Document RpKN6xL2z0xp9Y45jgZDzDb5v

Amirican Journal or ErtotMioiccY Copyright 1981 by The Johns Hopkins University School of Hygiene and Public Health All rights reserved Vol. 114. No. 5 Printed in U.5.A POWER CONSIDERATIONS IN EPIDEMIOLOGIC STUDIES OF VINYL CHLORIDE WORKERS JAMES J. BEAUMONT' and NORMAN E. BRESLOW*1 Beaumont, J. J. (NIOSH, Cincinnati, OK 45226) and N. E. Breslow. Power considerations in epidemiologic studies of vinyl chloride workers. Am J Epidemiol 1931;114:725-34. Nine retrospective mortality studies of workers exposed to vinyl chloride were reviewed to determine whether differences in their hypothesis testing results might be due to differences in statistical power. Where possible, the power of each study was calculated for cancer of the lung, brain and liver. When power was taken Into consideration, the results for liver and brain cancer were found to be consistent with an etlologlc role for vinyl chlorlde; For luna cancer, the data were not consistent with an etlologlc role, jn that two studies with very high power yielded negative results. epidemiologic methods; respiratory tract neoplasms; brain neoplasms; liver neoplasms; vinyi chloride The nine mortality studies of workers exposed to vinyl chloride that have been completed to date disagree in their.hypothesis testing results Tor some causes of death, and for those causes it is difficult to draw conclusions about excess risk (1-12). The studies that are negative for a cause of death are especially difficult to interpret, since they may or may not have had the statistical power to detect an ex cess risk if, in fact, one existed. To aid in the interpretation of the studies, their statistical power with respect to three Received for publication November 14, 1980. and in final form April 13, 1981. 1 Industrywide Studies Branch F-8, National Inatitutc for Occupational Safety and Health, 4676 Columbia Parkway, Cincinnati, OH 45226 (address for reprint requests). 1 Dept, of Biostatistics, School of Public Health and Community Medicine, U. of Washington, Seat tle, WA 98195. The authors thank Jay Lubin, Richard Waxweiler, Thomas Fischbach. Noel Weiss and Wtllium Halperm for their valunble advice. Their special thanks go to Philip Landrigan for encouraging this approach. This paper was presented at the Conference to Re evaluate the Tnxi.-ity nT t*in'I Chloride. Pnlyvmvl (* Meei.ie mu) hi net lira ) A Hu vkik-m. Korllille. Ml), V-rei, ?n yi 1D-0. sites of cancer--liver, brain and lung-- was calculated, and their hypothesis test ing results, positive or negative, were considered in the context of power. Methods Power calculations Statistical power is the probability of not overlooking an excess risk, i.e., of not making a Type II statistical error. To aid in the interpretation of this frequently confusing subject, a brief review of Tvpe I and Type II errors follows. Investigators are most familiar with Type I errors. If the true state of nature is the null hypothesis (no increase in risk), then a Type I error is wrongly rejecting the null hypothesis and declaring that there is an increase in risk. The probabil- . ity of a Type I error is known as alpha, or more commonly, the "level .of signifi cance." For example, when an inves tigator finds an excess and declares it "significant at the 0.05 level," in a sense what he or she is saying is that there is less than a 5 per cent chance of having nmde n Type I error. Tvpe H errors nro less funilinr but. 725 OS Cl oootv) 726 3S.VJMONT AND 3RESL.OW nevertheless, very important (13). Under lying this concept is the fact that when the true state of nature, is the alternative hypothesis (increased risk)r the research I' goal i_s_tojietect it (i.e., reject the null hy pothesis). Suppose one has specified an ^ alpha level (0.05, for example) for testing a null hypothesis of no increased risk for a particular exposure. If an exposure is harmful with a relative risk ofi?, then not rejecting the null hypothesis (i.e., wrongly accepting