Estimacion farmacocinetica que soporta la inocuidad del timerosal en vacunas de influenza

1. Risk Analysis
DOI: 10.1111/risa.12124
A Comparative Pharmacokinetic Estimate of Mercury in
U.S. Infants Following Yearly Exposures to Inactivated
Influenza Vaccines Containing Thimerosal
Robert J. Mitkus,1,∗ David B. King,1,2 Mark O. Walderhaug,1 and Richard A. Forshee1
The use of thimerosal preservative in childhood vaccines has been largely eliminated over the
past decade in the United States because vaccines have been reformulated in single-dose vials
that do not require preservative. An exception is the inactivated influenza vaccines, which are
formulated in both multidose vials requiring preservative and preservative-free single-dose
vials. As part of an ongoing evaluation by USFDA of the safety of biologics throughout their
lifecycle, the infant body burden of mercury following scheduled exposures to thimerosal
preservative in inactivated influenza vaccines in the United States was estimated and compared to the infant body burden of mercury following daily exposures to dietary methylmercury at the reference dose established by the USEPA. Body burdens were estimated using kinetic parameters derived from experiments conducted in infant monkeys that were exposed
episodically to thimerosal or MeHg at identical doses. We found that the body burden of
mercury (AUC) in infants (including low birth weight) over the first 4.5 years of life following
yearly exposures to thimerosal was two orders of magnitude lower than that estimated for exposures to the lowest regulatory threshold for MeHg over the same time period. In addition,
peak body burdens of mercury following episodic exposures to thimerosal in this worst-case
analysis did not exceed the corresponding safe body burden of mercury from methylmercury
at any time, even for low-birth-weight infants. Our pharmacokinetic analysis supports the
acknowledged safety of thimerosal when used as a preservative at current levels in certain
multidose infant vaccines in the United States.
KEY WORDS: MeHg; modeling; pharmacokinetics; safety; thimerosal
1. INTRODUCTION
tally contaminated, as might occur with repeated
puncture of multidose vials. Since the 1930s,
thimerosal has been used as the preservative of
choice for vaccines formulated in multidose vials because of its effective antimicrobial activity and nonreactivity with vaccine components that could lead to
a loss of potency. In the late 1990s, as the number of
thimerosal-containing childhood vaccines increased,
concern arose that the higher levels of exposure
of infants and children to the thimerosal metabolite, ethylmercury, might lead to neurotoxicity, based
on comparisons with the related organomercurial,
methylmercury.(1,2) While recognizing the absence of
evidence of harm from exposure to low levels of
thimerosal used in vaccines in the late 1990s, as a
The U.S. Code of Federal Regulations (CFR)
generally requires the addition of a preservative
to multidose vials of vaccines to prevent microbial
growth in the event that the vaccine is acciden1 Office
of Biostatistics and Epidemiology, USFDA Center for
Biologics Evaluation and Research, Rockville, MD, USA.
2 Co-first author; current address: Office of New Animal Drug
Evaluation, Center for Veterinary Medicine, Rockville, MD,
USA.
∗ Address correspondence to Robert J. Mitkus, Office of Biostatistics and Epidemiology, USFDA Center for Biologics Evaluation
and Research, 1401 Rockville Pike, HFM-210, Rockville, MD
20852, USA; tel: 301-827-6083; robert.mitkus@fda.hhs.gov.
1
0272-4332/13/0100-0001$22.00/1
Published 2013. This article is a U.S. Government work and is in the public domain in the USA.

2. 2
precautionary measure, the American Academy of
Pediatrics (AAP), in a joint statement with the Public
Health Service (PHS), in July 1999 and later agreed
to by the American Association of Family Physicians
(AAFP), established the goal of removing thimerosal
as soon as possible from vaccines routinely recommended for infants.(3) Within a few years, vaccine
manufacturers voluntarily reformulated childhood
vaccines in single-dose vials, which do not contain
preservative.
However, subsequent evaluation by the National
Academy of Sciences Institute of Medicine (IOM),
which reviewed epidemiological evidence from the
United States, Denmark, Sweden, and the United
Kingdom, as well as studies of biological mechanisms
related to vaccines and autism, indicated that that
body of scientific evidence did not support a causal
relationship between thimerosal-containing vaccines
and autism.(4) The more recent epidemiological literature has also failed to support a causal relationship
between prenatal, neonatal, or postnatal exposure to
thimerosal in vaccines and a host of neuropsychological outcomes, including autism.(5–11) In 2006, the
American College of Medical Toxicology (ACMT)
ratified the conclusions of the IOM,(12) and in that
same year, the World Health Organization issued a
statement on thimerosal through the Global Advisory Committee on Vaccine Safety (GACVS), which
concluded that there was no evidence of toxicity in
infants, children, or adults exposed to thimerosal in
vaccines.(13) That statement applied to the full suite
of recommended infant and childhood vaccines containing thimerosal, which are used extensively outside the United States starting at birth. In 2012, following a more recent, comprehensive assessment of
the safety database for thimerosal, the World Health
Organization’s GACVS reaffirmed its previous statement and concluded that a link between thimerosal
at current levels in vaccines and neurotoxicity was
“biologically implausible.”(14) That conclusion was
based on an assessment of the best and most relevant
epidemiological, toxicological, and pharmacokinetic
data in humans and experimental animals.
