University of Southern Denmark
Benchmark dose calculation from epidemiological data
Budtz-Jørgensen, E.; Keiding, N.; Grandjean, P.
Published in:
Biometrics
DOI:
10.1111/j.0006-341x.2001.00698.x
Publication date:
2001
Document version:
Submitted manuscript
Citation for pulished version (APA):
Budtz-Jørgensen, E., Keiding, N., & Grandjean, P. (2001). Benchmark dose calculation from epidemiological
data.
Biometrics
,
57
, 698-706. https://doi.org/10.1111/j.0006-341x.2001.00698.x
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1
Benchmark Dose Calculation from
Epidemiological Data
Esb en Budtz-Jørgensen,
1
;?
Niels Keiding,
1
and Philipp e Grandjean
2
1
Department of Biostatistics, University of Cop enhagen
Blegdamsvej 3, DK-2200 Cop enhagen N, Denmark.
2
Institute of Public Health, University of Southern Denmark
Winslowparken 17, DK-5000 Odense C, Denmark.
?
email:
eb j@biostat.ku.dk
Summary
. A threshold for dose-dep endent toxicity is crucial for standards setting, but
may not b e p ossible to sp ecify from empirical studies. Crump (1984) instead prop osed to
calculate the lower statistical condence b ound of the b enchmark dose, which he dened
as the dose that causes a small excess risk. This concept has several advantages and has
b een adopted by regulatory agencies for establishing safe exp osure limits for toxic sub-
stances such as mercury. We have examined the validity of this method as applied to an
epidemiological study of continuous resp onse data asso ciated with mercury exp osure. For
mo dels that are linear in the parameters we derived an approximative expression for the
lower condence b ound of the b enchmark dose. We nd that the benchmark calculations
are highly dep endent up on the choice of the dose-eect function and the denition of the
b enchmark dose. We therefore recommend that several sets of biologically relevant default
settings b e used to illustrate the eect on the b enchmark results and to stimulate research
that will guide an a priori choice of prop er default settings.
Key words
: Condence limits; Environmental epidemiology; Exp osure standards; Mo del
dep endence; Multiple regression.
1 Intro duction
When regulatory agencies pro duce exposure limits, the decisions are based on available
do cumentation on adverse eects of the chemical in question (WHO, 1994). As thresholds
may b e dicult to derive from empirical studies, the b enchmark dose (BMD) (Crump,
1984, 1995) has b een dened as the dose of a toxic comp ound which increases the prob-
ability of an abnormal resp onse by a b enchmark resp onse (BMR), i.e., from
P
0
for an
unexp osed sub ject to
P
0
+BMR for a sub ject at the BMD. The BMDL is a statistical
lower condence limit of the BMD. An advantage of this approach is that it takes into
consideration b oth biological variation and statistical uncertainty.
2
The b enchmark metho d is applicable to b oth categorical and continuous exp osure data,
including epidemiological data that may involve a continuous exp osure scale, a graded
resp onse parameter, and potential confounding eects of covariates. Most recently, the
Reference Dose for methylmercury of the U.S. Environmental Protection Agency (EPA)
was based on b enchmark calculations, and a National Academy of Sciences (NAS) com-
mittee reviewed and approved the metho dology (2000).
The b enchmark calculations dep end on the default settings for several parameters: A 10%
BMR has b een prop osed for animal exp eriments on developmental toxicity (Allen et al.,
1994). However, a BMR of 5% was used by EPA and NAS, b ecause it corresp onds to a
doubling of the prevalence of a pathological response,
P
0
, which was dened as 5%. As
dose-resp onse function, the EPA (1997) used the average for the polynomial and Weibull
mo dels for dichotomous methylmercury eects, while for continuous resp onses, the NAS
committee (2000) chose a p ower function.
The present pap er provides a systematical statistical discussion of the b enchmark approach
as applied in environmental epidemiology. As our example, we use data from a large
epidemiological study p erformed on the Faro e Islands to investigate the health eects of
prenatal mercury exp osure. This study was identied by the NAS committee (2000) as
the critical epidemiological study of mercury toxicity. In adapting the original b enchmark
concept, the metho d must b e extended to allow confounder correction. An approximative
expression for the BMDL in linear mo dels is derived, and the mo del dep endence of the
b enchmark approach is investigated. Approximative condence limits for the excess risk at
a given dose are derived, and BMDL calculation in more complex linear mo dels is discussed
in regard to the wider applicability of this approach.