the exposure as harm less) js called a Type II error. The proba. _ bility of a Type II error is usually denoted beta (jQ). Conversely, the probability of correctly rejecting the null hypothesis and therefore of detecting the excess risk is called the power and is equal to 1 -- /3. Thus, power quantifies the ability of a particular study to dotcct an excess risk that truly exists. It is intuitively clear thut with a fixed amount of data there iu u greater likelihood of detecting a large-ex cess risk. Similarly, an increase in the amount of data increases the chance of observing a given risk, i.e., increases the PowerTht) api>rO)cin)atb pusVfar 1 - |3 of thu vinyl chloride studies to detect a relntive risk R at the alpha level of significance was calculated from the following for mula, which uses the fact that the square root transformation stabilizes the vari ance of the Poisson distribution (see the statistical appendix): Z,_fl = Za - 2(VF - WVE) Here Z,, denotes the upper 100a per centile of the standard normal distribu tion and E the expected number of cancer deaths based on general population rates. This approximation agrees well with exact power calculations based on Poisson probabilities made by Cutler et al. (14, 15). When the discreteness of the exact test based upon Poisson probabilities js accounted for, the approximate and exact power curves are virtually identical. A family of power curves based upon the approximation is shown in figure 1, where each curve is for a different rela tive risk. It can be seen that as the as sumed relative risk increases for a given number of expected deaths, the power also increases. Similarly, as the expected number of deaths increases for a given relative risk, the power also increases. Application to vinyl chloride literature The assumed relative risks for the power calculations were the median (ap proximate) standardized mortality ratios reported for each cancer site in the vinyl chloride literature. Power calculations are usually performed with a somewhat arbitrarily chosen relative_risk, but since relative risk inform.ation._was available from the vinyl chloride, studies, it wun thought best to make use of those data. So pa ru to' a sVTu iffpCi o * HT w o re 'm u d o'To r aiiulyrfen considering all person-yeurs, ut risk and for analyses considering only person-years after a minimum latency (time since first exposure), because in the former case the risk was diluted by the 10 Li 20 yeiUs ihut are ol^r, rbquhe.i fi,, cancer to develop alter exposure to a car cinogen. The median reported mortality ratio was not used in one instance: for overall lung cancer, where the median was 1.03, essentially no excess risk. Since some risk needs to be assumed to calcu late power, the arithmetic mean (approx imately 1.5) was used. The statistical powers of mortality studies of workers exposed to vinyl chloride were calculated with respect to three sites of cancer: liver, brain and lung. These three sites were chosen be cause they have been the subject of most of the discussion of causality in the vinyl chloride literature. The powers of the studies were subsequently plotted on power curves for two purposes: to show the variability in powers, and to relate positive and negative findings to power. For the purposes of this review, a positive finding was defined as an excess risk for a 2 0 0 0 3 7.Q?. BFG39732 POWER CONSIDERATIONS IN VINYL CHLORIDE STUDIES 727 EXPECTED DEATHS Figure. 