As mentioned, the decision to remove
thimerosal from routine infant vaccines in the
United States over a decade ago was a precautionary
one. It was based on a comparison of cumulative,
nominal doses of intramuscular vaccine thimerosal
to safe dietary doses of MeHg, but did not take into
account the differences in pharmacokinetics between
those two distinct organomercurials, especially their
distribution, metabolism, and excretion following
Mitkus et al.
absorption.(1,15) Since 2001, a number of studies
have been performed that have specifically investigated the pharmacokinetics of thimerosal either
alone or in comparison to MeHg within the same
study. Taken together, these studies have indicated
that thimerosal is cleared much more rapidly from
the bodies of infant or adult humans, nonhuman
primates, and rodents than is MeHg.(16–26) As a
result, comparisons of nominal doses of thimerosal
with nominal doses of MeHg will overestimate the
risk of thimerosal toxicity, while calculations of
cumulative external exposures to either compound
are misleading.(27) Despite the reasonableness of
those observations, however, no one has applied
this new pharmacokinetic information to estimate
internal mercury exposures from thimerosal at levels
currently found in infant vaccines in the United
States. This would be essential, because internal
exposures are more predictive of the potential
biological effects of xenobiotics, whether beneficial
or adverse, than nominal or external dose.(28,29)
Currently in the United States, only certain
inactivated influenza vaccines contain thimerosal
preservative. All other U.S. vaccines routinely
recommended for children six years of age or under do not contain thimerosal preservative or contain thimerosal only in trace amounts (≤1 μg mercury/dose). Inactivated influenza vaccines continue
to be marketed in both single-dose, preservative-free
and multidose, thimerosal-preservative-containing
(0.01%, w/v; 0.005% mercury, w/v) formulations in
the United States because the amount of available
preservative-free inactivated influenza vaccine is below the amount needed to immunize all infants and
children each season. Because some children may be
exposed to low levels of thimerosal from influenza
vaccines packaged in multidose vials, we have developed a quantitative pharmacokinetic model that estimates internal exposures to thimerosal at current
U.S. levels and compares them to predicted internal
levels of mercury from dietary MeHg exposures at
the USEPA reference dose (RfD).
2. METHODS
2.1. Mercury Exposures from Either Influenza
Vaccine or Diet
2.1.1. Vaccine Thimerosal
The most recent recommended immunization
schedule for persons aged 0–18 years(30) was utilized

3. Comparative Pharmacokinetic Estimate of Mercury in U.S. Infants
Table I. Earliest Maximum Mercury Exposures from Seasonal
Inactivated Influenza Vaccines Administered to Infants Over the
First 4.5 Years of Life According to the 2013 ACIP Vaccination
Schedule; Mercury Exposures Increase in Third Year of Life Due
to Increased Volume of Fluzone R Vaccine Administered at That
Age; Doses Normalized to Body Weight (bw) Are Based on the
5th and 50th Percentiles for Body Weight in U.S. Infants 0–60
Months of Age(35)
Postnatal Age
of Administration
Mercury
Exposure (μg)
Dose
(μg/kg bw)
12.5
(each)
12.5
12.5
25
25
1.5–2.0
Six months
(Two doses four weeks apart)
One and a half years
Two and a half years
Three and a half years
Four and a half years
1.1–1.4
0.9–1.1
1.6–1.9
1.4–1.7
3
servative) threshold in the range and was chosen
for this analysis. Because it is body-weight dependent, acceptable daily dietary levels of mercury in
the form of MeHg were calculated by multiplying the
RfD by the body weights (lower 5th and 50th percentiles) of infants over the first 4.5 years of life. Infant body weights were estimated using infant body
weight data collected from NHANES(35) as described
previously.(36) Bootstrapping was used to capture the
uncertainty in body weights for infants of both median and lower 5% quantile body weights. Dietary
absorption of MeHg was assumed to be 100% based
on results in human volunteers.(37)
2.2. Pharmacokinetic Model Construction
and Validation
to determine the course of influenza vaccination in
the United States over the first four to five years of
life. The exposures to mercury (Table I) are based
on the reported amounts contained in a recent list
of FDA-approved seasonal influenza vaccines(31) and
are independent of the body weight of the vaccinated infant. Of the 11 licensed, injectable seasonal
vaccine products, five are packaged in multidose
vials (Afluria , two FluLaval , Fluvirin , Fluzone )
that contain thimerosal (≤25 μg mercury/0.5 mL
dose). Of these five products, only Fluzone is licensed for use in infants as young as six months of
age. The other products are not indicated for children under three (FluLaval ), four (Fluvirin ), or
five (Afluria ) years of age. Therefore, Fluzone administered from a multidose vial according to the
2013 Advisory Committee on Immunization Practices (ACIP) seasonal vaccination schedule would
provide the maximum theoretical exposures to mercury in the youngest children (six months to four
years of age). These exposures may not be typical,
however, given the possibility that a child may receive Fluzone in a single-dose vial or prefilled syringe or the live attenuated, intranasal influenza vaccine FluMist , both of which are thimerosal-free.
R
R
R
R
R
R
R
R
R
R
R
2.1.2. MeHg at Its RfD
Four health-based guidelines have been published for dietary MeHg: 0.1 μg/kg bw/day(32)
(bw, body weight); 1.6 μg/kg bw/week (0.23 μg/kg
bw/day);(33) 0.3 μg/kg bw/day;(26) and 0.4 μg/kg
bw/day.(34) Although these values are quite similar,
the USEPA RfD for MeHg is the lowest (most con-
2.2.1. Source and Justification of Data for the Model
As mentioned, several pharmacokinetic studies have been performed for thimerosal in humans,
nonhuman primates, and rodents. Of these, we
considered those performed in either human or nonhuman primates to be the most relevant to humanhealth risk assessment, based on known physiological, phylogenetic, and taxonomic kinship and
concordance in previous cross-species pharmacokinetic comparisons.(38,39) This smaller set of studies includes those by Pichichero et al. in human
infants,(17–19) the study by Barregard et al. in human
adults,(20) and that by Burbacher et al. in infant nonhuman primates.(16) Of this group, the study by Burbacher et al. provided the only direct, intrastudy comparison of the pharmacokinetics of thimerosal with
that of MeHg when administered to infant nonhuman primates at identical doses starting at birth.
Briefly, Burbacher et al. exposed infant macaques to either thimerosal (IM) or MeHg (PO)
at identical, weekly doses of 20 μg/kg bw for four
weeks starting from birth and reported mercury levels in blood weekly thereafter. The dosing regimen in
that study was designed to mimic the repeat, episodic
dosing schedule of human infants (outside the United
States) beginning at birth. In the absence of a similar head-to-head study in human infants, it is the
most relevant study on which to base a comparative
assessment of infant mercury exposure or risk from
thimerosal relative to MeHg. In addition, application of the results from that study to human infants
was considered warranted given the almost identical
blood half-lives of mercury in human infants (three
to seven days) and infant nonhuman primates (two

4. 4
Mitkus et al.
