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On the translation of uncertainty from toxicokinetic to toxicodynamic models – The TCDD example
Chemosphere 67 (2007) S365–S374 www.elsevier.com/locate/chemosphere
On the translation of uncertainty from toxicokinetic to toxicodynamic models – The TCDD example Harald Heinzl a b
a,*
, Martina Mittlbo¨ck
a,1
, Lutz Edler
b,2
Core Unit for Medical Statistics and Informatics, Medical University of Vienna, Spitalgasse 23, A-1090 Vienna, Austria Department for Biostatistics, German Cancer Research Center, Im Neuenheimer Feld 280, D-69120 Heidelberg, Germany Accepted 26 May 2006 Available online 16 January 2007
Abstract When estimating human health risks from exposure to TCDD using toxicokinetic and toxicodynamic models, it is important to understand how model choice and assumptions necessary for modeling add to the uncertainty of risk estimates. Several toxicokinetic models have been proposed for the risk assessment of dioxins, in particular the elimination kinetics in humans has been a matter of constant debate. For a long time, a simple linear elimination kinetics has been common choice. Thus, it was used for the statistical analysis of the largest occupationally exposed cohort, the German Boehringer cohort. We challenge this assumption by considering, amongst others, a nonlinear modified Michaelis–Menten-type elimination kinetics, the so-called Carrier kinetics. Using the area under the lipid TCDD concentration time curve as dose metrics, we model the time to cancerrelated death using the Cox proportional hazards model as toxicodynamic model. This risk assessment set-up was simulated in order to quantify uncertainty of both the dose (TCDD body burden) and the risk estimates, depending on the use of the kinetic model, variations of carcinogenic effect of TCDD and variations of latency period (lag time). If past exposure is estimated assuming a linear elimination kinetics although a Carrier kinetics actually holds, then high exposures in reality will be underestimated through statistical analysis and low exposures will be overestimated, respectively. This bias will carry over on the estimated individual concentration–time curves and the therefrom derived TCDD dose metric values. Using biased dose values when estimating a dose–response relationship will finally lead to biased risk estimates. The extent of bias and the decrease of precision are quantified in selected scenarios through this simulation approach. Our findings are in concordance with recent results in the field of dioxin risk assessment. They also reinforce the general demand for the scheduled uncertainty assessments in risk analyses. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Uncertainty assessment; Simulation study; Carrier kinetics; Workplace exposure; Exposure reconstruction; Area under the lipid concentration time curve (AULC)
1. Introduction Polychlorinated dibenzo-p-dioxins and dibenzofurans (PCDDs/PCDFs) as well as dioxin-like polychlorinated
*
Corresponding author. Tel.: +43 1 40400 6686; fax: +43 1 40400 6687. E-mail addresses: [email protected] (H. Heinzl), [email protected] (M. Mittlbo¨ck), [email protected] (L. Edler). 1 Tel.: +43 1 40400 2276; fax: +43 1 40400 2278. 2 Tel.: +49 6221 42 2392; fax: +49 6221 42 2397. 0045-6535/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.chemosphere.2006.05.130
biphenyls (PCBs) constitute a family of chemicals which are present in both occupational and daily human environments and which are considered as hazardous to humans. International health organizations such as the WHO and the IARC have classified dioxins as human carcinogens and risk specific dose levels have been derived recently (IARC, 1997; WHO, 2000, see also; Gies et al., 2004). Although these efforts of estimating human health risks of PCDDs/PCDFs and dioxin-like PCBs try hard to take statistical uncertainty into account, (e.g. applying 95% confidence intervals or using the Benchmark Dose Lower
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Confidence Limit, as starting point of low-dose extrapolation), most risk assessments do not account for a comprehensive assessment of the uncertainty of risk measures reported to the risk managers. One difficulty for doing so is due to the complexity of the nature of this uncertainty; another obstacle is the lack of methods and algorithms to translate uncertainty from exposure assessment via toxicokinetic modeling to the final risk estimate obtained in a toxicodynamic model. Estimation of human health risks from exposure to PCDDs/PCDFs and dioxin-like PCBs depends on the assessment of exposure to the hazardous compound as well as on its toxicokinetic and toxicodynamic behavior in the human body, or, when risk assessment is based on animal data, in the respective organism examined in a bioassay. Modeling these processes constitutes a basic prerequisite for any quantitative risk assessment, including assessment of the uncertainty of risk estimates. Obviously, the modeling process itself, as part of the risk assessment task, affects the development of valid risk estimates. Due to the wealth of information available on exposure and effects in humans and animals on the prototype compound 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD), an elaboration of uncertainty methods and algorithms for this compound serves as an excellent example. Such an analysis should allow a quantitative evaluation of the uncertainty of TCDD risk estimates, and it should exhibit how toxicokinetic model uncertainty carries over to uncertainty of the dose metrics and the dose–response relationship from which parameters for the risk management interventions are then obtained. In the following, we restrict our uncertainty assessment on the cancer endpoint for convenience and earlier work done in this field. Cancer is usually considered as a slowly evolving disease. An increase in TCDD dose may result in an increase of the observable cancer response not until some latency time period (in the following called lag time) has elapsed. This fact needs careful consideration when a dose–response relationship is to be established. Toxicokinetic models have been developed capable to reconstruct TCDD exposure concentrations during a lifetime, see e.g. Dixit et al. (2003). Thereby, time-dependent TCDD dose metrics like the area under the concentration–time curve were constructed for each person. These measures were then used to determine the exposure level of cohorts, see e.g. occupational cohorts described in Crump et al. (2003). TCDD concentration–time curves of individuals are calculated by combining exposure matrices with individual residence data or, in the case of occupational exposure, by using job exposure matrices and workplace data. Usually, one obtains individual exposure estimates by the socalled back-calculation method. This is mainly a statistical regression model, which relates TCDD concentrations to the exposure matrices and then reconstructs an individual exposure history using all information available for that person. In the case of TCDD, rather high exposures that had occurred in the 1950s could be reconstructed from gen-
erally lower body burdens determined in the 1980s and 1990s when TCDD concentration measurements in human body compartments became accomplishable. This reconstruction is a rather delicate statistical task because of extrapolation beyond the observed range of measurements. Standard statistical model checking techniques of regression (e.g. residual analysis) do not apply and therefore extrapolated results cannot be verified in the usual way. The validity of the results rises and falls with that of the underlying model assumptions. High lipophilicity and slow elimination require careful monitoring of the body fat compartment when TCDD toxicokinetics is modeled in humans. Two, for some time common, but nowadays questionable model assumptions for estimating past TCDD exposure are the assumption of lifetime constancy of the total lipid volume (TLV) of the human body and the assumption of simple linear elimination kinetics of TCDD. Modified Michaelis–Menten kinetics (also known as Carrier kinetics) has been suggested to link the TCDD elimination rate with the TCDD body burden, i.e. the concentration of TCDD in the body (Carrier et al., 1995a,b). Under the Carrier kinetics, TCDD elimination would be faster, or nearly the same rate, or slower than under the simple linear elimination kinetics when the individual would be highly, moderately or slightly contaminated, respectively. In other words, the elimination rate is not constant but depends on the amount of TCDD available for elimination. If exposure would be estimated assuming a linear elimination kinetics although a nonlinear Carrier kinetics actually holds, then a so-called compression effect could bias the outcome data of the toxicokinetic model: truly high exposures will be underestimated with the back-calculation method and low exposures will be overestimated, respectively (Heinzl and Edler, 2002). Consequently, the estimated individual concentration–time curves will be biased and this bias will carry over into TCDD dose metric values and risk estimates (Edler et al., 2004). The present study addresses these issues in detail by the use of extensive computer simulations. Carcinogenicity of TCDD is assumed and effect size and lag time of the carcinogenic effect are varied. However, the statistical analysis strategy is the same procedure as used for the statistical analyses of the Boehringer dioxin cohort (Becher et al., 1998). This allows the assessment of how the estimated half-lives, back-calculated workplace exposure levels, and the subsequently computed cancer risk estimates are affected if the assumptions of statistical analysis differ from toxicokinetic reality. The paper is organized as follows. Section 2 contains a description of the simulation study conditions. The results are presented in Section 3. In Section 4, we discuss potential consequences of our results for the risk assessment of TCDD, and present a strategy to include ex post uncertainty assessments in the risk management process.
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2. Methods
2.2. Design of the simulation study
2.1. The Boehringer cohort
For the uncertainty assessment, various assumptions of the original statistical analysis of Becher et al. (1998) were challenged by means of a computer simulation study. The simulation study was designed to mimic the essential features of the Boehringer cohort’s exposure history. The simulated data were generated under various assumptions reflecting different possible states of the true nature of the elimination kinetics. These data were then analyzed using the statistical evaluation strategy described in Becher et al. (1998). This approach allows the study of the impact of the various assumptions/scenarios on the statistical estimates obtained from the toxicokinetic and, consequently, also from toxicodynamic modeling. To be precise, the simulation study consisted of five main steps (see the rectangles in Fig. 1), briefly described in the next sections (for a more detailed description, see Heinzl and Mittlboeck, 2004).
