Document N2KKG4D85OjvLk6EvMqL4pBvD

STATISTICS IN MEDICINE, VOL. IS, SSI-605 (1996) MISCLASSIFICATION OF SMOKING HABITS AS A SOURCE OF BIAS IN THE STUDY OF ENVIRONMENTAL TOBACCO SMOKE AND LUNG CANCER PETER N. LEE AND BARBARA A. FOREY P.N. Lee Statistics and Computing Ltd., 17 Cedar Road, Sutton, Surrey, SAf2 5DA, U.K. SUMMARY The relationship of environmental tobacco smoke to lung cancer risk in lifelong non-smokers is commonly studied using marriage to a smoker as the index ofexposure. As smokers tend to marry smokers, relative risk estimates will be biased if some current or former smokers are misctassified as lifelong non-smokers. This paper shows how various factors affect the magnitude of the bias and describes a method for obtaining tnisclassification-adjusted relative risk estimates. Application of the method to US. and Asian data for women suggests misclassificatiou is an important determinant of the slight excess risk observed in non-smokers married to smokers. Reasons why our conclusions differ from those of others are discussed, as are other difficulties in interpreting the association between spousal smoking and lung cancer risk. 1. INTRODUCTION Error in the variables studied can bias the relationship of a risk factor to a disease. In 2 x 2 tables, random misclassification of exposure or disease biases relative risk (RR) estimate towards unity.1-3 How the bias relates to the misclassification rate, and the disease and exposure frequency has been described.4 Additional information on accuracy of exposure data can be used to obtain unbiased RR estimates.5 Random misclassification of exposure understates true associations, but random misclassification of confounding variables may not. How misclassification affects RR estimates adjusted for a single confounder with two levels has been studied.6'7 With large ( ~ 30 per cent) errors in the confounder, adjustment has little effect. Even for smaller ( ~ 10 per cent) errors, about half the confounding effect remains after adjustment. Tzonou et al.6 note that `Generally, in the presence of strong risk factors which have potentially large confounding effects and which may have been imprecisely measured, the etiological significance of factors observed to be relatively weakly associated with disease must be treated with caution. Since 1981, the possible association of lung cancer with environmental tobacco smoke (ETS) exposure has been extensively studied. Since this association, if it existed, would be much weaker than that with active smoking, and since it is hard to quantify precisely the many aspects ofactive smoking correlated with risk, ETS studies usually consider only lifelong non-smokers. The exposure index usually used, and that for which an association has been claimed,7, * is marriage to a smoker, there being far more data for females than males. Some 10 years ago9 one of us (PNL) pointed out that, as smokers tend to marry smokers, misclassification of some current or former CCC 0277-6715/96/060581-25 1996 by John Wiley & Sons, Ltd. Received January 1995 Revised June 1995 http://legacy.library.ucsf.edu/tid/mid32d00/pdf S' 582 P. LEE AND B. FOREY smokers as lifelong non-smokers would bias the spousal smoking RR. Since then many attempts have been made to quantify the bias,7, 10 _ 12 with conflicting conclusions about its importance. This paper reviews the issue of bias from smoking misclassification in ETS/lung cancer studies. Section 2 considers misclassification in a 2 x 2 table assuming no true ETS effect, and describes the relationship of the observed spousal smoking/lung cancer association to various factors and assumptions. It is shown that misclassification of smokers as non-smokers causes much greater bias than misclassification, either of non-smokers as smokers or of spousal smoking. Restricting u attention to misclassification of smoking subjects, Section 3 considers the possibility of a true ETS effect, acting multiplicatively or additively with active smoking. It also reveals errors in published methodologies for bias adjustment.7, t0 Section 4 allows for different misclassification rates for different types of smokers, and shows how to estimate bias based on observed rather than true underlying data. Weaknesses in the methods of the U.S. Environmental Protection Agency (EPA)8 are demonstrated, and an alternative methodology described. Using this, and the complex set of misclassification rates used by EPA,8 the estimated biases are shown to be virtually the same as those estimated using a single misclassification rate, of ever smokers as never smokers. After considering plausible values of the between-spouse smoking concordance rate and of the ever-smoker/never-smoker misclassification rate, the simplified methodology is then, in Section 5, applied to U.S. data. In Section 6 the methodology is applied to data from Asian studies, accounting for possible higher misclassification rates. Section 7 discusses other issues affecting interpretation of the ETS/lung cancer relationship, and in Section 8 the main findings are reviewed and discussed. 2. MISCLASSIFICATION IN A 2 x 2 TABLE; NO TRUE EFFECT OF ETS EXPOSURE 2.1. The simplest situation Consider N married individuals of which a proportion s smokes. Let the proportion whose spouse smokes be for non-smokers and in2 for smokers. Assume in2 > mi. Let the lung cancer risk for a given period be y for non-smokers and Ry for smokers, and be independent of spouse smoking. Assume a random proportion p (> 0) of smokers are misclassified as non-smokers. Expected numbers of subjects before (`true data') and after (`observed data') misclassification are then: Group Smoking habits Subject Spouse True data Population Cases Observed data Population Cases Ji-tli 1 Non-smoker Non-smoker a =JV(1 -s)(l - "til A -- ya a* = a + pc A* y(a + pRc) 2 Non-smoker Smoker b = JV(1 -- s)ffl| B = yb b* = b + pd B* = y(b + pRd) 3 Non-smoker All u = N(1 - s) U = yu u* = u 4- pv V* = >'( + pRv) 4 Smoker Non-smoker c = JVs(l -- m2) C = yRc C*=(l -p)c 5 Smoker Smoker d = JVsm2 D = yRd d* = (1 - p)d 6 Smoker All v = Ns V=yRv a* -- (l -- p)u V* = y(l - p)Rt> Asterisks indicate observed rather than true data. Upper and lower case letters indicate cases and the population, respectively. The bias calculations do not depend on the scaling factors N and y. The mathematics below deals only with expected values, and not sampling distributions. 2501854149 http://legacy.library.ucsf.edu/tid/mid32d00/pdf i ! MISCLASSIFICATION OF SMOKING HABITS AS A SOURCE OF BIAS 583 2.2. Effect of misclassification on the concordance ratio The association of husbands' and wives' smoking habits is often measured by the concordance ratio k -- ad/bc -- nt2(l -- -- m2). Since m2>m1, k > 1. The observed concordance ratio k* -- a*d*/b*c* satisfies the conditions 1 < k* < k. 2.3. Effect of misclassification on the active smoking risk The observed active smoking RR, obtained by dividing risks in groups 6 and 3 (ignoring spousal smoking) is R* = R(u 4- pe)/{tt + pRo). It satisfies 1 < R* < R. The ratio of observed to true excess risks (R* -- 1)/(R -- 1) equals {1 -- s)/(l -- s + pKs) and declines as the misclassification rate, proportion of smokers and true risk increase. 2.4. Effect of misclassification on the spousal smoking risk The observed spousal smoking RR, obtained by dividing risks in groups 2 and 1 (in non-smokers), is E* = (a + pc)(b + pRd)/(b + pd)(a + pRc) and satisfies E* > I. Thus misclassification creates an apparent risk from spousal smoking when no true effect exists. We refer to this as the `misclassification bias'. 2.S. Maximum misclassificatiou bias and rate E* can be expressed in terms of the observed population by: E* = [<* + d*(R - l)p/(l - p))*]/[(a* + c*(R - l)p/(l - p))ft*]. E* is a maximum when R is infinite. E* then equals k*, so the bias cannot exceed the observed concordance ratio. When R is infinite, R* = (u + pv)/pv = u*(l -- p)/v*p, and p = u*j(u* + which is thus the maximum misclassification consistent with the observed active smoking data. 2.6. Factors affecting the magnitude of the misclassification bias Defining Q = e*(R -- l)p/a*(l -- p), E* = (1 + k*Q)/(1 4- Q). E* increases monotonically with k* and Q. Given an observed distribution of smoking habits (a*, c* and k*) E* thus increases strongly with the misclassification rate (being, for small p, approximately proportional to p) and with the active smoking RR (being proportional to (R -- 1)). This formulation also suggests E* increases with the concordance ratio and with the proportion of smokers. Defining 2 =. m3/wi > 1, E* can be expressed as the cross-product ratio of four ratios of observed to true data: Cases: Spouse smoker hi = (b + pRd)/b = 1 + pRsz/(1 -- s) = 1 + 5X Cases: Spouse non-smoker h2 - 1 + pRs(l - m:z)/(1 - s)(l - nu) = 1 + S2 Population: Spouse smoker h3 " 1 + psz/(l - s) = I + <5j Population: Spouse non-smoker ft* = 1 + ps(l -- m,z)/( 1 -- s)(l -- mx) = 1 + 34 For small p, are small, so E* can be estimated approximately by (1+^)(1 +&*) E* = -- 1 + 5t + (l+<52)(l-t-53) p(R - l)s(z - I) -- <52 -- <53 = 1 + (1 - s)(l - mi) ' 2501854150 http://legacy.library.ucsf.edu/tid/mid32d00/pdf 584 P. LEE AND B. FOREY Table I. Variation in misclassiflcation bias according to variation in p, R -- 1, s, m: and fc Misctassification rate (P) Excess smoking risk (R-l) OOt 4 9 19 002 4 9 19 0-05 4 9 19 Proportion smoking 0*2 04 0*6 02 04 06 0*2 04 06 02 04 06 0*2 04 06 0*2 04 06 02 0*4 06 0-2 04 0-6 0-2 04 06 Proportion of spouses who smoke On,) 0*1 20 30 1*009 1*023 1*050 1*020 1-051 1-105 1*041 1*101 M98 1*016 1*043 1-091 14)37 1*093 1*193 1076 1*187 [ 366 1*018 1045 1-091 1*039 1*095 1183 1*078 1-181 1*318 1032 1081 1165 1071 . 1*174 1*335 M44 1*334 1-589 1042 1-099 1179 1-090 1-197 1 321 1172 1*338 1*482 14)77 1*180 1-321 1165 1*361 1-583 1-318 1*626 1*889 0*3 Concordance ratio (fc) 40 20 3-0 4*0 24) 0-5 30 1*023 1*059 T125 14)51 1-129 1*267 1*105 1*260 1*511 1*045 1112 1*227 1*098 1*241 1*463 1*200 1466 1*824 1-106 1*247 1*437 1-228 1500 1*803 1*443 1*876 2*241 1008 1020 1043 1017 14W3 109! 