Fig. 1. Structure of the Bayesian hierarchical model for thimerosal. The statistical model for MeHg was structured analogously.
to nine days) following single, episodic exposures to
thimerosal.(16–19) At FDA’s request, the individual
infant macaque blood concentration data from the
study were kindly provided by the study’s authors,
Drs. Thomas Burbacher and Danny Shen. The provision of the individual animal data by the original
study’s authors at FDA’s request does not constitute
their approval of the methods or conclusions of this
article.
2.2.2. Model Description and Justification
In order to provide an analysis that was independent and that would also provide multiple plausible
fits of the data for the purpose of ascertaining the
uncertainty in internal exposure of infants to mercury following influenza vaccinations, the nonhuman
primate data from Burbacher et al. were reanalyzed
using a Bayesian approach (Fig. 1). To fully capture
the biological heterogeneity in the data, the Bayesian
hierarchical model allowed each monkey to have its
own unique set of pharmacokinetic parameters (e.g.,
rate constants, volume of distribution), which were
based on the individual blood concentration–time
data. A Bayesian censoring model was created to
deal with individual animal data that were missing or
below the limit of detection.
The Bayesian hierarchical model, much like an
equivalent multilevel mixed model, has many advantages. First, because the model is a multilevel
model where there are both subject- and populationlevel predictions, this approach generally allows for
better fits to the experimental data because the
residuals for the subject-level predictions are usually smaller than the residuals associated with the
population-level prediction in an equivalent singlelevel model. Second, because the model allows
each monkey to have its own unique pharmacokinetic parameters, the intersubject variation of pharmacokinetic parameterization can be studied and

5. Comparative Pharmacokinetic Estimate of Mercury in U.S. Infants
5
Fig. 2. The population-level prediction (solid black) for mercury concentration in blood following multiple doses of thimerosal (IM) is
shown along with the predicted response for monkey 5 (red) and monkey 14 (blue) (colors visible in online version). The dotted lines
represent the 2.5% lower and 97.5% upper bounds on prediction. The blue and red dots correspond to the actual blood concentration
measurements published by Burbacher et al.
differentiated. The model was hierarchical in the
sense that each of the monkey-specific parameters
(the first level of hierarchy) was itself assumed to be
a random draw from some probability density with
distributional parameters centered with means and
variances common to the population of all monkeys
(the second level of hierarchy). The values of the
pharmacokinetic parameters for the overall population were, therefore, inferred by first estimating the
parameters for each monkey involved in the biological study and then utilizing the collection of these
subject-specific parameter estimates as data for inference toward the population-level parameters. The
parameter constants at the third and highest level of
hierarchy, in turn, established the prior distribution
for the population pharmacokinetic parameters; the
process of prior elicitation that defined the plausible envelope for the distribution of population-level
pharmacokinetic parameters is described in the Appendix. Bayesian posterior inference on the parameters of the model was carried out by Markov Chain
Monte Carlo (MCMC) sampling of the posterior distribution using OpenBugs(40) and the JAGS package
in R.(41)
2.2.3. Model Validation
We conducted at least five validation steps during model development. First, the predicted values of
the population model and the monkey-specific models were plotted against observed values to visually
assess the fit of the model (representative examples
in Figs. 2 and 3). Each figure includes the population prediction and the predictions for two specific
monkeys along with the 95% predictive confidence
interval (CI). Most data points are within the 95%
predictive CI of the monkey-specific model. In addition, there are as many blue and red curves (subjectspecific predictions) above the black curve (population prediction) as below it. Therefore, there was
good agreement between the subject-specific predictions and the subject-level data, as well as consistency

6. 6
Mitkus et al.
Fig. 3. The population-level prediction (solid black) for mercury concentration in blood following multiple, equivalent doses of MeHg (PO)
is shown along with the predicted response for monkey 1 (red) and monkey 10 (blue) (colors visible in online version). The dotted lines
represent the 2.5% lower and 97.5% upper bounds on prediction. The blue and red dots correspond to the actual blood concentration
measurements published by Burbacher et al.
between the population prediction and the animalspecific estimates. Second, we based the posterior inference of pharmacokinetic parameters on a production sample of 10,000 posterior samples following a
burn-in period of 10,000. Visual evidence for posterior convergence was verified via trace plots, and
quantitative evidence was based upon the evaluation
of the Raftery and Lewis diagnostic test statistic.(42,43)
Third, the overall quality of model fit was assessed quantitatively by means of posterior predictive checking.(44) Specifically, for each MCMC simulation, we randomly generated a simulated response
for each monkey and measurement time and then
compared the sum of squared residuals between
these simulated responses and the model predictions.
These quantities were in turn compared with the sum
of squared residuals between the simulated prediction and the actual data. A Bayesian p-value was then
computed by measuring the number of times in the
simulation that the sum of squared residuals for the
posterior predictive distribution was larger than the
sum of squared residuals from the data at hand and
dividing by the number of simulations. The Bayesian
p-value for the one-compartment model applied to
the MeHg data was 0.54, and that for the twocompartment model applied to the thimerosal data
was 0.562, indicating an acceptable fit to the data for
both models. Fourth, the deviance information criterion (DIC(43) ) was applied to compare models with
simpler parameterizations to more complex ones,
with a model with a lower DIC value being preferred.
Fifth, we conducted a Bayesian sensitivity analysis to determine whether the quality of fit would
substantially change if we changed the center of our
prior distributions for model parameters at the third
level of hierarchy. The sensitivity analysis was conducted by running the baseline MCMC simulation
and then perturbing the parameters one at a time and
then running alternate MCMC simulations with this
new prior distribution. For each set of simulations,

7. Comparative Pharmacokinetic Estimate of Mercury in U.S. Infants
we compared how changing the prior distribution
changed the overall fit of each model by means of
computing the log-likelihood value for each simulated MCMC run. Specifically, we investigated 11 different choices for prior distributions and investigated
how each change affected the log-likelihood score.