Occupational cohort studies produced important evidence for the International Agency for Research on Cancer (IARC) evaluation concluding that TCDD is carcinogenic to humans (IARC, 1997; McGregor et al., 1998; Steenland et al., 2004). One of these cohorts was the so-called Boehringer cohort comprising more than 1500 workers mainly engaged in the production of herbicides from 1950 until 1984 in Germany (Flesch-Janys et al., 1995; Becher et al., 1998). In that plant, one was able to identify about 20 different working areas of different exposure types. Information on the exposure was obtained between 1985 and 1994 when TCDD measurements from blood or body fat samples were taken from 245 workers. For the analysis, these areas were clustered into five main areas of sufficiently different TCDD exposure levels. There was, e.g. one working area of the 1950s (see the working area 1 below) which was extremely contaminated, such that some workers still had a high dioxin concentration in their blood more than 30 years later. Their estimated daily TCDD exposure exceeded the largest estimates for the other working areas by more than 20 times. TCDD is a highly lipophilic compound that rapidly distributes in the human body lipids (within days or few weeks), whereas its elimination is a slow process (a matter of years). These observations usually lead to the assumption of a one-compartment mass-balance equation for describing the amount A(t) of TCDD in the body lipids at time t by dAðtÞ=dt ¼ intakeðtÞ eliminationðtÞ: This generic model was adapted for the Boehringer cohort data (Flesch-Janys et al., 1995; Becher et al., 1998) assuming that the total lipid volume (TLV) of the body remained constant over lifetime and that TCDD elimination followed a simple linear kinetics, that is, elimination(t) = keA(t) where ke denotes the elimination rate constant. After adjusting TCDD measurements for German background exposure levels, ke was estimated from data of workers for whom multiple measurements between 1985 and 1994 were made. Working exposure levels in different working areas were estimated by summation of intake over the respective areas. The estimated exposure levels were used together with individual lifetime work history data to compute individual time courses of TCDD exposure for all workers of the cohort. In particular, for modeling the toxicodynamics, the area under the TCDD concentration curve over the time of exposure was used as the dose metrics representing accumulated TCDD exposure. This dose was then the primary explanatory variable in a Cox proportional hazards regression model of cancer mortality (Cox, 1972; Flesch-Janys et al., 1995; Becher et al., 1998).
2.2.1. Simulation of whole cohort Each simulated cohort consisted of 500 (virtual) workers starting to work in 1950 within one of five working areas. The areas exhibited different TCDD exposure levels and each worker’s individual exposure was randomly drawn from a lognormal distribution with mean intakes of 3500, 150, 40, 5 and 0 ngTCDD/kgfat/year, respectively. Mean background exposure intake was set to 1 ngTCDD/kgfat/ year. The dispersion of the lognormal distribution was chosen such that the 99th percentile was two-times the mean intake. The highest workplace exposure of 3500 ngTCDD/ kgfat/year mean intake was assumed as having occurred only in the 1950s (working area 1). Stop of exposure was assumed at plant closure in 1984. Hiring, change of working areas during employment, termination of contract, retirement and death of the workers were simulated using
Fig. 1. Block diagram of the simulation study. There are five main simulation steps, which are represented by rectangles. The circles represent simulation results.
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standard randomly occurring events and random choices between options available at specific time points. For the toxicodynamic model, each worker was assumed as of being under permanent hazard to develop cancer. The increase in cancer hazard was dynamically linked to TCDD exposure via the area under the lipid concentration time curve (AULC) dose metrics. Both the up-to-date and the 10-years-lagged AULC were considered. The dose– response relationship between TCDD and cancer was simulated for the three different effect sizes of no, small and strong effects, respectively. For a (virtual) worker with cancer, an increased mortality hazard was assumed and – provided he was still active in the company – retirement was entailed. At the closing of the plant, each simulated cohort consisted of around 1200 workers representing the male part of the original Boehringer cohort. Four different toxicokinetic scenarios concerning the elimination kinetics were considered: I: Simple linear elimination kinetics, elimination(t) = keA(t), with a total body lipid volume (TLV) which is constant over the worker’s life time II: Simple linear elimination kinetics, elimination(t) = keA(t), with a TLV varying with worker’s age III: Modified simple linear elimination kinetics, elimination(t) = kTS[LVliver(t)/TLV(t)]A(t), according to Thomaseth and Salvan (1998) and a TLV varying with worker’s age IV: Modified Michaelis–Menten-type elimination kinetics, elimination(t) = kC[fmin + (fmax fmin)C(t)/{K + C(t)}]A(t),
according to Carrier et al. (1995a,b) with body weight and a TLV varying with workers age. In the case of a simple linear kinetics (I and II), an elimination half-life of 7 years was assumed (Becher et al., 1998). The age-varying TLV values (scenarios II–IV) were randomly generated by adapting formulas and results as reported by Thomaseth and Salvan (1998). This step in the simulation study could also be called forward simulation. The simulated data from this step are called simulated true values in order to distinguish them from simulated observed values of the next step (Fig. 1). 2.2.2. Measurement conditions The next step of the simulation (see Fig. 1) had to reflect the data collection in the Boehringer cohort. It was assumed that the job-exposure matrix could be reconstructed for all cohort members, as it had been the case in the original evaluation when company-internal records were available. Note that, TCDD measurements were only available for a small number of workers of the Boehringer cohort. Since a considerable portion of them had repeated TCDD measurements, we simulated two TCDD measurement times in 1990 and 1995. At each of the two time
points, each (virtual) worker still living had a chance of 15% to participate in that examination. Whenever a (virtual) worker participated in the first examination, then the chance to participate in the second investigation was set to 60%. The results of this step are the simulated observed values (Fig. 1). 2.2.3. Workplace exposure back-calculation The available simulated observed TCDD values were used for exposure back-calculation that was performed as in the original statistical analyses of the Boehringer cohort (for details see Becher et al., 1998). Simple linear elimination kinetics and constant TLV over lifetime were assumed. The former was the commonly used elimination kinetics at analysis time and the latter was enforced due to lack of appropriate data during the operating period of the plant. Technically, back-calculation was a three-part approach (Becher et al., 1998). First, a simple and robust adjustment for background exposure was performed. Second, the elimination rate constant ke from all workers with more than one TCDD measurement above background level was estimated, and third, from all available TCDD measurements above background level and using the corresponding jobexposure data, the exposure levels of the various working areas were estimated by employing a linear regression model without intercept. If negative exposure estimates were obtained, they were set to zero. Becher et al. (1998) were well aware of the problematic assumption of a constant TLV over lifetime. They tried to overcome it at least partly by applying some form of ad hoc adjustment for the period between the end of workplace exposure and measurement time. This strategy was adopted in the simulation study as well. The results of this simulation step will be estimated working area exposure levels and half-life estimates for the cohort (Fig. 1). These results will refer to a simple linear elimination kinetic back-calculation when the actual forward exposure simulation is performed using the different elimination kinetic approaches I–IV (see Section 2.2.1 above). Additionally, three different types of TCDD effect strengths on cancer (no, small, strong) and two different latency times for cancer (0 and 10 years) will be studied. 2.2.4. Estimation of individual concentration–time curves for whole cohort The cohort’s back-calculated exposure levels and halflife together with individual job-exposure matrices are used to estimate individual lipid concentration–time curves for all cohort members (Fig. 1). Individual dynamic exposure indices can be constructed from these curves, which are always based on the simple linear elimination kinetics, irrespectively whose elimination kinetics has been used in the forward simulation of the cohort. Here only the time-dependent AULC with three different lag times (0, 10 and 20 years) is considered as dynamic exposure index (dose metrics).
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2.2.5. Assessing the relationship between exposure and cancer mortality (dose–response modeling) For the assessment of the dose–response relationship between TCDD exposure and cancer mortality, the AULC is used as a time-dependent explanatory variable in a Cox proportional hazards regression model (Cox, 1972; FleschJanys et al., 1995; Becher et al., 1998). Total cancer mortality time is considered as outcome variable. The Cox model then results in hazard ratios as cancer risk estimates for a unit increase in the AULC (Fig. 1). These hazard ratios will be compared for the combination of the elimination kinetics I–IV, different types of TCDD effect strengths on cancer (no, small, strong) and different true latency times for cancer (0 and 10 years) used for forward simulations, and different lag times (0, 10 and 20 years) used for AULC construction in the Cox model, respectively. 2.3. Further technical details of the simulation The SAS software system was used for statistical computations (SAS Institute Inc., Cary, NC, USA). 100 cohorts were simulated whenever the elimination kinetic scenarios I, II and III were considered. The Carrier elimination kinetics of scenario IV resulted in a computationally time-consuming procedure so that only 50 cohorts were simulated then. Contrary to Heinzl and Edler (2002) and Edler et al. (2004), where ad hoc estimates were used, the parameters of the Carrier elimination kinetics, kC, fmin, fmax and K, were set here to values as provided by Carrier et al. (1999). 3. Results In the following, the distributions of the simulation results will be described by median values, lower and upper quartiles. 3.1. Workplace exposure back-calculation Table 1 shows the distribution of the simulation results of the back-calculation analysis described in Section 2.2.3. After adjusting for background exposure in a first step, the half-life of a simple linear kinetics, half-life = log(2)/ke, was estimated from the simulated worker’s data who had TCDD measurements (above background) in 1990 and 1995. Under elimination kinetics I and II, the true half-life was set to a value of 7 years and the half-life estimates for both scenarios are close to it. However, the half-life estimates under the elimination kinetic scenarios III and IV are also quite close to this value. This indicates that the gradients of the TCDD concentration versus time curves under the various elimination kinetic scenarios are obviously quite close 5–10 years after the closing of the virtual plant. The last step of the back-calculation analysis gives estimates of the workplace exposure levels. Table 1 shows
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that the estimates for working areas 2–5 are quite close to the true values for elimination kinetic scenarios I–III. A quite different and more variable outcome is observed for working area 1 under elimination kinetic scenarios I– III. Working area 1 only existed in the 1950s with a mean exposure of 3500 ngTCDD/kgfat/year. All the results for elimination kinetic scenario IV (the Carrier kinetics) are completely different when compared with the other scenarios. For working area 1, one realizes an increasing bias from scenarios I to III. In other words, if the time-varying agedependent change in body lipids is ignored in the analysis due to lack of data, then the effective exposure level will be underestimated. If a strong cancer effect is assumed, then this underestimation will even be larger. This is quite natural as those virtual workers who in the simulation have randomly drawn TCDD exposures below the mean exposure level of that working area will more probably survive until the (virtual) TCDD measurement times. Note that an assumed lag time of 10 years for developing cancer is weakening this effect, since then the chance to experience TCDD measurement in 1990 or 1995 has increased. Technically, the whole problem is called informative missingness and is in concordance with what can be observed in real highrisk cohorts. The simulation shows clearly that a back-calculation based on the simple linear elimination kinetics would completely fail when the elimination kinetics IV (the Carrier kinetics) would hold. Working area 1 of highest exposure would be incredibly underestimated; areas 2 and 3 would still suffer underestimation, whereas for areas 4 and 5 we would observe an exposure overestimation. Figs. 2a and b provide an explanation for this. The Carrier elimination kinetics is not linear. It reaches a saturation level for constant high exposure, but it eliminates high amounts of TCDD from the body much faster than a linear kinetics can do (Fig. 2a). However, in the case of low exposure, it eliminates the compound at a much slower rate than any linear elimination kinetics (Fig. 2b). Notice that the back-calculation is based on the measurement of TCDD values in the 1990s and on this basis of information, we go back in time using the simple linear elimination kinetics. It is obvious that such an approach cannot work if the underlying elimination kinetics is of the nonlinear Carrier type. Consequently, if scenarios I–III would be true, then a back-calculation procedure based on the assumptions of scenario I would yield biased exposure estimates, but this bias would not be too bad. However, if the Carrier elimination kinetics (as in scenario IV) would be true, then the TCDD exposure of highly contaminated workers would be drastically underestimated when back-calculation was based on a simple linear kinetics. In contrast, the effects of minor or no exposure would be overestimated to some extent. In other words, the TCDD dose metrics is considerably compressed if a linear kinetics is used to reconstruct an actually underlying Carrier kinetics.
