Document G6KVQwn4mzBb3mzv6ayOVGY97

^<ra, UfcC 41981 /`fU AhxiciU* Jouxnm. or Ert&CMiouieY Copyright 1991 by Th* Johor Hopkioa Uoivonity School of Hygitnt m4 Public Hoolth All right* roMrvod * Ij- Vol. 114. No. S PHnud in USA POWER CONSIDERATIONS IN EPIDEMIOLOGIC STUDIES OF VINYL CHLORIDE WORKERS JAMES J. BEAUMONT and NORMAN E. BRESLOW* Beaumont, J. J. (NIOSH, Cincinnati, OH 45226) and N. E. Breslow. Power considerations in epidemiologic studies of vinyl chloride workers. Am j Epidemiol 1961;114:725-34. Nine retrospective mortality studies of workers exposed to vinyl chloride wore 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 wss csleulated for cancer of the lung, brain and liver. When power was taken Into consideration, the results for liver and brain cancer we re found to be consistent with an etiologic role for vinyl chloride. For lung cancer, the data were not eonsistent with an etlologic role, in that two studies with very high power yielded negative results. epidemiologic methods; respiratory tract naopiasms; brain neoplasms; liver neoplasms; vinyl chloride The nine mortality studies of workers exposed to vinyl chloride that have been completed to date disagree in their hy pothesis testing results for 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 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 a cause of death are especially difficult to interpret, 6ince 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 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 Type I and Type II errors follows. Investigators are most familiar with Received for publication November 14, I960, asd in final form April 19.1991. 1 Industrywide Studio* Branch F-8, National In stitute for Occupational Safety and Health, 4876 Columbia Parkway, Cincinnati, OH 45Z26 (addreaa for reprint requests). 1 Dept, of Biostatiatics, School of Publie Health and Cotanaunity Medieine, U. of Washington, Seat tle, WA 98196. The author* thank Jay Lubia, Richard Waxweiler, Thomas FUchbsch, Noel Weiss and William Halperin for their valuable advice. Their special go te Philip Landrigan for encouraging this 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, I960. Type I errors. If the true state ofnature 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 made a Type I error. Type II errors are less familiar but, 726 For Distributed by CMA SPECIAL ??.0C.PAMS DIVISION BamssBBSssr. Ref. Nte.. - Pt^A**** Pa t2 //6, APOOOt6896 726 BEAUMONT AND BRESLOW nevertheless, very important (13). Under lying this concept is the fact that when the true state ofnature is the alternative hypothesis (increased risk), the research goal is to detect it (i.e., reject the null hy pothesis). Suppose one has specified an alpha level (0.05, for example) for testing a null hypothesis ofno increased risk for a particular exposure. If an exposure is harmful with a relative risk off?, then not rejecting the null hypothesis (i.e., wrongly accepting the exposure as harm less) is called a Type II error. The proba bility of a Type II error is usually denoted beta 03). 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 detect an excess risk that truly exists. It is intuitively clear that with a fixed amount of data there is a 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 power. The approximate power 1 - 0 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): Z1-, - z. - 2(VR - 1XVT) Here Zn denotes the upper 100s 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 is 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 information was available from the vinyl chloride studies, it was thought best to make use of these data. Separate assumptions were made for analyses considering all person-years at 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 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. 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 ,V 11 B U 5 O a PlCVRX. 1. ratio studies particular cance at t! Poisson te It was t was carcir should be power sho the studii general, t exposure' ofJ2 acros assumptu cause, as( differed ir The hii vinyl chic in table 1 tions vari study by 1 APOOOt 6897 POWER CONSIDERATIONS IN VINYL CHLORIDE STUDIES 727 EXPECTED DEATHS Ficurx. i. Approximate powor eurvas for various assumed relative risks in standardized mortality ratio studies {for onesided comparisons with alpha * 0.06). 