Figure A1 and Tables AI and AII demonstrate that
the fit is not significantly changed by the choice in
prior distribution. Each box plot in the figure was
computed by calculating the log-likelihood score for
each of the 10,000 MCMC simulations. The box plots
are very similar across the scenarios, suggesting that
the overall fit of the model is robust to changes in assumptions about the prior distributions.
2.3. Estimation of Mercury Retention in
Human Infants
Based on the shape of their blood time course
curves, we, like the original study authors,(16) modeled the distribution of mercury into one compartment (central) for MeHg and two compartments
(central and peripheral) for thimerosal. This classical pharmacokinetic approach was consistent with
the use of either one- or two-compartment models
to describe the distribution of these organomercurials in the human body previously.(18–20,32,45) Body
burden of mercury following exposure to either
thimerosal-containing influenza vaccines or dietary
levels of MeHg at the RfD was calculated using the pharmacokinetic parameters derived from
the Bayesian models in Table II. Specifically, mercury retention was estimated over the first four
to five years of life by substituting the respective, relevant exposures (μg) to either thimerosal
(IM) or MeHg (PO), along with the rate constants derived from the Bayesian analysis, into Equations (A.1) through (A.3). Differential equations
were solved and time course graphs were generated using R(46) or Biokmod(47) in conjunction with
Mathematica 8 (Wolfram Research, Champaign, IL,
USA).
The areas under the mercury body burden curves
(AUCs) following daily exposure to acceptable daily
doses of MeHg or episodic exposures to thimerosal
were calculated using Equations (A.14) and (A.15),
respectively. Results of multiple Bayesian simulations were used to obtain a predictive Bayesian confidence limit for the AUC following exposure to either
MeHg or thimerosal. The body burden for infants of
both median and lower 5% body weights was then
plotted, and the respective AUCs calculated, along
7
with their respective lower 2.5% and upper 97.5%
bounds following 5,000 MCMC simulations.
3. RESULTS
3.1. Body Burden of Mercury Following Repeated
Exposures to Thimerosal or MeHg at the RfD
Fig. 4 presents levels of mercury in infants following single doses of influenza vaccine that contain thimerosal (up to 2 μg/kg bw; Table I) or daily
oral consumption of acceptable doses of MeHg(32)
over the course of the first 4.5 years of life. It is
clear from the graph that there is no long-term accumulation of mercury in the body following single, yearly exposures to thimerosal. Integrating under the concentration–time curve (from time zero to
1,700 days, or 4.5 years) yielded a median AUC for
thimerosal of 700 μg Hg-days in infants (Table III).
On the other hand, integrating under the median
curve for this time period for MeHg exposures at the
RfD in the lowest-weight infants yielded an AUC of
100,000 μg Hg-days (120,000 for median-weight infants). Comparing the AUC of 700 μg Hg-days for
thimerosal mercury to those from MeHg at the RfD
(100,000 or 120,000) over the first 4.5 years of life
yields a margin of exposure (safety) of 143 or 171.
This indicates that the body burden of mercury from
vaccine thimerosal in infants over the first 4.5 years
of life is at least 140-fold lower than the body burden of mercury from acceptable daily levels of dietary MeHg over the same time period. Fig. 4 also
indicates that an infant’s peak body burden of mercury at the time of his or her first influenza vaccination at 180 days of life is two- to threefold less than
the median acceptable body burden of MeHg in either median- or low-weight infants.
3.2. Uncertainty in Body Burden Estimates Over
Time (AUC)
Table III contains a Bayesian posterior summary
of the uncertainty (upper and lower 2.5% quantiles
and standard deviation) surrounding the AUC values corresponding to the median time course curves
for both thimerosal and MeHg. As mentioned, AUC
estimates for MeHg took into account both the variability in the pharmacokinetic parameters in infant
monkeys (Table II) and the variability of infant body
weights(35) as modeled by Mitkus et al. Therefore,
this uncertainty analysis provides an estimate of the

8. 8
Mitkus et al.
Table II. Posterior Summary of the Population-Level Parameters for the Two-Compartment Pharmacokinetic Model for Thimerosal and
the One-Compartment Pharmacokinetic Model for MeHg
Quantiles
Compound
Population-Level Parameter
Mean
Std. Dev.
2.5%
25.0%
50.0%
75.0%
97.5%
Thimerosal
Thimerosal
Thimerosal
Thimerosal
Thimerosal
MeHg
MeHg
MeHg
Vc = exp(μV )
K12 = exp(μk12 )
K21 = exp(μk21 )
Ka = exp(μka )
Ke = exp(μke )
Vc = exp(μV )
Ka = exp(μka )
Ke = exp(μke )
1.62
0.20
1.08
3.92
0.18
1.76
19.42
0.017
0.24
0.20
1.26
4.96
0.04
0.09
37.86
0.005
0.98
0.03
0.10
0.68
0.13
1.59
2.16
0.007
1.54
0.08
0.40
1.43
0.16
1.69
5.42
0.014
1.66
0.13
0.73
2.37
0.17
1.75
10.21
0.018
1.78
0.23
1.32
4.34
0.20
1.82
19.76
0.021
2.01
0.80
4.16
16.51
0.30
1.95
94.52
0.027
Fig. 4. Simulated kinetics of mercury following exposures to thimerosal or MeHg in the body over the first 4.5 years of life. Thimerosal:
mercury retention in central (purple) and peripheral (magenta) compartments following single ACIP-recommended exposures (up to 25
μg) (colors visible in online version). MeHg: body burden of mercury following daily ingestion of USEPA safe levels by infants of median
(orange: median curve) or lower fifth percentile (red: median curve; blue: lower 5% bound) BW. MeHg time course curves were generated
by simultaneously drawing samples from both the simulated body weight distributions and the pharmacokinetic parameter distributions.
