Document KzK8b48k4MBqg5qGeYoy8DjDN

: J, et ai. Epiervix and cornd New York. . The relation! cervix. Am J 5 of a cervical iblic Health s of cancer of ith special em1 Dissertation, if Minnesota, W, Jr. Funda.t in surgery. , Chiurgecon. lar substances Pathol 1926; ;er R. ProtecL-cysteine or fleets of fresh tna cigarettes. Sgibneva V. sear^Af the nonflHr the i Bd 1977,59: :z B. Ascorbic Cancer Res mical carctno197*223. i; metabolism Cancer Res remical carci- istics. Dietary 1974. DHEW Hyattsville, American Journal or Epidemiology Copyright 1981 by The Johns Hopkins University School of Hygiene and Public Health All rights reserved Vol. 114. No. 5 Printed in USA A POWER CONSIDERATIONS IN EPIDEMIOLOGIC STUDIES OF VINYL CHLORIDE WORKERS JAMES J. BEAUMONT*1 *and NORMAN E. BRESLOW3 Beaumont, J. J. (NIOSH, Cincinnati, OH 45226) and N. E. Breslow. Power considerations in epidemiologic studies of vinyl chloride workers. Am J Epidemiol 1981;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 etiologic role for vinyl chloride. For lung cancer, the data were not consistent with an etiologic role, in that two studies with very high power yielded negative results. epidemiologic methods; respiratory tract neoplasms; brain neoplasms; liver neoplasms; vinyl chloride The nine mortality studies of workers sites of cancer--liver, brain and lung-- exposed to vinyl chloride that have been was calculated, and their hypothesis test completed to date disagree in their hy ing results, positive or negative, were pothesis testing results for some causes of considered in the context of power. death, and for those causes it is difficult to draw conclusions about excess risk Methods (1-12). The studies that are negative for Power calculations I a cause of death are especially difficult to Statistical power is the probability of interpret, since they may or may not have not overlooking an excess risk, i.e., of not had the statistical power to detect an ex making a Type II statistical error. To aid cess risk if, in fact, one existed. To aid in in the interpretation of this frequently the interpretation of the studies, their confusing subject, a brief review of Type I statistical power with respect to three and Type II errors follows. Investigators are most familiar with f. Received for publication November 14, 1980, and Type I errors. If the true state of nature is in final form April 13, 1981, the null hypothesis (no increase in risk), 1 Industrywide Studies Branch F-8, National In stitute for Occupational Safety and Health, 4676 then a Type I error is wrongly rejecting Columbia Parkway, Cincinnati, OH 45226 (address the null hypothesis and declaring that for reprint requests), there is an increase in risk. The probabil 1 Dept, of Biostatistics, School of Public Health and Community Medicine, U. of Washington, Seat ity of a Type I error is known as alpha, or tle. WA 98195. more commonly, the "level of signifi The authors thank Jay Lubin, Richard Wax- cance." For example, when an inves weiler, Thomas Fischbach, Noel Weiss and William Halperin for their valuable advice. Their special tigator finds an excess and declares it thanks go to Philip Landrigan for encouraging this "significant at the 0.05 level," in a sense approach. This paper was presented at the Conference to Re evaluate the Toxicity of Vinyl Chloride, Polyvinyl Chloride and Structural Analogues, Rockville, MD, March 20-21, 1980. what he or she is saying is that there is less than a 5 per cent chance of having made a Type I error. Type II errors are less familiar but, 725 r &S 001617 726 BEAUMONT AND BRESLOW nevertheless, very important (13). Under the approximation is shown in figure 1, lying this concept is the fact that when where each curve is for a different rela the true state of nature is the alternative tive risk. It can be seen that as the as hypothesis (increased risk), the research sumed relative risk increases for a given goal is to detect if (i.e., reject the null hy number of expected deaths, the power also pothesis). Suppose one has specified an increases. Similarly, as the expected alpha level (0.05, for example) for testing number of deaths increases for a given a null hypothesis of no increased risk for a relative risk, the power also increases. particular exposure. If an exposure is harmful with a relative risk off?, then not Application to vinyl chloride literature rejecting the null hypothesis (i.e., The assumed relative risks for the wrongly accepting the exposure as harm power calculations were the median (ap less) is called a Type II error. The proba proximate) standardized mortality ratios bility of a Type II error is usually denoted reported for each cancer site in the vinyl beta (/3). Conversely, the probability