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-. jeass-HE &**-*&&ED BY COPYRIGHT LAW A 'V * TITLE 17 0. S. CODE AmcmcaH Jouxnal or ErioCMioLOCT Copyright 1980 by Tl Johns Hopkins University School of Hygiene and Public Health All rights reserved Vol. 112, Mo. 6 Printtd in USA. o O EPIDEMIOLOGIC INVESTIGATION OF OCCUPATIONAL CARCINOGENESIS USING A SERIALLY ADDITIVE EXPECTED DOSE MODEL * rn A. H. SMITH,*-* R. J. WAXWEILER* and H. A. TYROLER* (D Smith, A. H. (Dept, of Community Health, Wellington Clinical School of Medicine, Wellington Hospital, Wellington 2, New Zealand), A. J. Waxweiler and H. A. Tyroler, Epidemiologic investigation of occupational carcinogenesis using a serially additive expected dose model, Am J Epidemiol 112:787-797, 1980. The epidemiologic identification of occupational carcinogens Is compli cated by several problems Including worker mobility between jobs, variation over time of chemicals and processas used, and the long latency period be tween exposure and discovery of a tumor. In the light of these problems, a method using the cumulative dose concept has been developed which In volves calculating the expected yearly exposure for each case from work histories of all noncases dose to the case in year of birth and year of hire. The data required for use of the method include Information concerning exposure to the chemicals being studied for each job In each calendar year of the study. Use of the method is illustrated with a study of angiosarcoma of the liver and vinyl chloride exposure in a polymerization plant The value of the method Ilea In the wealth of information generated concerning the association between chemical exposures and cancer, indudlng exposure level relationships, la tency Information, and the possibility that two chemicals might be acting In dependently or jointly. The serially additive expected dose model is likely to prove particularly useful In the analysis of data collected by occupational health surveillance systems, as well as retrospective studies of the type Illus trated. TC O in CD 5 -O angiosarcoma; cancer; epidemiologic methods; occupational diseases; K. vinyl chloride The epidemiologic identification of oc cupational carcinogens is generally com plicated by several features of the expo sure of workers to industrial chemicals. Received for publication December 13, 1979, and in final form March 2S, 1980. Abbreviation: SAED; serially additive expected dote. ` Occupational Health Studiee Group, Univereity of North Carolina at Chapel Hill, NC. ' Reprint requests to Dr. A. H. Smith. Current ad dress: Department of Community Health, Wel lington Clinical School of Medicine, Wellington Hospital, Wellington 2, New Zealand. 1 National Institute for Occupational Safety and Health, Cincinnati, OH. The helpful suggestion by Dr. David Deubner are gratefully acknowledged. and also by certain aspects of the car cinogenic process itself. The major prob lems have been presented and discussed elsewhere (1-4) and will only be briefly outlined here. Our main objective is to present a method of data analysis which deals with many of these problems in the identification of likely carcinogenic agents in the work environment. The model used requires exposure information which, although not usually obtained in occupational studies, is generally avail able with the cooperation of the com panies involved. A major problem in occupational cancer studies is that worker movement from job 787 uec 044191 788 SMITH, WAXWHLER AND TYROLER to job within industrial plants is accom panied by variation in exposure to any suspect carcinogen. In some instances movement between different companies is sufficiently frequent to add to this prob lem. In addition, the chemicals used by. workers in individual jobs change over time with the introduction of new produc tion methods and with changes in the products themselves. In many industries, workers are exposed to a large number of different chemicals, further complicating the isolation of carcinogenic agents. Even when the same chemicals are used in the same amounts, changes in work practices and plant ventilation alter exposure levels. With regard to the carcinogenic process itself, the mqjor complicating factor is the long latency period between exposure to a carcinogen and the diagnosis of cancer. Unless ongoing surveillance systems are operational, this means that exposure in formation must be sought for 20--30 years prior to conducting a study. The risk of cancer may depend on the level, duration, and continuity of exposure, and accurate information of this kind may be difficult to obtain retrospectively over such a long period of time. An additional complicat ing feature of the carcinogenic process is that more than one chemical may be in volved, either independently, orjointly in an interactive manner. The method of data analysis which we present here was constructed in an at tempt to deal with as many of these prob lems as possible. Much of the data re quired is obtained routinely in occupa tional cancer studies other than those which merely compare disease incidence or mortality with that in the general population. The additional information required is the average exposure level for each job in each calendar year under study, although the method can still be used when classification is limited to ex posed and nonexposed jobs. Exposure in formation allowing a simple ranking of job exposure can be utilized and was made available for this study by the companyfrom interviews of personnel with a knowledge of past and current jobs within the study plant and from records of chem ical usage. The method can also incorpo rate actual chemical exposure measures, when they are available. Method The basis of the serially additive ex-3? pected dose (SAED) method in descriptive.^; terms is to compare the observed exposure 77 of each case in a study with the exposures -1- of fellow workers close to the case in year ~ of birth, and in age at commencement of % work for the company in the study. If the-1 total work force in a plant is referred to as the cohort, thee each case can be thought *> of as belonging to a subcohort of workers.7: with approximately the same year and y age of commencing work in the In . each year that a case worked, his expo sure can be compared with the other .7 members of his subcohort who were work- ing in that year. If the exposure being 7,- studied is causally related to the disease % of interest, then the cases should, on av- y- erage, be exposed for longer periods 2-- and/or to higher levels of the causative : agent than other workers in their sub- cohorts who did not get the disease. If the > exposure is not causally related to the - disease then we would expect case expo sures to approximate those of their sub- cohorts. Thus for each case, we calculate an expected and observed exposure, tak ing into account both exposure level and - duration. The exposure data required for the- analysis consist of some measure of expo- _ sure to a given chemical for each job in a -~ plant, for each calendar year involved in the study. The exposure measures should ideally be interval measures, but can also consist of ranked exposure data if this is-' all that is available. Ranked data will be- used to illustrate the application of the ' method with a 0 to 5 scale of exposure for;, ` ucc 044192 occupational cancer dose model 789 Tabu 1 Exposure ratings used to classify jobs 0 -- No exposure - 1 ~ Minimal exposure to low levels: (Chemical in building--not handled, low vapor pressure and dust level, probably works on different floor) ' 2 - Moderate exposure: (Works around the chemical, but exposure is minimal) 3 -- Works in area subject to occasional high excursions: (Normally exposure is minimal but oc* casional spills, leaks, or dust exposure may occur) 4 Works in areas where level is high: (Exposure levels in the area are frequently high. Might con sider that some risk is involved if chemicql is very toxic) 5 < Intimate contact--skin or high inhalation: (Such as poly cleaners in the old days--handling slurry) Chemical #J Job identification no. i 2 3 Tabu 2 Chemical exposure ratings specific for job identification number and calendar year for a given chemical 1942 1943 Calendar yaar 1944 1945 1946..