internal exposure to mercury in infants who may be
at the tails of the population distribution for body
weight and pharmacokinetic clearance. AUCs for
thimerosal and MeHg in low- or median-birth-weight
infants with the fastest mercury kinetics (2.5% quantile, Table III) are 550 and 66,000 or 80,000 μg Hgdays, respectively. That equates to a margin of exposure of 120–145. AUCs for thimerosal and MeHg in
lower- or median-birth-weight infants with the slowest mercury kinetics (97.5% quantile, Table III) are
much higher: 1,500 and 250,000 or 300,000 μg Hgdays, respectively; and the margin of exposure for
that comparison is 167–200. AUCs for internal mer-
cury exposure from thimerosal, as predicted by our
Bayesian models, therefore, are always at least 120fold lower than the respective AUCs for MeHg, including the most conservative comparison using the
lowest-weight babies with the fastest mercury kinetics. Peak body burdens of mercury following episodic
exposures to thimerosal were also always lower than
the corresponding level of acceptable mercury from
methylmercury in low-birth-weight infants with the
fastest kinetics (Fig. 4). Taken together, these results
indicate that mercury in the body following maximal
theoretical exposures to thimerosal preservative in
inactivated influenza vaccine packaged in multidose

9. Comparative Pharmacokinetic Estimate of Mercury in U.S. Infants
9
Table III. Posterior Summary of the Bayesian Estimates for the Area Under the Body Burden Curve (with Confidence Limits) from Birth
to 1,700 Days of Age (4.5 Years) Following Episodic Exposures to Thimerosal or Daily Safe Exposures to MeHg
Posterior Statistics—AUC (μg Hg · Day)
Kinetics (Fast → Slow):
Thimerosal
Safe MeHg—infants at the lowest 5% quantile for body weight
Safe MeHg—infants at the median body weight
vials does not at any time exceed the body burden
of mercury that is based on a highly conservative
threshold for dietary MeHg. In addition, a potentially sensitive subpopulation (low-birth-weight infants) will not be exposed to unsafe levels of mercury
from vaccine thimerosal following single or repeated
exposures in the United States.
4. DISCUSSION AND CONCLUSION
In 2001, Ball and colleagues at the Center for Biologics Evaluation at the FDA published an assessment of thimerosal exposures from infant vaccines
and reported that some infants could be exposed to
cumulative levels of mercury from vaccines that were
higher than the EPA threshold for MeHg.(1) Because
the clinical significance of that apparent risk was unknown, the authors noted that lowering exposures
to thimerosal in vaccines was consistent with the
larger aim of reducing exposures to mercury in general. Today, the inactivated influenza vaccine packaged in multidose vials is the only U.S. infant vaccine that contains thimerosal at other than residual
amounts.
Since the original analysis of Ball et al., it has
become increasingly clear that there are significant differences in pharmacokinetics between the
organomercurials, thimerosal and MeHg, and that
these differences govern their respective toxicities. It
has been shown, for example, that mercury is cleared
from the blood and brain much faster following exposure to thimerosal than to MeHg in infant nonhuman primates.(16) Peak blood or brain mercury levels have also been shown in several species to be
lower following exposures to thimerosal (or EtHg)
relative to an equivalent dose of MeHg administered
via the same (IM/IM) or real-world (IM/PO) routes
of exposure,(16,21–24) and those studies illustrate the
acknowledged differences in disposition and tissue
uptake between the two compounds.(48–51) In addi-
2.5% Quantile
Median
Mean
97.5% Quantile
Std. Dev.
550
66,000
80,000
700
100,000
120,000
780
110,000
140,000
1500
250,000
300,000
300
57,000
70,000
tion, thimerosal is more quickly and extensively metabolized to inorganic mercury in the brain than is
MeHg,(16,48) and that process of dealkylation may
be a detoxification step.(49,52) Taking together these
three major pharmacokinetic differences, one would
expect, therefore, greater toxicity from MeHg than
from thimerosal when administered at equivalent
doses, given the higher and longer bioavailability of
the former.
These established differences in pharmacokinetics between thimerosal and MeHg imply that
comparing nominal exposures to mercury from
thimerosal in infant vaccines directly to nominal
exposures at the MeHg RfD will overestimate
thimerosal risk.(27) This is the case because, fundamentally, comparisons of nominal (external) exposures do not take into account differences in physiological ADME processes (absorption, distribution,
metabolism, excretion), which normally serve to reduce internal exposures to xenobiotics in the body
following exposure. Therefore, we expanded the
original comparison of Ball et al. in order to provide
a more reliable (i.e., internal) estimate of thimerosal
exposures. First, we utilized body burden, not nominal dose, as our metric for internal exposures to
either thimerosal or MeHg, and we performed our
comparison accordingly. Second, in the models that
we built to estimate the body burden of either
thimerosal or MeHg, we explicitly took into account
the major pharmacokinetic difference between these
two organomercurials, which is the faster clearance
of thimerosal from the body. And, third, in the absence of comparative repeat-dose pharmacokinetic
data for thimerosal and MeHg in human infants, we
utilized results from the only published study that
(1) compared the clearance of thimerosal with that
of MeHg; (2) when administered at equivalent doses;
(3) in an infant model; (4) according to an episodic,
repeat-dosing regimen; and (5) that started at birth:
the infant nonhuman primate study by Burbacher
et al.

10. 10
Specifically, we generated (Bayesian) statistical
models for thimerosal and MeHg that were based on
the individual animal blood mercury concentration
data from that study. Several visual and quantitative
validation tests indicated that our Bayesian models
were robust and fit the experimental data well. Pharmacokinetic rate constants were then derived from
our two data-based models and applied to a real-life
human exposure scenario, in order to estimate the
body burden of mercury in U.S. infants following
exposures to thimerosal in vaccines or dietary MeHg
at its RfD. Direct cross-species application of the parameters was considered reasonable based on the essentially identical blood half-lives of thimerosal (average four to five days) in infant human and nonhuman primates.(16–19) As far as we are aware, this is the
first time such an estimate of mercury body burden
from thimerosal has been made for human infants.