1035 1*087 1*174 14)15 1*038 1079 1033 1*082 1*161 14)67 1-158 1-287 1*036 14)86 M61 1*077 M75 1-295 1*150 1*306 1-456 1*012 1*032 14)70 14)28 14)71 1-150 1057 1*144 1*292 1*016 14)41 1-088 1-035 1*090 1*192 1*073 1*184 1*377 1*024 . 1031 1*062 1079 M30 1-165 1054 14)69 M35 1-172 1*269 1-346 1-Hl 1-141 1*265 1-341 1-491 1-643 1*059 1142 1*266 1*127 1*292 1*504 i*25t 1*526 1-806 1-074 1181 1-342 1-162 1*377 1*660 1-323 1-692 24)86 1-007 14)17 14)37 1*015 1*038 1080 14)31 1077 1-155 1010 1026 1-057 1022 1057 1-123 14)46 1*118 1-242 1-013 1-033 1070 1-029 1072 1-144 1059 1-141 1-261 1020 1051 1*107 1-044 MIC 1-225 1090 1-219 1-420 1031 1-048 1077 1-117 1-145 1-227 1-068 1-104 1-157 1-245 1-273 1-441 1-133 1-207 1-280. 1*452 t-432 1*732 4-0 1012 14)31 1068 14)27 14)69 1-149 1-056 1*143 1*298 1024 1061 1*130 1053 1-134 1-276 1*109 1-269 1*526 1057 1-142 1-280 1-126 1*302 1-556 1*254 1*570 1*954 The bias increases with the misclassiflcation rate, the smoking excess risk, the proportion of smokers and the concordance ratio (here parameterized indirectly by z) and decreases with the proportion of spouses who smoke. Table I shows how E* actually (not approximately varies with these parameters. The same relationships apply. 2.7. Case/control rather than prospective study E* can be calculated by dividing an estimate {h1/h2) based on case data by an estimate (h3/h^) based on population data. If the controls are representative of the population, and if misclassiflcation is independent of case-control status, the above procedures can also be applied to case-control study data. Note misclassiflcation of cases produces upward bias, while misclassiflcation of controls produces downward bias. For small p, the upward bias = hjh2 al + Rj and the downward bias -- h3lhAa 1 4- g, where g = ps(z -- 1)/ (1 -s)(l - mi). 2.8. Risk of disease associated with misclassiflcation In Section 2.1 misclassiflcation of smoking was assumed random, with the same risk in nusclassifled and correctly classified smokers. This may well be untrue in practice. Misclassified 2501854151 .ucsf.edu/tid/mid32d00/pdf MISCLASSIFICATION OF SMOKING HABITS AS A SOURCE OF BIAS 585 smokers may have smoked less and/or longer ago, suggesting a lower risk than smokers who report their smoking. On the other hand, misclassification may be common in subjects who have ignored doctor's advice to give up smoking following a visit relating to symptoms rendering them at higher than average risk. If correctly classified smokers have w times the risk of misclassified smokers, and R' and R" are their risks, relative to true non-smokers, we can solve R' -- wR" and (1 - p)R' 1- pR" -- R to give R" = R/(p + (1 -- p)w) and R' = wR/(p + (1 -- p)w). The observed active smoking RR is then given by R* = R'{u + pv)/(ti -f pR"v}. R* is usually < R, but this need not be so, for example, if p is small and tt is much larger than v, R* cs R' which is > R if w > 1. The observed spousal smoking RR is given by the same formulae as in Sections 2.4 --2.6 with R replaced by R". Assuming the risk of misclassified smokers exceeds that of non-smokers, positive misclassification bias will occur. 2.9. Misclassification associated with spousal smoking habits The random misclassification assumption also means that rates are independent of spousal smoking. This may also be untrue, with people married to a non-smoker less willing to admit smoking. If the misclassification rate is when the spouse smokes and p2 when the spouse does not, E` = (a 4- PzC)\b +- pLRd)/(b + pid){a + piRc). It is clear pt causes positive bias and p2 negative bias. Given plt E' declines with increasing p2, the overall bias ceasing to be positive (' = 1) if Pi/Pi = k- If P2 > kpt, negative bias will occur. 2.10. Misclassification of non-smokers as smokers So far it has been assumed no non-smokers are misclassified as smokers. Now if q is the proportion of misclassified non-smokers, we have: Group Smoking habits Subject Spouse 1 Non-smoker Non-smoker 2 Non-smoker Smoker 3 Non-smoker All 4 Smoker Non-smoker 5 Smoker Smoker 6 Smoker All Observed data Population Cases a** = (1 -- q)a + pc b** -- (1 -- q)b 4- pd u** = (1 -- q)u 4- pv c** 5= qa + (1 -- p)c d** = qb -t- (1 -- p)d v** = qu + (1 -- p)v y((! -- q)a + pRc) y((i -- q)b + pRd) y(U -- q)u + pRv) y(qu + (I -- p)Rv) If p + q < 1, as should always be true in practice, the observed concordance ratio k** = a**d**/b**c** satisfies 1 < k** < k* < k. The observed active smoking RR is given by R** = (qu + (1 -- p)Ru)((l -- q)u + pv)/(qu + (1 - p)u)({l - q)u + pRc). If p + q < 1, R** satisfies 1 < R** < R* < R. The observed spousal smoking RR is given by ** = ({1 _ q)a + pc){(l -- q)b + pRd)/{(l -- q)b + pd)((l -- q)a -1- pRc). 2501854152 http://legacy.library.ucsf.edu/tid/mid32d00/pdf 586 P. LEE AND B. FOREV Writing p** -- p/(l -- <7) it is clear the formula for E** is identical to that in Section 2.4, with p** replacing p. Thus, for example, a 5 per cent misdassification rate of smokers as non-smokers causes the same bias as a 5-26 per cent rate in both directions. Misdassification of smokers is dearly a much more important cause of bias than is the reverse misdassification, which has no effect on its own and only slightly reduces the spurious RR estimate otherwise. Because of this, and as false claiming of smoking is probably quite rare, most attempts to quantify the bias have ignored this reverse misdassification. 2.11. Misdassification of spousal smoking So far it has been assumed subjects but not spouses are misclassified. If r is the proportion of smoking spouses misclassified we have: Group Smoking habits Subject Spouse Observed data Population Cases 1 Non-smoker Non-smoker a*** -- (a + pc) -5- r(fi + pd) y((a + pRc) + r(b + pRd)) 2 Non-smoker Smoker it*** = (1 - r)(b + pd) >'(1 - r)(b + pRd) 3 Non-smoker All u*** = a + pv y(u + pRv) I 4 Smoker Non-smoker c*** " (1 -- p)(c + rd) 5 Smoker Smoker = -p)(l -r)d 6 Smoker AH V*** -- (1 -- p)i> y(l - The observed concordance ratio k*** = a***d*'**/b***c*** is a more severely biased estimate of *' k, satisfying 1 < k*** <.k* <k. Misdassification of spousal smoking does not affect the observed active smoking risk, so The observed spousal smoking RR is given by *** = (a -f pc + r(b + pd))(b + pRd)/(a + pRc + r(b + pRd))(b + pd). If p = 0, E*** = 1, so that misdassification of spousal smoking causes no apparent effect of spousal smoking when no true risk exists. Assuming p > 0, E*** satisfies 1 < E*** < E*. For tf small p, (E*** -- 1)/(E* -- 1) approximately equals a*/(a* + rb*). For small r this is close to 1, implying that ignoring misdassification of spousal smoking only leads to slight overestimation of" the spousal smoking RR, which arises mainly from misdassification of smoking by the subject. The above calculations assume misdassification of subject and spousal smoking are independent. If they are positively correlated, which might occur, if, say, both were reported by as the same respondent, E would be reduced. If all smokers who deny their smoking also deny their II spouse's, the observed spousal smoking RR will be < 1. 2.12. Summary The results above show that misdassification of a subject's smoking habits leads to underestimation of the strength of the active smoking/lung cancer relationship and of the concordance between husbands' and wives' smoking habits, consistent with the general thesis that random misdassification leads to underestimation of the strength of positive associations. By contrast, providing there is positive concordance between spouses' smoking habits, random misdassification ofsome subjects who smoke as non-smokers leads to an apparent relationship of spousal smoking to risk in non-smokers when no true relationship exists. The size of the i j 2501854153 http://legacy.library.ucsf.edu/tid/mid32d00/pdf MISCLASSIFICATION OF SMOKING HABITS AS A SOURCE OF BIAS 587 misclassification bias depends on the niisclassification rate, the excess active smoking risk, the proportion of smokers, the concordance ratio, and the proportion of spouses who smoke. It is little affected by niisclassification of non-smokers as smokers, or of smoking by spouses, which will be ignored hereafter. More crucial to the size of the bias are the possibilities that niisclassification rates may depend on risk of disease or on spousal smoking habits. If smokers with a relatively low risk of lung cancer or who are married to non-smokers tend to be more likely to deny smoking, the bias will be less than indicated by the formula in Section 2.4. 3. MISCLASSIFICATION IN A 2 x 2 TABLE: TRUE EFFECT OF ETS EXPOSURE 3.1. Multiplicative and additive model Let the risk be y for non-smokers married to non-smokers, with RRs in groups 1,2,4 and 5 in the ratios 1:E:R: RE and 1:E:R:E + R - 1 for the multiplicative model and for the additive model. Expected numbers of subjects after misclassification are then: Group Smoking habits Subject Spouse Population 1 Non-smoker Non-smoker a* = a + pc 2 Non-smoker Smoker b* = b + pd 3 Non-smoker All U* U + pV 4 Smoker Non-smoker c* -- (1 -- p)c 5 Smoker Smoker d* - fl - P)d 6 Smoker All u* =5 [1 -- p)v Observed data Cases Cases (multiplicative) (additive) y(a [ pRc) yE(b + PRd) Aa + PRc) y{Eb H- p(E + R - 1)4) By summation yR(l - p)c yR(l - p)c -- p)d y(E + R- 1)(1 -p)d By summation The changed assumptions, which only affect risks, do not change the effect of misclassification on the concordance ratio (see Section 2.2). 3.2. Effect of misclassification on the active smoking relative risk For the multiplicative model, the observed active smoking RR is given by Rm -- R(c 4- Ed)(u + pv)jv({a + pRc) -1- E(b + pRd)). This is biased even without misclassification {p -- 0) due to failure to adjust for spousal smoking. When adjustment for spousal smoking is made, the active smoking RR will be biased downwards by misclassification. For example, within subjects with non-smoking spouses, the observed active smoking RR will be given by the expression R(a + pc)/(a + pRc), which is < R. For the additive model, the observed active smoking RR is given by R* -- (Rc + (E + R -- l)d)(H + pv)/v{(a + pRc) + Eb + p(E + R -- l)d). The ratio of risks in smokers to non-smokers, among those married to a smoker is equal to (JS + R -- 1)/E. As this is < R, the active smoking RR will be biased downwards even when there is no misclassification and when adjustment is made for spousal smoking. 