- 0002 5s55 221 1 2 S 0 1973 2 5 0 84 4 4 4 1 l 1 each of 12 chemicals examined (table 1). Panels of employees familiar with the past conditions in the plant assigned each job an exposure rank for each calendar year of the study (table 2). These exposure data are then linked with work histories identifying the jobs each worker had in the plant and the calendar time period in volved. Exposure dose is estimated by multiplying the exposure level and the duration worked at that level. These "doses" are accumulated over each calen dar year. A worker exposed at level 1 for all of a calendar year accumulates 365 dose units; if he spends 200 days at level 2, and the remainder of the year at level 1 he accumulates 565 dose units. (Strictly speaking, the doses should be calculated for work days only, but the accumulation over calendar days is easier.) The fact that both the observed and expected doses are obtained in the same manner pre vents bias being introduced. The calculation of the expected dose for each year a case works is obtained from the cohort dose matrix (figure 1). This is a three-dimensional matrix defined by age of first employment, year of first employ ment, and calendar year. During employ ment in the industry, each noncase con tributes to the relevant cells of this ma trix the number ofdays spent in the given calendar year at each of the possible expo sure levels. For example, an employee aged 22 when first employed in 1944 who spends 200 days of that year at level 2 and 165 days at level 1 would contribute to the corresponding cell shown in figure 1 the number of days at the two levels. The properties of the cohort dose matrix are such that entries into any one cell are based on workers of the same age in the corresponding calendar year, who were first employed at the same age. Once data from each noncase have been entered into the cohort dose matrix, the 790 SMITH, WAXWEILER AND TYROLER parison is somewhat restrictive; compari either direction. When the cohort being sons might be made with subcohorts hav- studied is small, the moving sum accumuing approximately the same year of birth lation may need to span more than five and age at first employment. This is done years. in the SAED model by using a moving The cohort dose matrix is then used to sum accumulation of data in the cohort calculate the expected dose for each year dose matrix. In the application to be pre that a case works. Table 3 presents the sented we define a subcohort for compari first two years of work for a case who was son with a case as consisting of all non aged 22 when first employed in 1944. In cases whose year of first employment and his first year he worked 115 days, 50 at age at first employment are within two level 0, followed by 65 at level 5. He thus years ofthose ofthe case. Since in the first accumulated a dose of50 x 0 + 65 x 5 year of employment of a case there are 325 dose units. The noncase members of no noncases working who were first "'his subcohort accumulated 600 days at employed in the two subsequent years, level 0,1350 days at level 1, etc. The total the expected values for this first year are number of days of work in 1944 was 3165, calculated only from noncases who and the total subcohort dose was 4830 started work in the.same year as the case, units, or 1.53 per day. The case worked for while in the second year of work the non 115 days in that year, so his expected dose cases first employed in the year before under the null hypothesis is 115 x 1.53 = and the year after the year of hire of the 176 dose units. His actual exposure was case are included. In subsequent years the 325 dose units. estimation is from the whole subcohort The above calculations relate to one ucc 044194 s > OCCUPATIONAL CANCER DOSE MODEL 791 __ 1944 Total Tabu 3 - Example of rigla used to calculate the observed and expected dose units for a case in two calendar years* k Exporti* !wel Cam diyt Cut dot* unit* Subcohort dtyi 0 50 0 10 0 2 0 -0 30 0 40 0 5 65 325 115 325 600* 1350 540 400 175 100 3165 Subcobovt dost unit* 0 1350 1080 1200 700 500 4630 1945 0 0 0 1205 0 1 365 365 800 800 20 0 1500 3000 30 0 340 1020 4 0 0 110 440 6 0 0 50 250 Total 365 365 4005 5510 * Because the moving average variable was set at 2, the value 600 can be interpreted as meaning that the group of persons whose age when first employed was between 20-24 and whose year when first em ployed was between 1942--1946 worked a total of 600 days at exposure level 0 jobs during 1944. Tabu 4 The total observed ease dose units for each case ofangiosarcoma, the expected case dost units, and the difference calculated by the SAED* analysis method Cam Obaemd total cbm doae unit* Ezptcttd total cut dou unit* Difference 1 15,728 2 25,765 3 17,145 4 27,232 5 10,264 6 16,413 7 40,412 8 5,375 9 21,820 10 34,372 11,103 12,689 11,366 12,514 14,350 7,553 16,605 2,613 10,014 21,555 +4,625 + 13,076 +5,779 +14,713 -4,086 +8,860 +23,807 +2,762 + 11,806 + 12,817 Average 21,453 * Serially additive expected dose. 12,036 +9,416 year ofwork. Doses can be summed over a worker's entire work history to give his observed total dose. The expected dose for each year can likewise be summed. Some results are presented in table 4 for the exposure of 10 cases of angiosarcoma of the liver to vinyl chloride monomer. For all but one of the cases the observed total doses are greater than the expected total doses with a mean difference of 9417 (p " 0.004 by paired f-test, p 0.01 by Wilcoxin signed ranks test). The SAED analysis also facilitates examination of the relationship between dates of exposure and dates of diagnosis (alternatively, dates ofdeath) ofthe cases. vjm :i^ii.'',u:,,iii'; f. %&iii&& Al<- jt tv .'jj.i 792 . SMITH. WAXWEIUBR AND TYROLER M*vt ..,i'f;.. No. oT yean prior lo death i 2 3. 4 S 6 7 8 9 10 11 12 13 14 1G 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Totals Tarlc 6 Tht total cate dote untfi ofvinyl chloride for each angioiarcoma cate and the expected total i < dote unit* No. of eases working (total of 10 cases} Casa days of work Subcohort days of work Casa dose units Expected cue dess units Difference between ebeerred and expected ease dose units 2 4 7 9 9 9 9 9 9 9 9 9 9 f 8 8 6 8 8 8 6 4 3 3 3 3 2 2 2 1 299 1,082 2,665 3,196 3,286 3,266 3,285 3,285 3,126 3,285 3,285 3,285 3,285 3,269 2,803 2,749 2,670 2,458 2,920 2,495 1,848 1,209 1,096 1,096 1,096 763 730 730 399 174 23,523 87,533 171,672 224,090226,932 229,741 233,626 239,066 243,653 247,948 251,083 257,741 259,848 249,430 279,338 293,761 276,032 261,656 291,071 236,498 160,202 103,944 107,942 110,643 96,261 83,802 79,025 63,288 46,529 14,119 890 3,112 7,666 10,132 9,946 9,866 10,495 11,471 11,277 10,600 10,236 10,036 10,877 11,293 10,426 9,688 7,616 6,260 7,766 8,082 6.443 3,670 i860 4,604 4,876 3,400 3,285 3,493 1,996 870 663 1,942 4.337 6,346 6,472 6,640 6,568 6,700 6,399 6,773 6,944 6,988 6,122 6,197 6,380 6,323 4,794 4^97 6,618 4,945 3,636 2,464 2,276 2,378 2,621 1,646 1,668 1,778 972 487 327 1,170 3,328 4,787 4,473 4,316 4,927 6,771 6,878 4,727 4,292 4,048 4,765 6,096 6,046 4,266 2,821 1,663 2.138 3,137 2307 1,216 2,106 2,226 2,364 1,754 1,617 1,716 1.023 383 04,929 6,438,792 214,626 120,362 94,164 "Hto. ;.