Retrospective assessment of exposure through modeling in a study on cancer risks among workers exposed to phenoxy

Retrospective assessment of ex posure through modeling in a study on cancer risks among workers exposed to phenoxy herbicides, chlorophenols and dioxins. Scand J Work Environ Health 1994;20:262-71. OBJECTIVES - The study aimed at developing a model for the retrospective assessment of exposures in epidemiologic studies when little or no data on past exposures are available. METHODS - A deterministic model was developed for the level of exposure by industrial hygienists involved in an international study on cancer risks among phenoxy herbicide or chlorophenol manu facturing workers and pesticide sprayers. The general source-receptor model was used as the concep tual framework for the model. RESULTS - The model included variablesrelated to job, the emission of chemicals, contact with chem icals, personal protection, and other relevant determinants of exposure. Cumulative dose indices were calculated from the duration of exposure (from the work histories) and the level of exposure (from the model). CONCLUSIONS - Deterministic modeling in complex exposure situations may provide more valid and reliable results than its conventional alternative, subjective assessment by an expert.

Exposure assessment in retrospective epidemiologic studies can be carried out by several methods depending on the resources and information available. The measures of dose chosen, such as cumulative or average exposure, often require an estimation of the level of exposure over time. The more accurate methods of estimating exposure levels use stochastic (statistical) modeling in which missing exposure data are calculated from a model fitted into the results of historical industrial hygiene measurements assumed to follow the log-normal distribution within worker groups defined by plant, job title, and work area. Occasionally the distribution of different tasks within the worker groups is also taken into consideration. Stochastic modeling has been used to study health hazards in the mineral industries (l) and in coal mines (2 262 only from relatively recent times, a similar procedure can be followed, but any trends in exposure levels over time have to be estimated from knowledge of historical changes in the factors affecting exposure. In some cases, as in studies of silicon carbide workers (3) and railroad workers (4), the level of exposure in the defined worker groups has been assumed to have been constant over time. Exposure to other agents occurring as a measured agent at the same time can be assessed with the use of a conversion factor (5). However, like all group-based assessment methods, stochastic modeling is not able to account for the idiosyncrasies of individual workers. It also tends to be insensitive to exceptional exposure patterns occurring temporarily or occurring in workplaces where industrial hygiene measurements have not been made. Because comprehensive exposure data are rarely available, less accurate methods have to be employed. If the significant factors determining the level of exposure can be identified, they can be used to construct a deterministic model, which, as a distinction from stochastic models, does not include a random term (6,7). Some models may have both deterministic and stochastic features. For example, a sophisticated stochastic model to estimate exposure to ethylene oxide included factors influencing the level of exposure (8). Even though the deterministic models are generally based on recent measurements, they can be used retrospectively if informa-tion about the determinants is available or it can be inferred over time. This approach was used in the reconstruction of exposures in the manufacture of man-made mineral fibers (9). The general idea of deterministic modeling can also be used when only very few data are available . Determinants of exposure can be considered as multiplicative weighting factors, which are applied to the basic level of exposure expressed in absolute or relative units. Often, the basic level is defined by any combination of occupation, task, or plant. This approach has been used to estimate exposures among painters (10), resin manufacturing workers (5), and welders (II ). This method, although based on many simplifying assumptions, is more systematic than its conventional alternative, professional judgment, where an industrial hygienist intuitively assigns the levels of exposure case by case in a complex exposure situation.
In this paper we present a deterministic modeling method which was applied to the spraying of herbicides and to the manufacture of phenoxy herbicides and chlorophenols.

Epidemiologic study
The International Agency for Research on Cancer (IARC) has compiled a cohort of 2 I 183 workers from II countries to study possible cancer risks from phenoxy herbicides, chlorophenols, and their contaminants (12). The results of a mortality and cancer morbidity analysis of the cohort have recently been published (13). The available exposure data, together with information on processes and work environments, have also been summarized (14,15).