of chloride literature. Power calculations correctly rejecting the null hypothesis are usually performed with a somewhat and therefore of detecting the excess risk arbitrarily chosen relative risk, but since is called the power and is equal to 1 -- /3. relative risk information was available Thus, power quantifies the ability of a from the vinyl chloride studies, it was particular study to detect an excess risk thought best to make use of these data. that truly exists. It is intuitively clear Separate assumptions were made for that with a fixed amount of data there is a analyses considering all person-years at greater likelihood of detecting a large ex risk and for analyses considering only cess risk. Similarly, an increase in the person-years after a minimum latency amount of data increases the chance of (time since first exposure), because in the observing a given risk, i.e., increases the power. The approximate power 1 -- (3 of the vinyl chloride studies to detect a relative 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): former case the risk was diluted by the 10 to 20 years that are often required for cancer to develop after 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. Z,_fl = Za - 2(VR ~ 1 )(VE) The statistical powers of mortality studies of workers exposed to vinyl Here Za denotes the upper 100a per chloride were calculated with respect to centile of the standard normal distribu three sites of cancer: liver, brain and tion and E the expected number of cancer lung. These three sites were chosen be deaths based on general population rates. cause they have been the subject of most This approximation agrees well with of the discussion of causality in the vinyl exact power calculations based on Poisson chloride literature. The powers of the probabilities made by Cutler et al. (14, studies were subsequently plotted on 15). When the discreteness of the exact power curves for two purposes: to show test based upon Poisson probabilities is the variability in powers, and to relate accounted for, the approximate and exact positive and negative findings to power. power curves are virtually identical. For the purposes of this review, a positive A family of power curves based upon finding was defined as an excess risk for a 100 80 4 POWER CONSIDERATIONS IN VINYL CHLORIDE STUDIES 5.0, 3.CL 60 727 R&S 001619 1.5 20 10 EXPECTED DEATHS Figure. 1. Approximate power curves for 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 differed 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 al, (3) 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 overlap of about 800 workers in the studies by Waxweiler et al. (4) and Wax- weiler (5). It should be noted that the studies were dissimilar in many other ways. As can be seen in table 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 dif ferent: four of the five American studies 728 BEAUMONT AND BRESLOW used United States rates, the fifth used Texas rates; and the British, Swedish and German studies used their respective na XXX X X tional rates. There were also minor differ ences in the International Classification of Diseases codes included for the specific X XX XX X cancers. Finally, there were probably dif ferences in age composition which could be important if an effect were dependent O X XX xxxxxx 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 had a bearing on the XXXX XX ability of the studies to detect excess risk. Liver cancer was reported in the four studies listed in table 2 and graphically presented in figure 2. When the results were tested for statistical significance XXXXXX with a one-sided Poisson test, it was found that three of the four studies showed sig nificant excesses (4, 5, 8, 11). The powers <O E_ ^oooo AA A AA were all very high, despite the fact that the expected numbers of deaths were in all instances small. The small expected numbers would normally have led to low statistical powers, but the high estimated ^ to I(Nfi O) cm oco tCfoo'-i Mor- (O'T MlO OUt-) M C'J relative risks had a large effect on the cal culations. The powers of the studies are shown in two columns in table 2 and on two lines in figure 2 because the calcula tions assumed different relative risks for analyses considering all person-years at t0to> 0ut-l)0to)00c--0 ^ oo o> U) (O to or- co- or- or-> oe-- or- risk and for analyses considering only person-years after a minimum latency (relative risks of 5 and 10, respectively, were assumed for liver cancer). The results for brain cancer (table 3) were more variable, in that three of five .5 & studies had statistically significant find . -C3 4* o s.