**> occupational cancer dose model 793 For each case in the study one can calcu were mostly accumulated by the cases in late for each year prior to death his ob this study 4-16 years prior to death, al served and expected dose. (If the case does though some cases were exposed 30 years not work in a given year, both observed prior to death. and expected are Set to zero.) Table 5 A search can also be made for a doseshows the output from the latency response relationship by an exposure analysis program for the 10 angiosarcoma level analysis comparing the number of cases. Column seven, the difference be-' days each case has worked at each level of tween the observed case dose and the ex exposure, with the expected number of pected case dose per case in the study, is days. For example, consider a case who plotted in figure 2 after dividing by 10 to worked for 200 days in 1965 at dose level obtain the average per case. It can be seen 2. If his subcohort had a total of 20,000 from this plot that the greatest average work days during that calendar year with difference occurred nine years prior to 2000 at dose level 2, then his expected death, and that it was over 400 dose units number of days during 1965 at dose level in the interval 4-16 years prior to diag 2 is 365 x 2000/20,000 = 36.5. The ob nosis. Excess exposures to vinyl chloride served and expected values can be ac cumulated over the total work history, and the values for each case added. Re sults for vinyl chloride and 10 cases of an giosarcoma of the liver are shown in table 6. It can be seen that cases worked longer than expected at leVels 3, 4 and 5. Any excess at some levels must be accom panied by a deficit at other levels and the deficit here is at levels 0,1 and 2. An in teresting and unexpected finding was the strong association with exposure level 3, which includes jobs involving occasional high excursions from normally minimal levels (table 1). The model can be adapted to assess whether or not more than one chemical is involved. The angiosarcoma cases were Ficuxs 2. Avenge difference between observed investigated for 19 individual chemicals. angiosarcoma case does units and expected dose While the strongest relationship in terms units of vinyl chloride. Tails 8 Comparison ofobserved and expected numbers ofdays the 10 angiosarcoma ease* worked at tach exposure level of vinyl chloride Cam days 0 7,467 1 369 Dow level 23 6,539 14,249 4 23,193 5 13.112 Expected case days Ratio Difference 12,831 0.58 -5,364 15,633 0.02 -15,264 21,879 0.30 -15,340 1,933 7.37 + 12,316 8,091 2.87 + 15,102 4,562 2.87 +8,550 64,929 64,929 ucc 044197 Wm w* t; . [j 794 SMITH, WAXWEILER AND TYROLER of statistical significance was with vinyl chloride, an association was also noted with caprylyl chloride exposure (p =* 0.005, f-test). This raises a question as to which is more likely to be the carcinogen; or if both are carcinogens, whether they are acting independently or jointly. To answer this question, an additional di mension was added to the model so that each cell from the model shown in figure 1 becomes a two-dimensional matrix (table 7) giving the number of days of exposure for the cohort members at each combina tion of levels of the two chemicals. This information enables calculation of the conditional expectation of exposure. If a case worked in a job with exposure 2 to vinyl chloride, then the expected exposure to caprylyl chloride was calculated from data in the corresponding column vector (see table 7). Observed and expected doses Tabu 7 Representation ofa ctU ustd in the cohort dose matrix to assets two chemical*, vinyl chloride and caprylyl chloride. Xu is the number of day* for the corresponding calendaryear, age first employed, and year first employed, that were spent at level i of caprylyl and levelj of vinyl chloride exposure Vinyl ehtorid* l*v*l 0 1 23A 5 Caprylyl chloride level 0 X. x., x. X-, x#* X. 1 X,. X,, Xb x,, x,, x,, 2 X. x Xb X,. x* 3 X, X,, x,, Xj* XH X* 4 X* X,, X*. Xo x fi XH x,, x,, Xu x x,, were accumulated with the results shown in table 8. It can be seen that, given the exposure to vinyl chloride, the observed case exposure to caprylyl chloride was very close to that expected. In contrast, given the exposure levels to caprylyl chloride, there remained some difference between observed exposure to vinyl chloride and that expected. Thus, in spite of the fact that these exposures are corre lated in that jobs with exposure to vinyl chloride tend also to involve exposure to caprylyl chloride, the model suggests that caprylyl chloride is not involved. If a dif ference had remained between observed and expected exposure doses to caprylyl chloride given vinyl chloride exposures, then differences could have been calcu lated for each level of vinyl chloride expo sure to attempt to differentiate between independent and joint action. Discussion The method presented deals with sev eral problems of occupational cancer studies. Worker movement between jobs and variation in job exposure levels ac cording to calendar years are incorpo rated into the estimation of exposure dose. Latency intervals and exposure levels associated with the cancer can be estimated. Several different chemical as sociations can be sought for and the possi bility that two chemicals might be acting jointly to induce cancer can be investi gated. This information is obtained in a manner which avoids bias from potential confounding due to differences between Table 8 Observed, and conditional and unconditional expected case dose unit* of exposure to vinyl chloride and caprylyl chloride for angiosarcoma cases. The p values for differences between observed 4 and expected values are in parentheses Observed dost units Unconditional expocted dote unit* Condition*! expected do** unite givtn exposure ltvclj to th* other ch*mieml Vinyl chloride Caprylyl chloride 21,433 11,493 12,036 (0.004) 3,730 (0.005) 19,450 (0.055) 11,579(0.9) ucc 044" y'3 9 OCCUPATIONAL CANCER DOSE MODEL 795 cases and noncases in age, calendar year come more readily available (12, 13). In of exposure, and age when first employed. the meantime, retrospective assessment Other variables such as race and smoking of exposure by means of company records can be included when appropriate by de of chemicals and processes used and riving cohort dose matrices for each race interviews with personnel familiar with group and for smokers and nonsmokers past conditions can generate data enhanc separately. ing the power of occupational cancer The method shares certain features of studies. cohort studies and certain features of Cancer latency is usually defined start case-control studies. Cases are ascer ing from the point in time of first expo tained for a defined work population or sure, although attention may also be cohort, and all work histories are utilized. given to the midpoint or end of the expo However, the analysis follows the case- sure period (14-16). Rather than fixing control study pattern. The advantages of attention to these points in exposure time, using case-control methods of analysis of the SAED model allows one to examine cohort data include the fact that bias due the period of time during which the expo to potential