1. Approximate power curves Tor various assumed relative risks in standardized mortality ratio studies (for one-sided comparisons with alpha = 0.05). particular cancer with statistical signifi cance at the 0.05 level, using a one-sided Poisson test. It was expected that if vinyl chloride was carcinogenic for an organ site, there should be a pattern: the studies with high power should, in general, be positive, and the studies with low power should, in general, be negative. This assumed that exposure would result in a constant value of R across the various populations. The assumption was somewhat tenuous be cause, as discussed below, the populations dilTcred in a number of respects. Results The historical prospective studies of vinyl chloride exposed workers are listed in table 1. The sizes of the study popula tions varied considerably, from 255 in the study by Nicholson et ai. C5> to 9677 in the Equitable Environmental Health study (6, 7). The reports were not entirely in dependent; for example, many of the workers in the study by Ott et al. (10) were included in the Equitable Environ mental Health study, and there was an bveriap of about S00 workers in the studies by Waxweiler et al. (4) and Waxweiler (5). It should be noted that the studies were dissimilar in many other ways. A3 can be seen'in tabic 1, a minimum exposure of 1-5 years was required in some studies, while others required only one day. Some studies reported findings based upon all person-years at risk, some included person-years at risk only after a mini mum time since first exposure, and some reported both types of analysis. The con trol (standard) populations used were diffeierit: four of the five: American studies i 728 BEAUMONT AND BRESLOW XXX X X X XX XX X u X XX xxxxxx XXXX Q v, H .V 5 a1 < 1* f- := 5 e e- 21' 8.-S * we U? uy!0! - o o o o o IA: A A A A A a 5! r* to <0 -- ") <7> C t* ^ cm o r- C^ O CM VO 04 9 Cp-- CM --CM *COr OJ OO- 'V tfJ C~ * -3 c 3 0rO0J to 10 <0 CO rQ* fO) <07) pO- V 0 CpoO*) Ofa) 1p<0n* toto>) U`o) .i3. 3 a a; 3 c a ~1 ~3 5 Us- -"C*SW4>Sbm ,W1--- <-o.2-- --^3,, 0*w" ---<*9 gS'S *3*i II "" _ X. x -3 t. .--2 cc ^** o2;i U, 2 ^> WO*'*' Pi C3Q O- ffl used United States rates; the fifth used Texas rates; and the British, Swedish and German studies used their respective na tional rates. There were also minor differ ences in the International Classification of Diseases codes included for the specific cancers. Finally, there were probably dif ferences in age composition which could be important if an effect were dependent upon age. While it was felt that none of these dissimilarities was important enough to prevent comparison of statistical powers, it should be noted that factors other than power"could have bad a bearing on the ubility of the studies to detect excess risk. Liver cuncer was reported in the four studies listed in table 2 and graphically presented in figure 2. When the results were touted for HtnliHticnI Kignificiinco With q iiiio'tiii&t! i'olfefiiUi |txt, IL W|jfi found that three of the lour studies showed sig nificant excesses (4, 5, 8, 11). The powers wore all very high, despite the fact that _. the expected numbers of deaths were in 3 all instances small. The small expected numbers would normally have led to low f statistical powers, hut the high estimated 3 relative risks had a large effect on the'cah culations. The powers of the studies are |- shown in two columns in table 2 and on 8 two lines in figure 2 because the calcula"f tions assumed different relative risks for I analyses considering all person-years at & risk and for analyses considering only J; person-years after a minimum latency >; % (relative risks of 5 and 10, respectively, 3 S were assumed for liver cancer). - The results for brain cancer (table 3) 2 g were more variable, in that three of five . S. studies had statistically significant findf; ings (5-7, 11), and that the powers 2 = ranged from 12 per cent to a maximum of 5 8 approximately 80 per cent. In figure 3, the ^ 3 range of powers is presented graphically. It can be seen that, in general, the studies o j with high power had positive findings and those with low power had negative find ings. Of the eight studies of lung cancer, only BFG39734 POWER CONSIDERATIONS IN VINYL CHLORIDE STUDIES 729 Tadle 2 Liver cancer: results and powers of epidemiologic studies of vinyl chloride Author Fox and Collier (1,2) Waxweiler (5) (10+ latency) Waxweiler et al. (4) (15 + latency, 5 + exposure) Byren et al. (11) (10+ latency) Reinl et nl. (8) Observed deaths 4 10 8 Expected deaths 1.6 2.3 0.5 Mortality. ratio 2.44 4.27 15.09 Excen p < 0.05? - + + Power (%) If RR - S.O URH 10.0 93 98 92 7 0.4 16.08 86 4 1.0 4.13 + 80 4 0.7 5.89 + 98 12 0.9 15.23 + 76 . 