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Table 1 Results of the simple linear elimination kinetic back-calculation when applied to ‘‘actual’’ exposures simulated using four different elimination kinetic approaches Assumptions for forward simulation
Back-calculation estimates derived using a simple linear elimination kinetics
Elimination kinetics
Cancer effect
Cancer latency (years)
Half-life (years)
I
No Small
– 0 10 0 10
7.1 7.1 7.1 7.2 7.1
(7.0, (7.0, (7.0, (7.1, (7.0,
– 0 10 0 10
6.7 6.8 6.8 6.7 6.8
– 0 10 0 10 – 0 10 0 10
Strong II
No Small Strong
III
No Small Strong
IV
No Small Strong
Expected median/mean values
Workplace exposure rates (ng TCDD/kg fat/year) Working area 1
Working area 2
7.2) 7.2) 7.2) 7.4) 7.3)
3109 3123 3128 1702 1783
(2730, 3821) (2695, 3614) (2698, 3535) (0.0, 3160) (0.0, 3141)
146 147 146 139 143
(137, (140, (139, (131, (135,
153) 153) 154) 145) 150)
39.2 38.1 39.7 37.7 38.9
(34.5, (34.8, (37.4, (35.3, (36.1,
42.9) 41.7) 42.5) 40.2) 41.1)
5.3 4.7 5.4 4.9 5.4
(1.6, (1.7, (1.6, (3.7, (4.0,
9.7) 7.6) 7.9) 6.0) 6.3)
1.0 0.0 0.0 0.8 0.5
(0.0, (0.0, (0.0, (0.0, (0.0,
5.9) 5.1) 4.6) 2.9) 2.3)
(6.6, (6.7, (6.7, (6.6, (6.6,
6.9) 7.0) 7.0) 6.9) 6.9)
2702 2534 2645 1660 1821
(2369, 3109) (2024, 3219) (2155, 3076) (0.0, 2495) (0.0, 2676)
141 138 138 137 139
(134, (129, (133, (132, (131,
151) 145) 147) 143) 145)
37.8 38.1 37.0 37.7 37.4
(34.4, (33.7, (33.8, (34.7, (35.5,
41.1) 42.3) 40.4) 39.5) 40.2)
5.9 5.5 5.2 5.0 4.6
(2.6, (2.6, (2.8, (3.9, (3.5,
11.3) 8.6) 9.3) 6.4) 6.1)
0.7 1.5 1.2 0.2 0.6
(0.0, (0.0, (0.0, (0.0, (0.0,
5.7) 5.3) 5.4) 1.8) 2.5)
7.1 7.1 7.2 7.0 7.0
(6.9, (6.9, (6.9, (6.8, (6.9,
7.3) 7.3) 7.3) 7.2) 7.2)
2251 (1874, 2721) 2175 (1784, 2766) 2282 (1814, 2750) 776 (0.0, 1991) 1169 (0.0, 1995)
135 133 135 130 133
(127, (128, (127, (122, (124,
144) 141) 142) 137) 140)
36.3 37.8 36.1 35.8 35.2
(32.3, (34.3, (32.8, (33.6, (32.8,
39.8) 40.9) 39.3) 38.3) 37.6)
5.3 5.4 4.8 4.9 4.5
(0.9, (1.6, (2.4, (3.7, (3.3,
10.7) 8.8) 8.0) 5.6) 5.7)
1.9 0.2 1.3 0.3 0.0
(0.0, (0.0, (0.0, (0.0, (0.0,
6.5) 6.6) 7.5) 2.4) 1.8)
6.7 6.9 6.8 6.6 6.7
(6.5, (6.6, (6.5, (6.4, (6.4,
7.0) 7.1) 7.1) 6.9) 7.0)
63.5 (45.5, 93.4) 61.1 (39.6, 87.6) 66.4 (40.4, 97.6) 6.6 (0.0, 165.6) 20.3 (0.0, 96.6)
28.8 28.5 28.6 31.2 31.4
(27.0, (27.1, (26.6, (30.0, (29.1,
17.9 17.6 18.8 18.9 18.9
(16.5, (16.5, (16.5, (17.4, (17.4,
19.1) 18.8) 19.9) 21.0) 20.2)
7.1 7.1 7.3 7.4 7.4
(6.3, (6.7, (6.5, (6.9, (6.5,
8.2) 7.8) 8.1) 8.6) 8.2)
5.5 5.0 5.5 5.8 5.5
(4.7, (3.9, (4.8, (4.5, (4.4,
6.6) 6.2) 7.2) 6.5) 8.1)
3325/3500
143/150
–/–
Working area 3
30.1) 30.2) 30.5) 34.4) 33.2)
Working area 4
38.0/40.0
4.8/5.0
Working area 5
0.0/0.0
The distributions of the estimated half-life (years) and workplace exposure levels (ngTCDD/kgfat/year) are described by medians and lower and upper quartiles (in parentheses). The order of the five working areas corresponds to decreasing true workplace exposure expected from the simulation settings. True median and mean exposure level values are given in the last row. The simulations were performed for the four elimination kinetics I–IV (see Section 2.2.1), three different types of TCDD effect strengths on cancer (no, small, strong), and two different latency times for cancer (0 and 10 years).
3.2. Risk estimates
4. Discussion and conclusion
The impact of carrying-over the uncertainty in TCDDdose estimates onto cancer hazard ratios is shown in Table 2. In the cases of no TCDD cancer effect, hazard ratios of one are to be expected throughout. In the cases of a small or strong cancer effect, the expected hazard ratios would need some elaborate computation; however, they can be expected in the magnitude of the effects observed under elimination kinetic scenario I. The estimated hazard ratios under scenario III show a slight bias if a strong TCDD effect on cancer is assumed. Under elimination kinetics IV (the Carrier kinetics), the spread of the estimated coefficients increases and in the case of a strong cancer effect a considerable positive bias is observed as well. Note that a positive bias corresponds to an overestimate of carcinogenic potency. Both, the increased spread and the positive bias of estimated hazard ratios, are natural consequences of the TCDD dose compression discussed above. These consequences of dose compression on a dose–response relationship (that is, amongst others, a much steeper dose–response curve) are simply exemplified in Figs. 3a and b.
The results of the uncertainty analysis performed in this study show that the results of the Boehringer cohort evaluation may crucially depend on assumptions laid down during the statistical analysis. If exposure is estimated by assuming linear elimination kinetics although a Carrier kinetics actually holds, then a compression effect will be usually observed, that is, high exposures in reality will be underestimated through statistical analysis and low exposures will be overestimated, respectively. Consequently, the estimated individual concentration–time curves will be biased and this bias will carry over on TCDD dose metric values and cancer risk estimates. In summary, if the Carrier model represents actual elimination kinetics, then the use of a simple first-order kinetic model will result in a substantial overestimate of carcinogenic potency (Table 2). There is a note of caution to be sounded in order to prevent too simplistic conclusions from our study. The present study setting mimics the main statistical analyses of the Boehringer cohort, that is, both exposure back-calculation and dose construction (via AULC) are based on simple lin-
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Fig. 2. Exemplification of TCDD concentration in body lipids over time for the four elimination kinetics I–IV (see Section 2.2.1). (a) A workplace exposure of 3500 ngTCDD/kgfat/year in the 1950s followed by a workplace exposure of 150 ngTCDD/kgfat/year until the closing of the plant in 1984. (b) A workplace exposure of 5 ngTCDD/kgfat/year over the same time period. In both Figures, an additional background exposure of 1 ngTCDD/ kgfat/year is assumed.
ear elimination kinetics. Therefore, before the discussion concerning the carcinogenic potential of dioxins, in particular in the low-dose range, can be reasonably resumed, it seems advisable to re-analyse the available data sets of human exposure by using the Carrier kinetics for both exposure back-calculation and dose construction.
