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/.~ . |. TB 1315 SMOKING : LUNG AND BLADDER CANCER Comments on the reply by Stevens and Mool~avkar to my letter (TB 1240) Author: P.N.Lee Date : 21.10.80 Stevens and Moolgavkar's reply to my letter, published with it in the October 1980 issue of the Journal of National Cancer Institute (TB 1240) betrays an incredible lack of understanding both of the implausibility of their mathematical model and the degree to which it misfits published data on lung cancer incidence by duration and amount smoked. They state that the logistic model is widely used in the analysis of epldemio- loglcal studies and that this is based on an assumption of multlpllcatlvity of relative risks. This may be so, but multipllcatlvlty of risks relatlng to two (or more) factors is easy to understand whereas multipltcattvity of risks relating to doses of the same factor is not. The former would, for example, happen if a disease only occurred if event A caused by Factor 1 and event B caused by Factor 2 both happened. If P1 and P2 are the probabilities of each individual event occurring the probability of disease is given P1P2, the product of the two probabilities. Hultlplicativity of the effects of two factors would not be expected to occur, however, on physically plausible models, if the two factors had the aame mode of action and this is the case where the "two factors" are two half-doses of the same thing. I may not be conversant with the literature but I have never heard of any dose- response relationship where each dose (here cigarette) is supposed'to multiply risk by a given factor. The constant used by Stevens and I~oolgavkar is equivalent to each cigare~te smoked multiplying the risk (compared to a non-smoker of the same age) by 1.00001 so that we have the following example consequences of their formula: Number of cigarettes Number per day of years smoked Relative Risk 0 20 1 10 20 2.07 20 20 4.30 30 20 8.92 40 20 18.49 50 , 20 38,34 0 40 I 20 40 18.49 40 40 341.88 0 60 1 20 60 79.51 40 60 6321.36 0 0 0 --.,j 0
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D 2. Stevens and Moolgavkar states that data on the effect of people who have .smoked such high doses as In the example I quoted 40 cigarettes a day for forty yearsp are sparse and that my example is therefore inappropriate. This is a ridiculous comment. In Kahn's study 63 lung cancer deaths occurred in current cigarette smokers of 39+cigarettes a day of age 55-64 giving a death rate of 316 per 100,000 per year. This compared with 25 lung cancer deaths occurring in never smokers of the same age with a death rate of 10 per 100,000 per year. These smokers will have smoked at least 40 ~igarettes a day for at least 40 years on average with a resultant expected relative risk of at least 342 accordlng to the formula of Stevens and Hoolgavkar. Had their formula been correct one would have expected among 88 lung cancer deaths, to observe 84.0 in the heavy smokers and 3.1 in the non-smokers an observation highly significantly discrepant from the true situation (X2= 15%.5, P<O.O0001), Assumlng 50 years average duration of smoking and 40 years average number af cigarettes smoked, the ~esults for the 65-74 year old man are even more discrepant. (Heavy smoker : observed deaths = 50, expected = 97.7; non-smokers: observed deaths = 49, expected 1.3, ~2 = 1751.%, P<0.O0001). Hammond's data which shows a 17-fold extra risk in smokers of 40+ cigarettes a day compared with never smokers for men aged 55-69 based on 50 and 27 lung c-seer deaths respectively is also enormously discrepant from the 400-fold or more extra risk predicted by Stevens and Moolgavkar's formula. While, in my examples, I am extrapolating outside the range of cigarette consumption units of their fitted formula and that as they say, extrapolatlon outside the range of data in statistical analyses is fraught with uncertainty, the f~ut that extrapolating leads to such nonsensical findings surely implies they ought to look for