confounding variables can be sure of the cancer cases is greater than avoided without the assumptions re that of comparable noncases. The advan quired for multivariate analyses (5). A tages and disadvantages of such informa particular advantage with occupational tion concerning cancer latency have been studies is that observed and expected ex discussed in greater detail elsewhere (17). posures can be derived for each calendar Calculation of the average and range of year, a variable which is difficult to incor the timea between first exposure or last porate into a multivariate model. exposure and diagnosis in occupational Exposure variables currently employed cancer studies is influenced by the fact in occupational health studies include the that, unlike angiosarcoma of the liver, simple binary categorization of workers most cancers have relatively low occupa according to whether they worked in a tional attributable risks and some of the given job or plant area for any time at all, occupationally exposed cases will usually or for a minimum period such as five have had their cancer induced by years (6-8). Occasionally estimates of nonoccupational causes leading to possi exposure to a postulated causal agent are ble bias in measures of latency. Estima made for each job in an industry and dis tion of latency using the SAED model out ease incidence is compared between those lined deals with this situation since, on exposed at different levels (7,9). Cumula average, the occupational exposure of tive dose as in the method presented has cases whose cancer was nonoccupation- been used in studies of the effects ofradia ally induced should be the same as that of tion (10) and asbestos exposure (11) and comparable noncase workers. If the occu gives a more precise index of exposure re pational exposure is indeed causal, the sulting in greater power in testing years during which the average case ex hypotheses concerning occupational posure is greater than that expected iden carcinogenesis. Collection of additional tifies the period during which causal ex information is required, but the costs of posures were accumulated. collecting this information are relatively The use ofthe SAED model with ranked small compared with the total costs of oc exposure data can be criticized since the cupational cancer studies. In the future, dose accumulation assumes a continuous health surveillance systems may be im scale. However, the SAED model itself is plemented in many industrial plants and not dependent on having ranked data. the type of information required will be When exposure measures are available 796 SMITH WAXWEILER and tyrolee it is suggested that they be placed in than one chemical is involved. We have rank order and categorized into approxi illustrated its use with a known associa mately five exposure Bteps. Jobs for which tion between vinyl chloride and angio measures are not available could be as sarcoma of the liver, and have also used it signed to an exposure level in each in a study of lung cancer in the same calendar year on the basis of information plant (18) in conjunction with methods concerning manufacturing processes and generating risk estimates. The SAED chemicals used and the accumulation of model, or adaptations of it, may have doses would involve the average of avail widespread application in future occupy able exposure measures pertaining to tional health surveillance systems, in ad- ; each level. When no exposure measures dition to its use for retrospective studies. are available, the justification for using subjectively determined ranked data as if RinuNcu .~ it were on a continuous scale is that this 1. Enteriine PE: Pitfalls in epidemiological re should generally lead to increased statis search. An examination of the asbestos litera tical power over the use of binary expo sure data. Increased statistical power will ture. J Occup Med 18:150-156,1976 2. Gamble J, Spirtas R: Job classification and utilization ofcomplete work histories in occupa result if those jobs assigned the higher tional epidemiology. J Occup Med 18:299-404, exposure rankings do indeed involve noticeably more exposure than those as 1976 3. Mancuao TF, Coulter EJ: Methodology in indus trial health studies. Arch Environ Health signed the lower rankings. The exposure 6:210-226,1963 measure becomes virtually continuous once accumulated over calendar time and 4. Redmond CK, Brcslin PP: Comparison of meth ods for assessing occupations! hazards. J Occup Med 17:313-317, 1975 the paired f-test, or Wilcoxin's test, can be 5. Smith AH, Kark JO, Cassel JC. et al: Analysis used to test differences between observed and expected values. of prospective epidemiologic studies by minimum distance case-control matching. Am J Epidemiol 105:567-574, 1977 A second statistical criticism of the' 6. Lloyd JW, Lundin FE, Redmond CK, et ah method relates to the fact that the same noncase can contribute in at least some Long-term mortality study of steel workers. IV. Mortality by work area. J Occup Med 12:151-157,1970 years to the estimation of the expected 7. McMichael AJ, Spirtas R, Kupper LL, et ah Sol exposure doses of more than one case. Each expected exposure dose is calculated vent exposure and leukemia among rubber workers: An epidemiologic study. J Occup Med 17:234-239,1975 from many noncases. The predominant 8. Waxweiler RJ, Stringer W, Wagoner JK, et ah source of the variance of the difference be tween observed and expected case doses is Neoplastic risk among workers exposed to vinyl chloride. Annals NY Acad Sci 271:40--48,1976 9. Tabershaw IR, Gaffey WR; Mortality study of the variance of the observed case doses. workers in the manufacture of vinyl chloride The contribution of some noncases to the and its polymers. J Occup Med 16:509-518, estimation of expected doses for more' 10. 1974 Lundin FE, Wagoner JK, Archer VE: Radon than one case can therefore have very lit Daughter Exposure and Respiratory Cancer. tle effect on the (-test or Wilcoxin's test Quantitative and Temporal Aspects. US Dept used to measure statistical significance. HEW, 1971 11. Enterline P, DeCoufle P, Henderson V: Mortal We claim that the wealth of informa ity in relation to occupational exposure in the tion generated by use of the SAED model asbestos industry. J Occup Med 12:897-903, outweighs these statistical problems. The 1972 12. Barrett CD, Belk HD: A computerized occupa model allows one to test for the associa tional medical surveillance program. J Occup tion of individual chemicals with cancer, Med 19:732-736, 1977 13. Kerr PS: Recording occupational health data for examine dose response relationships and future analysis. J Occup Med 20:197--203,1978 latency phenomena, and assess if more 14. Armenian HK, Lilienfeld AM: The distribution ucc 044200 'IlhaBUJ-ELW^lgllMUl 1 OCCUPATIONAL CANCER DOSE MODEL 797 of incubation periods of neoplastic diseases. Am J Epidemiol 99:92-100,1974 15. Cobb S, Miller M, Wald N: On the estimation of the incubation period in malignant disease. J Chronic Dis 9:385-393, 1959 16. Polednak AP: Latency periods in neoplastic dis eases. Am J Epidemiol 100:354-356, 1974 17. Smith AH, Checkoway H, Goldsmith DF, et ak An analytic procedure for investigation of cancer latency in matched case control studies illustrated with occupational data. Paper pre sented at Society for Epidemiologic Research meeting, June 1978. Am J Epidemiol 108:226 (abstract), 1978 IS. Waxweiler RJ: An epidemiologic investigation of lung cancer in a multixenobiotic occupational environment. PhD Dissertation, University of North