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Furthermore, note that although the simulation study tries to mimic the main features of a real occupational cohort, its results should be considered with the usual reserve. Emphasis should therefore not be placed on absolute numerical values of the simulation results, but rather on the relative comparison between the various scenarios, which allow the most interesting insight. The uncertainty assessment presented in this work relies on various assumptions. The effect of latency periods or lag times in the process of cancer development is still an area of research and estimates vary considerably not only between tumors which would be an issue of correct modeling, but also within tumors which could be a problem of limited knowledge, in particular when accounting for genetic variation. The sole utilization of the area under the lipid concentration–time curve as exposure index (i.e. dose metrics) in this investigation may be crucial and needs to be challenged in further studies. Further issues of concern could be laboratory measurement inaccuracies or workplace misclassifications as there is some evidence in Edler (1999) which directly relates to the Boehringer cohort. We also want to make an important clarification with respect to the usage of an uncertainty assessment. An uncertainty assessment, as it was performed here for the Boehringer Cohort addressing the original analysis of Becher et al. (1998), does not aim at blaming the former analysis for its erstwhile assumptions. In contrast, an uncertainty assessment does only make sense if the primary modeling and data analysis is performed in a sound and accurate manner. The role of an uncertainty assessment is to challenge those statistical assumptions of the primary analysis for which alternatives have meanwhile emerged. Challenging assumptions will naturally provoke the question for the plausibility of the considered alternatives, in the present case, for the plausibility of the concentrationdependent TCDD elimination kinetics of Carrier et al. (1995a,b). Repeated TCDD measurements of two highly exposed Viennese women support the Carrier kinetics for TCDD (Geusau et al., 2002). A combined evaluation of the Seveso and Ranch Hand data sets also adds to the plausibility of the Carrier toxicokinetics (Michalek et al., 2002). Recent evaluations of Viennese and Seveso data have produced a similar message (Aylward et al., 2005a). Actually, in the latter case a refined structure of the Carrier kinetics has been developed and employed as a term was added to account for the amount of TCDD eliminated through partitioning from circulating lipids across the lumen of the large intestine into the fecal content (Aylward et al., 2005a). The refined model is called concentration- and age-dependent model of elimination abbreviated as CADM. Recently, the CADM has been used to reconstruct TCDD exposure for the NIOSH cohort (Aylward et al., 2004, 2005a,b). Emond et al. (2004a,b, 2005) extrapolate
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Table 2 Results of the dose–response evaluation. In a Cox proportional hazards model, total cancer mortality was regressed on the time-dependent AULC values chosen as dose metrics Assumed cancer effect
Assumed cancer latency (years)
AULC lag in Cox model (years)
Estimated hazard ratios for different elimination kinetics assumed for forward simulation I
II
III
IV
No
–
0 10 20
1.000 (0.999, 1.001) 1.000 (0.999, 1.001) 1.000 (0.998, 1.001)
1.000 (0.999, 1.001) 1.000 (0.999, 1.001) 1.000 (0.998, 1.002)
1.000 (0.999, 1.001) 1.000 (0.998, 1.002) 1.000 (0.998, 1.002)
0.999 (0.960, 1.030) 0.998 (0.947, 1.034) 0.988 (0.911, 1.065)
0 10 20 0 10 20
1.003 1.004 1.005 1.003 1.003 1.004
(1.002, (1.003, (1.003, (1.002, (1.002, (1.003,
1.004) 1.005) 1.006) 1.003) 1.004) 1.005)
1.004 1.004 1.005 1.003 1.004 1.005
(1.003, (1.003, (1.004, (1.002, (1.002, (1.003,
1.005) 1.005) 1.007) 1.004) 1.005) 1.007)
1.004 1.005 1.006 1.004 1.004 1.006
(1.003, (1.003, (1.004, (1.002, (1.003, (1.004,
1.006) 1.007) 1.009) 1.005) 1.006) 1.007)
1.019 1.020 1.013 1.021 1.019 1.018
(0.983, (0.979, (0.971, (0.979, (0.975, (0.960,
1.039) 1.052) 1.076) 1.045) 1.055) 1.083)
0 10 20 0 10 20
1.028 1.037 1.056 1.022 1.030 1.046
(1.013, (1.016, (1.026, (1.013, (1.017, (1.025,
1.061) 1.087) 1.127) 1.048) 1.069) 1.112)
1.030 1.039 1.053 1.023 1.030 1.047
(1.019, (1.021, (1.032, (1.015, (1.020, (1.029,
1.058) 1.081) 1.103) 1.046) 1.067) 1.105)
1.055 1.074 1.094 1.034 1.043 1.062
(1.024, (1.028, (1.040, (1.019, (1.025, (1.035,
1.070) 1.094) 1.134) 1.049) 1.071) 1.112)
1.180 1.219 1.260 1.187 1.248 1.313
(1.139, (1.172, (1.192, (1.133, (1.182, (1.208,
1.235) 1.291) 1.374) 1.270) 1.349) 1.455)
Small
0
10
Strong
0
10
The computation of the AULC values is based on the simple linear elimination kinetics, thereby the back-calculated half-life and exposure estimates of the respective cohort are used (see Table 1). The distributions of the hazard ratio estimates from Cox model are described by medians and lower and upper quartiles (in parentheses). The hazard ratios correspond to a unit change in the AULC. The results are shown for the four elimination kinetics I–IV (see Section 2.2.1), three different types of TCDD effect strengths on cancer (no, small, strong) and two different latency times for cancer (0 and 10 years) assumed for forward simulation, as well as the three different lag times (0, 10 and 20 years) used for AULC construction in the Cox model.
a physiologically based pharmacokinetic model for rodents to the Viennese and Ranch Hand data sets. Their considerations also strongly support the hypothesis of a dose– dependent TCDD elimination kinetics. Interestingly, the additionally considered TCDD elimination term of the CADM is relatively unimportant at elevated body burdens, but becomes relatively important at low body burdens (Aylward et al., 2005a). For an application of the CADM in the setting of the present study, we would expect that if exposures would be estimated by assuming linear elimination kinetics although the CADM actually holds, then – analogous to the Carrier kinetics – high exposures in reality would have been most probably underestimated through statistical back-calculation. This as well as other implications of the CADM should be explored in further work. The development of the Carrier kinetics and the CADM and the considerations of Emond et al. (2004b, 2005) have considerably increased the understanding of the toxicokinetic and toxicodynamic properties of TCDD in humans. However, as long as those properties are not fully understood, any risk estimate should be considered with caution and supplied with an uncertainty analysis which takes the uncertain knowledge base into account. This is one conclusion to be drawn from the Boehringer Cohort example. The Boehringer Cohort example provides also further insight into the course of action of performing a risk assessment and the scheduling of uncertainty analyses after the primary statistical analysis. Risk management may be tempted to delay regulative decisions as new uncertainty analyses may cast doubt on them in the future. Such a
policy would, however, completely misunderstand the role of uncertainty analysis. We want to stress here that uncertainty analysis never lays blame on anybody. In fact, an uncertainty analysis points out the inevitable uncertainty in risk management decisions and the demand for future re-evaluation of a risk management decision whenever scientifically relevant new aspects emerge. A formal instrument called ex post uncertainty assessment was suggested by Heinzl et al. (2005) to cope with this situation. Whenever newly emerging scientific aspects may seriously question the foundations of the original risk assessment at a later date, there will be a need to address such novel aspects by an ex post uncertainty assessment. The goal is to provide an evaluation of the limits of the available knowledge under the light of the newly emerging scientific aspects, strikingly expressed as ‘‘tell us by how much we can be wrong and still be ok’’ (Bois and Diack, 2005). It was suggested by Heinzl et al. (2005) that this ex post uncertainty assessment should be supervised and fostered by an expert panel formed by toxicologists, statisticians, epidemiologists, risk assessors, risk managers and other stakeholders, both from science and society. The time schedule for the ex post uncertainty assessment, the above mentioned expert panel and a fund-raising scheme should be already set up during the original risk assessment, latest, however, at the time of the original risk management decision. At the lapse of time - and in the case of an unforeseen but vitally important event even before the lapse of time – the expert panel would have to decide on what new scientific aspects would justify an ex post uncertainty assessment.
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Fig. 3. Schematic representation of a dose compression effect. (a) A simple linear dose–response relationship. In (b) the dose scale is compressed around a value of 2.5, that is, dose values originally larger than 2.5 have been decreased and dose values originally smaller than 2.5 have been increased. Consequently, the estimated slope of the regression line increases.
Acknowledgments Parts of this research were performed when one of the authors (H.H.) was visiting scientist at the German Cancer Research Center in Heidelberg, Germany. He was supported by Grant J 1823 (Erwin Schro¨dinger Fellowship) from the Austrian Science Fund. The authors thank two anonymous reviewers for helpful comments that improved the presentation of the paper. References Aylward, L., Brunet, R., Starr, T., Delzell, E., Cheng, H., Beall, C., 2004. Exposure reconstruction for the TCDD-exposed NIOSH cohort using a concentration- and age-dependent model of elimination. Organohalogen Compounds 66, 3394–3400. Aylward, L.L., Brunet, R.C., Carrier, G., Hays, S.M., Cushing, C.A., Needham, L.L., Patterson Jr., D.G., Gerthoux, P.M., Brambilla, P., Mocarelli, P., 2005a. Concentration-dependent TCDD elimination kinetics in humans: toxicokinetic modeling for moderately to highly
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Heinzl, H., Edler, L., 2002. Assessing uncertainty in a toxicokinetic model for human lifetime exposure to TCDD. Organohalogen Compounds 59, 355–358. Heinzl, H., Mittlboeck, M., 2004. Design aspects of a computer simulation study for assessing uncertainty in human lifetime toxicokinetic models. In: Compstat 2004, Proceedings in Computational Statistics. PhysicaVerlag, Heidelberg, pp. 199–211. Heinzl, H., Mittlboeck, M., Edler, L., 2005. On the role of ex post uncertainty assessment for risk management. International Journal of Risk Assessment and Management 5, 206–215. IARC, 1997. Polychlorinated dibenzo-para-dioxins and polychlorinated dibenzofurans. In: IARC Monographs on the Evaluation of Carcinogenic Risks to Humans, vol. 69. International Agency for Research on Cancer, Lyon. McGregor, D.B., Partensky, C., Wilbourn, J., Rice, J.M., 1998. An IARC evaluation of polychlorinated dibenzo-p-dioxins and polychlorinated dibenzofurans as risk factors in human carcinogenesis. Environmental Health Perspectives 106 (Suppl. 2), 755–760.