1 25280005 EXPECTED DEATHS Ficuiie 2. Approximate powers of vinyl chloride studies reporting results for liver enneer 10.0 <* nMumcd relnlive risk after n minimum latency. 5.0 nanumed rplntive risk overall. REINL * Rcinl et nl. (8V, RYRM " HV'ei'H^.l'Iv^US = l,'a'x"n.l*Jolllcfl.2l:'vAX = *t (4* hitd \ViTtfildr 16*- twnvinlrtrH statistical! y significant resuTtsTlVlhO) (table 4 and figure 4). Again, there was a wide range of powers, from 14 per cent to almost 100 per cent, but here the studies with very high power were negative, an uniikeiv occurrence :I vinyl chloride is indeed a human lung carcin ogen^ l -- " Discussion The data regarding liver cancer in vinyl chloride exposed workers suggested to o CO VO '-J u> .I I 730 DEAUMONT AND 3RESLOW 0ri 1 04 o XX GO to c~i 'cfs ++ I ++ I o0* tWo5 01 e* CoO ci o> p CO CO to -< a *2 d O) co co oM*- co ddd aa> 8. o <9 2. *+* Oo lwO CC -* Jci *v. a(i it. 2 | +1 + 25s > w>c +xd U J2 X 2^ 3 tO* UCT w C-- cVu>o, ,ac2<:u strongly that the chemical is carcinogenic for the liver. Three of the four studies re ported statistically significant excess risks (4, 5, 8, 11), and the nonsignificant study (1, 2) reported a small excess (4 ob served, 1.6 expected). The statistical pow ers of the studies were high (all above 75 percent) due to the high observed relative risk. Even without knowledge of the animal studies, and without knowledge that angiosarcoma of the liver is ex tremely rare, one might conclude from these data that vinyi chloride is car cinogenic for the liver. The powers of the studies that reported brain cancer ranged from 12 per cent to 80 per cent. The expected trend for a causa tive association was seen, in that the studies with high power were statistically significant and the studies with low power wore, with one oxception, noiiHig-' nificant. The most reasonable interpreta tion, therefore, is that the data are consis tent with an etiologic hypothesis for vinyl chloride and cancer of the brain. Only two of eight studies reportinglung cancer results snowedaig.mficanLfi3ses.aft5 ('475, 9). While some of the negative re sults could be"jxplained BjfloMTstaElsfical power, two studies that were negative had very high power '(lt| 2, 6,.7_L The lack of trend is evidence that vinyl chloride may not be a lung carcinogen, or that the ac tual relative risks were much lower than the assumed values of 1.5 and 2.0, in which case the powers were also much lower. It should be noted that one of the two negative studies with high power (by Fox and Collier (1, 2)) was also negative for liver cancer. Since it is generally ac cepted that vinyl chloride is a liver car cinogen, it may be that the exposures in that study were minimal. The other nega tive study with high power (Equitable) did not report liver cancer results, but did find a significant excess of brain cancer, which may constitute evidence of sub stantive exposure. Examination of "positive" and "nega- 25260006 BFG39736 POWER CONSIDERATIONS IN VINYL CHLORIDE STUDIES 731 EXPECTED DEATHS Fiqurx 3. Approximate powers of vinyl chloride studies reporting results for brain cancer: 3.0 * assumed relative risk after a minimum latency, 2.0 ~ assumed relative risk overall. BYREN Byren et al. (11); JIEINI, - R.