The major outcome of the modeling efforts reported here has been the estimation of the mercury body burden in infants from either thimerosal
at U.S. exposure levels or MeHg at its oral RfD.
This is a significant advance over previous estimates
that calculated (only) external exposures to these
compounds.(1) Although Pichichero et al. measured
blood levels of mercury in human infants following single or repeat doses of thimerosal,(17–19) those
studies, which are still highly relevant, did not assess
the effect of controlled dietary MeHg exposures on
blood levels of mercury or conduct additional pharmacokinetic analyses to estimate parameters such as
rate constants that could then be applied to estimate
a more comprehensive metric of internal exposure
(body burden) over several years, as we have done
here.
Although we view our study to be an advance
over previous efforts, one of its limitations is its
comparison to the regulatory threshold for MeHg.
That comparison is highly conservative because the
RfD for MeHg is designed to be protective of possible adverse effects following daily exposure for a
lifetime, while exposure to thimerosal is small and
episodic, hence the conservatism. In addition, regulatory thresholds for short-term exposures to xenobiotics are normally above those for long-term exposures because toxicity thresholds trend lower as
length of exposure becomes higher. However, because an acute or short-term threshold (e.g., “RfD,”
“minimal risk level”) for either MeHg or thimerosal
does not exist, the RfD for MeHg was the next best,
although imperfect, comparator. This means that the
margins of exposure reported here (i.e., ≥120) ac-
Mitkus et al.
tually underestimate the true margin of safety for
thimerosal by some factor. For that reason, we support future assessments of thimerosal safety that
move away from comparisons with MeHg.
In summary, using pharmacokinetic parameters
(rate constants) derived from the most relevant available study of exposure of infant nonhuman primates
to either thimerosal or MeHg, we have estimated the
body burden of both thimerosal and MeHg in human
infants. We have demonstrated that children, including those of low birth weight, who receive the recommended schedule of annual inactivated influenza
vaccines formulated with thimerosal as a preservative in multidose vials in the United States will
receive over 100 times less internal exposure to mercury on a time-integrated basis over the first 4.5
years of life as compared to the USEPA regulatory threshold for dietary MeHg over a similar interval. Peak mercury levels from thimerosal in the
body were also always below the regulatory threshold for MeHg over the same time period. By taking
into account the significant pharmacokinetic differences between thimerosal and MeHg that have been
elucidated over the past decade and by not relying
on nominal dose as the exposure metric, our study
significantly improves upon the previous estimates
of Ball et al. Together with the robust human epidemiological data for thimerosal, our results, which
are based on a “worst-case” comparison, support the
continued safety of this preservative at levels currently used in multidose inactivated influenza vaccines in the United States.
ACKNOWLEDGMENTS
We thank Drs. Burbacher and Shen for kindly
providing the individual infant macaque blood concentration data from their paper.(16) The provision of
the individual animal data by the original study’s authors at FDA’s request does not constitute approval
of the methods or conclusions of the article by the
original study’s authors.
APPENDIX: MATHEMATICS OF THE
BAYESIAN PHARMACOKINETIC MODELS
In the one-compartment pharmacokinetic
model for MeHg, mercury is absorbed into the blood
from the GI (rate constant ka ) and removed from the
blood at a rate proportional to the elimination rate
constant ke . The rate of movement of MeHg into and
out of a single, central compartment is described by

11. Comparative Pharmacokinetic Estimate of Mercury in U.S. Infants
A=
the following equation:
dX1 /dt = ka XGI (t) − ke X1 (t),
dX1 /dt = k21 X2 (t) + ka XM (t) − (ke + k12 )X1 (t),
(A.2)
(A.3)
where dX1 /dt and dX2 /dt refer to the rates of change
of thimerosal mercury within the central and peripheral compartments, respectively, and XM refers to
the amount of mercury at the site of intramuscular
injection.
˜ j=1
When K doses {D(t j )} K are administered at the
K
˜
dosing times {t j } j=1 , the superposition principle in
differential equations ensures that the blood concentration in the blood is given by
f1 (t) =
˜
j:t j <t
˜
FD(t j )ka
˜
exp (−ke (t − t j ))
Vc (ka − k)
(A.4)
˜
˜
−exp (−ka (t − t j )) I[t − t j ]
for the one-compartment model, and
f2 (t) =
˜
j:t j <t
˜
FD(t j )
˜
Aexp (−ka (t − t j ))
Vc
˜
+B exp (−α(t − t j ))
˜
˜
+C exp (−β(t − t j )) I[t − t j ]
(A.5)
for the two-compartment model, where Vc is the effective volume of the central compartment, F is the
bioavailability, I[•] is an indicator function that has
a value of 1 whenever the argument (t − t0 ) > 0 and
is 0 otherwise, and the parameters {α, β, A, B, C} are
given by:
α, β =
(k12 + k21 + ke ) ±
(k12 + k21 + ke )2 − 4k21 ke
2
ka (k21 − α)
ka (k21 − ka )
,B=
,
(α − ka )(β − ka )
(ka − α)(β − α)
C=
ka (k21 − β)
(Ref. 53).
(ka − β)(α − β)
(A.1)
where dX1 /dt refers to the rate of change of MeHg
within the central compartment; and XGI refers to
the amount of MeHg at the port of entry following
oral, dietary exposure (GI). In the two-compartment
model for thimerosal, mercury is absorbed from the
site of IM injection (rate constant ka ) into the central
compartment (well-perfused tissues) and distributes
between the central compartment and the peripheral
compartment (less well-perfused tissues; rate constants k12 and k21 ). Elimination takes place from the
central compartment (rate constant ke ). The differential equations describing the time course of mercury
in either compartment are described as follows:
dX2 /dt = k12 X1 (t) − k21 X2 (t),
11
Often, when dealing with data for a single method
of administration, the bioavailability F is statistically
unidentifiable; accordingly, we estimate the effective
central-compartment volume Vc = Vc /F in all the results that follow.