3.3. Effect of inisclassificutiou on the spousal smoking relative risk For the multiplicative model, the observed spousal smoking RR is given by ES = E{a + pc)(b -)- pRd)Kb + pd)(a 4- pRc) - EE*. 2501854154 http://legacy.library.ucsf.edu/tid/mid32d00/pdf 588 P. LEE AND B. FOREY Thus any circumstances causing a given bias in the simple model described in Section 2 will multiply a true risk associated with spousal smoking by the same factor. For the additive model, the observed spousal smoking RR is given by E*A - (a + pc){Eb + p(E + R -- 1)d)J{b + pd){a + pRc). This satisfies E% < Em- Given p, j increases with increasing E, starting at the value E* when E = 1. The increase in EX is less steep than that in E, so that E% = E when E = a*d/b*c, which is approximately equal to the concordance ratio k. For higher values of E, EX will underestimate E, though this is unlikely in practice since estimates of concordance ratio usually substantially 1 exceed estimates of spousal smoking relative risk. 3.4. Estimates of Wald and of the US National Research Council In 1986, Wald et al} and the US National Research Council7 used an additive model to correct spousal smoking RR estimates for bias. The methodology used was similar to that described here. However, it was applied using observed data to estimate s, m, and R, ignoring the fact that these data would themselves be subject to misclassification. This resulted in understatement of the bias. | jl Thus, Wald et al.,i0 using estimates of s -- 0-50, p = 0-07, mL -- 0-59, m2 = 0-81, R -- 2 and T E = 1-3 calculated the observed spousal smoking RR should be 1-3454, that is, an upward bias by 3-5 per cent. In fact, after accounting for misclassification, appropriate estimates of.;, mt and R are 0-5376, 0-5721 and 2-3079. The observed spousal smoking RR can then be estimated as 1-3725, that is, an upward bias by 5-6 per cent, almost 60 per cent more than Wald et at.10 calculated. 4. MISCLASSIFICATION IN A 2 xN TABLE 4.1. The Wells-Stewart method In their report, the EPA8 described and used the method of Wells and Stewart to correct individual study RR estimates for smoking misclassification. The method has two notable features. First, rather than simply classify subjects as smokers or non-smokers, four groups are considered: regular; occasional; former smokers, and lifelong non-smokers. The association with spousal smoking (which remains classified in two groups) is studied in observed lifelong non-smokers, which contain true lifelong non-smokers together with misclassificd regular, occasional and former smokers, the misclassification rate varying by smoking group. Second, the method is based on observed data. While in Sections 2 and 3 above, emphasis is on describing how observed RRs depend on the misclassification rate, given true underlying values of parameters such as s, mt, m2, k, E and R, the Wells-Stewart method aims at estimating the true value of E, given assumed misclassification rates, and observed values ofthe parameters, including the spousal smoking RR. Elsewhere, Lee13 discusses the Wells-Stewart method in detail. He points out the method depends on many inadequately explained and justified assumptions and imprecisely known parameters, and refers to errors in the method. Thus: (i) it was assumed, totally implausibly, that the spousal smoking RR multiplies the former smoking RR, but not the current smoking RR; (ii) the multiplicative model was applied to observed RRs when logically it would only apply (were it appropriate) to true RRs, that is, RRs before misclassification; (iii) the estimated RR for current (versus never) smoking was applied to current regular smoking, but current smokers include both regular and occasional smokers; (iv) in estimating the observed smoking habit distribution of the cases, the frequency of all former smokers (long-term and short term) has been multiplied by a risk factor derived for long-term smokers only; and (v) the actual method of 2501854155 http://legacy.library.ucsf.edu/tid/mid32d00/pdf MISCLASSIFICATION OF SMOKING HABITS AS A SOURCE OF BIAS 589 estimating corrected numbers of never smokers, given the observed distribution of cases and controls by self and spouse's smoking habits and the assumed misclassiflcation rates, is mathematically erroneous. In the following we describe an alternative procedure which is simpler, exact and involves fewer assumptions. As with the EPA method, it estimates E based on observed data, and allows various categories of smokers to be misclassified (though it can also be applied to the simple smoker/non-smoker case). 4.2. Adjusting the spousal smoking relative risk using observed data -- assumptions and notation Let subjects who smoke be categorized into n increasing levels (; -- 1,The notation previously used is extended by a subscript for smoking level. The true distribution of smoking in controls is then: Spouse Non-smoker Smoker Total Subject Never Level 1 . Level i Level n a Cl Ci c,,- b di di d, u Vl 1>w with asterisks used for the observed distribution. For a multiplicative model, the true RRs are: Spouse Non-smoker Smoker Subject Never Level 1 - Level f Level n 1 i?T R, R,, E RiE R,E R,,E The true distribution for cases (ignoring scaling factors) is given by multiplying corresponding elements in the two tables. Upper case letters indicate the result, for example, Dt = d.R.fi for a multiplicative model. For an additive model, R,E is replaced by Rj + E -- 1. Let ptj be the probability a smoker at level i is misclassified at a lower level j. The relationship between true and observed distributions (for controls or cases, for spouse non-smoker or smoker) can be written down easily, for example, with n = 2 and considering cases married to a smoker: B* Di = Dt = B -f + PioDx P21D2 (1 -- P20 -- Pz These formulae can be inverted to estimate true from observed data. Following the EPA, it is assumed there is no misclassiflcation of never smokers as smokers or of spousal smoking and that misclassiflcation of smoking by the subject is independent of spousal smoking and of disease status. 2501854156 http://legacy.library.ucsf.edu/tid/mid32d00/pdf s i. i1 W tfi fii 590 P. LEE AND B. FOREY 4.3. The estimation procedure -- Step 1: obtaining observed and true smoking habit distributions for controls The case-control study for which the RR is to be adjusted provides estimates of observed number of never smokers by spousal smoking, a* and b*, which can be summed to give u*. Data on the total number of subjects who smoke, t* = Tvf, can be obtained directly in some studies, or indirectly from an estimate of smoking frequency in the population, s*, by t* = s*u*/(l -- s*). t* can then be multiplied by estimates or the relative frequency of smoking in the n categories to give vf. Given a?, bf and v*, and estimates of the concordance ratio for each smoking level, kf, c* and df can then be estimated by solving c* + df = vf and kf = a*df /b*c*. This gives the whole of the table for observed controls from which, as described in Section 4.2, the table for true controls can then be estimated. 4.4. The estimation procedure - Step 2: obtaining smoking habit distributions for cases regardless of spouse smoking . The study for which the RR is to be adjusted provides estimates of observed numbers of never smokers by spousal smoking, A* and B*, which can be summed to give U*. Given estimates of the observed smoking RR in the various categories, Rf, estimates of V* can then be obtained by R* = V?u*/pfU*. Alternatively, if the total number of smokers in the cases, T* -- ii'*, is known and estimates of the excess risks of smoking in the various categories, Xf, relative to category n{Xf = 1), are available, estimates of V* can be obtained from 2n equations: Rf = V*u*/ofU* (i = i,...,n), Rf - 1 + X?(R% " 1) (i = 1, ,n - 1), and T* = EF(*. The relationships of Section 4.2 are then used to give V and Vt, the total number of true cases subdivided by subject's smoking. 4.5. The estimation procedure - Step 3: estimating tbe true spousal smoking relative risk Assume a starting value of E = ltr perhaps the observed value of the spousal smoking RR E = B*a*[A*b* or a value somewhat less. Solve E -- Ba/Ab and U = A +- B to give A aU/(a + bE) and B -- U -- A. For the multiplicative model R( -- Ci a/Ac^ Rt = Dib/Bd( and Cf 4- Dt = Vs. Solving gives Ct = AbciVt/(Badt + AbCi) and hence >, and R,. ^^ For the additive model, the second equation is replaced by (R; + -- l)/ = Dib/Bdi, and solving gives C, AcdbVfi - BddE - 1})ABad, + Abc,E) and hence Di and R,. The whole table for true cases has now been obtained, and using the relationships in Section 4.2, the complete table for observed cases can then be estimated. If the estimate of B* exceeds the actual study value assume a lower value of if it is less try a higher value. The whole procedure is then repeated iteratively until the estimate of B* equals that observed. This gives the value of E adjusted for smoking habit misclassification. The relationships of Section 4.2 then allow completion of the table of observed case data and hence of observed RRs. 95 per cent confidence limits of E and E can be estimated in the normal way from the true and observed 2x2 tables {, b. A, B and a*, b*. A*, B*), 2501854157 http://legacy.library.ucsf.edu/tid/mid32d00/pdf MISCLASSIFICATION OF SMOKING HABITS AS A SOURCE OF BIAS 591 4.6. Example As in the EPA report, data from Correa ei a/.14 study are used to illustrate the method. The data observed are as follows: Smoking habits Subject . Non-smoker Non-smoker Non-smoker Smoker Smoker Ail Observed number of subjects Controls Cases a*= 72 b* = 61 (* = 119 A* = 8 B* = 14 T* = 244 Associated with these data are estimates of 52-8 per cent for the observed proportion of subjects who had never smoked and of 2-066 and 12-396 for the observed spousal and active smoking RRs. Following to a considerable extent the EPA report,8 we assume; 1. Three levels of smoking by the subject: former {z = 1), occasional (i -- 2), and regular (i = 3). .2 Former smokers are 35-5 per cent of ever smokers (o* = 0-355t*). 