^.s j i <N o " C y w to _. a o oj . q j iu ;ZCo ^OxcJs -a5xeT3> W"333e2r 2^^dCJ _dgCCJj og--3v o-J n>,a3 ings (5-7, 11), and that the powers ranged from 12 per cent to a maximum of approximately 80 per cent. In figure 3, the range of powers is presented graphically. It can be seen that, in general, the studies with high power had positive findings and those with low power had negative find ings. Of the eight studies of lung cancer, only Fox and C Waxweilei (10+ t Waxweile (15+ U exposu Byren et: (10+ 1; Reinl et Figur relative BYREN two y suits ( there per ce the st negat Sfth Used edish and active naior diver sification e specific aably difich could spendent none of t enough 1 powers, her than T, on the ;ss risk, the four phically results ificance is found ved sigpowers ict jtfk ffetWm 'tpected i to low imated ;he calies are and on alculasks for ars at ? only itency tively, ble 3) if five findiwers um of 3, the cally. udies s and find- onl POWER CONSIDERATIONS IN VINYL CHLORIDE STUDIES 729 Table 2 Liver cancer: results and powers of epidemiologic studies of vinyl chloride *r Author Observed Expected deaths deaths Mortality ratio Excess p < 0.05? Power (%) Ifftfl - 5.0 KRR = 10.0 : Fox and Collier (1, 2) Waxweiler (5) r?.v' ' (10+ latency) 4 1.6 2.44 10 2.3 4.27 8 0.5 15.09 - 93 98 92 Waxweiler et al. (4) (15+ latency, 5 + exposure) Byren et al. (11) (10+ latency) 7 0.4 16.08 4 1.0 4 0.7 4.13 5.89 + + 80 86 98 Reinl et al. (8) 12 0.9 15.23 4- 76 EXPECTED DEATHS Ficure 2. Approximate powers of vinyl chloride studies reporting results for liver cancen 10.0 = assumed relative risk after a minimum latency, 5.0 = assumed relative risk overall. REINL = Reinl et al. (8); BYREN = Byren et al. (11); FOX - Fox and Collier (1, 2); WAX = Waxweiler et al. (4) and Waxweiler (5). two yielded statistically significant re sults (4, 5, 9) (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 unlikely occurrence if vinyl chloride is indeed a human lung carcin ogen. Discussion The data regarding liver cancer in vinyl chloride exposed workers suggested R&S 001621 <N W C4 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 per cent) 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 vinyl 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 were, with one exception, nonsig 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 reporting lung cancer results showed significant excesses (4, 5, 9). While some of the negative re sults could be explained by low statistical power, two studies that were negative had very high power (1, 2, 6, 7). 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- Figur relative REINL EQUIT five" light i severs dence For ex relath bininf bers f) help i which combi for tH the pi relati also ; homo Reinl bine< cancc inogenic udies ret excess gnificant ;ss (4 ob.cal powabove 75 ; relative e of the lowledge r is ex;de from is car- reported ent to 80 a causa;hat the :istically ith low nonsig-erpr e cd for vmyl ing lung excesses ative reatistical .tive had ; lack of 'ide may t the acver than 2.0, in io much ie of the ower (by negative rally acver carsures in er nega* uitable) , but did cancer, of sub- POWER CONSIDERATIONS IN VINYL CHLORIDE STUDIES 100 731 80 WAX >10 (+) 3.0 EQUIT (+) 60* WAX (+) 2.0 FOX (-) 40 WAX >15 (-) REINL (-) 20 BYREN (+) & EXPECTED DEATHS Figure 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); REINL = Reinl et al. (8); FOX = Fox and Collier (1, 2); WAX = Waxweiler et al. (4) and Waxweiler (5); EQUIT = Equitable Environmental Health (6, 7). tive" hypothesis testing results in the light of statistical power is only one of several approaches to reviewing the evi dence of carcinogenicity for a substance. For example, one can compute a 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 a combined overall relative risk of 5.17 (p < 0.00001), and also a significant (p = 0.002) result in homogeneity testing, largely due to the Reinl (8) relative risk of 15.23. The com bined relative risk for overall brain cancer is 1.74 (p < 0.01); 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 risk for overall lung cancer is 1.06 (nonsignificant), with some evidence (homogeneity p = 0.06) that the results from Waxweiler (4, 5) and Bufller (9) are out of step with the others (relative risks of 1.49 and 2.89, respec tively). Close examination of the individual studies can also be helpful in searching for reasons for differing results. 