Let yik denote the kth blood concentration measurement made on the ith monkey subject and let tik
denote the time of the blood measurement. A basic statistical model for the blood concentration of
MeHg under the one-compartment model would be
yik = f1 (tik|ka , ke , V) + εik,
(A.6)
where f1 (t|ka , k, V) is given by Equation (A.4), the
residuals εik are independent and identically distributed (iid) with εik ∼ N(0, σ 2 ), and the variance σ 2
denotes the residual variance or the lack of fit error.
The structure of the two-compartment model statistically utilized to fit the concentration of EtHg is given
by:
yik = f2 (tik|ka , ke , k12 , k21 , V) + εik,
(A.7)
which has identical assumptions as Equation (A.5).
The problem with the statistical models in Equations
(A.6) and (A.7) is that:
(1) They assume that every monkey has exactly
the same set of pharmacokinetic parameters
and so does not account for biological heterogeneity between monkeys.
(2) The models assume that the residuals εik are
caused by a simple and unexplainable source
of error with uniform variance σ 2 . Because of
this, the model does not distinguish between
variation caused by monkey-to-monkey variation (biodiversity) and other unexplainable
errors.
To more accurately model the biological heterogeneity that is present among animal subjects
and more faithfully account for the hierarchical
data structure, a more appropriate model would assume that each of the monkeys involved in the
Burbacher et al. experiment is endowed with its
own monkey-specific set of pharmacokinetic parame17
ters. Let ka [i], ke [i], k12 [i], k21 [i], V[i] i=1 denote the
monkey-specific rate constants and effective volumes

12. 12
Mitkus et al.
for the ith monkey. The index i will be utilized to
represent the data and parameters particular to the
ith monkey in all that follows. The one-compartment
model for the blood concentration of mercury from
MeHg is:
˜
yik = f1 (tik|ka [i], ke [i], V[i]) + εik,
˜
(A.8)
and the equivalent two-compartment model for the
blood concentration of thimerosal mercury has the
form:
yik = f2 (tik|ka [i], ke [i], k12 [i], k21 [i], V[i]) + εik,
˜
(A.9)
with the residuals εik in Equations (A.8) and (A.9)
˜
assumed to be independent and normally distributed
having a monkey-specific residual variance σ 2 [i]
˜
(εik ∼ N(0, σ 2 [i])). We note that because the sta˜
tistical models in Equations (A.8) and (A.9) fit
each monkey with its own separate monkey-specific
set of pharmacokinetic parameters, the residuals εik
˜
in Equations (A.8) and (A.9) will necessarily be
smaller, on average, than the residuals εik in Equations (A.6) and (A.7). Moreover, the lack of fit, or
residual variance specific to each monkey σ 2 [i] =
˜
Var(εik) in Equations (A.8) and (A.9) will similarly
˜
be smaller than σ 2 as well.
Because we allow different pharmacokinetic parameters for each monkey, we assume that each
monkey-specific parameter is itself a random draw
from an overall population distribution. In our onecompartment Bayesian model for MeHg we assume
that the monkey-specific pharmacokinetic parameters are distributed by:
2
ka [i] ∼ LogNormal(μka , σka ),
2
ke [i] ∼ LogNormal(μke , σke ),
2
V[i] ∼ LogNormal(μV , σV ),
(A.10)
and for the two-compartment pharmacokinetic model for EtHg we similarly assume that:
ka [i]
ke [i]
k12 [i]
k21 [i]
V[i]
∼
∼
∼
∼
∼
2
LogNormal(μka , σka ),
2
LogNormal(μke , σke ),
2
LogNormal(μ12 , σ12 ),
2
LogNormal(μ21 , σ21 ),
2
LogNormal(μV , σV ),
(A.11)
where {μka , μke , μk12 , μk21 , μV } are the means of the
logarithm for the population of the respective phar2
2
2
2
2
macokinetic parameters, and σka , σke , σk12 , σk12 , σV
are the respective population variances of the logarithms of each parameter. In our specification we
utilize a log normal distribution in order to ensure
that each of the pharmacokinetic parameters is posi-
tive. The population-level parameters themselves are
unknown and are of primary interest for estimation,
so following Bayesian methodology we introduce yet
another level of hierarchy and let the populationlevel parameter means and variances be specified by
2
2
μka ∼ N(μka0 , σka0 ) σka ∼ Unif(0, θa ),
2
2
μk ∼ N(μk0 , σk0 ) σk ∼ Unif(0, θk),
2
2
μV ∼ N(μV0 , σV0 ) σV ∼ Unif(0, θV ),
(A.12)
for the one-compartment model of MeHg and similarly let
μka
μke
μk12
μk21
μV
∼
∼
∼
∼
∼
2
2
N(μka0 , σka0 ) σka ∼ Unif(0, θa ),
2
2
N(μke0 , σke0 ) σke ∼ Unif(0, θe ),
2
2
N(μk120 , σk120 ) σk12 ∼ Unif(0, θ12 ),
2
2
N(μk210 , σk210 ) σk21 ∼ Unif(0, θ21 ),
2
2
N(μV0 , σV0 ) σV ∼ Unif(0, θV ),
(A.13)
be the analogous prior population-level parameters
for the two-compartment model for thimerosal mercury. In both models, we specify the lack-of-fit error with a vague Gelman prior σ 2 [i] ∼ Unif(0, θ ) and
˜
then the Bayesian model is completely specified.(43)
The Bayesian model is an empirical Bayesian
model (“objective Bayesian”) in the sense that the
distributional parameters of the prior were specified by setting them equal to the maximum likelihood estimators from Tables III and IV in Burbacher et al. Bayesian posterior inference on the
parameters of the model was then carried out by
MCMC sampling utilizing the Metropolis-Hastings
algorithm to simulate 10,000 samples from the posterior distribution.(43) To ensure that the MCMC algorithm had converged, a burn-in of 1,000 posterior
simulations was utilized and posterior convergence
was verified via trace plots. The posterior summary
of the two models mentioned above generally concur with the parameter estimates and corresponding
standard errors given by Burbacher et al. As stated,
we obtained quantitative evidence for the quality of
fit of our statistical model by means of posterior predictive checking.(44)
To establish the priors for the population vari2
2
2
2
2
˜
ances {σka , σke , σk12 , σk21 , σV , σ 2 }, we utilized an analysis by Renwick and Lazarus to inform our decision
making.(54) In that paper, the pharmacokinetics of 60
different compounds were studied, and the interindividual variation was found to be roughly 3.2 (that
study currently serves as a basis for a default threefold uncertainty factor for pharmacokinetic variability in human-health risk assessment). On the log
scale, this variation translates to 1.16. We padded

13. Comparative Pharmacokinetic Estimate of Mercury in U.S. Infants
the interindividual variation somewhat as insurance
against compound-specific peculiarities and set the
2
2
2
2
2
prior for each variance σka , σke , σk12 , σk21 , σV , σ 2 ∼
˜
Unif(0, 3), so θa = θk = θ12 = θ21 = θV = θe = θ = 3.