3. 90 per cent of current smokers are regular smokers (u* = 0-9 [v* + *)). 4. The concordance ratio for ever/never smokers is 2-8 (a* Ed* = 2-3f>te+). 5. The concordance ratio for former/never smokers is 2-2 (fcf = 2-2). 6. The concordance ratios for occasional/never and regular/never smokers are the same m = k*3)= 7. The observed excess risks for former and occasional smokers are, respectively, 9 per cent and 20 per cent of those for regular smokers. 8. There is a multiplicative model between the true risks. 9. The true to observed misclassification probabilities (ptj) are True Regular (3) Occasional (2) Former (1) Never (0) Regular (3) ------ Observed (j) Occasional (2) Former (1) Never (0) 0-0000 -- 0 0107 00910 0-0107 0-1770 0-1081 Assumption 8 is the main difference from the EPA assumptions. Their multiplicative model applied to observed rather than true smokers, and did not apply to current smokers. Following Section 4.3 (with minor adaptation as the concordance ratios are not given level by level) the data, together with assumptions 1 to 6, lead to the following table of observed control data: Spouse Non-smoker Smoker Total Never 72 61 133 Subject Former 14-751 27-494 42-245 Occasional 2-054 5-622 7-676 Regular 18-484 50-596 69080 This is essentially identical to Table B-13 of the EPA report. 2501854158 http://legacy.library.ucsf.edu/tid/mid32d00/pdf 592 P. LEE AND B, FOREY The misclassification probability matrix can now be applied to convert tbese to true control data: Spouse Non-smoker Smoker Total Never 69-569 55-907 125-476 Subject Former Occasional 16-026 29-423 45-449 2-806 7-680 10 486 Regular 18-888 51-702 70-590 Using assumption 7, and the procedures in Section 4,4, we estimate the following table of data and risks, ignoring spousal smoking: Observed data Cases Relative risk True data Cases Relative risk Never 22 1.00 16-316 1-00 Former 18-449 2-640 17170 2-905 Subject Occasional 5-897 4-645 8-056 5-908 Regular 219-655 19-223 224-458 24-453 Ever 244 12-396 249-684 15-176 , t! Finally, the iterative procedures of Section 4.5, in conjunction with the multiplicative model assumption, lead to: :h ijlj i Multiplicative model Never Subject Former Occasional Regular Observed data - spouse non-smoker Cases 8 Relative risk 1-00 Observed data - spouse smoker Cases 14 Relative risk 2-066 True data -- spouse non-smoker Cases 6-877 Relative risk 100 True data -- spouse smoker Cases 9-440 Relative risk 1-708 4-255 2-596 14-194 4-646 4-151 2*621 13-018 4-476 1039 4-553 4-858 7-777 1-419 5-118 6-637 8-742 38-702 18.845 180-953 32-188 39-548 21-182 184-910 36-181 The misclassification corrected spousal smoking RR is thus 1-708, so that misclassification has caused upward bias by a factor 2-066/1-708 = 1-209. An additive model would lead, as shown below, to a corrected RR of 1-900, a bias of 1087. The latter is closer to the EPA bias estimate of 1-10 (corrected RR = 1-89), presumably as the RRs in the current smoking groups are less dependent on spousal smoking, so being more consistent with their assumptions. 2501854159 http://legacy.library.ucsf.edu/tid/mid32d00/pdf MISCLASSIFICATION OF SMOKING HABITS AS A SOURCE OF BIAS Additive model Never Observed data - spouse non-smoker Cases 8 Relative risk 1-00 Observed data -- spouse smoker Cases 14 Relative risk 2 066 True data -- spouse non-smoker Cases 6458 Relative risk I-00 True data -- spouse smoker Cases 9-859 Relative risk 1-900 Subject Former Occasional 5-438 3-318 13011 4-259 5*188 3-487 11-982 4-387 1-452 6-364 4-445 7-116 1-984 7-618 6-072 8-517 Regular 57-643 28-067 162-012 28-819 58-903 33-596 165-555 34-496 593 4.7. Simplification of the model In the example above, the upward bias depends on assumed values of six misclassification probabilities. To simplify further work, the relationship of the bias to these probabilities was investigated further. First, it was clear the values of the misclassification probabilities from regular or occasional to former smokers had little effect on the bias. Setting these to zero changed the bias only from 1-2093 to 1-2167 (multiplicative model) or from 10873 to 1-0871 (additive). Second, it was also clear misclassification of regular smokers as never smokers contributed most to the bias. With other misclassification rates set to zero and using a multiplicative model, the biases resulting from misclassification of regular, occasional or former smokers only were, respectively, 1*1021,1-0416 and 1-0427. These represent excess biases that are, respectively, 47, 19 and 20 per cent compared with the bias, 1-2167, associated with all three misclassification probabilities combined. These excess biases are in the ratio 1:0-407:0-418, quite close to that predicted 1:0-368:0-378 by assuming bias is proportional to the product of misclassification rate, observed excess risk, observed concordance ratio and observed frequency of the smoking category in the controls, an approximate formula suggested by Section 1. For the additive model, the biases resulting from misclassification of regular, occasional and former smokers only were, respectively, 1-0480, 1-0190 and 1-0040. These represent excess biases that are respectively 55, 22 and 5 per cent compared with the combined bias of 1-0871, Thirdly, for both multiplicative and additive models the bias from the full analysis described in Section 4.6 was quite close to that arising from a simpler model with only one smoking level, in which 1-75 per cent of ever smokers were misclassified as never smokers, with the concordance ratio set as 3-0. Thus, for a multiplicative model, this simpler model gave a bias of 1-1850 compared with 1-2093 for the full model. For the additive model, the simpler model gave 1-0806 and the full model 1-0873. These general conclusions were confirmed using data from other studies. Table II summarizes results for the Correa study14 and for four other large U.S. studies.15-13 These show misclassifi cation to former smokers is unimportant, misclassification of regular smokers as never smokers accounts for about half of the total bias and that the assumptions used are similar in effect to using the simpler model with a misclassification rate of 1-75 per cent and a concordance ratio of 3-0. The biases for the multiplicative and additive models are similar where the observed spousal i 2501854160 http://legacy.library.ucsf.edu/tid/mid32d00/pdf 594 P. LEE AND B, FOREY Table II. Biases from five studies in U.S. females under various assumptions Study Correa14 Brownson15 Fontham16 Garfinkel11 Stockwell18 Observed spousal risk Multiplicative model 1. Bias from full model 2. Bias ignoring misclassifica- tion to former smokers 3. Bias from misclassification of regular smokers only % of excess bias (3 of 2) 4. Bias from `simpler' model Additive model 1. Bias from `full' model 2. Bias ignoring misclassifica- tion to former smokers 3. Bias from misclassificatioD of regular smokers only % of excess bias (3 of 2) 4. Bias from `simpler' model 2-066 1-209 1-217 F102 47-1 1-185 1-087 1-087 1-048 55-1 1-081 0-972 1-117 1-120 1-059 48-7 1-102 1-132 1137 1-062 45-6 1-114 1-263 1-099 1-102 1-050 489 1-088 1-088 1-090 1-044 486 1-077 1-233 1-045 1-046 1-0235 50-9 1-040 1-039 1-040 1-021 51-5 1-035 1-600 1-089 1-092 1-046 49-5 1-080 1-060 1-061 1-032 55-2 1-055 RR is near unity (Brown son, Fontham, Garfinkel). For larger spousal risks (Stockwell, Correa) the bias from the multiplicative model is larger. 5. APPLICATION OF THE METHODOLOGY TO DATA FOR U.S. FEMALES 5.1. Introduction The simplified methodology of Section 4 is now applied to available data for U.S. females. Studies conducted in the U.S. and in Asia (considered in Section 6) are the main contributors to the evidence, and data for females are much more extensive than for males. The U.S. data are described in Section 5.2, followed by discussion, in Sections 5.3 and 5.4, of appropriate ranges of concordance ratios and misclassification rates to use. The methodology is applied in Section 5.5, and the results compared with those of others in Section 5.6. 5.2. U.S. epidemiological data on lung cancer and spousal smoking in females Table III summarizes relevant data from 13 U.S. studies.14-26 (Data from one study27 are ignored, being based on only nine lung cancer cases, and only one in ever smokers whose risk, unusually, was less than in never smokers.) Points to note about the studies are: (i) Only one study21 was prospective. For this study, `number of controls' are number of subjects at the start of the study. (ii) Most studies concerned all histological types of lung cancer but three'4'19'26 considered specific types only. (iii) The index of exposure varied. Ten studies concerned spousal smoking but varied as to whether smoking of products other than cigarettes was considered, and when smoking occurred. Three studies19,20- 25 concerned at home exposure, not specifically from the spouse. For one study19 the index related only to heavier exposure. 