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. Detailed examination of this anomaly might be informative. There are other consid- R&S 001623 732 BEAUMONT AND BRESLOW Table 4 Lung cancer: results and powers of epidemiologic studies of vinyl chloride Study Fox and Collier (1,2) (15+ latency) Waxweiler (5) (10+ latency) Waxweiler et al. (4) (15+ latency, 5+ exposure) Equitable Environmental Health (6, 7) (1 + exposure) (15+ latency, 1+ exposure) BulTler et al. (9) (5+ latency, 2.29+ exposure) Byren et al. (11) Duck et ul. (12) Reinl et al. (8) Ott et al. (10) Observed deaths 46 28 42 39 11 45 41 5 4 3 16 22 4 Expected deaths 51.2 26.0 28.2 24.9 5.7 44.3 39.2 1.7 1.0 1.8 15.5 24.6 5.2 Mortality ratio 0.90 1.08 1.49 1.56 1.94 1.02 1.05 2.89 3.81 1.68 1.03 0.95 0.77 Excess p < 0.05? _ + + + _ + + __ - Power (%) If RR = 1.5 If RR = 2.0 94 100 77 99 63 91 100 14 21 15 55 , 75 27 ... ..(A* t>Z9t00 S'Sd to to J-* v: ts rt t. >71 s 2 2-? 2- # 5! > n 3 {j cl m d> p. o ST. <T> P JJ' r n It 2 3 g 2< C /ft/ \ POWER CONSIDERATIONS IN VINYL CHLORIDE STUDIES 733 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 = Buffler et al. (9): BYREN = Byren et al. (11); OTT = Ott et al. (10): DUCK = Duck et al. (12); REINL = Reinl et al. (8); WAX = Waxweiler et al. (4, 5); EQUIT = Equitable Environmental Health (6, 7); FOX = Fox and Collier U, 2). erations, such as dose-response, degree of exposure, concomitant exposures, and confidence limits for risk ratios, that also need to be kept in mind. While consid eration of statistical power cannot pro vide a complete answer, it is one more useful way of looking at epidemiologic evidence. References 1. Fox AJ, Collier PF. Low mortality rates in in dustrial cohort studies due to selection for work and survival in the industry. Br J Prev Soc Med 1976;30:225-30. 2. Fox AJ, Collier PF. Mortality experience of workers exposed to vinyl chloride monomer in the manufacture of polyvinyl chloride in Great Britain. Br J Ind Med 1977;34:1-10. 3. Nicholson WJ, Hammond EC, Seidman H, et al. Mortality experience of a cohort of vinyl chloride-polyvinyl chloride workers. Ann NY Acad Sci 1975;246:225-30. 4. Waxweiler RJ, Stringer W, Wagoner JK, et al. Neoplastic risk among workers exposed to vinyl chloride. Ann NY Acad Sci 1976:271:40-8. 5. Waxweiler RJ. An epidemiologic investigation of lung cancer in a multixenobiotic environ ment. Ph.D. Dissertation. Chapel Hill, NC: University of North Carolina, 1978. 6. Tabershaw IR, Gaffey WR. Mortality study of workers in the manufacture of vinyl chloride and its polymers. J Occup Med 1974;16:509-18. 7. Equitable Environmental Health, Inc. Epidemi ologic study of vinyl chloride workers. Final re port submitted to Manufacturing Chemists As sociation, 1978. 8. Reinl W, Weber H, Greiser E. Diseases caused by vinyl chloride. Special report of the State In dustrial Physician, Dusseldorf, West Germany, 1978. 9. Buffler PA, Wood S, Clayton E, et al. Mortality experience of workers in a vinyl chloride monomer production plant. J Occup Med 1979;21:195-203. 10. Ott MG, Langner RR, Holder BB. Vinyl chloride exposure in a controlled industrial environ ment. Arch Environ Health 1975;30:333-9. 11, Byren D, Engholm G, Englund A, et al. Mortal ity and cancer morbidity in a group of Swedish R&S 001625 734 BEAUMONT AND BRESLOW VCM and PVC production workers. Environ Health Perspect 1976;17:167-70. 12. Duck BW, Carter JT, Coobes EJ. Mortality study of workers in a polyvinylchloride produc tion plant. Lancet 1975;2:1197-9. 13. Freiman JA, Chalmers TC, Smith H. et al. The importance of beta, the Type II error, and sam ple size in the design and interpretation of the randomized control trial. N Engl J Med 1978;299:690-94. 14. Cutler SJ, Schneiderman MA, Greenhouse SW Some statistical considerations in the study 0f cancer in industry. Am J Public Health 1954;44:1159-66. 15. Molina EC. Poisson's exponential binomial limit. Huntington, NY: Robert E. Krieger Pub. lishing Company, 1973. 16. Armitage P. Statistical methods in medical re search. Oxford: Blackwell Scientific Publica tions, 1971. Appendix The approximate power formula assumes that the observed number of deaths from the cause of interest follows a Poisson distribution with mean RE, where E is the ex pected number based on standard population rates and R is the ratio of rates (relative risk) for the study as opposed to the standard population. It follows that for large values oi RE, the square root of the observed deaths is approximately normally distributed with mean VRE and variance V* (16). Now, if a random quantity has a normal distri bution with mean m and variance cr2, its power 1 - p to reject the null hypothesis m = Mo at the a level of significance is given by Zv/|_0 *_" 4*7/a -- M M'O <x Substitution of m " VRE, Mo = VE, and cr = 14 into this expression yields the re quired result. The homogeneity test for the combined relative risk uses the chi-square distribu tion with n -- 1 degrees of freedom. The equation is XV<2 n-U (O, - d,)2 6E, where n 0, E, and 6 the number of studies, the observed deaths from the ith study, the expected deaths from the ith study, the combined relative risk estimate.