Because these prior distributions were uniformly distributed over the entire plausible range of variances,
this prior specification had little influence in the
estimation procedure. The specification of priors for
the population means {μka , μke , μk12 , μk21 , μV } was
a bit trickier as some biologically plausible understanding about the true value of these parameters
must be applied in order to ensure algorithm convergence. Accordingly, in order to prevent conflicts
between priors and likelihoods, we adopted an empirical Bayesian approach, which substitutes point estimates utilizing the data for certain parameters. To
obtain point estimates on pharmacokinetic parameters, we fit a one- or two-compartment model to the
data for each monkey utilizing the nonlinear regression algorithm from SAS, PROC NLIN (SAS institute, Cary, NC, USA).
Once the nonlinear estimates for each monkey
were obtained, we set the expected value of the
mean of the prior distribution equal to the sample
average from the regression estimates for the logarithms of the parameters (not shown). By doing this,
we would ensure that the center of the prior distribution would be roughly in the same neighborhood where the posterior mode would likely be. In
order to ensure that the prior distributions for the
population means {μka , μke , μk12 , μk21 , μV } were sufficiently diffuse, we were motivated to choose the
2
2
2
2
2
variances {σka0 , σke0 , σk120 , σk210 , σV0 } as large as possible. The logic behind the selection of these variances follows closely from Renwick and Lazarus, in
which the mean coefficient of variation in pharmacokinetic parameters for the 60 compounds involved
in the study was a maximum of 137%. In all cases,
the distributions for the population means had coefficients of variation larger than 137%. The complete
prior specification for the population means in the
one-compartment model for MeHg was:
μka ∼ N(−2.09, 10),
μk ∼ N(1.04, 2),
μV ∼ N(0.26, 10),
and the similar prior specification for the twocompartment model for thimerosal was:
μka ∼ N(0.58, 1),
μke ∼ N(−0.81, 10),
13
μk12 ∼ N(−0.98, 1.5),
μk21 ∼ N(−0.7, 1),
μV ∼ N(0.2, 100).
To compute the area under the body burden
curve (AUC) for mercury, we used appropriate formulas for the integral of the mass (body burden) under both the one- and two-compartment models. Following the exposure to safe daily doses of MeHg, the
formula for the integral from 0 to T is:
T
AUC(T) = V
f1 (t)dt
0
=
t j ≤T
F D(t j )
+
ke
t
j ≤T
F D(t j )ka
(ka − ke )
(A.14)
exp (−ke (T − t j )) exp (−ka (t − t j ))
.
−
ke
ka
×
Following the episodic exposures to thimerosal,
the formula for AUC of the body burden is given
by:
AUC(T) = V
fcentral (t) + fperipheral (t) dt+
D(t j )
(A+ D) (B + E) (C + F)
+
+
ka
α
β
D(t j )
=
(A+ D) exp (−ka (T − t j ))
ka
t j ≤T
−
t j ≤T
(B + E) exp (−α(T − t j ))
α
(C + F) exp (−β(T − t j ))
,
+
β
+
(A.15)
where fcentral (t), fperipheral (t) are the equations for the
concentration time-course in the central and peripheral compartments and the constants A through F are
given by:
A=
ka (k21 − α)
ka (k21 − ka )
,B=
,
(α − ka )(β − ka )
(ka − α)(β − α)
C=
k12 ka
ka (k21 − β)
,D=
,
(ka − β)(α − β)
(α − ka )(β − ka )
E=
k12 ka
,
(ka − α)(β − α)
F=
k12 ka
(Ref. 53).
(ka − β)(α − β)

14. 14
Mitkus et al.
Fig. A1. The log-likelihood score for each of the 11 models explored during the sensitivity analysis. Each box plot is constructed from 10,000
MCMC iterations of the model.
Table AI. Table of Parameter Values Explored in the Sensitivity
Analysis
Parameter
μv0
μka0
μke0
μk120
μk210
Baseline Value
Low Value
High Value
0.2
0.75
− 0.81
− 1.06
− 0.75
0
0.5
−1
− 1.25
−1
0.4
1
− 0.5
− 0.8
− 0.5
A Bayesian sensitivity analysis was conducted to
determine whether the quality of fit would substantially change if we changed the center of our prior
distributions for model parameters at the third level
of hierarchy. We investigated 11 different choices
for prior distributions and investigate how each
change affected the log-likelihood score. Figure A1
and Tables AI and AII demonstrate that the fit
was not significantly changed by the choice in prior
distribution.
Table AII. Table of Parameter Values Explored in the
Sensitivity Analysis
Model
Parameter Perturbation
1
2
3
4
5
6
7
8
9
10
11
Baseline case
Low μv0
High μv0
Low μka0
High μka0
Low μke0
High μke0
Low μk120
High μk120
Low μk210
High μk210
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