2501854161 edu/tid/mid32d00/pdf Tabic III. Data from 13 studies of lung cancer and spousal smoking in U.S. females Study Year Ntunher of controls Number of cases Histological Index ofexposure % reference type exposed Neer smoked Ever Never smoked Ever cooked smoked Spousal smoking No Yes Total Total No Yei Total Total Brownson tf a/. Browwon ft d. Buffer fr aJ. Curren i a!. Ponthjun d Garfinkd OtrfintMl *t d. Hurnbte et at. Jinerich ri al. 199213 19H" 19S3'4 1994" 198I11 lUSS1' 19S7" 1990" 40 7 47 568 598 1164 32 103 m 72 01 113 487 766 1253 81859 94880 176739 148 254 71 91 38 so 402 162 124 19 15 4 !9 - 213 218 431 279 8 33 41 119 S 14 22 -- 218 433 651 6S It 153 -- 43 91 (34 Ill 5 IS 20 -- 6f 76 144 K*b and Wynder 19S41* K*b*l 199013 Stockwt!l et et Wuat. 1992'* 1985" 10 15 25 - u 13 24 45 97 142 " \l 35 53 30 35 91 - is 44 62 22 33 SJ 87 9 19 28 33 Adenocarcinoma Presence of person 12-B smoking 4 +- hours/day ,, All types Spouse smoked 51-3 412 All typos Household member 83-7 smoked regular))1 244 All except Spouse ever smoked 45-9 broochoalvcolar cigarettes All types Spouse ever smoked 61-1 tobacco -- All types Spouse currently smoked cigarettes 53*7 - All types Spouse ever smoked 63-2 223 All types Spouse ever smoked 562 " All types Spoute smoked 59-7 cigarettes while living with ibe subject - All types -- All types Spouse ever smoked 604) Exposed )p adulthood 68-3 at home - All types Spouse smoked 604 12C Adenocarcinoma Spouse smoked GOO Spousal rid: (95% limits) 1-52 (0-59-5*96) 097(078-121) (V80 (0-34-1 W) 2-07 fO-81 -MS) 126(1 04-1-54) 1-17 (0-85-161) 1-23 (0-81-1-87) 2-34 (0-81 6-75) 0-75 (0*47-1-20} 1-68 (0-39-6*90) 1-00(0*0-120) " 1 29(1-04-1608 MS (0-90-1-54) 2-20 (0-S&6-60) 1 0-79 (0*25-2*45) 050 (0-46-176) 160 fO-SO-3-20) Ml (0-54-3.G7) -- 160 (o-so-a-oo) 1-20 (050-3-30) % smoked 2S-S [430] 58-7 47-2 [43-0] 22-0 [346] 40*7 [42KJJ 42*0 [430] [420] 61-3 Artis* risk 4*30 [SO] 7-06 12-40 [*0] 5-58 [6-0] 16-28 [8-0] 390 [o] [SO] 2-71 Z9J-PS810&Z http://legacy.library.ucsf.edu/tid/mid32d00/pdf 596 P. LEE AND B. FOKEV (iv) The crude spousal RR corresponds to the 2x2 table of unexposed and exposed never smoking controls and cases. For the prospective study,21 the RR and numbers of controls are in fact age standardized, crude data not being presented. (v) Adjusted spousal RRs are as reported, with the potential confounding variables considered varying by study. (vi) Some studies14'19,30-22,26 gave direct data on numbers of ever smoking cases and controls, from which estimates of proportions of ever smokers and of active smoking RRs could be calculated directly. For other studies, estimates were either taken from other publications or, shown in square brackets, calculated from other studies conducted at a similar time. The data in Table III are as used by EPAs except: (a) three additional studies1 s-1 *2 3 have been included; (b) the Fontham et al. study data are updated from a recent report;16 (c) for the Garflnkel case-control study21 data were used for `spouse ever smoked' rather than `spouse smoked at home', the former index being more consistent with that used in other studies; (d) numbers for the Janerich et al. study,23 given for the sexes combined by EPA, have been estimated separately Tor females;12 and (e) ever smoking RRs have been used for the Wu et al. study26 whereas EPA gave current smoking risks. Ignoring misclassification, the data show some evidence of a positive association for spousal smoking. Fixed-effects meta-analysis28 gives an RR estimate of 1-13 (95 per cent Cl T01-T27) for the unadjusted data and M3 (95 per cent Cl 1-01-1-26) for the covariate-adjusted data. As adjustment for covariates had little effect, as the misclassification adjustment procedures are not designed to deal with data subdivided by covariates, and as the source papers rarely if ever present such subdivided data anyway, misclassification adjustment will (in Sections 5.5 and 6) be applied to the data unadjusted for covariates. 5.3. Concordance ratios EPA assumed that, for the 2x2 table subject: never/ever smoker; spouse: never/ever smoker, the concordance (cross-product) ratio is 2-8, and that, for the 2x2 table subject; never/ex-smoker; spouse: never/ever smoker, is 2-2. A value of 3'2 for the concordance ratio subject; never/current smoker; spouse; never/ever smoker, was also provided, but not used in the adjustment procedure, as this would lead to over definition. As support for these estimates, EPA cited four references,29-32 but gave no detailed data. In fact, the first reference29 gives no relevant data at all, the second30 only gives data relevant to a different concordance ratio, while the third31 only gives data relevant to the first of the three concordance ratios (giving a value of 1-74 for women and 2-49 for men). Only the fourth reference32 gives a joint breakdown of smoking habits of subjects and spouses by never/ex/current status and even that was estimated indirectly, and suggests concordance ratios ! of 2-4, 1-9 and 2-8 rather than 2-8, 2*2 and 3-2, ii ; EPA also assumed that for current smokers the association with spousal smoking was the same for occasional and regular smokers. In fact, the only study cited32 actually showed that the more the subject smoked the more likely the subject was to be married to a smoker. The concordance ratio estimates of EPA are not solidly based. Elsewhere12 Lee summarizes data from 17 studies. Four provide estimates of the subject: never/ever smoker; Spouse: i never/ever smoker concordance ratio. For females the estimates were 1-74,2-67,2-19 and 2-65.For i. males, the estimates (whose expected values are the same due to symmetry) were 2-49,1-95,2-32 and 3-10, The mean of these values is 2-39. The remaining studies provided 16 independent estimates of the subject: non-current/current smoker; spouse: non-current/current smoker 2501854163 http://legacy.library.ucsf.edu/tid/mid32d00/pdf t MISCLASSIFICATION OF SMOKING HABITS AS A SOURCE OF BIAS 597 concordance ratio which ranged from 2-56 to 6-04, with a mean of 3-98. Based on the 3x3 table of Lee,31 the non-current/current concordance ratio should be about 1-36 times higher than the never/ever concordance ratio. If so, the mean of 3-98 for the former ratio implies a value of 2-93 for the latter ratio, rather higher than the mean of 2-39 for the four studies providing direct data. This look at the data suggests an appropriate value of the never/ever concordance ratio is almost definitely in the range 2 to 4, probably below 3 and probably nearer 3 than 2. However, we should bear in mind there is highly significant variation between estimates for different studies. Concordance may depend, among other things, on national characteristics, the exact questions asked and the circumstances of interview. Limited evidence12 suggests no clear relationship with age, however. 5.4. Misclassification rates Evidence on the extent of misclassification has been discussed by Lee11,12'33 and Wells.8,3*'33 There are two main sources of data, studies in which biochemical markers of smoke uptake are used to validate statements about current smoking, and studies in which statements made on different occasions about smoking are checked for consistency. It is useful to summarize the evidence from these studies, so highlighting difficulties in obtaining reliable rate estimates for use in adjustment procedures. As increases in carbon monoxide and thiocyanate commonly occur from sources other than smoking, both Lee and Wells have restricted attention to studies using cotinine, a major metabolite of nicotine, as a biochemical marker of uptake. Although there are some dietary sources of nicotine, these cannot produce cotinine levels typical even of a light smoker.36 Cotinine levels of current smokers are about two orders of magnitude higher than those of ETS exposed non-smokers. Although there may be slight overlap between levels in very light smokers and very heavily ETS-exposed non-smokers, it seems generally accepted that a cut-offof 10 per cent of the level of average smokers can be used to distinguish true smokers. A 30 per cent cut-off is often used to distinguish regular smokers. Reviewing evidence from cotinine studies, virtually all conducted in the U.S., U.K. or other Western populations, some points emerge. First, misclassified smokers (that is, self-reported non-smokers above the cut-off) have lower cotinine levels than self-reported smokers; occasional smokers more often deny smoking than regular smokers (but see Section 6). Second, with similar cut-offs there is wide variation in the proportion of non-smokers found to be smokers. Studies in which smokers are advised to give up smoking often report very high proportions of 15-40 per cent. Even ignoring such studies, as Lee and Wells have done, there is still marked heterogeneity, proportions ranging from under 1 per cent to over 6 per cent.12 Clearly, study circumstances affect misclassification rates, and, as the cotinine and ETS/fung cancer studies may not be comparable, there is uncertainty in extrapolating results from one study type to another. Wells suggests misclassification rates from `general population studies' may be much higher than those from `epidemiological studies', but this runs counter to the conclusions of Velicer et a/.37 that the less the likelihood of intervention the greater the accuracy of self-report. In any case the distinction between such study types is unclear. Many cotinine studies only record current smoking habits, and some studies only report data for self-reported non-smokers. Misclassification adjustment requires knowledge, not of the proportion of non-smokers found to be current smokers, but of the proportion of current smokers reporting they are lifelong non-smokers. Wells estimates 1-07 per cent of true regular smokers and 17*7 per cent of true occasional smokers are misclassified as never smokers. Elsewhere33 Lee presents data from more studies showing, in total, 68 per cent higher rates of misclassification of current smoking. 