*'nl t al <fl; F'X ' F"x nd 'kjU'er `I, WAX - Wa'wpHer "t pi. (^> ai"l W-uweiK (M| K-`jil|> p<i*iiii'i,|p btivif,>iii,,i.ii|pi h>"'iii' ' b tive" hypothesis testing results in the light of statistical power is only one of several approaches to reviewing the evi dence of cnrcinngehicity for n substance. For oxrunpie, one cnn Compute n combined relative risk for each cancer site (by com bining the observed and expected num bers from the studies), and then, with the help of homogeneity testing, determine which studies are compatible with the combined risk estimate (see the Appendix for the homogeneity test). Liver cancer in the present review has n combined ovorntt relative risk of 5.17 (p < 0.00001), and also a significant (p = 0.002) result in homogeneity testing, largely due to the Rcinl tS) relative risk of 15.23. The com bined relative risk for overnll brain cunu'r is i.74 ip G.uii; here the results are more homogeneous (p = 0.10), al though Byren (11) is somewhat of an out lier with a relative risk of 6.12. Finally, the combined relative rUk for overall lung cancer in i,06 (nonsighincunt), with" some _evldehcTTRTmogeneity~pJp~(L0 that the results from Waxweiler (4, 5) and Bufflcr (9) are out of step with the others (relative risks of .1.49 /and ,2.89 ...respec-/ tively). J Close examination of the individual studies cnn also be helpful in searching for rcunonH for differing rosulls. For example, the expected number of deaths from liver cancer in the Byren study (11) is unusually large relative to the expected numbers for brain and lung. Detnilcd examination of this anomaly might be informative. There are otner conaid- <T) o m P PQ 25280007 732 ? 1 ' i < BEAUMONT AND BRESLOW 0 C4 1 CS an * oO> C(OO oo i^c iOn iCn- r<N 12 i i i 14 V ii 2> O ao CJ) CO Cl <3 T If? o C tf " S ft cQicio. .mn ,-r;.tiojjoo i<oj> ri'. ^ n rN jr ^ c S a 12 - CIOMO) CO <N o QO to (0 cs a. hn c<oi ani n id oi 3 CO im in ^ in ^ C4 C a 1l l-s (O CO M A ** 04 -V CO l^Ofn-*tio^reocDcC^4 Tr a ._. 8-1 s. 8. ~s|s + 5 3 3 . p s- . C/3 j SsSsSe ^>u* oZ>? ^ ~ ~ c --; 2m * 3(H k\c3o u 3 " = -= .4 _ ~ *""* -r? -r "S * -- * TM r mJjo+i5+cnl.s-i ^.0+(5t --C 5a * ---- a2-C> s: 3cr <_o -- E m c" a a (2 5 BFG39738 25260008 POWER CONSIDERATIONS IN VINYL CHLORIDE STUDIES 733 25260009 Figure 4. Approximate powers of vinyl chloride studies reporting results for lung cancer: 2.0 " assumed relative risk after a minimum latency, 1.5 = assumed relative risk overall. BUFF = BuiTler et al. (9); BYREN = Byren et al. (11); OTT - Ott et al. (10): DUCK - Duck etal. (12); REINL - Reinl et al. (8); WAX =* Waxweiler et al. (4, 5): EQUIT * Equitable Environmental Health (6, 7); FOX =* Fox and Collier (1, 2). erations, such as dose-response, degree of Neoplastic risk among workers exposed to vinyl exposure, concomitant exposures, and. ___ chTo?WcrAHn NY Acad Sci 1976:271:40-8. 5. Waxweiler RJ. An epidemiologic investigation confidence limits for risk ratios, that also_ of lung canrcr in a multixenobiotic. environ need to be kept in mind. While consid eration of statistical power cannot pro vide a complete answer, it is one more ment. Ph.D. Dissertation. Chapel Hill, NC: University of North Carolina, 1978. fi. Tabershavr !R. Gzi!cy \VR. Mortality study of" workers in the manufacture of vinyl chlorideN^ useful way of looking at epidemiologic evidence. and its polymers. J Occup Med 1974:16:509-18. 7. Equitable Environmental Health, Inc. Epidemi- ologic study of vinyl chloride workers. Final re References port submitted to Manufacturing Chemists As sociation, 1978. 1. Fox AJ. Collier PF. Low mortality rates in in 8, Reinl W, Weber H. Greiser E. Diseases caused dustrial cohort studies due to selection for work by vinyl chloride. Special report of the State In '' and survival in the industry. Br J Prev Soc Med dustrial Physician, Dusseldorf, West Germany, 1976:30:225-80. 1978. ----. 2. Fox AJ. Collier PF. Mortality experience of 9. llufner PA, Wood S. Clayton E. et nl. Mortality workers exposed to vinyl chloride monorrtrr in experience d(~workerx'Tn~h"'Wnyl chloride the mimuliu'ture of polyvinyl chloride in Great monomer production plant. J Occup Med Britain. Br J Ind Med 1977;34:1-10. 1979;21:195-203. 3. Nicholson WJ, Hammond EC. Seidman H. et al. 10. Ott MG. Langner RR. Holder BB. Vinyl chloride Mortality experience of a cohort of vinyl exposure in a controlled industrial environ chloride-polyvinyl chloride workers. Ann NY ment. Arch Environ Health 1975:30:333-9. Acad Sci 1975:246:225-30. 11. Byren D. Enghotm G. Englund A, et al. Mortal- od n O u> VO wJ u> VO