a better model. To state, as they do, that my reference to multistage models is not relevant is absurd. Multistage models are based on a plausible theory and its mathematical predictions flt numerous aspects of the close/time response of lung Cancer well. Choo%tng to use an alternative model with obvious fla~s seems crazy to me. Less important is the point I made regarding their misuse of TRC Research Paper i data on percentage of smokers where they ignored the large age variation in their model-fitting. Better estimates to use could surely have been derived by dividing the § year age group data on manufactured cigarettes per adult (Table 14) by that per smoker (Table 17). I do not ~ntent to write a further letter as I suspect it would be a waste of time. However, I have carried out some model fitting work of my own a year or so ago and when 1 get time to finish it off I intend to draft a paper for publication on it. P.N.Lee 21.10.80
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TB 1240 -.:? 07"- • il "t i . ! a ! ' --, ~,.%-, ,,;-e* _~:u=~ to the Editor ~mohlng: Lung end Bladder Cancer ;n~: In their paper "FJtimation of Relative Risk From Vital Data" Smoking and Cancers of the Lung and Bladder" in the December 1979 issue of ]NCI. Stevens and Moolgavkar use incorrect data on tobacco con- mmption. Table 12 ol the seventh edition of "Starts- tin of Smoking in the United Kingdom," which they use as source material, clearly shows a marked varia* tion in consumption by age. especially in the early postwar y~rs (1948-50), when the percentage of smokers of manufactured cigarettes was 68,% for men $5-5g years old and 38% for men 60 or more years old. .Although Stevens and Moolgavkar give separate figures in their table la (or every 5-y~r age group from 35-39 to 75-79 years, they ignore this variation and as. sume that Ihe average tigure of 63% for all men ]6 T~rs or over can be used lor each age group. This same false assumption of age invariance, which is likely to have a great influence on the fit of their mathematical model, is also made for the data on females. In view of the considerable amount of work that has been performed with the use of multistage models of cancer.~':'~ I was surprised th.'tt the authors used a complcte|y different model without discussing the ad- vantages or disadvantages of ahernative models or without really looking closely at the prolxrtics nf their own model, in which relati"e risk for a smoker is X', wher~ X is a constant (4,$) and n is proportional to the cumulative number of cigarettes smoked (n=l for smokers o[ 20 cigarettes/day [or 20 yr). I! they had looked more closely at the dose-response properties of their model, which predicts that a pet;son who had smoked 40 cigareues/day and who had smoked for 40 years would have 80 times the risk of a smoker who had smoked l0 cigarettes/d~y for the same duration. the inappropriateness of the model would have been highlighted. Such enormous relative risks by amount smoked, which are predicted to be even larger for longer durations, do not approximate the findings se~n in Hammond's data (quoted by the authors) or in any of the numerous large epidemiologic studies. P. N. L~, M,A. 2~ Cedar Road Sutton, Surrey $M2 5DG, England s AIt.,~rrs~Gt P. Dm.L R. Stochastic modeh for carcinogrnesh. Pro- ¢eedlnKs of the four|h ~,rEeley ,ympofium on mathematics! .atistics and prohabi|itlr. I~ah'l:19-]l& ! r~ltJ, g. P~.rn g. C.JK:SI,"IIt' m.,ki.g and broach|al car(ira.no: 12kite and time :eklti+m,+hips amnvtg reguLtr stnnkerl, and llfcta,tK tmn.qmok;.rt. J Epidrtrtitfl C'-mnm.n |trahh 1978:Si:.~0~-MS. ) P|'TU R. Epldt'uticd,=g7. mtdtista~e ,'av, l'ds att~ sh~.