Carolina, 1978 \ ucc 044201 COVERED BY COPYRIGHT LAW TITLE 17 U. S. CODE. AMERICA* JOUXNAi or EriDCMlOLOCT Copyright < 1980 by The Johni Hopkin* University School of Hygiene end Public Health All rights reserved A** Vol. 112, Ho. Printed in USJL. FILE COPY DO NQ r r c v o v c EPIDEMIOLOGIC INVESTIGATION OF OCCUPATIONAL CARCINOGENESIS USING A SERIALLY ADDITIVE EXPECTED DOSE MODEL A. H. SMITH,14 R. J. WAXWEELER? /uvo H. A. TYROLER*1 Smith, A. H. (Dept, of Community Health, Wellington Clinical School of Medicine, Wellington Hospital, Wellington 2, New Zealand), R. J. Waxweiler and H. A. Tyroler. Epidemiologic Investigation of occupational carcinogenesis using a serially additive expected dose model. Am J Epidemiol 112:787-797, 1980. The epidemiologic identification of occupational carcinogens is compli cated by several problems including worker mobility between Jobs, variation over time of chemicals and processes used, and the tong latency period be tween exposure and discovery of a tumor. In the light of these problems, a method using the cumulative dose concept has been developed which in volves calculating the expected yearly exposure for each case from work histories of all noncases close to the case In year of birth and year of hire. The data required for use of the method include information concerning exposure to the chemicals being studied for each Job in each calendar year of the study. Uss of the method is illustrated with a study of angiosarcoma of the liver and vinyl chloride exposure in a polymerization plant The value of the method lies in the wealth of information generated concerning the association between chemical exposures and cancer, including exposure level relationships, la tency information, and the possibility that two chemlcala might be acting In dependently or Jointly. The serially additive expected dose model Is likely to prove particularly useful in the analysis of data collected by occupational health surveillance systems, as well as retrospective studies of the type Illus trated. angiosarcoma; cancer; epidemiologic methods; occupational diseases; vinyl chloride The epidemiologic identification of oc cupational carcinogens is generally com plicated by several features of the expo sure of workers to industrial chemicals, Received for publication December 13, 1979, and in final form March 25, 1980. Abbreviation: SAED; serially additive expected dose. 1 Occupational Health Studies Group, University of North Carolina at Chapel Hill, NC. 1 Reprint requests to Dr- A. H. Smith. Current ad dress: Department of Community Health, Wel lington Clinical School of Medicine, Wellington Hospital, Wellington 2, New Zealand. 1 National Institute for Occupational Safety and Health, Cincinnati, OH, The helpful suggestions by Dr. David Deubner are gratefully acknowledged. and also by certain aspects of the car cinogenic process itselL The major prob lems have been presented and discussed elsewhere (1-4) and will only be briefly outlined here. Our main objective is to present a method of data analysis which deals with many of these problems in the identification of likely carcinogenic agents in the work environment. The model used requires exposure information which, although not usually obtained in occupational studies, is generally avail able with the cooperation of the com panies involved. A major problem in occupational cancer studies is that worker movement from job 787 j*-> Mrm : ^3 788 SMITH, WAXWEILER AND TYROLER to job within industrial plants is accom panied by variation in exposure to any suspect carcinogen. In some instances movement between different companies is sufficiently frequent to add to this prob lem. In addition, the chemicals used by. workers in individual jobs change over time with the introduction of new produc tion methods and with changes in the products themselves. In many industries, workers are exposed to a large number of different chemicals, further complicating the isolation of carcinogenic agents. Even when the same chemicals are used in the same amounts, changes in work practices and plant ventilation alter exposure levels. With regard to the carcinogenic process itself, the major complicating factor is the long latency period between exposure to a carcinogen and the diagnosis of cancer. Unless ongoing surveillance systems are operational, this means that exposure in formation must be sought for 20-30 years prior to conducting a study. The risk of cancer may depend on the level, duration, and continuity of exposure, and accurate information of this kind may be difficult to obtain retrospectively over such a long period of time. An additional complicat ing feature of the carcinogenic process is that more than one chemical may be in volved, either independently, or jointly in an interactive manner. The method of data analysis which we present here was constructed in an at tempt to deal with as many of these prob lems as possible. Much of the data re quired is obtained routinely in occupa tional cancer studies other than those which merely compare disease incidence or mortality with that in the general population. The additional information required is the average exposure level for each job in each calendar year under study, although the method can still be used when classification is limited to ex posed and nonexposed jobs. Exposure in formation allowing a simple ranking of job exposure can be utilized and was made available for this study by the company from interviews of personnel with a knowledge of past and currentjobs within the study plant and from records of chem ical usage. The method can also incorpo rate actual chemical exposure measures when they are available. * Method g rfl The basis of the serially additive ex-'X pected dose (SAED) method in descriptive terms is to compare the observed exposure ~ of each case in a study with the exposures of fellow workers close to the case in year - of birth, and in age at commencement of '= work for the company in the study. If the < total work force in a plant is referred to as the cohort, then each case can be thought of as belonging to a subcohort of workers with approximately the same year and age of commencing work in the plant. In each year that a case worked, his expo sure can be compared with the other members of his subcohort who were work- ' mg in that year. If the exposure being . studied is causally related to the disease : of interest, then the cases should, on av- ' erage, be exposed for longer periods and/or to higher levels of the causative agent than other workers in their sub cohorts who did not get the disease. If the " exposure is not causally related to the disease then we would expect case expo sures to approximate those of their sub- . cohorts. Thus for each case, we calculate an expected and observed exposure, tak ing into account both exposure level and duration. The exposure data required for theanalysis consist of some measure of expo sure to a given chemical for each job in a plant, for each calendar year involved in the study. The exposure measures should ideally be interval measures, but can also consist of ranked exposure data if this is all that is available. Ranked data will be used to illustrate the application of the method with a 0 to 5 scale of exposure for , ucc 044203 mmmi* OCCUPATIONAL CANCER DOSE MODEL 789 Table I Exposure ratings used to classify jobs 0 = No exposure - 1 = Minimal exposure to low levels: (Chemical in building--not handled, low vapor pressure and dust level, probably works on different floor) " 2 = Moderate exposure: (Works around the chemical, but exposure is minimal) 3 = Works in area subject to occasional high excursions.' (Normally exposure is minimal but oc casional spills, leaks, or dust exposure may occur) 4 = Works in areas where level is high: (Exposure levels in the area are frequently high. Might con sider that some risk is involved if chemical is very toxic) 5 = Intimate contact---skin or high inhalation: (Such as poly cleaners in the old days--handling slurry) Chemical Job identification no. i 2 3 Table 2 Chemical exposure ratings specific for job identification number and calendar year for a given chemical 1942 1943 Calendar year 1944 1945 1946 ... 