The cohort study, which was based on a crude assessment of exposure, was supplemented by a nested case-referent study on soft-tissue sarcomas and non-Hodgkin ' s lymphomas. Altogether II cases of soft-tissue sarcoma and 32 cases of non-Hodgkin's lymphoma were identified from within the cohort, and the patients were each individually matched by gender, age, and country with five referents . The details and results of the epidemiologic study will be published in another paper (in preparation).

General pro cedure for exposure assessment
The exposure assessment of the cases and their referents was based on cumulative exposure (CE), defined as a product of the duration of exposure (D) and the estimated level of exposure (L). Exposures occurring five years before selection into the study were ignored in the calculation of the CE scores. Exposures were assessed and ranked by a team of three industrial hygienists unaware of the case-referent status of the subjects. The principles and criteria of exposure assessment were discussed, applied to some typical examples, and agreed upon before the assessment. For consistency, the work was di-Scand J Work Environ Health 1994, vol 20, no 4 vided in such a way that the exposures of all of the cases and referents from a given country were assessed by the same hygienist. The team checked the results, discussed the problems arising during the estimation, and arrived at the final decisions.
The procedure used in the assessment had the following principal steps : qualitative exposure assessment, determination of the duration of exposure, estimation of the level of exposure, calculation of cumulative exposure, and ranking of the subjects (figure I). Each of the steps is described in more detail in the following sections.

Qualitative exposure assessment
The assessed agents are shown in table I. They include phenoxy herbicides, chlorophenols, polychlorinated dioxins and furans, and other agents found in phenoxy herbicide or chlorophenol manufacturing. Some individual agents were grouped for practical reasons. The grouping of agents was mainly based on similarity of chemical structure and expected biological activity. For example, 2,4-dichlorophenoxyacetic acid (2,4-D), 2,4-dichlorophenoxypropionic acid (2,4-DP), and 2,4-dichlorophenoxybutyric acid (2, and their salt, amine, and ester derivati ves were grouped together on the assumption that their toxic properties relate to the (similar) chlorophenoxy part of these molecules. Chlorinated dioxins and furans were merged because they occur as genuine complex mixtures. Some chemicals, such as 2,4dichloro-, 2,4,5-trichloro-, and methylchloro-derivatives of phenoxy acids, were examined both as individual agents and as grouped into wider categories (phenoxy herbicides) to allow statistical analysis at two hierarchical levels. Nonphenoxy herbicides sprayed or manufactured by the subjects were also recorded qualitatively, but semiquantitative assess-   ment of exposure turned out to be questionable because of the lack of accurate inform ation on period s of exposure.
The occupat ional histories of the sets of six subje cts (one case and five referents -disease status "blinded"), includin g information about plant or sprayer cohort, departm ents or jobs, periods of employment, and the end of the assessment period, were used as the basic material. In the qualitative assessment of exposure, unexposed subjects (L = 0, D =°a nd CE =0) were identified agent by agent at the cohort level with the help of the company questionnaires and the cross-tabulation of occurrence of exposure by agent and plant or cohort. The following assumpti ons were made in the assessment: (i) chlorophenols and other raw materials or process chemicals present as impurities in phenoxy herbicide prod-264 ucts do not entail significant exposure among sprayers and other workers handling phenoxy herbicides only as end products; (ii) significant exposure to 2,3,7,8-tetrachloro-p-dibenzo dioxin (TCDD) among the subjec ts occurs only in the manufacture or spraying of 2,4,5-trichlorophenoxyacetic acid (2,4, 5-T ), 2,4,5-trichlorophenoxypropionic acid (2,4,5-TP), and 2,4,5-trichlorophenol (2,4,5-TCP), and (iii) there is no significant carry over of vapors or dusts between production departments unless it is specifically noted in the company questionnaire.

