birth weight. It is important to consider also the possibility that “efforts to persuade mothers to give up smoking during pregnancy” may result in emotional stress and feelings of guilt among mothers who may have tried to quit smoking and did not succeed. Professor Child Health and Deuelopment School of Public Health University of California Berkeley, California 94720
1. Yerushalmy of Biostatistics Studies
REFERENCES
Shapiro, S,, Schlesinger, E., and Nesbitt, R. E, L.: Infant, Perinatal, Maternal and Childhood Mortality in the United States, Boston, 1968, Harvard University Press, p. 51. 2. Yerushalmy, J.: Am. J, Epidemiol. 93: 443, 1971. I.