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- c XX ! tional rates. There were also minor differ ences in the International Classification of Diseases codes included for the specific XX XX cancers. Finally, there were probably dif ferences in age composition which could be important if an effect were dependent XX xxxxxx upon age. While it was felt that none of these dissimilarities was important enough to prevent comparison ofstatistical powers, it should be noted that factors other than power could have had a bearing on the XXXX ability ofthe 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 s V z \ ill- !5 25 Ie* if- i xxxxxx >se O O o o a A A AA AA were tested for statistical significance 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 were all very high, despite the fact that the expected numbers of deaths were in I all instances small. The small expected ^ numbers would normally have led to low .1 statistical powers, but the high estimated jj relative risks had a large effect on the cal- S< P"S| ateS- cOr-*a^s eUSi 2 e--* i culations. The powers of the studies are | shown in two columns in table 2 and on i s two lines in figure 2 because the calcula- | tions assumed different relative risks for I analyses considering all person-years at S & risk and for analyses considering only V a ia ia Q SA AS S person-years after a minimum latency 3 (relative risks of 5 and 10, respectively, ! Jf were assumed for liver cancer). ~ The results for brain cancer (table 31 i i S | were more variable, in that three of five * jL studies had statistically significant find- I f I ings (5-7, 11), and that the powers s ranged from 12 per cent to a maximum of jj approximately 80 per cent. In figure 3, the S range of powers is presented graphically, ji i a 2 `s = .s g t It can be seen that, in general, the studies fiS** JT S c 3 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 WAxwtiiei (10+ h Wtxwailar (15+ 1 txpoau; Byrea it i (10+ ti Raial t a FlGUX relative BYRSN two y Suits ( there per ce the st negat: APOOO16899 POWER CONSIDERATIONS IN VINYL CHLORIDE STUDIES 729 Tail*2 Liver cancer: results and poioert ofepidemiologic studiet of vinyl chloride Fox and Collier (1, 2) Waxweiler (5) (10+ latency) Waxweiler et aL (4) (15+ latency, 5+ exposure) Byren et aL (11) (10+ latency) Heini at al. (8) Observed deaths 4 10 8 Expected deaths 1.6 2.3 0.5 Mortality ratio 2.44 4.27 15.09 EXcom p < 0.057 - + Power (%) IfJW - 5.0 IfAH - 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 EXPECTED DEATHS Fiov*i 2. Approximate power* ofvinyl chloride studiet reporting results for liver cancer: 10.0 " assumed relative risk after a minimum latency, 5.0 - assumed relative risk overall. REINL " Reinl et aL (8): BYREN - Byrea 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 ofpowers, 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 BEAUMONT AND BRESLOW ss $s I ++ + * 2 1? S 3 22 S NNN SI n s -? s a ! * - Ix 55 s g g* iii C u MV" + ^--"> ^ S03 'm I S'I 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, 116 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, 6, 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 conrrtute evidence of sub stantive expo-: Exammat,v 'positive" and "nega- 100 so 60 a Ul 3 oa 40 20 0 FlOt'U 3 raistiv* rii RETNL - 1 EQUIT - ] tive" hy light of several t dence of Far ex&n relative bining t bers fror help of which combine for the t the pres< relative also a s homogei Reinl (8 bined r cancer i Brain cancer: result* APOOO16901 POWER CONSIDERATIONS IN VINYL CHLORIDE STUDIES 731 EXPECTED DEATHS Figure 3- Approximate powers of vinyl chloride studies reporting results for brain cancen 3.0 " assumed relative risk sfler c minimum latency, 2.0 * assumed relative risk overall. BYREN " Byren et al. (11); REINL Reinl et al. (8); FOX - Fox and Collier U, 2); WAX - Waxweiler et sL (4) and Wajcweiler (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 Buffler (9) are out of step with the others (relative risks of 1.49 and 2.39, 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- APOOOf6903 * --m " 4' 4K> Uo G hJ r> O 4> 1Z 001 E9 6G 00 f oc-uhji LZ *- LLO Z`9 9L - 960 rtz 99 .. CO'I rsi 91 _ rot ri 4 1U' 01 H + 6trz n _ 90 