[blerrn mut~o .tt'nlcity Irst,t. In: OriRin'. ,z4 human ru.cer. Cnld Sprln~ Harl~tr. ,N.Y.: G=|d SprinR l|:.L~w Puhl. 1977:l-|OS-|t28. Sin: Lee begins by saying that we u,e "incorrect" dam on tobacco consumption. I~'e assume that he means we use correct data inappropriately. We are re'ell aware of the variation in propornon of smokers by age, and ideally we would have liked to have been able to u.re the exact proportion n/ Stub/tees in each J.year age group in our analysis. However, the data are presented for only 2 age group* (ages 35-$9 yr and >--60 yr) over the age range 35-29 years. Due to the large discon- tinuity between the reported proportions in the 2 groups, we believed that it was best tO me the average that is also reported in the same table. Analysis of the data with the use of the proportions/or each of the broad rather than the average age groups yields a good fit and a similar estimate of relative risk (3.75), but this procedure leads to a discontinuit7 in the parameters that represent the effects of age. Lee also suggests that we have not considered the implication., of our dose.response relationship. The example he cites is inappropriate because data on the effect of such high doses are sparse. Hammondt states that his estimate, of relative risk are subject to large sampling errors in all consumption categories. This problem i* most acute in people smoking more than 40 cigarettes/day because there is a very small number of deaths in this group. Indeed, Wynder et aLe report risks in the hundreds for this level of consump- tion relative to risks /or nonsmokers. Again, these estimates art based on small numbers. In the English data we analyzed, the range of cigarette consumption units is 0,034-2.768 (tables la and lb in our paper). Over this range, our dose.response relationship (illus- trated in detail in our table 3) gives a good description o/ the mortality data in England and Wales over J$ years. Let's example of 40 cigarettes/day for 40 years equals 4 units and, as is well known, extrapolation outside the range of data in statistical analyses is fraught with uncertainty.. Nonetheless, until better data on such high levels of consumption are available, we believe that multipticativity of relative risks is reason- able over the range o[ consumption that is humanly possible. Indeed, there is precedent for assumption o/ multiplicatiue relative ri~ks in epidemiology. For ex. ample, the logistic model is widely used in the analysis of ca~e-control studies. Our finding that cumulative consumption determines relative risk imp~es that, in any study examining the effect of daily consumption, duration of smoking acts as an effect modifier. Finally, Let's reference to multistage models is not re&vane. We are not proposing a model /or the pathogenesis of lung cancer. Rather, our statistical model attempts to obtain a simple functional form for Ha.Mmo~n EC. Smoking in reladon to the death rat~ of one millitm men and wt~m~t. N:til ~ncer ttist Mottogt" 1966:19:1~-20-1.. Wv.~ntt EL, .M~tt'rrnl K, B~xrl";t: EJ. The epidemioloRy at hml~ cantrl. JAMA 19TO1213:2"22|-2~. e87 J..C~. vat_ 65, NO. 4. OCTO~rR 1950 L~
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- 4. SO Letters to the EdRor dose repomt. This information can then be mrd in conjunction with mt~lHstage models to identrfy tenta- tively the number and nature of stages affected by smoking. Our results on dose response are not entirely coruistent with those of Doll and Peto.J However, that is the subject of another paper. R2CHARO G. STEVENS SURESII H, ~OOLGAt;KAR institute /or Cancer Research Philadelphia. Pennsylvania 19111 J Dtn.L R, Pvro R. Ci~aretle smoking and bronchial carcinoma: Dote and time ~lationships among regular smoken and lifelong tmn-slnnkets. J tepidemiol Commlffl Health 1978;~2:3021-qtlJ. THsomy of Chromosome #'[3 in Spontaneous Mammary Tumors of GR, C3H, and Noninbred Swiss Mice Sin: In studying the article published in JNCI by Dofuku. Utaknji, and Matsuzawa.I I found that the • k.a~'otypes as presented are misleading. The authors state that their figure, show trisomy o{ chromosome The identification of the chromosomes in figure ! appears to be correct, but according to table !. the minor has a modal chromosome number of 40. The figure shows 41 chromosomes, however, and it cannot represent the true tumor stemline. The