Determination of du ration of exposure
The duration of exposure took into consideration the overlap in the occurrence of exposure and the periods of employment extracted from the detailed work records of the subjects under study. It was expressed in years (12 months calculated for each year). For sprayers, the actual length of the spraying time was used whenever available. If the spraying time was unknown, the annual spraying season was assumed to have lasted three months. For some of the potentially exposed subjects, there was no overlap between the occupational history and the occurrence of exposure resulting in assignment to the unexposed category (D =0, L =0 and CE =0). To improve the validity of the cumulative exposure, an allowance for a latency period was made by omitting the last five years of the follow-up in the calculation of the duration of exposure.

Estimation of level of exposure
Biological monitoring is the preferable method for assessing worker exposure to phenoxy acids and chlorophenols. The predominant route of exposure is often through the skin, and air sampling may therefore seriously underestimate exposure. However, it was not possible to estimate the level of exposure accurately because both biological monitoring and industrial hygiene data were rather scarce until the 1980s (14,16).
To obtain semiquantitative estimates of exposure and a reasonable basis for ranking, a simple exposure model was developed. The underlying conceptual framework was the source-receptor model of exposure (17). According to this model the level of exposure is determined by workplace conditions and by the worker's proximity to the source of exposure, which mainly depends on the tasks involved. The "tasks" in the model can be replaced by "job" if the distribution of tasks is similar within the job. The workplace conditions mainly affecting the level of exposure are the rate of emission of contaminant Scand J Work Environ Health 1994, vol 20, no 4 from the source (emission), spread of contaminant due to air movement and surface contamination (transport), and personal protective equipment and work habits (reception). Other factors directly or indirectly influencing the potential for exposure include the size of the workroom, the ventilation systems, the location of the workplace relative to other production areas, the production rate, and health and safety regimes, such as the frequency of plant cleaning. Because a significant part of exposure in this study took place through skin contact, there was no solid basis for accurate calculation procedures, which in some cases may be applied in the estimation of inhalatory exposures. The source-receptor model could therefore be used only as a general guideline and its application took place according to the rules that follow.
In the present study, the characteristics of the job were regarded as the basic factor influencing the estimated level of exposure. In addition, the main factors that significantly modified the basic level were considered to be the emission of agents, the average daily contact time of the workers with the contaminants, the use of personal protective equipment, and certain other factors. These modifying factors were treated as mutually independent and multiplicative weighting factors (w) in the model. The resulting model can be written as follows: where L = level of exposure (in relative units), L. = job-related level of exposure, we = emission factor, we =contact factor, w p =personal protection factor, w = other factors.
"The job-related levels of exposure L. (table 2) were based mainly on the opinions of the} industrial hygiene team and limited exposure data. The IARC company questionnaire also included a request to rank departments and jobs according to the level of exposure to polychlorinated dibenzo-p-dioxins (PCDD) and polychlorinated dibenzo-p-furans (PCDF), but replies were obtained only from a few plants. No direct exposure data were available from most of the plants and cohorts, and therefore general data reported in the literature were mainly used. The exposure of phenoxy herbicide applicators was studied rather extensively in the 1980s, and the mean concentrations of phenoxy acids in urine usually ranged from <I to 8 mg· I-I. Exposure of forestry workers was usually heavier than that of agricultural workers. Exposure of manufacturing workers to phenoxy herbicides has been monitored by biological samples only in one plant not included in this study. The urine samples of formulation workers contained an average of 1.4 mg . I-I of 2,4-D. In one tetrachlorophenol plant included in this study the mean concentration of chlorophenols in the urine of synthesis workers was 2.3 mg . I-I, and in the urine of packers it was 1.9 mg . II. The mean concentrations of pentachlorophenol reported from four pentachlorophenol plants not included in this study ranged from <I to 2.4 mg . 1-1 among unspecified production workers, but the analytical method used probably underestimated the exposure. Because phenoxy herbicides and chlorophenols can be absorbed by the skin, the results from air samples available from several plants were not regarded as reliable in the setting of the L. values. In addition, levels of TCDD below the parts per billion range have been measured in the serum of workers exposed to phenoxy herbicides or chlorophenols. The exposure data have been described in more detail elsewhere (14,16). Different tasks within a job can entail different levels of exposure. Because almost no information was available about the proportional distribution of tasks, the possible variation of tasks between workers of the same job group could not be taken into account, and only one basic value was used for each job. The departments and jobs for which exposure was estimated to be low were given the relative value of I. On the basis of available exposure data, the highest potential for exposure was considered to have occurred among synthesis workers, finishing workers, and herbicide sprayers, and they were given the value 10. Other exposed jobs were distributed according to the evaluation of the team between these two extreme values. In the special case in which workers were rotated between several operations or departments and the work histories did not allow discrimination between different work periods, L. was calculated as the time-weighted average. For' example, if a worker shared evenly the workhours between synthesis (L = 10) and formulation (L. = 5), L. = 7.5 for agents present in both operations, L. ='5 for , agents present only in synthesis, and L j = 2.5 for agents present only in formulation.