0002 5555 221 1 2 5 0 1973 2 5 0 84 4 4 4 1 1 1 each of 12 chemicals examined (table 1). Panels of employees familiar with the past conditions in the plant assigned each job an exposure rank for each calendar year of the study (table 2). These exposure data are then linked with work histories identifying the jobs each worker had in the plant and the calendar time period in volved. Exposure dose is estimated by multiplying the exposure level and the duration worked at that level. These "doses" are accumulated over each calen dar year. A worker exposed at level 1 for all of a calendar year accumulates 365 dose units; if he spends 200 days at level 2, and the remainder of the year at level 1 he accumulates 565 dose units. (Strictly speaking, the doses should be calculated for work days only, but the accumulation over calendar days is easier.) The fact that both the observed and expected doses are obtained in the same manner pre vents bias being introduced. The calculation of the expected dose for each year a case works is obtained from the cohort dose matrix (figure 1). This is a three-dimensional matrix defined by age of first employment, year of first employ ment, and calendar year. During employ ment in the industry, each noncase con tributes to the relevant cells of this ma trix the number of days spent in the given calendar year at each of the possible expo sure levels. For example, an employee aged 22 when first employed in 1944 who spends 200 days of that year at level 2 and 165 days at level 1 would contribute to the corresponding cell shown in figure 1 the number of days at the two levels. The properties of the cohort dose matrix are such that entries into any one cell are based on workers of the same age in the corresponding calendar year, who were first employed at the same age. Once data from each noncase have been entered into the cohort dose matrix, the 790 SMITH, WAXWEILER AND TYSOLER case exposure dose can be compared with within two years of first employment and the matrix values. However, this com within two years of birth of the case in parison is somewhat restrictive; compari either direction. When the cohort being sons might be made with subcohorts hav studied is small, the moving sum accumu ing approximately the same year of birth lation may need to span more than five and age at first employment. This is done years. in the SAED model by using a moving The cohort dose matrix is then used to sum accumulation of data in the cohort calculate the expected dose for each year dose matrix. In the application to be pre that a case works. Table 3 presents the sented we define a subcohort for compari first two years of work for a case who was son with a case as consisting of all non aged 22 when first employed in 1944. In cases whose year of first employment and his first year he worked 115 days, 50 at age at first employment are within two level 0, followed by 65 at level 5. He thus years of those of the case. Since in the first accumulated a dose of 50 x 0 + 65 x 5 =* year of employment of a case there are 325 dose units. The noncase members of no noncases working who were first his subcohort accumulated 600 days at e*. employed in the two subsequent years, level 0,1350 days at level 1, etc. The total the expected values for this first year are number of days of work in 1944 was 3165, calculated only from noncases who and the total subcohort dose was 4830 started work in the same year as the case, units, or 1.53 per day. The case worked for while in the second year of work the non 115 days in that year, so his expected dose cases first employed in the year before under the null hypothesis is 115 x 1.53 = and the year after the year of hire of the 176 dose units. His actual exposure was case are included. In subsequent years the 325 dose units. estimation is from the whole subcohort The above calculations relate to one 044205 occupational cancer dose model 791 -- X*sx 1944 Total Table 3 Example of data used to calculate the observed and expected dose units for a case in two calendar years* a Exposure level 0 i 2 3 4 5 Cut day* 50 0 0 0 0 65 115 Cam dose units 0 0 ,0 0 0 325 325 Sub cohort day* 600* 1350 540 400 175 100 3165 Subcohort dose unit* 0 1350 1080 1200 700 500 4830 1945 0 0 0 1205 0 1 365 365 800 800 20 0 1500 3000 3 0 0 340 1020 40 0 110 440 5 0 0 50 250 Total 365 365 4005 5510 * Because the moving average variable waa set at x2, the value 600 can be interpreted as meaning that the group of persona whose age when first employed was between 20-24 and whose year when first em ployed waa between 1942-1946 worked a total of 600 days at exposure level 0 jobs during 1944, Tabu 4 The total observed case dose units for each case ofangiosarcoma, the expected case dose units, and the difference calculated by the SAED* analysis method Cue Observed total case doe* unit* Expected total caaa dose unita Difference 1 15,728 2 25,765 3 17,145 4 27,232 5 10,264 6 16,413 7 40,412 8 5,375 9 21,820 10 34,372 11,103 12,689 11,366 12,514 14,350 7,553 16,605 2,613 10,014 21,555 +4,625 + 13,076 +5,779 + 14,718 -4,088 +8,860 +23,807 +2,762 + 11,808 + 12,817 Average 21,453 * Serially additive expected dose. 12.036 +9,416 year of work. Doses can be summed over a worker's entire work history to give his observed total dose. The expected dose for each year can likewise be summed. Some results are presented in table 4 for the exposure of 10 cases of angiosarcoma of the liver to vinyl chloride monomer. For all but one of the cases the observed total doses are greater than the expected total doses with a mean difference of 9417 (p = 0.004 by paired f-test, p = 0.01 by Wilcoxin signed ranks test). The SAED analysis also facilitates examination of the relationship between dates of exposure and dates of diagnosis (alternatively, dates of death) ofthe cases. No. or years prior lo death i 2 3,, 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Totals Table G The total case dote unite of vinyl chloride for each angiosarcoma case and the expected total case dose units No. or cases working (total of 10 cun) 2 4 7 9 9 9 9 9 9 9 9 9 9 r9 8 8 8 8 8 8 6 4 3 3 3 3 2 2 2 1 Caw day* of work 299 1,082 2,655 3,196 3,285 3,285 3,285 3,285 3,125 3,285 3,285 3,285 3,285 3,269 2,803 2,749 2,570 2,458 2,920 2,495 1,848 1,209 1,095 1,095 1,095 753 730 730 399 174 Subcohort day* of work 23,523 87,533 171,672 224,090' 226,932 229,741 233,626 239,066 243,553 247,948 251,083 257,741 259,848 249,430 279,338 293,751 275,032 261,666 291,071 236,498 150,202 103,944 107,942 110,643 96,261 83,802 79,025 63,288 46,529 14,119 Case dose units 890 3,112 7,665 10,132 9,945 9,855 1Q,495 11,471 11,277 10,500 10,236 10,036 10,877 11,293 10,426 9,688 7,616 6,260 7,766 8,082 6,443 3,670 4,380 4,604 4,875 3,400 3,285 3,493 1,995 870 Expected eaw dose units 563 1,942 4,337 6,345 6,472 6,540 5,568 6,700 6,399 6,773 5,944 5,988 6,122 6,197 5,380 6,323 