2501854164 http://legacy.library.ucsf.edu/tid/mid32d00/pdf 598 P. LEE AND B. FOREY Various studies have compared smoking as reported by subjects on two occasions, some years | apart. In a large study in Scotland, for example, cited by Lee,12 10-1 per cent of ex-smokers and | 2*5 per cent of current smokers at initial interview later claimed never to have smoked. Such I !! I studies may underestimate misclassification, as smokers may deny smoking on both occasions. j Data from six other studies were summarized by Wells,8 from which similar estimates of 11-7 per f cent for ex-smokers and 3-9 per cent for current smokers were calculated. The individual study | estimates varied considerably, however, for ex-smokers ranging From 0 0 per cent to 26*8 per cent. Compared with subjects who consistently report being ex-smokers, subjects reporting past 5 smoking on only one occasion tend to report having given up longer ago and to have smoked less when they were smoking.32 Because of this, Wells, in the EPA report,8 assumed that inconsistent i ex-smokers could be assigned the excess risk of long-term ex-smokes, estimated as 9 per cent of * that of current smokers. As some recent ex-smokers deny smoking this estimate may be , somewhat too low. i The misclassification estimates ofWells are similar in effect to assuming about 1*75 per cent of average ever smokers are misclassified as never smokers. Based on higher misclassification rates found in a more extensive data review, Lee13 estimated 2*5 per cent would be more appropriate. Taking into account other points (multiple report studies may miss subjects denying on each occasion; some recent ex-smokers may deny smoking), the figure would be slightly higher than , this. However, there are considerable uncertainties. An appropriate figure is probably in the range * 2-3 per cent but could, not implausibly, be anywhere in the range 1-4 per cent. ' Strictly, bias calculations should allow for a smoker being more ready to deny his habit if married to a non-smoker. The limited data on this12 do not suggest this is a major issue. Full investigation would require a study with cotinine measured for both husband and wife. There is no evidence whether, given actual smoking habits, subjects who deny smoking are more or less at risk of lung cancer than those who admit it. in a Danish prospective study (Gyntelberg, personal communication), five deaths occurred from ischaemic heart disease among men who had reported not smoking but with cotinine levels consistent with current smoking. This compared with 0-8 expected for men of similar age reporting smoking (p < 0-001). 5.5. Effect of misclassification adjustment on spousal risk estimates Table IV presents meta-analysis RRs for the U.S. data assuming: (i) various levels of misclassification; (ii) various concordance ratios; and (iii) either a multiplicative or an additive model. The combined RR risk estimate decreases with increasing misclassification, and (for a non-zero misclassification) with increasing concordance. For low misclassification rates, estimates from the multiplicative and additive models are very similar, but for higher misclassification rates, the additive model gives slightly lower RR estimates. Even with an estimated misclassification rate as low as 0*5 per cent, the RR estimate becomes non-significant. For a rate of 1-75 per cent and a concordance ratio of 3-0, shown above to give results comparable to EPA's more complex assumptions, the unadjusted RR of 1-13 reduces to 1-05. Assuming a 2-5 per cent misclassification rate, as noted to be reasonable, the association essentially disappears, with RR 1-01 (95 per cent Cl 0-90-1-14) for a concordance of 3 0. While there is uncertainty about the true misclassification rate and concordance ratio, these analyses are consistent with the slight excess lung cancer risk observed in relation to smoking by the husband, being due not to ETS exposure, but to an artefact arising from misclassification of some smokers as non-smokers. 2501854165 http://legacy.library.ucsf.edu/tid/mid32d00/pdf MISCLASSIFICATION OF SMOKING HABITS AS A SOURCE OF BIAS 599 Table IV. Lung cancer risk associated with spousa! smoking (95 per cent Cl) after adjustment for misclassification of smoking habits - based on meta-analysis of data from 13 studies in U.S. females (see Table III) Misclassification rate (%) Multiplicative model Concordance ratio Additive model 2-0 3-0 4-0 2-0 3-0 4-0 0 113 1-13 1-13 113 1-13 1-13 (101-1-27) (1-01-1-27) (1-01-1-27) (1-01-1-27) (1-01-1-27) (1-01-1-27) 0-5 1-11 Ml 1-10 1-11 Ml M0 (0-99-1-25) (0-99-1-24) (0-98-1-24) (0-99-1-25) (0-99-1-24) (098-1-24) 1-0 1-10 108 107 1-10 1-08 1-08 (0-98-1-23) (0-96-1-22) (0-96-1-21) (0-98-1-24) (0-96 1-22) (0-96-1-21) 1-5 1-08 1-06 1-05 1-08 1-06 105 (0-96-1-22) (0-94-1-19) (0-93 1-18) (0-96-1-22) (0-94-1-19) (0-93-M8) 1-75 107 1-05 103 1-08 1*05 1-03 (0-95-1-21) (0-93-118) (0-92-1-16) (0-96-1-21) (0-93-1-18) (0-92-M6) 2-0 1-06 1-03 102 1-07 104 102 (0-94-1-20) (0-92-1 17) (0-90-1-15) (0-95-1-20) <0-92 1-17) (0-90-M5) 2-5 105 1-01 0-99 105 1-01 0-99 (0-93-118) (0-90-1 -14) (0-88-1-12) (0-93-1-18) (0-89-M4) (0-87-1-11) 30 103 0-99 0-96 1-03 0-98 0-95 (091-1-16) (0-87-1-11) (0-85-1-08) (0-91-1-17) (0-84-1-16) (084--1-08) 4-0 1-00 0-94 0-90 0-99 092 OSS (0-88-1-13) (0-83-1-06) (0-80-1-02) (0-87--1-12) (0-81-1-04) (078-1-00) 5.6. Difference from conclusions reached by others In 1986 the NRC7 summarized data from 13 studies, five in the U.S.A. They estimated an overall adjusted RR of 1-34 (95 per cent Cl 1-18--1-53). After misclassification adjustment the RR was estimated to be about T25, and at least T15. Although (see Section 3.4) the methodology used was incorrect, the conclusions were similar to those derived from Table IV. Thus the NRC suggested a bias of 1-34/1-25 = 1-07 and at most 1-34/1-15 = 1-17. Applied to the unadjusted U.S. estimate of 1-13 for the updated data, these biases would give adjusted figures of 1-06 and 0-97. The NRC conclusion that misclassification bias could not explain the association was not due to inadequate adjustment but to the much higher RR they started with. In this context, it is notable that there has been a striking tendency for more recent studies to report lower RRs. Thus, while the 22 worldwide studies reporting findings up to 1988 provided a covariate-adjusted meta-analysis RR estimate of 1-35 (95 per cent Cl 1-20-1-52) for spousal smoking, the 15 studies reported later provide a RR estimate of only 1-01 (95 per cent Cl 0-91-1T1). The analysis of Wald er al.t0 also conducted in 1986, was similar to that of the NRC, being based on the same 13 studies. However, as they assumed an exceptionally low misclassification rate, a lower bias estimate of only 1-35/1-30 = 1-04 was calculated. The recent EPA report considered data from 11 U.S. studies, with an RR estimate of 1-22 (95 per cent Cl 1-04-1-44) reducing to 1-19 (95 per cent Cl 101-1-38) after adjustment. Assuming a 1-75 per cent misclassification rate, and a concordance ratio of 3-0, our analysis reduces an RR of 1-13 (95 per cent Cl 1-01-1-27) to 1-05 (95 per cent Cl 0-93-1-18). There are three main reasons why our misclassification adjusted RR is much lower than that of EPA, and non-significant: (i) our analysis includes three studies not considered by EPA,1S- la-3S one1 a large study. Overall i 2501854166 http://legacy.library.ucsf.edu/tid/mid32d00/pdf 600 P. LEE AND B. FOREY the three studies show no association with spousal smoking (RR 10i; 95 per cent Cl 0-82-1-23); (ii) the individual study data we used give slightly lower RRs (see Section 5.2). Thus our estimate for the same 11 studies EPA used is 1-20 (95 per cent Cl 1*05-1-38) rather than 1*22; (iii) the actual bias estimated by EPA, of 1-03, is substantially lower than we estimate, 1-08, using apparently similar assumptions. The most notable difference is for the largest study,1* where we estimate 1-08 and the EPA only 101. This study was unusual as urine samples were used to determine cotinine levels. As no self-reported lifelong non-smoking women with lung cancer were found to have cotinine levels consistent with regular smoking, the EPA assumed a misclassification rate of zero for regular smoking for this study. This assumption is wholly unjustified. Urine samples were taken in hospital after diagnosis. Since many smokers give up smoking at time of diagnosis of lung cancer, it is unusual for smoking to be permitted in hospitals, and cotinine has a relatively short half life of about a day, one cannot infer that none of those cases who were regularly smoking around the time of diagnosis reported being lifelong never smokers. 6. EFFECT OF MISCLASSIFICATION IN ASIAN FEMALES Of 37 studies of ETS and lung cancer worldwide, 16 have been conducted in Japan, China or Hong Kong.*78 Based on 1918 lung cancer cases in females, an overall RR estimate, unadjusted for covariates or misclassification, is a marginally significant 1*16 (95 percent Cl 1-03 1-31). For these data, misclassification adjustment at about the level suggested by EPA8 (that is, using an ever/never smoker misclassification rate of 1-75 per cent, a concordance ratio of 3-0, and an additive model) has very little effect, reducing the RR only by 0-01 to 1-15 (95 per cent Cl 1-02-1-30). This trivial adjustment, as EPA8 also reported, is due to the few Asian women who smoke and the lower RR when they do. However, this assumes misclassification rates in Asian and Western populations are similar, as the evidence on misclassification comes almost exclusively from Western populations. Great doubt has been cast on this assumption by a recent study39 of 400 married Japanese women, in which as many as 20-8 per cent of current smokers (as determined by cotinine) reported being never smokers. The misclassified smokers had very similar cotinine levels to smokers who admitted smoking. While the circumstances of interview (door-to-door interviews) and age range (20-55) differed from the ETS/lung-cancer studies, the findings fit in with a long-held suspicion that misclassification rates may be much higher in Japanese than U.S. women, smoking by women being socially unacceptable in Japan. A concordance ratio of 3-0 and a 20 per cent misclassification rate applied to the overall Asian data would totally eliminate the association (RR = 0-99,95 per cent Cl = 0-87-1-12), while even >0 l( a 10 per cent rate would render it non-significant (RR = 1-09, 95 per cent Cl 0-97-1-23). The Japanese study actually suggested rather a higher concordance than seen in Western studies, further emphasizing the importance of bias due to misclassification. 