It was assumed that the L. of a given job, which is predominantly determined by the work tasks and proximity of the worker with the emission sources, was independent of the calendar time and constant in all situations. The agent-, plant-and time-specific factors were considered to affect the modifying weight factors we' We' w p ' and w o' Stepwise changes in the weight factors resulted in corresponding changes in the estimated level of exposure, and therefore for each plant-job combination a separate L-profile over calendar time was derived. Because the units used were relative, the values of L. (and consequently of Land CE) are mutually comparable and additive only for those agents for which L. was based on biological monitoring data (ie, for phenoxy herbicides and chlorophenols).
The emission factor W was assumed to be I unless there was good reason to believe, on the basis of the company questionnaire or other reliable sources of information, that the emissions in the plant were significantly higher or lower on the average than in other manufacturing plants. Examples of situations in which the value of w differed from unity follow: (i) shift from an old plant to a new plant assessed, on the basis of information provided by the company, to have a more-enclosed process (we = 0.5 for the process workers during the period when the new plant was in operation); (ii) manual charging or discharging of reaction vessels (w = 2 for the synthesis workers during the period~f manual work); (iii) dusty conditions arising from bagging (we = 2 for packers during the dusty period); (iv) process accident releasing TCDD or the occurrence of several cases of chloroacne (w =5, cases of chloroacne, or 10, TCDD-releasing accident, in the contaminated departments from the time of the accident or of the occurrence of chloroacne cases until the shutdown or thorough cleanup of the process); past experience has shown that accidents in which process material contaminated with TCDD has been released into the work environment have resulted in a high incidence of chloroacne among the workers involved (18)(19)(20)(21)(22).
The production volumes of chemicals were available from most plants, but their use in the estimation was discarded because interaction with other determinants of exposure was suspected. If several emission factors applied simultaneously, they were multiplied to obtain the total we ' The contact factor we' describing mainly the proportion of the workhours spent with specific exposure, was considered to be necessary because the plants usually manufactured several types of herbicides, chlorophenols, and other chemicals simultaneously. Similarly, herbicide sprayers also used nonphenoxy herbicides and other pesticides. The amounts of individual agents synthesized or sprayed varied significantly over time and plant. The mean proportion of the workday spent in contact with different types of chemicals could be crudely inferred on the basis of the company questionnaires which Cumulative exposure was calculate d by a computer program ign oring exposure for the last fiv e years before se lection into the case-referent study . For example, let us con sider a worker who work ed from I Ja nuary 1960 to I Jul y 1983 in the sy nthes is dep artment of a plant (ie, L = 10), whic h manufact ured phenoxy herbicides inclu ding 2,4-0 (40% of all phenoxy herbicides; ie, we =0.4). Produ ction was shifte d to a new plant with mor e-clo sed process equipmen t (ie, we ch anges from 1.0 to 0.5, and the le vel of exposure drops) on I Janu ary 1975 , and since then exposur e has decreased gradually (a general ass umptio n co nce rn ing all plants; ie, w =0.75 in 1975-1980). No perso na l protect ion eq uipment was regularl y