4,794 4,697 6,618 4,945 3,636 2,454 2,275 2,378 2,621 1,646 1,668 1,778 972 487 Difference between obwrved and expected case dose units 327 1,170 3,328 4,787 4,473 4,316 4,927 6,771 6,876 4,727 4,292 4,048 4,765 6,096 6,046 4,265 2,821 1,663 2,136 3,137 2,807 1,216 2,105 2,226 2,354 1,754 1,617 1,715 1.023 383 64,929 5,436,792 214,526 120,362 94,164 OCCUPATIONAL CANCER DOSE MODEL 793 For each case in the study one can calcu were mostly accumulated by the cases in late for each year prior to death his ob this study 4-16 years prior to death, al served and expected dose. (Ifthe case does though some cases were exposed 30 years not work in a given year, both observed prior to death. and expected are set to zero.) Table 5 A search can also be made for a doseshows the output from the latency response relationship by an exposure analysis program for the 10 angiosarcoma level analysis comparing the number of cases. Column seven, the difference be-' days each case has worked at each level of tween the observed case dose and the ex exposure, with the expected number of pected case dose per case in the study, is days. For example, consider a case who plotted in figure 2 after dividing by 10 to worked for 200 days in 1965 at dose level obtain the average per case. It can be seen 2. If his subcohort had a total of 20,000 from this plot that the greatest average work days during that calendar year with difference occurred nine years prior to 2000 at dose level 2, then his expected death, and that it was over 400 dose units number of days during 1965 at dose level in the interval 4-16 years prior to diag 2 is 365 x 2000/20,000 = 36.5. The ob nosis. Excess exposures to vinyl chloride served and expected values can be ac cumulated over the total work history, and the values for each case added. Re sults for vinyl chloride and 10 cases of an giosarcoma of the liver are shown in table 6. It can be seen that cases worked longer than expected at leVels 3, 4 and 5. Any excess at some levels must be accom panied by a deficit at other levels and the deficit here is at levels 0,1 and 2. An in teresting and unexpected finding was the strong association with exposure level 3, which includes jobs involving occasional high excursions from normally minimal levels (table 1). The model can be adapted to assess whether or not more than one chemical is involved. The angiosarcoma cases were FtGUKE 2. Average difference between observed investigated for 19 individual chemicals. angiosarcoma case dose units and expected dose While the strongest relationship in terms units of vinyl chloride. HI- Tabu 6 Comparison of observed and expected numbers of days the 10 angiosarcoma cases worked at each exposure level of uinyl chloride Case days Expected case days Ratio Difference 0 7,467 1 369 12,831 0.58 -5,364 15,633 0.02 -15,264 Dow level 23 6,539 14,249 21,879 0.30 -15,340 1,933 7.37 + 12,316 4 23,193 8,091 2.87 + 15,102 5 13,112 4,562 Z87 +8,550 64,929 64,929 Ear, p;ir 794 SMITH. WAXWEILER AND TYHOLER of statistical significance was with vinyl chloride, an association was also noted with caprylyl chloride exposure (p = 0.005, f-test). This raises a question as to which is more likely to be the carcinogen; or if both are carcinogens, whether they are acting independently or jointly. To answer this question, an additional di mension was added to the model so that each cell from the model shown in figure 1 becomes a two-dimensional matrix (table 7) giving the number of days of exposure for the cohort members at each combina tion of levels of the two chemicals. This information enables calculation of the conditional expectation of exposure. If a case worked in a job with exposure 2 to vinyl chloride, then the expected exposure to caprylyl chloride was calculated from data in the corresponding column vector (see table 7). Observed and expected doses were accumulated with the results shown in table 8. It can be seen that, given the exposure to vinyl chloride, the observed case exposure to caprylyl chloride was very close to that expected. In contrast, given the exposure levels to caprylyl chloride, there remained some difference between observed exposure to vinyl chloride and that expected. Thus, in spite of the fact that these exposures are corre lated in that jobs with exposure to vinyl chloride tend also to involve exposure to caprylyl chloride, the model suggests that caprylyl chloride is not involved. If a dif ference had remained between observed and expected exposure doses to caprylyl chloride given vinyl chloride exposures, then differences could have been calcu lated for each level of vinyl chloride expo sure to attempt to differentiate between independent and joint action. Table 7 Representation ofa cell used in the cohort dose matrix to assess two chemicals, vinyl chloride and caprylyl chloride. Xu is the number of days for the corresponding calendar year, age first employed, and year first employed, that were spent at level i of caprylyl and level j of vinyl chloride exposure Caprylyl chloride level 0 I 2 3 4 5 Vinyl chloride level 0 1 234 Xw X., X, x x X|# Xm x,, Xu XjQ x,, Xn x,, X,, X* X,, x,, Xa x,, x x, x,, X x X*o xs, Xja XM XM & X,, x,s X,, XM x-> X,, Discussion The method presented deals with sev eral problems of occupational cancer studies. Worker movement between jobs and variation in job exposure levels ac cording to calendar years are incorpo rated into the estimation of exposure dose. Latency intervals and exposure levels associated with the cancer can be estimated. Several different chemical as sociations can be sought for and the possi bility that two chemicals might be acting jointly to induce cancer can be investi gated. This information is obtained in a manner which avoids bias from potential confounding due to differences between Table 8 Observed, and conditional and unconditional expected case dose units of exposure to vinyl chloride and caprylyl chloride for angiosarcoma cases. The p values for differences between observed and expected values are in parentheses Observed dose units Unconditional expected dose unite Conditional expected dose units given exposure levels to the other chemiesl Vinyl chloride Caprylyl chloride 21,433 11,493 12,036 (0.004) 3,730 (0.005) 19,450 (0.055) 11,579 (0.9) HOC 044209 9 OCCUPATIONAL CANCER DOSE MODEL 795 cases and noncases in age, calendar year come more readily available (12, 13), In of exposure, and age when first employed. the meantime, retrospective assessment Other variables such as race and smoking of exposure by means of company records can be included when appropriate by de of chemicals and processes used and riving cohort dose matrices for each race interviews with personnel familiar with group and for smokers and nonsmokers past conditions can generate data enhanc separately. ing the power of occupational cancer The method shares certain features of studies. cohort studies and certain features of Cancer latency is usually defined start case-control studies. Cases are ascer ing from the point in time of first expo tained for a defined work population or sure, although attention may also be cohort, and all work histories are utilized. given to the midpoint or end of the expo However, the analysis follows the case- sure period (14-16). Rather than fixing control study pattern. The advantages of attention to these points in exposure time, using case-control methods of analysis of the SAED model allows one to examine cohort data include the fact that bias due the period of time during which the expo to potential confounding variables