7. OTHER ISSUES AFFECTING INTERPRETATION OF DATA ON ETS AND LUNG CANCER 7.1. Other sources of bias Misclassification of smoking is not the only source of bias relevant to the relationship of spousal smoking to lung cancer. Others include; (i) Inaccuracy of exposure. Misclassification of spousal exposure will (see Section 2.10) underestimate any true risk. Also, as some non-smokers married to non-smokers are exposed to ETS, the RR for non-smokers married to smokers, as traditionally calculated, 2501854167 http://legacy.library.ucsf.edu/tid/mid32d00/pdf MISCLASSIFICATION OF SMOKING HABITS AS A SOURCE OF BIAS 60i will underestimate their risk relative to a truly noil-exposed population. Layard40 reviews the difficulties in adjusting for background risk. (ii) Inaccuracy ofdiagnosis. Without autopsy, a false-positive clinical diagnosis of lung cancer is common 41 In many of the Asian and European studies a high proportion of cases were diagnosed without histological confirmation. (iii) Recall bias. Almost all the ETS/lung cancer studies are case-control, in which recall of smoking, ETS, and other exposures may be affected by disease presence. (iv) Confounding. For many lifestyle risk Factors for many diseases, prevalence is not only increased in smokers, but is also somewhat increased in ETS-exposed never smokers. A recent study42 concluded that `confounding by multiple risk factors may be an important issue in passive smoking studies'. (v) Publication bias. Spousal smoking RR estimates tend to be lower for studies with large numbers of cases.12'45 Based on the latest data, this difference is significant (p = 0-01) with (covariate-adjustedj RRs of 1-07 (95 per cent Cl 0-97 T-l 7), 1-35 (95 per cent Cl M4-1-59) and 1-42 (95 per cent Cl 1-07--1-90) for studies with, respectively, more than 100, 50-100, and less than 50 cases. This is consistent with publication bias. A technique for carrying out a meta-analysis whilst adjusting for publication bias has been proposed.44 (vi) Study quality. Elsewhere43 Lee defined a study as having a serious weakness if any ofseven criteria were present. 16 studies can be classified `inferior' using these criteria including 9 out of 10 of the studies with the highest RRs. The overall RR (adjusted for covariates) for the `inferior' studies is 1-29 (95 per cent Cl 1-15-1-45), significantly {p < 0-01) greater than that for the 21 `superior' studies, which, at 1-03 (95 per cent Cl 0-93-M4), show no significant association with spousal smoking. 7.2. Evidence from other indices of ETS exposure Early ETS/lung cancer studies presented data only for husband's smoking, and published meta-analyses have tended to concentrate on this index. This includes the EPA report,8 which considered these results at length but did not give even basic results for any other index, although considerable evidence has accumulated for workplace and childhood ETS exposure. Based on 15 individual sex-spedfic RR estimates from 12 studies, a combined RR estimate (adjusted for covariates) for woricplace exposure is 1-00 (95 per cent Cl 0-91-1-08). Based on 15 estimates from 14 studies, the RR estimate for childhood exposure is 0-96 (95 per cent Cl 0-87-1-06). This compares with 1-14 (95 per cent Cl 106-1-23), based on 37 studies, for husband's smoking. Concentration on the index showing an association, at the expense of others which do not, is a major form of publication bias. Two alternative extreme views of the conflict between the spousal and the workplace/childhood results are possible. One is that spousal smoking is much more susceptible than the other indices to misclassification, and perhaps also confounding, bias as concordance is much stronger for spouses than for co-workers or for parents and their children. The other is that working with a smoker and having a parent smoke in childhood are both very poor markers of actual exposure, spousal smoking finding an association as it is the only adequate marker. This second explanation seems weak. Working with a smoker is clearly correlated with increased ETS exposure (though probably less so than is marriage to a smoker), and, if ETS exposure really increased risk, an association with lung cancer incidence would be expected. 7.3. Dose-response relationships Our methodology compares risk in non-smokers according to whether or not the husband smoked, regardless of how much he smoked. The EPA report8 stressed the existence of 2501854168 http://legacy.library.ucsf.edu/tid/mid32d00/pdf 602 P. LEE AND B. FOREY a dose-response relationship, with RR estimates generally highest in the women whose husbands smoked the most. In interpreting this finding it should be noted that studies reporting relatively high RRs For spousal smoking are much more likely to present data by amount smoked than those that do not. Thus, for the 19 studies which presented dose-response data, the overall spousal smoking RR (adjusted for covariates) was 1-36 (95 per cent Cl 1-23-1-51), highly significantly (p < 0-001) greater than the RR of 0-93 (95 per cent Cl 0-83-1-04) for the 18 studies which did not. This form of publication bias means RR estimates for non-smoking women married to heavily smoking husbands are strongly biased upward. It may also be that, given a choice of indices of ETS exposure, an author may only present detailed findings for the index showing the clearest trend- Other biases may affect the dose-response relationship. Thus, as concordance increases with amount smoked, smoking misclassification will also contribute to the observed dose response, 7.4. Histological type The association oflung cancer with active smoking is much greater for squamous carcinoma than for adenocarcinoma. If ETS is seen, crudely, as a smaller dose of active smoking, it might be expected, had it any effect at all, to be more strongly associated with risk of squamous carcinoma. Findings for those ETS/lung cancer studies reporting results separately by histological type do not fit in with this expectation. While for some studies the results do seem more consistent with a relationship with squamous carcinoma, there are an equal number where the relationship seems more with adenocarcinoma, as well as some studies with similar, or a lack of, relationship with either.43 7.5. Plausibility Active smoking is strongly associated with risk of lung cancer and ETS and mainstream smoke contain many chemicals in common, albeit in different relative concentrations. It can be argued (especially by adherents of the `no-threshold' hypothesis) that an association of ETS with lung cancer is to be expected. However, the amount of particulate matter Otar') retained by passive smokers is thousands of times lower than that retained by active smokers. If, as many believe, `tar' retention is relevant to lung carcinogenesis, and the dose-response relationship is approximately linear, the observed spousal smoking RR (about 1-15-1-20) would be much higher than expected on dosimetric grounds (about 1-01-1-02). Based on this argument, most of the observed association could be due to bias.8 8. DISCUSSION Misclassification of smoking habits leads to underestimation of the association of lung cancer with active smoking. Given positive concordance between smoking habits of spouses, however, random misclassification of some smokers as non-smokers will result in overestimation of the association of lung cancer with ETS in studies of non-smokers where marriage to a smoker is the index of exposure. Sections 2 and 3 show how this bias depends on various factors. It tends to increase with an increasing misclassification rate of smokers as non-smokers, concordance, proportion of subjects who smoke, and proportion of spouses who smoke. Misclassification of non-smoking subjects as smokers or of smoking by spouses has little effect on the bias, and the mathematics is simplified by ignoring these possibilities. Bias estimates can be materially affected if misclassification of smoking is not random. Section 4 accounts for one important form of non-randomness, arising as current regular smokers are less likely to deny smoking than are W W 2501854169 http://legacy.library.ucsf.edu/tid/mid32d00/pdf MISCLASSIFICATION OF SMOKING HABITS AS A SOURCE OF BIAS 603 occasional or long-term ex-smokers. However, various other mechanisms may cause tion-randomncss. If, for example, smokers tend to be much more likely to deny smoking if their spouse does not smoke, the bias will be reduced and may even be reversed. If, on the other hand, smokers who are ill and at more risk of developing lung cancer are also more likely to deny smoking, the bias may be increased. Without hard data indicating the existence or importance of these forms of non-randonness, we make no attempt to account for them. However, there is need for further research here, for example, a study where smoking by husbands and wives is both assessed and separately validated using cotinine assays. Section 4 considers the possibility that misclassification may vary by type of smoker, and improves the correction method used by EPA, which has numerous errors. Given known misclassification rates and concordance ratios, and various other assumptions, the methodology allows estimation of true numbers of cases and controls in the various smoking categories from the observed data, and hence of the misclassification-adjusted RR associated with marriage to a smoker. RR estimates for individual studies can then be meta-analysed. This method is problematic due to the large number of misclassification rates and concordance ratios assumed, with data sparse or non-existent for many of them. Luckily matters are simplified by noting (see Section 4.7) that for many studies the bias implied by the assumed values of the misclassification rates and concordance ratios is virtually identical to that implied by a simpler model with only two smoking categories (never, ever), a single misclassification rate of 1-75 and a single concordance ratio of 3-0. In Section 5 this simpler model is applied to data for U.S. females. With the misclassification rate of 1-75 and concordance ratio of 3-0, a marginally significant unadjusted meta-analysis RR of 1-13 drops to a non-significant 1-05. In fact the misclassification rate could well be higher than 1-75 per