used (ie, w = I). If this worker was followed unt il I Janu ary ' i 985, the calculation of 0 and CE for ex posure to 2,4 -D wo uld proceed as foll ows: itoring in some plants and subco horts have probably decre ased exposure since the mid-I 970 s through sma ll improvements in the area of personal hygiene, the handling of chemicals, and the cle aning of the work environment. Another signi ficant cha nge co ncerns the level of ex posure to polychlorin ated dioxins and furans . In man y manu facturing pl ant s, pro cess parameters have been adju sted to minimize the sidereactions in whi ch the se toxic compo unds are for med. Their co ncentratio ns in the end products have consequently decreased. The values used for W o were the following : (i) for compo unds other than TCDD and PCDD and PCDF in manufa cturing plants included information about the distribution of the workhours by pr oduct and the production volumes by product in five-year intervals. Another factor that res tricted the cont act of the workers with the process emi ssion s was the devel opm ent of automatic process co ntro l, which tended to move workers from the vici nity of the emi ssion s mainly into ventilated control rooms. Examples of the values used for we foll ow : (i) 10% of workhours spent in synthesis of a specific herbi cid e (we = 0.1 , ie , 10%) and (ii) most of the time spent in a venti lated control roo m (w = 0.5 ).
Local vent ila tion wa s discussed as a determinant, but there were no cases in which the documentation wo uld have warranted the use of a decreased value for we' If sev era l contact factors applied si multaneou sly, the y were multiplied to obtain the total we' Becau se the co mpany questionnaires did not usually contain any qu antitative dat a on raw material s, pro cess che micals, intermediates or impurities, the w for these che micals had to be inferred from the produ cti on volumes of phenoxy herbi cides or chloroph enol s and from the proce ss description s. A set of rule s was made for the inferen ce of we' Exampl es follow: (i) we for TCDD equals either we for 2,4 ,5-T and 2,4,5-TP in phenoxy plants and spraying, or w.. for 2,4 ,5-TCP in chl orophenol plant s because TCDD is present in these products; (ii) w.. for PCDD and PCDF equ als either the summed wc for all phen oxy herbicides exc ep t meth ylchl orophen oxy acetic, propi onic or butyric ac id (MCPA, MCPP, or MCPB ) in phenoxy plants and spray ing or the summed we fo r pent a-, tetra-and trichl oroph enol s in chloro pheno l plant s because PCDD and PCDP are present as impurities in these products; (iii) we for p-chl oro-ocresol (PCOC) equals wr for MCPA, MCPP, and MCPB in phenoxy plants because PCOC is their raw material ; (iv) we for gamma-butyro lactone equ als the summed w,. for MCPB and 2,4-DB in phenoxy plants becau se it is their raw material ; (v) wc fo r phenol equ al s either we for 2,4-0, 2,4-DP, and 2,4-DB in phenoxy pl ants or the summed w,. fo r chl oroph en ols in chlorophenol plants applying the chl orination proce ss because phenol is the raw material of these produ cts.
Th e per sonal protecti on fact or w , was assessed fro m the information pro vided by the /comp any questionn aire s. The use of respirators or prot ection of the skin was uncomm on in manufacturing plants, except du ring so me shor t-term tasks with high potenti al for exposure. In sprayi ng, the use of personal protection had proba bly increa sed slig htly o ver the yea rs. Applying the value of 0.5 for W , when appro priate protective equipment of the ski n and respi ratory tract were frequ ently used , was discussed , but inaccurate documentation of worker protectio n in the co mpa ny questionn aires did not war rant the use of th is va lue .