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On the translation of uncertainty from toxicokinetic to toxicodynamic models – The TCDD example Harald Heinzl a b
a,*
, Martina Mittlbo¨ck
a,1
, Lutz Edler
b,2
Core Unit for Medical Statistics and Informatics, Medical University of Vienna, Spitalgasse 23, A-1090 Vienna, Austria Department for Biostatistics, German Cancer Research Center, Im Neuenheimer Feld 280, D-69120 Heidelberg, Germany Accepted 26 May 2006 Available online 16 January 2007
Abstract When estimating human health risks from exposure to TCDD using toxicokinetic and toxicodynamic models, it is important to understand how model choice and assumptions necessary for modeling add to the uncertainty of risk estimates. Several toxicokinetic models have been proposed for the risk assessment of dioxins, in particular the elimination kinetics in humans has been a matter of constant debate. For a long time, a simple linear elimination kinetics has been common choice. Thus, it was used for the statistical analysis of the largest occupationally exposed cohort, the German Boehringer cohort. We challenge this assumption by considering, amongst others, a nonlinear modified Michaelis–Menten-type elimination kinetics, the so-called Carrier kinetics. Using the area under the lipid TCDD concentration time curve as dose metrics, we model the time to cancerrelated death using the Cox proportional hazards model as toxicodynamic model. This risk assessment set-up was simulated in order to quantify uncertainty of both the dose (TCDD body burden) and the risk estimates, depending on the use of the kinetic model, variations of carcinogenic effect of TCDD and variations of latency period (lag time). If past exposure is estimated assuming a linear elimination kinetics although a Carrier kinetics actually holds, then high exposures in reality will be underestimated through statistical analysis and low exposures will be overestimated, respectively. This bias will carry over on the estimated individual concentration–time curves and the therefrom derived TCDD dose metric values. Using biased dose values when estimating a dose–response relationship will finally lead to biased risk estimates. The extent of bias and the decrease of precision are quantified in selected scenarios through this simulation approach. Our findings are in concordance with recent results in the field of dioxin risk assessment. They also reinforce the general demand for the scheduled uncertainty assessments in risk analyses. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Uncertainty assessment; Simulation study; Carrier kinetics; Workplace exposure; Exposure reconstruction; Area under the lipid concentration time curve (AULC)
1. Introduction Polychlorinated dibenzo-p-dioxins and dibenzofurans (PCDDs/PCDFs) as well as dioxin-like polychlorinated
*
Corresponding author. Tel.: +43 1 40400 6686; fax: +43 1 40400 6687. E-mail addresses: [email protected] (H. Heinzl), [email protected] (M. Mittlbo¨ck), [email protected] (L. Edler). 1 Tel.: +43 1 40400 2276; fax: +43 1 40400 2278. 2 Tel.: +49 6221 42 2392; fax: +49 6221 42 2397. 0045-6535/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.chemosphere.2006.05.130
biphenyls (PCBs) constitute a family of chemicals which are present in both occupational and daily human environments and which are considered as hazardous to humans. International health organizations such as the WHO and the IARC have classified dioxins as human carcinogens and risk specific dose levels have been derived recently (IARC, 1997; WHO, 2000, see also; Gies et al., 2004). Although these efforts of estimating human health risks of PCDDs/PCDFs and dioxin-like PCBs try hard to take statistical uncertainty into account, (e.g. applying 95% confidence intervals or using the Benchmark Dose Lower
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Confidence Limit, as starting point of low-dose extrapolation), most risk assessments do not account for a comprehensive assessment of the uncertainty of risk measures reported to the risk managers. One difficulty for doing so is due to the complexity of the nature of this uncertainty; another obstacle is the lack of methods and algorithms to translate uncertainty from exposure assessment via toxicokinetic modeling to the final risk estimate obtained in a toxicodynamic model. Estimation of human health risks from exposure to PCDDs/PCDFs and dioxin-like PCBs depends on the assessment of exposure to the hazardous compound as well as on its toxicokinetic and toxicodynamic behavior in the human body, or, when risk assessment is based on animal data, in the respective organism examined in a bioassay. Modeling these processes constitutes a basic prerequisite for any quantitative risk assessment, including assessment of the uncertainty of risk estimates. Obviously, the modeling process itself, as part of the risk assessment task, affects the development of valid risk estimates. Due to the wealth of information available on exposure and effects in humans and animals on the prototype compound 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD), an elaboration of uncertainty methods and algorithms for this compound serves as an excellent example. Such an analysis should allow a quantitative evaluation of the uncertainty of TCDD risk estimates, and it should exhibit how toxicokinetic model uncertainty carries over to uncertainty of the dose metrics and the dose–response relationship from which parameters for the risk management interventions are then obtained. In the following, we restrict our uncertainty assessment on the cancer endpoint for convenience and earlier work done in this field. Cancer is usually considered as a slowly evolving disease. An increase in TCDD dose may result in an increase of the observable cancer response not until some latency time period (in the following called lag time) has elapsed. This fact needs careful consideration when a dose–response relationship is to be established. Toxicokinetic models have been developed capable to reconstruct TCDD exposure concentrations during a lifetime, see e.g. Dixit et al. (2003). Thereby, time-dependent TCDD dose metrics like the area under the concentration–time curve were constructed for each person. These measures were then used to determine the exposure level of cohorts, see e.g. occupational cohorts described in Crump et al. (2003). TCDD concentration–time curves of individuals are calculated by combining exposure matrices with individual residence data or, in the case of occupational exposure, by using job exposure matrices and workplace data. Usually, one obtains individual exposure estimates by the socalled back-calculation method. This is mainly a statistical regression model, which relates TCDD concentrations to the exposure matrices and then reconstructs an individual exposure history using all information available for that person. In the case of TCDD, rather high exposures that had occurred in the 1950s could be reconstructed from gen-
erally lower body burdens determined in the 1980s and 1990s when TCDD concentration measurements in human body compartments became accomplishable. This reconstruction is a rather delicate statistical task because of extrapolation beyond the observed range of measurements. Standard statistical model checking techniques of regression (e.g. residual analysis) do not apply and therefore extrapolated results cannot be verified in the usual way. The validity of the results rises and falls with that of the underlying model assumptions. High lipophilicity and slow elimination require careful monitoring of the body fat compartment when TCDD toxicokinetics is modeled in humans. Two, for some time common, but nowadays questionable model assumptions for estimating past TCDD exposure are the assumption of lifetime constancy of the total lipid volume (TLV) of the human body and the assumption of simple linear elimination kinetics of TCDD. Modified Michaelis–Menten kinetics (also known as Carrier kinetics) has been suggested to link the TCDD elimination rate with the TCDD body burden, i.e. the concentration of TCDD in the body (Carrier et al., 1995a,b). Under the Carrier kinetics, TCDD elimination would be faster, or nearly the same rate, or slower than under the simple linear elimination kinetics when the individual would be highly, moderately or slightly contaminated, respectively. In other words, the elimination rate is not constant but depends on the amount of TCDD available for elimination. If exposure would be estimated assuming a linear elimination kinetics although a nonlinear Carrier kinetics actually holds, then a so-called compression effect could bias the outcome data of the toxicokinetic model: truly high exposures will be underestimated with the back-calculation method and low exposures will be overestimated, respectively (Heinzl and Edler, 2002). Consequently, the estimated individual concentration–time curves will be biased and this bias will carry over into TCDD dose metric values and risk estimates (Edler et al., 2004). The present study addresses these issues in detail by the use of extensive computer simulations. Carcinogenicity of TCDD is assumed and effect size and lag time of the carcinogenic effect are varied. However, the statistical analysis strategy is the same procedure as used for the statistical analyses of the Boehringer dioxin cohort (Becher et al., 1998). This allows the assessment of how the estimated half-lives, back-calculated workplace exposure levels, and the subsequently computed cancer risk estimates are affected if the assumptions of statistical analysis differ from toxicokinetic reality. The paper is organized as follows. Section 2 contains a description of the simulation study conditions. The results are presented in Section 3. In Section 4, we discuss potential consequences of our results for the risk assessment of TCDD, and present a strategy to include ex post uncertainty assessments in the risk management process.
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2. Methods
2.2. Design of the simulation study
2.1. The Boehringer cohort
For the uncertainty assessment, various assumptions of the original statistical analysis of Becher et al. (1998) were challenged by means of a computer simulation study. The simulation study was designed to mimic the essential features of the Boehringer cohort’s exposure history. The simulated data were generated under various assumptions reflecting different possible states of the true nature of the elimination kinetics. These data were then analyzed using the statistical evaluation strategy described in Becher et al. (1998). This approach allows the study of the impact of the various assumptions/scenarios on the statistical estimates obtained from the toxicokinetic and, consequently, also from toxicodynamic modeling. To be precise, the simulation study consisted of five main steps (see the rectangles in Fig. 1), briefly described in the next sections (for a more detailed description, see Heinzl and Mittlboeck, 2004).