can be sure of the cancer cases is greater than avoided without the assumptions re that of comparable noncases. The advan quired for multivariate analyses (5). A tages and disadvantages of such informa particular advantage with occupational tion concerning cancer latency have been studies is that observed and expected ex discussed in greater detail elsewhere (17). posures can be derived for each calendar Calculation of the average and range of year, a variable which is difficult to incor the times between first exposure or last porate into a multivariate model. exposure and diagnosis in occupational Exposure variables currently employed cancer studies is influenced by the fact in occupational health studies include the that, unlike angiosarcoma of the liver, simple binary categorization of workers most cancers have relatively low occupa according to whether they worked in a tional attributable risks and some of the given job or plant area for any time at all, occupationally exposed cases will usually or for a minimum period such as five have had their cancer induced by years (6--8). Occasionally estimates of nonoccupational causes leading to possi exposure to a postulated causal agent are ble bias in measures of latency. Estima made for each job in an industry and dis tion of latency using the SAED model out ease incidence is compared between those lined deals with this situation since, on exposed at different levels (7, 9). Cumula average, the occupational exposure of tive dose as in the method presented has cases whose cancer was nonoccupation- been used in studies of the effects of radia ally induced should be the same as that of tion (10) and asbestos exposure (11) and comparable noncase workers. If the occu gives a more precise index of exposure re pational exposure is indeed causal, the sulting in greater power in testing years during which the average case ex hypotheses concerning occupational posure is greater than that expected iden carcinogenesis. Collection of additional tifies the period during which causal ex information is required, but the costs of posures were accumulated. collecting this information are relatively The use ofthe SAED model with ranked small compared with the total costs of oc exposure data can be criticized since the cupational cancer studies. In the future, dose accumulation assumes a continuous health surveillance systems may be im scale. However, the SAED model itself is plemented in many industrial plants and not dependent on having ranked data. the type of information required will be When exposure measures are available 796 SMITH, WAXWEILER AND TYROLER it is suggested that they be placed in than one chemical is involved. We have rank order and categorized into approxi illustrated its use with a known associa mately five exposure steps. Jobs for which tion between vinyl chloride and angio measures are not available could be as sarcoma of the liver, and have also used it signed to an exposure level in each in a study of lung cancer in the same calendar year on the basis of information plant (18) in conjunction with methods concerning manufacturing processes and generating risk estimates. The SAED chemicals used and the accumulation of model, or adaptations of it, may have doses would involve the average of avail widespread application in future occupa- able exposure measures pertaining to tional health surveillance systems, in ad each level. When no exposure measures dition to its use for retrospective studies. are available, the justification for using subjectively determined ranked data as if ReraxENCC* it were on a continuous scale is that this should generally lead to increased statis tical power over the use of binary expo sure data. Increased statistical power will result if those jobs assigned the higher exposure rankings do indeed involve noticeably more exposure than those as signed the lower rankings. The exposure measure becomes virtually continuous once accumulated over calendar time and the paired f-test, or Wilcoxin's test, can be 1. Enterline PE: Pitfall* in epidemiological re search. An examination of the asbesto* litera ture. J Occup Med 18:150-156, 1976 2. Gamble J, Spirtaa R: Job classification and utilization of complete work histories in occupa tional epidemiology. J Occup Med 18:299-404, 1976 3. Mancuso TF, Coulter EJ: Methodology in indus trial health studies. Arch Environ Health 6:210-226, 1963 4. Redmond CK, Breslin PP: Comparison of meth ods for assessing occupational hazards. J Occup Med 17:313-317, 1975 5. Smith AH, Kark JD, Cassel JC, et al: Analysis used to test differences between observed and expected values. of prospective epidemiologic studies by minimum distance case-control matching. Am J Epidemiol 105:567-574, 1977 A second statistical criticism of the' 6. Lloyd JW, Lundin FE, Redmond CK, et al: method relates to the fact that the same noncase can contribute in at least some Long-term mortality study of steel workers. IV. Mortality by work area. J Occup Med 12:151-157, 1970 years to the estimation of the expected 7. McMichael AJ, Spirtas R, Kupper LL, et al: Sol exposure doses of more than one case. Each expected exposure dose is calculated vent exposure and leukemia among rubber workers: An epidemiologic study. J Occup Med 17:234-239, 1975 from many noncases. The predominant 8. Waxweiler RJ, Stringer W, Wagoner JK, et al: source of the variance of the difference be tween observed and expected case doses is Neoplastic risk among workers exposed to vinyl chloride. Annals NY Acad Sei 271:40-48, 1976 9. Tabershaw IR, Gaffey WR: Mortality study of the variance of the observed case doses. workers in the manufacture of vinyl chloride The contribution of some noncases to the and its polymers, J Occup Med 16:509-518, estimation of expected doses for more' 1974 10. Lundin FE, Wagoner JK, Archer VE; Radon than one case can therefore have very lit Daughter Exposure and Respiratory Cancer. tle effect on the f-test or Wilcoxin's test Quantitative and Temporal Aspects. US Dept used to measure statistical significance. HEW. 1971 11. Enterline P, DeCoufle P, Henderson V: Mortal We claim that the wealth of informa ity in relation to occupational exposure in the tion generated by use of the SAED model asbestos industry. J Occup Med 12:897-903, outweighs these statistical problems. The 1972 12. Barrett CD, Belk HD: A computerized occupa model allows one to test for the associa tional medical surveillance program. J Occup tion of individual chemicals with cancer, Med 19:732-736, 1977 examine dose response relationships and 13. Kerr PS: Recording occupational health data for future analysis. J Occup Med 20:197-203,1978 latency phenomena, and assess if more 14. Armenian HK, Lilienfeld AM: The distribution _ ucc 044211 i T OCCUPATIONAL CANCER DOSE MODEL 797 of incubation periods of neoplastic diseases. Am J Epidemiol 99:92-100, 1974 15. Cobb S, Miller M, Wald N: On the estimation of the incubation period in malignant disease. J Chronic Dis 9:385t393, 1959 16. Polednak AP: Latency periods in neoplastic dis eases. Am J Epidemiol 100:354-356, 1974 17. Smith AH, Checkoway H, Goldsmith DP, et al: An analytic procedure for investigation of cancer latency in matched case control studies illustrated with occupational data. Paper pre sented at Society for Epidemiologic Research meeting, June 1978. Am J Epidemiol 108:226 (abstract), 1978 18. Waxweiler RJ: An epidemiologic investigation of lung cancer in a multixenobiotic occupational environment. PhD Dissertation, University of North Carolina, 1978 "'-l t* J*'f