1 Z6C 16 - Z 1 ov 4 >61 rs LL Y6 rt - WJI + + -* WO > ^ Mig 99 1 OKI HOI 000 X|i|M*H 60S m os zib "n*f rpuaino pCuia Jo ttipnjt OftfajotwjfMttiJo UMwtf pint y riavj, y zz 91 e* y 9 \y so li 6C SO BZ 90 W |0*MW|U com* ia no <) l 1* |U*If (SO r t vna (||>|ll4ll*lXtl ^WMOdxa 4-627'>*lul -19) (6)'!1* -UJnll (4JDMdl 4 I 'itw^ll 161) (Miiaodaa 41 ml '9) 911*411 I*1U9UIIKMIAU^| l|l|V^!nl>3 (unMdu 4 9 491) <m i (feudal 4 01) (9) |6 (XM9|K| 4 91) Pu* WA <r*s ;jnkim Suirj POWER CONSIDERATIONS IN VINYL CHLORIDE STUDIES 733 PtGUU 4. Approximate power* 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 ai. (Ill; OTT - Ott et al. (10); DUCK - Duck et al. (12); REINL - Rein] et al. (8); WAX Waxweiler et al. (4.5); EQUIT Equitable Environmental Health (6, 7); FOX " Fox and Collier (1, 2). eratione, 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. Rzjzunces 1. Fox AJ, Collier FF- Low mortality rates in in dustrial cohort studies due to selection for work and survival in the industry. Br J Prav Soc Med 1976;30:225-30. 2. Fox AJ, Collisr PF. Mortality experience of workers exposed to vinyl chloride monomer in the manufacture of polyvinyl chloride In Great Britain. Br 3 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 Sd 1975;246:225-30. 4. Waxweiler RJ, Stringer W, Wagoner JK, et at Neoplastic risk among workers exposed to vinyl chloride. Ann NY Acad Sd 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, 1976. 6. Tabershaw IR, Gaffey WR. Mortality study of workers in the manufacture of vinyl chloride and its polymers. J Oeeup Med 1974;16:509-16. 7. Equitable Environmental Health, Inc. Epidemi ologic study of vinyl chloride worker*. Final re port submitted to Manufacturing Chemists As sociation, 1978. 9. Reinl W, Weber H, Grelser E. Diseases caused by vinyl chloride. Special report of the State In dustrial Physician, Dusseldorf. West Germany, 1976. 9. Buffler PA, Wood S, Clayton E, et aL Mortality experience of workers in a vinyl chloride monomer production plant. J Oceup 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. Syren D, Engholm G, Englund A, et al. Mortal ity and cancer morbidity in a group of Swedish .t* * * * , ^ * ^ ^ * ^ -- ~ r |1T1. 734 BEAUMONT AND BAESLOW VCM and PVC production workers. Environ 14. Cutler SJ, Schncidermen MA, Greenhouse SW. Health Perspecc 1976;17:167-70. Some statistical considerations in the study of 22. Duck BW, Carter JT, Coobea EJ. Mortality cancer in industry. Am J Public Health study of workers in a polyvinylchloride produc 1954;*4:1159-33. ii tion plant. Laoeet 1975;2:2197-9. 15. Molina EC. Poisson's exponential binomial 13. Fraiman JA. Chalmers TC, Smith H, t al. The limit. Huntington, MY: Robert E, Krieger Pub importance of beta, the Type Q error, and sam- lishing Company, 1973. pie size la the dasIsa and interpretation Of the 16. Anaitag# P. Statistical methods in medical re randomized control trial. N East J Med search. Oxford: Blackwell Scientific Publica 1978;299:690-94. 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, when E is the ex* peeted number baaed on standard population rates and J? is the ratio of rates (relative risk) for the study as opposed to the standard population. It follows that for large values of RE, the square root of the observed deaths is approximately normally distributed with mean VRE'and variance 'A (16). Now, if a random quantity has a normal distri bution with mean p, and variance a3, its power 1 - fi to reject the null hypothesis m at the a level of significance Is given by Zi-e 2. - J* <r Substitution of y. * \fRE, (in ** V'E, and <r % into this expression yields the re quired result. The homogeneity test for the combined relative risk uses the chi-square distribu tion with n-l degrees of freedom. The equation is y (O, - &,) where n 0, E, and 8 - the number of studies, ** the observed deaths from the zth study, * the expected deaths from the ith study, * T 0|/ ] (, the combined relative risk estimate. Akeiucan Je Copyrtiht Ail rlihu ru THE F yet SCI F mi. ate cis DO for an de tlrr ho ph ds re: me of Schiz< major ux a rare d mated tc to affectcommun ing and The ilinability, ment an Little schizoph Receive in final fa 'Deptc ofMedidz School of `Dept. School of * Dept.of Medici: Addrtu: 1006, Jot Ealtimon This w grants fro APOOOJ 6905