Occupational cohort studies produced important evidence for the International Agency for Research on Cancer (IARC) evaluation concluding that TCDD is carcinogenic to humans (IARC, 1997; McGregor et al., 1998; Steenland et al., 2004). One of these cohorts was the so-called Boehringer cohort comprising more than 1500 workers mainly engaged in the production of herbicides from 1950 until 1984 in Germany (Flesch-Janys et al., 1995; Becher et al., 1998). In that plant, one was able to identify about 20 different working areas of different exposure types. Information on the exposure was obtained between 1985 and 1994 when TCDD measurements from blood or body fat samples were taken from 245 workers. For the analysis, these areas were clustered into five main areas of sufficiently different TCDD exposure levels. There was, e.g. one working area of the 1950s (see the working area 1 below) which was extremely contaminated, such that some workers still had a high dioxin concentration in their blood more than 30 years later. Their estimated daily TCDD exposure exceeded the largest estimates for the other working areas by more than 20 times. TCDD is a highly lipophilic compound that rapidly distributes in the human body lipids (within days or few weeks), whereas its elimination is a slow process (a matter of years). These observations usually lead to the assumption of a one-compartment mass-balance equation for describing the amount A(t) of TCDD in the body lipids at time t by dAðtÞ=dt ¼ intakeðtÞ eliminationðtÞ: This generic model was adapted for the Boehringer cohort data (Flesch-Janys et al., 1995; Becher et al., 1998) assuming that the total lipid volume (TLV) of the body remained constant over lifetime and that TCDD elimination followed a simple linear kinetics, that is, elimination(t) = keA(t) where ke denotes the elimination rate constant. After adjusting TCDD measurements for German background exposure levels, ke was estimated from data of workers for whom multiple measurements between 1985 and 1994 were made. Working exposure levels in different working areas were estimated by summation of intake over the respective areas. The estimated exposure levels were used together with individual lifetime work history data to compute individual time courses of TCDD exposure for all workers of the cohort. In particular, for modeling the toxicodynamics, the area under the TCDD concentration curve over the time of exposure was used as the dose metrics representing accumulated TCDD exposure. This dose was then the primary explanatory variable in a Cox proportional hazards regression model of cancer mortality (Cox, 1972; Flesch-Janys et al., 1995; Becher et al., 1998).
2.2.1. Simulation of whole cohort Each simulated cohort consisted of 500 (virtual) workers starting to work in 1950 within one of five working areas. The areas exhibited different TCDD exposure levels and each worker’s individual exposure was randomly drawn from a lognormal distribution with mean intakes of 3500, 150, 40, 5 and 0 ngTCDD/kgfat/year, respectively. Mean background exposure intake was set to 1 ngTCDD/kgfat/ year. The dispersion of the lognormal distribution was chosen such that the 99th percentile was two-times the mean intake. The highest workplace exposure of 3500 ngTCDD/ kgfat/year mean intake was assumed as having occurred only in the 1950s (working area 1). Stop of exposure was assumed at plant closure in 1984. Hiring, change of working areas during employment, termination of contract, retirement and death of the workers were simulated using
Fig. 1. Block diagram of the simulation study. There are five main simulation steps, which are represented by rectangles. The circles represent simulation results.
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standard randomly occurring events and random choices between options available at specific time points. For the toxicodynamic model, each worker was assumed as of being under permanent hazard to develop cancer. The increase in cancer hazard was dynamically linked to TCDD exposure via the area under the lipid concentration time curve (AULC) dose metrics. Both the up-to-date and the 10-years-lagged AULC were considered. The dose– response relationship between TCDD and cancer was simulated for the three different effect sizes of no, small and strong effects, respectively. For a (virtual) worker with cancer, an increased mortality hazard was assumed and – provided he was still active in the company – retirement was entailed. At the closing of the plant, each simulated cohort consisted of around 1200 workers representing the male part of the original Boehringer cohort. Four different toxicokinetic scenarios concerning the elimination kinetics were considered: I: Simple linear elimination kinetics, elimination(t) = keA(t), with a total body lipid volume (TLV) which is constant over the worker’s life time II: Simple linear elimination kinetics, elimination(t) = keA(t), with a TLV varying with worker’s age III: Modified simple linear elimination kinetics, elimination(t) = kTS[LVliver(t)/TLV(t)]A(t), according to Thomaseth and Salvan (1998) and a TLV varying with worker’s age IV: Modified Michaelis–Menten-type elimination kinetics, elimination(t) = kC[fmin + (fmax fmin)C(t)/{K + C(t)}]A(t),
according to Carrier et al. (1995a,b) with body weight and a TLV varying with workers age. In the case of a simple linear kinetics (I and II), an elimination half-life of 7 years was assumed (Becher et al., 1998). The age-varying TLV values (scenarios II–IV) were randomly generated by adapting formulas and results as reported by Thomaseth and Salvan (1998). This step in the simulation study could also be called forward simulation. The simulated data from this step are called simulated true values in order to distinguish them from simulated observed values of the next step (Fig. 1). 2.2.2. Measurement conditions The next step of the simulation (see Fig. 1) had to reflect the data collection in the Boehringer cohort. It was assumed that the job-exposure matrix could be reconstructed for all cohort members, as it had been the case in the original evaluation when company-internal records were available. Note that, TCDD measurements were only available for a small number of workers of the Boehringer cohort. Since a considerable portion of them had repeated TCDD measurements, we simulated two TCDD measurement times in 1990 and 1995. At each of the two time
points, each (virtual) worker still living had a chance of 15% to participate in that examination. Whenever a (virtual) worker participated in the first examination, then the chance to participate in the second investigation was set to 60%. The results of this step are the simulated observed values (Fig. 1). 2.2.3. Workplace exposure back-calculation The available simulated observed TCDD values were used for exposure back-calculation that was performed as in the original statistical analyses of the Boehringer cohort (for details see Becher et al., 1998). Simple linear elimination kinetics and constant TLV over lifetime were assumed. The former was the commonly used elimination kinetics at analysis time and the latter was enforced due to lack of appropriate data during the operating period of the plant. Technically, back-calculation was a three-part approach (Becher et al., 1998). First, a simple and robust adjustment for background exposure was performed. Second, the elimination rate constant ke from all workers with more than one TCDD measurement above background level was estimated, and third, from all available TCDD measurements above background level and using the corresponding jobexposure data, the exposure levels of the various working areas were estimated by employing a linear regression model without intercept. If negative exposure estimates were obtained, they were set to zero. Becher et al. (1998) were well aware of the problematic assumption of a constant TLV over lifetime. They tried to overcome it at least partly by applying some form of ad hoc adjustment for the period between the end of workplace exposure and measurement time. This strategy was adopted in the simulation study as well. The results of this simulation step will be estimated working area exposure levels and half-life estimates for the cohort (Fig. 1). These results will refer to a simple linear elimination kinetic back-calculation when the actual forward exposure simulation is performed using the different elimination kinetic approaches I–IV (see Section 2.2.1 above). Additionally, three different types of TCDD effect strengths on cancer (no, small, strong) and two different latency times for cancer (0 and 10 years) will be studied. 2.2.4. Estimation of individual concentration–time curves for whole cohort The cohort’s back-calculated exposure levels and halflife together with individual job-exposure matrices are used to estimate individual lipid concentration–time curves for all cohort members (Fig. 1). Individual dynamic exposure indices can be constructed from these curves, which are always based on the simple linear elimination kinetics, irrespectively whose elimination kinetics has been used in the forward simulation of the cohort. Here only the time-dependent AULC with three different lag times (0, 10 and 20 years) is considered as dynamic exposure index (dose metrics).
H. Heinzl et al. / Chemosphere 67 (2007) S365–S374
2.2.5. Assessing the relationship between exposure and cancer mortality (dose–response modeling) For the assessment of the dose–response relationship between TCDD exposure and cancer mortality, the AULC is used as a time-dependent explanatory variable in a Cox proportional hazards regression model (Cox, 1972; FleschJanys et al., 1995; Becher et al., 1998). Total cancer mortality time is considered as outcome variable. The Cox model then results in hazard ratios as cancer risk estimates for a unit increase in the AULC (Fig. 1). These hazard ratios will be compared for the combination of the elimination kinetics I–IV, different types of TCDD effect strengths on cancer (no, small, strong) and different true latency times for cancer (0 and 10 years) used for forward simulations, and different lag times (0, 10 and 20 years) used for AULC construction in the Cox model, respectively. 2.3. Further technical details of the simulation The SAS software system was used for statistical computations (SAS Institute Inc., Cary, NC, USA). 100 cohorts were simulated whenever the elimination kinetic scenarios I, II and III were considered. The Carrier elimination kinetics of scenario IV resulted in a computationally time-consuming procedure so that only 50 cohorts were simulated then. Contrary to Heinzl and Edler (2002) and Edler et al. (2004), where ad hoc estimates were used, the parameters of the Carrier elimination kinetics, kC, fmin, fmax and K, were set here to values as provided by Carrier et al. (1999). 3. Results In the following, the distributions of the simulation results will be described by median values, lower and upper quartiles. 3.1. Workplace exposure back-calculation Table 1 shows the distribution of the simulation results of the back-calculation analysis described in Section 2.2.3. After adjusting for background exposure in a first step, the half-life of a simple linear kinetics, half-life = log(2)/ke, was estimated from the simulated worker’s data who had TCDD measurements (above background) in 1990 and 1995. Under elimination kinetics I and II, the true half-life was set to a value of 7 years and the half-life estimates for both scenarios are close to it. However, the half-life estimates under the elimination kinetic scenarios III and IV are also quite close to this value. This indicates that the gradients of the TCDD concentration versus time curves under the various elimination kinetic scenarios are obviously quite close 5–10 years after the closing of the virtual plant. The last step of the back-calculation analysis gives estimates of the workplace exposure levels. Table 1 shows
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that the estimates for working areas 2–5 are quite close to the true values for elimination kinetic scenarios I–III. A quite different and more variable outcome is observed for working area 1 under elimination kinetic scenarios I– III. Working area 1 only existed in the 1950s with a mean exposure of 3500 ngTCDD/kgfat/year. All the results for elimination kinetic scenario IV (the Carrier kinetics) are completely different when compared with the other scenarios. For working area 1, one realizes an increasing bias from scenarios I to III. In other words, if the time-varying agedependent change in body lipids is ignored in the analysis due to lack of data, then the effective exposure level will be underestimated. If a strong cancer effect is assumed, then this underestimation will even be larger. This is quite natural as those virtual workers who in the simulation have randomly drawn TCDD exposures below the mean exposure level of that working area will more probably survive until the (virtual) TCDD measurement times. Note that an assumed lag time of 10 years for developing cancer is weakening this effect, since then the chance to experience TCDD measurement in 1990 or 1995 has increased. Technically, the whole problem is called informative missingness and is in concordance with what can be observed in real highrisk cohorts. The simulation shows clearly that a back-calculation based on the simple linear elimination kinetics would completely fail when the elimination kinetics IV (the Carrier kinetics) would hold. Working area 1 of highest exposure would be incredibly underestimated; areas 2 and 3 would still suffer underestimation, whereas for areas 4 and 5 we would observe an exposure overestimation. Figs. 2a and b provide an explanation for this. The Carrier elimination kinetics is not linear. It reaches a saturation level for constant high exposure, but it eliminates high amounts of TCDD from the body much faster than a linear kinetics can do (Fig. 2a). However, in the case of low exposure, it eliminates the compound at a much slower rate than any linear elimination kinetics (Fig. 2b). Notice that the back-calculation is based on the measurement of TCDD values in the 1990s and on this basis of information, we go back in time using the simple linear elimination kinetics. It is obvious that such an approach cannot work if the underlying elimination kinetics is of the nonlinear Carrier type. Consequently, if scenarios I–III would be true, then a back-calculation procedure based on the assumptions of scenario I would yield biased exposure estimates, but this bias would not be too bad. However, if the Carrier elimination kinetics (as in scenario IV) would be true, then the TCDD exposure of highly contaminated workers would be drastically underestimated when back-calculation was based on a simple linear kinetics. In contrast, the effects of minor or no exposure would be overestimated to some extent. In other words, the TCDD dose metrics is considerably compressed if a linear kinetics is used to reconstruct an actually underlying Carrier kinetics.