objections to figures 2 and 3 are more serious: In figure 2. the second chromosome ~3 is a chrorno- some ~6: the second chromosome ~,9 is a chromosome #$: and the third chromosome ~13 is a chromosome ~g. These identifications show that the cell is diploid. In figure 3, chromosome #8 is a chromosome #12; the second chromosome ~I2 is a chromosome ~PS; the second chromou3me #10 is a chromosome #8; and the third chromosonte #13 is a chromosome Jtl0. This makes the cell diploid. Obviously. a definite statement is dilficult to give on the basis of two karyograms. However. irom the published picture~, the claim of the authon concemittg trisomF ~t$ dot's not appear to be well founded. l have studicd 5 spontaneous mammary carcinomas in C3H mice. All were diploid accorditlg to their trypsin-Giemsa handing pattern. It would be there/ore advisable if Dofuku ctal. could revise their identifica- tion of trimmy #13 in relation to mouse mammary tumors. Jac[ S~txa Department of Tumor Biology ICarolinska Institutes Stockholm, Sweden I OPel'KS" R, t'IAKt}JI T, .~I.~I"~I'rAlvA A. Tri'umty (d ehlnlllO.a.lle Iltq iS! '~t.t¢lllU.Ill¢,',lll~* m;]mmitly ttltltto[*t of C.R. (~$t. antS nonin|)rt.d Swi,u, nil.'. JN(;I 197~:67,:fi51-~i~6. JN[~. V{'IL 6$. N4}. I. ()CI'OBER |9~.0 Sin: Having ret,iewed the published as well a.t original kar'y'ot~..pes thoroughly after crtticai reading of Dr. Sptra's comments, we do not think that it is necessary. to ret,t.re our ident:fication and interpretation of the karyotypes. Our replies will be given in the order of Dr. Spira's comments; we refer to the Nesbitt and Frank¢ nomenclature of mouse chromosomes,t I) The reason /or the ka~otype with 41 chromo. tomes listed was that it clearly demonstrated that art extra chromosome was #13. tls a reference, a karyot~pe picture of the stemline cell with 40 chromosomes, which was obtained/rum the same tumor, is presented (lip. t). 2) The second chromosome #3 is not a chromosome #6 because the H2 band o/chromosome z3 is clearly shown, whereas chromosome a6 does not have the corresponding band. This second chromosome n9 may be di/licult to identify because it is overstretched and has an irregular banding pattern. The F.3 band o/ chromosome #9 stained lighter than usual, whereas the F2 band was more intense. Furthermore, the over- stretching caused the distance between El and E3 to become broader. The third chromosome #13 cannot be mistaken became it has all the characteristic banding patterns o~ chromosome #13 including band CI typical of this chromosome. 3) Frequently, chromosomes #8 and #12 are difficult to distinguish in tumor cells. In this karyotype, chro- mosome #8 has been identified as such because it has a larger size and the B3 band is more distinct than the BI in chromosome #8. In contrast, in chromosome aI2, band C3 combined with CI, which is often observable, looks bigger and stains darker than the E.band. The identification o/ the second chromosome #10 may be con/mini became it had a blurred Di band o/chromo. some #I0, bu~ the paleness o/ the bands was observed in other chromosomes of this particular karyotypc: band E2.4 of the second chromosome #14, C3 o] the second chromosome.el6, and so on. The Ihird chronto- some #13 is contracted, but it clearly shows the CI band characteristic of this chromosome, whereas no Juch band is present in chromosome #10 oJ this kar~otype. It is true that the identification of chromosomes o/ tumor cells is not ear)', particularly in the mouse, and a photographed picture is not as clear as the original one. We hope that the explanations presented dispel Dr. 5pira't uncertainty about our identification o[ the karyotypes. RYvtc:Hn DoFtmU, ,ll.D. Cell Biolog?t Cancer Institute Japanese Fotmdation for Cancer Research Kami-tkebukuro. Toshima-ku Tokyo lOS, ]apart o Nl:ssfr'r MN. IqtAS.K[ U. A ~yslt, m or Itomenclattlle for ~lltt |mtlq'ln~', Of IIl/lll~° c'[trfmto,~.lle~. ~'~|ftl*lllllr~Hll;ll 1973111:1 15-15.q. "--d Crx

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