All other factors deem ed to exert a significant effect o n the level of expos ure were incorpo rated into w o ' Health concern s and the start of biological mon -SCaI,d J Work Environ Health 1994, vol 20, no 4 Table 3. Exp osure c haracterist ic s of the referents of th e stu dy. The figures are mean valu es om itting ex pos ure du ring th e last f ive years before the end of the follo w-up . The scores, excep t those of t he duration of ex posure, are not mutually comparable because th e level has been expressed in agent-specific relat ive units'  The calc ulated mean values of cumulative exposure, the estimated level of exposure, and the duration of exposure of the exposed referents of the study are presented in table 3. The CE scores were then used in the statistical analysis both as continuous and categorical variables. Subj ects within each matched set were also ranked so that the perso n with the highest cumulative exposure within the set was give n the rank of one and the lowest the rank of six. To avoid a misclassification of exposure, similar ranks were give n to all of the unexposed perso ns (CE = 0) , all persons with light exposure (CE nonzero but < I; corresponding maximall y to one year of exposure at the level L = I), and those whose CE~1, but differ ed by less than 50% from the CE of subjects with adjacent ranks.

Discussion
The validity of the exposure estimates requires that the measu re of exposure and the model are correct and that the estimation is accurately carried out. Cumulat ive expos ure in its simplest form (leve l times dura tion) assumes inherently a linear relation between exposure and outcome, which in addition is indepe ndent of time. It may therefore be criticized as the measure of dose because the outcome under study may be nonlinear and depend on the time elapsed since first exposure (23). We allowed a fiveyear latency period for the cancers studied and thus omitted the most recent exposures . There are more sophisticated approac hes with which to weigh the 268 time sinee first exposure, but adopting them, as well as weighing the possible nonlinearity, would have been questionable because of the lack of information concerning the mechani sms of occupational carcinogenesis concerning non-Hodgkin' s lymphomas and soft-tissue sarcoma s. Cumul ative exposure omitt ing the last five years before the end of the follow-up was chosen because it was a feasible measure to be estimated and there was no solid basis for using more complex measure s.
An effor t was made to take into account the most significan t factors and temporal changes in the exposure conditio ns throu gh the introdu ction of timedependent weighting factors. Becau se there was no "go ld standard" (criterion) to compare with, it was impo ssible to measure to what extent this attempt was suceessful. However, each step of the assessment was considered by a team of experienced industrial hygienists and included in the model only if it was agreed that the incorporation improved the validity of the estimates. It is probable that this method provided more accurate exposure esti mates than the method used in the corres ponding cohort study (15), because tempor al and plant-specific factors could be more fully utiliz ed. Compari son of the results of the case-refe rent studi es and the cohort study can also be used as an internal validity test of the modeling method. The findings of the studies agreed to a large extent, but the magnitude of the risk in the case-referent studies was higher and therefore indicated that this ex posure assess ment exerc ise manage d to remove some of the nondifferential misclassification and thus provided more statistically significant results.
Some factors that may have been important could not be considered at all due to the lack of sufficien t information. One was the variation of exposure be-tween workers employed in the same job . For example, the mean concentration of chlorophenols in the urine of synthesis workers varied about twofold and that of the packers about tenfold in one of the chlorophenol plants under study (14). Between-worker variability of exposure in various other jobs has been reported to range from under twofold to over 1000fold (median about 25-fold when 5% of the values were excluded as outliers) (24). Omitting this factor may have caused misclassification, which in most cases tends to bias the point estimates of risk towards unity (misclassification between the exposed and unexposed) and to diminish the exposure-response relation (misclassification between the exposed classes).
Another assumption of the model was that the factors incorporated were independent (ie, a change in one factor did not automatically influence the values of other factors). Any interactions between factors would lead to over-or underestimation, which should be corrected by adding interaction terms into the model. The basic factors of the model -job characteristics, emissions, transport , and receptioncan be considered to be relatively independent, and no significant interactions were identified by the team during the assessment. Of the possible determinants , only the production volume was considered as reasonable to discard becau se it was known in some plants to be related to the changes in shift-work schedules and also to the proportion of workhours spent in contact with chemicals (incorporated into w) , The information obtained regarding historical changes in workhours and shift systems was not accurate enough to warrant the use of a weighting factor in this study. However, in situations in which more complete information is available, the effect of production volume could be incorporated. Relationships have been found between production rate and exposure levels (25).