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Table 1 Results of the simple linear elimination kinetic back-calculation when applied to ‘‘actual’’ exposures simulated using four different elimination kinetic approaches Assumptions for forward simulation
Back-calculation estimates derived using a simple linear elimination kinetics
Elimination kinetics
Cancer effect
Cancer latency (years)
Half-life (years)
I
No Small
– 0 10 0 10
7.1 7.1 7.1 7.2 7.1
(7.0, (7.0, (7.0, (7.1, (7.0,
– 0 10 0 10
6.7 6.8 6.8 6.7 6.8
– 0 10 0 10 – 0 10 0 10
Strong II
No Small Strong
III
No Small Strong
IV
No Small Strong
Expected median/mean values
Workplace exposure rates (ng TCDD/kg fat/year) Working area 1
Working area 2
7.2) 7.2) 7.2) 7.4) 7.3)
3109 3123 3128 1702 1783
(2730, 3821) (2695, 3614) (2698, 3535) (0.0, 3160) (0.0, 3141)
146 147 146 139 143
(137, (140, (139, (131, (135,
153) 153) 154) 145) 150)
39.2 38.1 39.7 37.7 38.9
(34.5, (34.8, (37.4, (35.3, (36.1,
42.9) 41.7) 42.5) 40.2) 41.1)
5.3 4.7 5.4 4.9 5.4
(1.6, (1.7, (1.6, (3.7, (4.0,
9.7) 7.6) 7.9) 6.0) 6.3)
1.0 0.0 0.0 0.8 0.5
(0.0, (0.0, (0.0, (0.0, (0.0,
5.9) 5.1) 4.6) 2.9) 2.3)
(6.6, (6.7, (6.7, (6.6, (6.6,
6.9) 7.0) 7.0) 6.9) 6.9)
2702 2534 2645 1660 1821
(2369, 3109) (2024, 3219) (2155, 3076) (0.0, 2495) (0.0, 2676)
141 138 138 137 139
(134, (129, (133, (132, (131,
151) 145) 147) 143) 145)
37.8 38.1 37.0 37.7 37.4
(34.4, (33.7, (33.8, (34.7, (35.5,
41.1) 42.3) 40.4) 39.5) 40.2)
5.9 5.5 5.2 5.0 4.6
(2.6, (2.6, (2.8, (3.9, (3.5,
11.3) 8.6) 9.3) 6.4) 6.1)
0.7 1.5 1.2 0.2 0.6
(0.0, (0.0, (0.0, (0.0, (0.0,
5.7) 5.3) 5.4) 1.8) 2.5)
7.1 7.1 7.2 7.0 7.0
(6.9, (6.9, (6.9, (6.8, (6.9,
7.3) 7.3) 7.3) 7.2) 7.2)
2251 (1874, 2721) 2175 (1784, 2766) 2282 (1814, 2750) 776 (0.0, 1991) 1169 (0.0, 1995)
135 133 135 130 133
(127, (128, (127, (122, (124,
144) 141) 142) 137) 140)
36.3 37.8 36.1 35.8 35.2
(32.3, (34.3, (32.8, (33.6, (32.8,
39.8) 40.9) 39.3) 38.3) 37.6)
5.3 5.4 4.8 4.9 4.5
(0.9, (1.6, (2.4, (3.7, (3.3,
10.7) 8.8) 8.0) 5.6) 5.7)
1.9 0.2 1.3 0.3 0.0
(0.0, (0.0, (0.0, (0.0, (0.0,
6.5) 6.6) 7.5) 2.4) 1.8)
6.7 6.9 6.8 6.6 6.7
(6.5, (6.6, (6.5, (6.4, (6.4,
7.0) 7.1) 7.1) 6.9) 7.0)
63.5 (45.5, 93.4) 61.1 (39.6, 87.6) 66.4 (40.4, 97.6) 6.6 (0.0, 165.6) 20.3 (0.0, 96.6)
28.8 28.5 28.6 31.2 31.4
(27.0, (27.1, (26.6, (30.0, (29.1,
17.9 17.6 18.8 18.9 18.9
(16.5, (16.5, (16.5, (17.4, (17.4,
19.1) 18.8) 19.9) 21.0) 20.2)
7.1 7.1 7.3 7.4 7.4
(6.3, (6.7, (6.5, (6.9, (6.5,
8.2) 7.8) 8.1) 8.6) 8.2)
5.5 5.0 5.5 5.8 5.5
(4.7, (3.9, (4.8, (4.5, (4.4,
6.6) 6.2) 7.2) 6.5) 8.1)
3325/3500
143/150
–/–
Working area 3
30.1) 30.2) 30.5) 34.4) 33.2)
Working area 4
38.0/40.0
4.8/5.0
Working area 5
0.0/0.0
The distributions of the estimated half-life (years) and workplace exposure levels (ngTCDD/kgfat/year) are described by medians and lower and upper quartiles (in parentheses). The order of the five working areas corresponds to decreasing true workplace exposure expected from the simulation settings. True median and mean exposure level values are given in the last row. The simulations were performed for the four elimination kinetics I–IV (see Section 2.2.1), three different types of TCDD effect strengths on cancer (no, small, strong), and two different latency times for cancer (0 and 10 years).
3.2. Risk estimates
4. Discussion and conclusion
The impact of carrying-over the uncertainty in TCDDdose estimates onto cancer hazard ratios is shown in Table 2. In the cases of no TCDD cancer effect, hazard ratios of one are to be expected throughout. In the cases of a small or strong cancer effect, the expected hazard ratios would need some elaborate computation; however, they can be expected in the magnitude of the effects observed under elimination kinetic scenario I. The estimated hazard ratios under scenario III show a slight bias if a strong TCDD effect on cancer is assumed. Under elimination kinetics IV (the Carrier kinetics), the spread of the estimated coefficients increases and in the case of a strong cancer effect a considerable positive bias is observed as well. Note that a positive bias corresponds to an overestimate of carcinogenic potency. Both, the increased spread and the positive bias of estimated hazard ratios, are natural consequences of the TCDD dose compression discussed above. These consequences of dose compression on a dose–response relationship (that is, amongst others, a much steeper dose–response curve) are simply exemplified in Figs. 3a and b.
The results of the uncertainty analysis performed in this study show that the results of the Boehringer cohort evaluation may crucially depend on assumptions laid down during the statistical analysis. If exposure is estimated by assuming linear elimination kinetics although a Carrier kinetics actually holds, then a compression effect will be usually observed, that is, high exposures in reality will be underestimated through statistical analysis and low exposures will be overestimated, respectively. Consequently, the estimated individual concentration–time curves will be biased and this bias will carry over on TCDD dose metric values and cancer risk estimates. In summary, if the Carrier model represents actual elimination kinetics, then the use of a simple first-order kinetic model will result in a substantial overestimate of carcinogenic potency (Table 2). There is a note of caution to be sounded in order to prevent too simplistic conclusions from our study. The present study setting mimics the main statistical analyses of the Boehringer cohort, that is, both exposure back-calculation and dose construction (via AULC) are based on simple lin-
H. Heinzl et al. / Chemosphere 67 (2007) S365–S374
Fig. 2. Exemplification of TCDD concentration in body lipids over time for the four elimination kinetics I–IV (see Section 2.2.1). (a) A workplace exposure of 3500 ngTCDD/kgfat/year in the 1950s followed by a workplace exposure of 150 ngTCDD/kgfat/year until the closing of the plant in 1984. (b) A workplace exposure of 5 ngTCDD/kgfat/year over the same time period. In both Figures, an additional background exposure of 1 ngTCDD/ kgfat/year is assumed.
ear elimination kinetics. Therefore, before the discussion concerning the carcinogenic potential of dioxins, in particular in the low-dose range, can be reasonably resumed, it seems advisable to re-analyse the available data sets of human exposure by using the Carrier kinetics for both exposure back-calculation and dose construction.