2 The Faroese Mercury Study
Methylmercury is a common contaminant in seafo o d and freshwater sh. While adverse
eects have b een unequivo cally demonstrated in p oisoning incidents, the implications of
lower-level exposures in sh eating p opulations have b een controversial (Grandjean, 1999).
This issue was therefore explored in a birth cohort of 1022 children from the Faro e Islands.
Information about the children's prenatal exp osure was obtained by measuring the mercury
concentrations in maternal hair at parturition and in cord blo o d. The latter biomarker
was thought to b e the b est indicator of the amount of the neurotoxicant that had reached
the fetal circulation. Because the eects of fetal exp osure to methylmercury are p ersistent,
the children underwent a detailed neuropsychological examination, at age 7 years, when
advanced neurob ehavioral testing would b e feasible. We shall use as an example the Boston
Naming Test, a cognitive task reecting language ability. This test was also used by the
NAS committee (2000) to calculate benchmark doses. In this test the child is presented
with drawings of ob jects, which the child has to name. As test score we use the numb er
3
of ob jects that the child failed to identify. Because of the large number of drawings
and b ecause on average about half of these drawings are identied the distribution of
this outcome variable, given important predictors, is approximately normal. In multiple
regression analysis Grandjean et al. (1997) estimated that a 10-fold increase in the cord
blo o d mercury concentration causes a test score decit of ab out 1.9 p oints (
p
<0.0001).
3 The Benchmark Approach for Exp erimental Data
The b enchmark concept was rst developed for standardized exp erimental dichotomous
(normal/abnormal) resp onses (Crump, 1984), and was later extended to also cover con-
tinuous resp onse data (Crump, 1995), which we shall consider. Let
Y
(
d
)
denote the re-
sp onse of a sub ject at exp osure
d
. Large resp onses are assumed to b e disadvantageous.
The denition of the b enchmark dose (BMD) is sp ecic to a dose-resp onse model. In this
section only mo dels of the following form will b e considered
Y
(
d
) =
f
(
d
) +
;
where
N
(0
;
2
)
, that is, at a given dose
d
the resp onse is assumed to b e normally
distributed with mean given by the dose-resp onse function
f
and standard deviation
. The
dose-resp onse function is monotone and may dep end on known and unknown parameters.
For example, Crump (1984, 1995) suggested a family of p ower functions, the so-called
K
-p ower mo del:
f
(
d
) =
0
+
d
K
, where
0
;
and
K
1
are parameters to b e estimated
from the data.
To dene the BMD it is necessary to specify the abnormal performance. For continuous
data, a cut-o level
(
x
0
)
can b e sp ecied ab ove which all resp onses are considered abnormal.
The probability of an abnormal resp onse in an unexp osed sub ject is then
P
0
=
P
f
Y
(0)
> x
0
g
= 1
f
x
0
f
(0)
g
;
(1)
where
is the standard cumulative normal distribution function. Rather than sp ecifying
x
0
directly one can also sp ecify the p ercentage of unexp osed sub jects whose resp onses are
considered abnormal, i.e.
P
0
,
x
0
can then be calculated by applying equation (1). Often
P
0
is set at 5%. The BMD is dened as the dose that results in an increased probability
of an abnormal test p erformance by a b enchmark resp onse (BMR), i.e., the BMD satises
P
f
Y
(
BMD
)
> x
0
g
P
0
=
BMR. Figure 1 gives a graphical illustration of the BMD
denition.
The BMDL is calculated as the statistical 95% lower (one-sided) condence b ound of the
BMD. In this way the p ower of the study is taken into account. The less the precision the
lower the BMDL.
4
The BMR is often set at 5% so that the corresp onding BMD will double the risk of an
abnormal resp onse, given that
P
0
is 5% (NAS, 2000). Everything else b eing equal, lower
BMRs will result in lower BMDs.
Figure 1: Hyp othetical dose-resp onse relation illustrating the concepts of b enchmark ap-
proach. The dose-resp onse curve indicates that when the dose increases so do es the exp ec-
ted resp onse. The distribution of resp onses in unexp osed sub jects is shown on the
y
-axis.
Resp onses ab ove the presp ecied
x
0
are considered abnormal. The risk of an abnormal
resp onse in unexp osed sub jects is
P
0
indicated by the shaded area. At the BMD the
resp onse distribution has been translated upward and the risk of an abnormal resp onse
has increased to
P
0
+BMR. The BMDL is placed somewhere b etween 0 and the estimated
BMD dep ending on the amount of information in the study.