One critical point in this estimation procedure is the assignment of the job-related levels (L values in table 2). The setting of these values wai based on the judgment of the team and rather limited data on exposure. Another team with different experience may have assigned different values and thereby influenced the final exposure estimates. In addition, the same basic level was applied independently of the plant and country. It is possible that, for example, laboratory workers may have rather high exposure in plants where their tasks include manual sampling of the process streams and products. We tried to overcome this difficulty by matching the country, which in many cases meant also matching the plant and comparing with each other only subjects who had worked in the same plant. However, if enough information is available on the tasks or ranks of jobs in the studied plants, a better procedure might be to assign plant-specific L values .
The degree of certainty of the different factors used in deriving exposure estimates varies by factor Scand J Work Environ Health 1994, vol 20, no 4 and agent. The duration of exposure was usually a precise measure based on individual work histories and plant information. The level of exposure was derived from a group-based model, in which the contributing factor s were all relatively crude estimates. The uncertainty of the level is also reflected in the cumulative exposure. However, what cumulative indices lose in certainty, they win in validity. Using only the duration of exposure as the measure of exposure would mean omitting often over 100-fold level-related exposure differences between worker groups . The estimates for phenoxy herbicides, chlorophenols, and their dioxin or furan impurities are also likely to be more accurate than those for other pesticides and solvents, because the company questionnaires provided more-detailed information on them.
The ranking system, which was used together with continuous and grouped CE scores, also deserves a critical comment. One advantage of using ranks is that it provides an alternative for examining the data to ensure that the findings are robust and do not depend highly on ways of categorizing data . Another advantage is that there is the possibility of expressing an uncertainty factor concerning the calculation of the exposure scores, by allocating the same rank value for subjects with approximately similar CE scores . On the other hand, deriving ranks from CE scores means replacing the best estimates by cruder values. The CE scores estimating the true quantity of exposure become ordinal ranks, and the possible exposure-response relation becomes distorted. In the present study, both approaches provided results that were essentially similar in relation to the direction of the odds ratios and the statistical significance of the associations. Hardly any new information was gained by ranking when it was used in connection with the more-accurate procedure based on cumulative exposure.
Simultaneous exposure to many agents, which has been described in more detail in another paper (14), was common in the study population, as is illustrated in table 4. Table 4 lists the Pearson correlation coefficients of the log CE scores (individual scores as continuous variables) for selected pairs of agents among all of the referents (N =2 I3) invol ved in the nested case-referent study of IARe. In a complex situation like this, confounding may occur. Should there be an agent causing the risk, its correlations will also show a spurious excess in the analysis. The modeling method may slightly decrease this kind of confounding bias because it decreases misclassification of the agent and confounders. Control of confounding by stratification or statistical modeling of the studied associations can be used, but residual confounding may still be left, especially if the agents are strongly correlated. However, confounding requires that the confounding agent is also associated with the disease under study. The epidemiologic study found significant associations in relation to exposure to  phenoxy herbicides and dioxins, but not in relation to other chemicals. Apart from some highly correlated agents in table 4, other agents can therefore probably be disentangled without a significant confounding bias.
In summary, simple deterministic modeling of exposure is a procedure which can be applied in the retrospective assessment of exposure in industrybased studies when few data on the levels of exposure are available. The results are likely to be less valid than assessment procedures based on a comprehensive set of measurements, but more valid and reliable than the subjective asses sment by an expert. The procedure requires knowledge of the industry under study for the development and use of the exposure model. Confounding due to the simultaneous presence of many etiologic agents may only slightly be influenced by expo sure modeling, but calculating intercorrelations of agents highlights such possibilities and may thus help in the interpretation of the results of epidemiologic studies. Misclassification of exposure is unavoidable, but its effect can be reduced by matching on the country level and by using standard rules for classifying subjects within each matched set. Although the present model was constructed mainly for the chemical industry, its starting point was the general source-receptor model, which is applicable to a wide range of industries and operations, provided that the factors of the model take into account the specific characteristics of exposure in the jobs being studied.