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Furthermore, note that although the simulation study tries to mimic the main features of a real occupational cohort, its results should be considered with the usual reserve. Emphasis should therefore not be placed on absolute numerical values of the simulation results, but rather on the relative comparison between the various scenarios, which allow the most interesting insight. The uncertainty assessment presented in this work relies on various assumptions. The effect of latency periods or lag times in the process of cancer development is still an area of research and estimates vary considerably not only between tumors which would be an issue of correct modeling, but also within tumors which could be a problem of limited knowledge, in particular when accounting for genetic variation. The sole utilization of the area under the lipid concentration–time curve as exposure index (i.e. dose metrics) in this investigation may be crucial and needs to be challenged in further studies. Further issues of concern could be laboratory measurement inaccuracies or workplace misclassifications as there is some evidence in Edler (1999) which directly relates to the Boehringer cohort. We also want to make an important clarification with respect to the usage of an uncertainty assessment. An uncertainty assessment, as it was performed here for the Boehringer Cohort addressing the original analysis of Becher et al. (1998), does not aim at blaming the former analysis for its erstwhile assumptions. In contrast, an uncertainty assessment does only make sense if the primary modeling and data analysis is performed in a sound and accurate manner. The role of an uncertainty assessment is to challenge those statistical assumptions of the primary analysis for which alternatives have meanwhile emerged. Challenging assumptions will naturally provoke the question for the plausibility of the considered alternatives, in the present case, for the plausibility of the concentrationdependent TCDD elimination kinetics of Carrier et al. (1995a,b). Repeated TCDD measurements of two highly exposed Viennese women support the Carrier kinetics for TCDD (Geusau et al., 2002). A combined evaluation of the Seveso and Ranch Hand data sets also adds to the plausibility of the Carrier toxicokinetics (Michalek et al., 2002). Recent evaluations of Viennese and Seveso data have produced a similar message (Aylward et al., 2005a). Actually, in the latter case a refined structure of the Carrier kinetics has been developed and employed as a term was added to account for the amount of TCDD eliminated through partitioning from circulating lipids across the lumen of the large intestine into the fecal content (Aylward et al., 2005a). The refined model is called concentration- and age-dependent model of elimination abbreviated as CADM. Recently, the CADM has been used to reconstruct TCDD exposure for the NIOSH cohort (Aylward et al., 2004, 2005a,b). Emond et al. (2004a,b, 2005) extrapolate
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Table 2 Results of the dose–response evaluation. In a Cox proportional hazards model, total cancer mortality was regressed on the time-dependent AULC values chosen as dose metrics Assumed cancer effect
Assumed cancer latency (years)
AULC lag in Cox model (years)
Estimated hazard ratios for different elimination kinetics assumed for forward simulation I
II
III
IV
No
–
0 10 20
1.000 (0.999, 1.001) 1.000 (0.999, 1.001) 1.000 (0.998, 1.001)
1.000 (0.999, 1.001) 1.000 (0.999, 1.001) 1.000 (0.998, 1.002)
1.000 (0.999, 1.001) 1.000 (0.998, 1.002) 1.000 (0.998, 1.002)
0.999 (0.960, 1.030) 0.998 (0.947, 1.034) 0.988 (0.911, 1.065)
0 10 20 0 10 20
1.003 1.004 1.005 1.003 1.003 1.004
(1.002, (1.003, (1.003, (1.002, (1.002, (1.003,
1.004) 1.005) 1.006) 1.003) 1.004) 1.005)
1.004 1.004 1.005 1.003 1.004 1.005
(1.003, (1.003, (1.004, (1.002, (1.002, (1.003,
1.005) 1.005) 1.007) 1.004) 1.005) 1.007)
1.004 1.005 1.006 1.004 1.004 1.006
(1.003, (1.003, (1.004, (1.002, (1.003, (1.004,
1.006) 1.007) 1.009) 1.005) 1.006) 1.007)
1.019 1.020 1.013 1.021 1.019 1.018
(0.983, (0.979, (0.971, (0.979, (0.975, (0.960,
1.039) 1.052) 1.076) 1.045) 1.055) 1.083)
0 10 20 0 10 20
1.028 1.037 1.056 1.022 1.030 1.046
(1.013, (1.016, (1.026, (1.013, (1.017, (1.025,
1.061) 1.087) 1.127) 1.048) 1.069) 1.112)
1.030 1.039 1.053 1.023 1.030 1.047
(1.019, (1.021, (1.032, (1.015, (1.020, (1.029,
1.058) 1.081) 1.103) 1.046) 1.067) 1.105)
1.055 1.074 1.094 1.034 1.043 1.062
(1.024, (1.028, (1.040, (1.019, (1.025, (1.035,
1.070) 1.094) 1.134) 1.049) 1.071) 1.112)
1.180 1.219 1.260 1.187 1.248 1.313
(1.139, (1.172, (1.192, (1.133, (1.182, (1.208,
1.235) 1.291) 1.374) 1.270) 1.349) 1.455)
Small
0
10
Strong
0
10
The computation of the AULC values is based on the simple linear elimination kinetics, thereby the back-calculated half-life and exposure estimates of the respective cohort are used (see Table 1). The distributions of the hazard ratio estimates from Cox model are described by medians and lower and upper quartiles (in parentheses). The hazard ratios correspond to a unit change in the AULC. The results are shown for the four elimination kinetics I–IV (see Section 2.2.1), three different types of TCDD effect strengths on cancer (no, small, strong) and two different latency times for cancer (0 and 10 years) assumed for forward simulation, as well as the three different lag times (0, 10 and 20 years) used for AULC construction in the Cox model.
a physiologically based pharmacokinetic model for rodents to the Viennese and Ranch Hand data sets. Their considerations also strongly support the hypothesis of a dose– dependent TCDD elimination kinetics. Interestingly, the additionally considered TCDD elimination term of the CADM is relatively unimportant at elevated body burdens, but becomes relatively important at low body burdens (Aylward et al., 2005a). For an application of the CADM in the setting of the present study, we would expect that if exposures would be estimated by assuming linear elimination kinetics although the CADM actually holds, then – analogous to the Carrier kinetics – high exposures in reality would have been most probably underestimated through statistical back-calculation. This as well as other implications of the CADM should be explored in further work. The development of the Carrier kinetics and the CADM and the considerations of Emond et al. (2004b, 2005) have considerably increased the understanding of the toxicokinetic and toxicodynamic properties of TCDD in humans. However, as long as those properties are not fully understood, any risk estimate should be considered with caution and supplied with an uncertainty analysis which takes the uncertain knowledge base into account. This is one conclusion to be drawn from the Boehringer Cohort example. The Boehringer Cohort example provides also further insight into the course of action of performing a risk assessment and the scheduling of uncertainty analyses after the primary statistical analysis. Risk management may be tempted to delay regulative decisions as new uncertainty analyses may cast doubt on them in the future. Such a
policy would, however, completely misunderstand the role of uncertainty analysis. We want to stress here that uncertainty analysis never lays blame on anybody. In fact, an uncertainty analysis points out the inevitable uncertainty in risk management decisions and the demand for future re-evaluation of a risk management decision whenever scientifically relevant new aspects emerge. A formal instrument called ex post uncertainty assessment was suggested by Heinzl et al. (2005) to cope with this situation. Whenever newly emerging scientific aspects may seriously question the foundations of the original risk assessment at a later date, there will be a need to address such novel aspects by an ex post uncertainty assessment. The goal is to provide an evaluation of the limits of the available knowledge under the light of the newly emerging scientific aspects, strikingly expressed as ‘‘tell us by how much we can be wrong and still be ok’’ (Bois and Diack, 2005). It was suggested by Heinzl et al. (2005) that this ex post uncertainty assessment should be supervised and fostered by an expert panel formed by toxicologists, statisticians, epidemiologists, risk assessors, risk managers and other stakeholders, both from science and society. The time schedule for the ex post uncertainty assessment, the above mentioned expert panel and a fund-raising scheme should be already set up during the original risk assessment, latest, however, at the time of the original risk management decision. At the lapse of time - and in the case of an unforeseen but vitally important event even before the lapse of time – the expert panel would have to decide on what new scientific aspects would justify an ex post uncertainty assessment.
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Fig. 3. Schematic representation of a dose compression effect. (a) A simple linear dose–response relationship. In (b) the dose scale is compressed around a value of 2.5, that is, dose values originally larger than 2.5 have been decreased and dose values originally smaller than 2.5 have been increased. Consequently, the estimated slope of the regression line increases.
Acknowledgments Parts of this research were performed when one of the authors (H.H.) was visiting scientist at the German Cancer Research Center in Heidelberg, Germany. He was supported by Grant J 1823 (Erwin Schro¨dinger Fellowship) from the Austrian Science Fund. The authors thank two anonymous reviewers for helpful comments that improved the presentation of the paper. References Aylward, L., Brunet, R., Starr, T., Delzell, E., Cheng, H., Beall, C., 2004. Exposure reconstruction for the TCDD-exposed NIOSH cohort using a concentration- and age-dependent model of elimination. Organohalogen Compounds 66, 3394–3400. Aylward, L.L., Brunet, R.C., Carrier, G., Hays, S.M., Cushing, C.A., Needham, L.L., Patterson Jr., D.G., Gerthoux, P.M., Brambilla, P., Mocarelli, P., 2005a. Concentration-dependent TCDD elimination kinetics in humans: toxicokinetic modeling for moderately to highly
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