cent, further reducing the RR estimate. Though there is some doubt as to the appropriate rate, misclassification can certainly explain most of the observed association of spousal smoking with lung cancer. As fewer Asian women smoke, and have lower active smoking RRs when they do, a given misclassification rate will cause far less bias in Asian than U.S. studies. However, evidence (which needs replicating) from Japan suggests misclassification rates may be much higher in Asian women. If so, misclassification may cause marked bias there. Until results of the IARC multicentre study are published, European data are rather sparse and are not considered here, Misclassification is only one reason to be wary of accepting the association of lung cancer risk with spousal smoking as indicative of a true effect of ETS. As discussed in Section 7, there are other sources of bias (such as confounding). There is also evidence of a lack of association with workplace or childhood ETS exposure. The very low particulate matter retention of passive smokers also suggests the association with spousal smoking may be mainly an artefact Our paper emphasizes the difficulties of interpreting weak associations in epidemiology, and the need to quantify the various sources of bias before coming to a firm conclusion. Though there are difficulties in quantifying the exact effects of smoking habit misclassification, our analyses show its likely importance and cast doubt on simple interpretation of the association between lung cancer and spousal smoking as indicative of a cause and effect relationship. . ACKNOWLEDGEMENTS We thank John Fry for computing assistance and Pauline Wassell for typing the numerous drafts of the manuscript. A number of colleagues provided helpful comments but we remain responsible for the views expressed. Finally, we thank various companies of the tobacco industry for financial support. 2501854170 http://legacy.library.ucsf.edu/tid/mid32d00/pdf 604 P. LEE AND B. FOREY REFERENCES 1. Bross, I. D. J, `Misclassification in 2 x 1. tables', Biometrics, 10, 478-486 (1954), 2. Newell, D. J. `Misclassification in 2x2 tables', Biometrics, 19, 187 (1963) 3. Goldberg, J. D. The effect of misclassification on the bias in the difference between two proportions and the relative odds in the fourfold table'. Journal of the American Statistical Association, 70, 561-567 (1975). 4. Copeland, K. T., Checkoway, H., McMichael, A. J. and Holbrook, R. H. `Bias due to misclassification in the estimation of relative risk', American Jounral ofEpidemiology, 105, 488--495 (1977). 5. Duffy, S. W., Maximovitch, D. M. and Day, N. E. `External validation, repeat determination, and precision of risk estimation in misclassified exposure data in epidemiology'. Journal ofEpidemiology and Community Health, 46, 620-624 (1992) 6. Tzonou, A., Kaldor, J., Smith, P. G., Day, N. E. and Trichopoulos, D. `Misclassification in case-control studies with two dichotomous risk factors'. Revue & Epidemiologies et de Sante Publique, 34, 10--17 (1986). 7. National Research Council, Environmental Tobacco smoke. Measuring Exposures and Assessing Health Effects. National Academy Press, Washington D. C-, 1986. 8. U.S, Environmental Protection Agency. Smoking and Tobacco Control, Monograph 4: Respiratory Health Effects of Passive Smoking: Lung Cancer and other Disorders', National Institutes of Health publication no. 93-3605, August 1993. 9. Lehnert, G, Garfinkel, L., Hirayama, T., Schmahl, D., Uberla, K., Wynder, E. L. and Lee, P. N. `Round table discussion'. Preventive Medicine, 13, 730-746 (1984). 10. Wald, N, J., Nanchahal, K, Thompson, S. G. and Cuckle, H. S. `Does breathing other people's tobacco smoke cause lung cancer?', British Medical Journal, 293, 1217-1222 (1986). 11. Lee, P. N. `Misclassification of smoking habits and passive smoking. A review of the evidence*. International Archives of Occupational and Environmental Health Supplement, Springer-Verlag, Heidelberg (1988) 12. Lee, P. N. Environmental Tobacco Smoke and Mortality, Karger, Basle 1992. 13. Lee, P. N. `Respiratory health effects of passive smoking: lung cancer and other disorders. A commen tary on issues relating to lung cancer in the May 1992 SAB review draft', submission to the Scientific Advisory Board of the U.S. Environmental Protection Agency, 1992. 14. Correa, P., Pickle, L. W,, Fontham, E,, Lin, Y. and Haenszel, W. `Passive smoking and lung cancer'. Lancet, 2, 595-597 (1983). 15. Brownson, R. C, Alavanja, M. C, R., Hock, E, T, and Loy, T. S, `Passive smoking and lung cancer in nonsmoking women', American Journal of Public Health, 82, 1525-1530 (1992). 16. Fontham, E. T. H, Correa, P., Reynolds, P., Wu-Williams, A., Buffler, P. A., Greenberg, R. S., Chen, V. W., Alterman, T., Boyd, P., Austin, D. F. and Liff, J. `Environmental tobacco smoke and lung cancer in nonsmoking women. A multicenter study". Journal of the American Medical Association, 271, 1752-1759 (1994). 17. Garfinkel, L., Auerbach, O. and Joubert, L. `Involuntary smoking and lung cancer: A case control study', Journal of the National Cancer Institute, 75, 463--469 (1985). 18. Stockwell, H. G., Goldman, A. L., Lyman, G, H., Nass, C. I., Armstrong, A. W., Pinkham, P. A., Candelora, E. C. and Brusa, M. R. `Environmental tobacco smoke and lung cancer in nonsmoking women*. Journal of the National Cancer Institute, 84, 1417-1422 (1992). 19. Brownson, R. C., Reif, J. S-, Keefe, T. J, Ferguson, S. W. and Pritzl, J. A. `Risk factors for adenocar cinoma of the lung', American Journal cf Epidemiology, 125, 25-34 (1987) 20. Buffler, P. A., Pickle, L, W, Mason, T. J. and Contant, C. The causes oflung cancer in Texas', in Mizell, M. and Correa, P. (eds). Lung Cancer. Causes and Prevention, Verlag Chemie International, New York, 1984. 21. Garfinkel, L. Time trends in lung cancer mortality among non-smokers and a note on passive smoking', Jouml of the National Cancer Institute, 66, 1061--1066 (1981). 22. Humble, C. G., Samet, J. M. and Pathak, D. R. `Marriage to a smoker and lung cancer risk', American Journal of Public Health, 77, 598-602 (1987) 23. Janerich, D. T., Thompson, W. D., Varela, L. R., Greenwald, P,, Chorost, S, Tucci, C., Zaman, M. B., Melamed, M. R,, Kiely, M, and McKneally, M. F. `Lung cancer and exposure to tobacco smoke in the household'. New England Journal of Medicine, 323, 632-636 (1990). 24. Kabat, G. C. and Wynder, E L. `Lung cancer in non-smokers'. Cancer, 53, 1214-1221 (1984). 25. Kabat, G. C. `Epidemiologic studies of the relationship between passive smoking and lung cancer*, 1990 Winter Toxicology Forum, Washington, 187-189 (1990) 2501854171 edu/tid/mid32d00/pdf MISCLASSIFICATION OF SMOKING HABITS AS A SOURCE OF BIAS 605 26. Wu, A. H., Henderson, B. E-, Pike, M. C. and Yu, M. C. `Smoking and other risk factors for lung cancer in women', Journal of the National Cancer Institute, 74, 747-751 (1985). 27. Butler, T. L. "The relationship of passive smoking to various health outcomes among Seventh-day Adventists in California', Dissertation, University of California, Los Angeles, 1988. 28. Flelss, J. L. and Gross, A. J. `Meta-analysis in epidemiology, with special reference to studies of the association between exposure to environmental tobacco smoke and lung cancer: a critique' Journal of Clinical Epidemiology, 44, 127-119 (1991). 29. Hirayama, T. `Cancer mortality in nonsmoking women with smoking husbands based on a large-scale cohort study in Japan', Preventive Medicine, 13, 680-690 (1984). 30. Sutton, G. C. `Assortative marriage for smoking habits'. Annals ofHuman Biology, 7, 449-456 (1980). 31. Akiba, S., Kato, H. and Blot, W. J. `Passive smoking and lung cancer among Japanese women'. Cancer Research, 46, 4804-4807 (1986). 32. Lee, P. N. `Passive smoking and lung cancer. Association a result of bias?'. Human Toxicology, 6, 517-524 (1987). 33. Lee, P. N. `An estimate of adult mortality in the United States from passive smoking', Environment International, 19, 91-96 (1993). 34. Wells, A. J. `An estimate of adult mortality in the United States from passive smoking a response to criticism'. Environment International, 17, 382-385 (1991). 35. Wells, A. J. `An estimate of adult mortality in the United States from passive smoking: A further reply'. Environment International, 19, 97--100 (1993). 36. Jarvis, M. `Dietary nicotine won't mislead on passive smoking unless subjects eat 90 kg tomatoes a day', British Medical Journal, 308, 62 (1994). 37. Velicer, W. F., Proehaska, J. O., Rossi, J. S. and Snow, M. G. `Assessing outcome in smoking cessation studies'. Psychological Bulletin, 111, 23 41 (1992). 38. Lee, P. N. `Lung cancer and ETS: Is the epidemiologic evidence conclusive?', American Statistical Association, Proceedings of the Section on Statistics and the Environment, 65-73 (1994). 39. Lee, P. N. `Marriage to a smoker may not be a valid marker of exposure in studies relating environ mental tobacco smoke to risk of lung cancer in Japanese non-smoking women'. International Archives of Occupational and Environmental Medicine, in press (1995). 40. Layard, M. W. The background adjustment in risk assessment of environmental tobacco smoke and lung cancer*. Environment International, 18, 453-461 (1992). 41. Lee, P. N. `Comparison of autopsy, clinical and death certificate diagnosis with particular reference to lung cancer. A review of the published data', /LPMJS, Suppl 45,102, 1 42 (1994). 42. Thornton, A. J., Lee, P. N. and Fry, J. S. `Differences between smokers, ex-SmokerS, passive smokers and non-smokers'. Journal of Clinical Epidemiology, 47,1143-1162 (1994). 43. Lee, P. N. `An assessment of the epidemiological evidence relating lung cancer risk in never smokers to environmental tobacco smoke exposure', in: Kasuga, H. (ed). Environmental Tobacco Smoke, Springer-Verlag, New York, 1993. 44. Sugita, M., Kamamori, M., Izuno, T. and Miyakawa, M. `Estimating a summarized odds ratio whilst eliminating publication bias in meta-analysis', Japanese Jorunal ofClinical Oncology, 22,354-358 (1992). 2501854172 http://legacy.library.ucsf.edu/tid/mid32d00/pdf