types aggregate in QTL regions, combined with
as an iv bolus to determine the contribution of nitric
14. E. S. Lander et al., Genomics 1, 174 (1987).
physiological profiling, provides a novel ap-
oxide to basal renal vascular tone. After 10 min of
15. J. Loscalzo, G. Welch, Progr. Cardiovasc. Dis. 38, 87
equilibration, a repeat infusion of the same two doses of
proach to facilitate the positional cloning of
ACh were administered to test for the degree of block-
16. N. K. Hollenberg et al., Medicine 57, 167 (1978).
genes underlying cardiovascular function and
ade of the synthesis of nitric oxide produced by L-
17. A. W. Cowley Jr. et al., Physiol. Genomics 2, 107
hypertension. While strategies for accomplish-
NAME. (Morphometric measurements): Heart and kid-
neys were removed, stripped of surrounding tissue, and
ing these goals will continue to evolve, this first
18. M. Stoll, A. W. Cowley Jr., A. S. Greene, data not
weighed to assess the degree of cardiac and renal
attempt at developing knowledge at a systems
hypertrophy. (Histology): The right kidney was immer-
19. E. S. Lander, L. Kruglyak, Nature Genet. 11, 241
biology level sets the stage for future improve-
sion-fixed in 10% buffered formalin and embedded in
paraffin, and prepared sections stained with H&E and
ments and provides investigators with a power-
PAS were evaluated for mean glomerular diameter and
20. We thank the Bioinformatics Research Center at
the degree of focal glomerulosclerosis.
Medical College of Wisconsin for the development of
8. B. R.Thumma et al., J. Exp. Bot. 52, 203 (2001).
the database, tools, and Web site; M. Granados, M.
Nobrega, M. Shiozawa, and M. Runte for assistance
9. L. L. Miner et al., Psychopharmacology 117, 62 References and Notes
with genotyping; A. Kwitek-Black for comparative
1. E. R. Bleecker, D. S. Postma, D. A. Meyers, Am. J.
mapping; and T. Kurth, K. Bork, P. Regozzi, and C.
10. K. G. Becker et al., Proc. Natl. Acad. Sci. U.S.A. 95, Respir. Crit. Care Med. 156, S113 (1997).
Thomas for excellent technical assistance. This work
2. C. Julier et al., Hum. Mol. Genet. 6, 2077 (1997).
was supported by National Heart, Lung, and Blood
11. J. Nadeau, W. Frankel, Nature Genet. 25, 381 (2000).
3. J. Krushkal et al., Circulation 99, 1407 (1999).
12. J. P. Rapp, Physiol. Rev. 80, 135 (2000).
4. C. L. Hanis et al., Nature Genet. 13, 161 (1996).
5. J. A. Todd, Proc. Natl. Acad. Sci. U.S.A. 92, 8560
13. A. C. Guyton et al., Annu. Rev. Physiol. 34, 13 (1972).
6. A user interface to the complete data set is found at
7. The total genome scan was carried out with an
average 10 cM spacing of markers following pheno-
typing with 239 measured or derived traits. After
testing for normalcy, 166 traits were analyzed in a
parametric genome scan using MAPMAKER/QTL (12,16). The remaining 73 traits were analyzed using the
nonparametric mapping algorithm (MAPMAKER/QTL
version 1.9b). (Phenotyping protocol, conscious): All
blood pressure measurements were made with the
animals unrestrained in their home cage as described
previously (17). Data were collected at a rate of 100
Hz and reduced to 1-min averages, except for time
Alain-Jacques Valleron,1 Pierre-Yves Boelle,1 Robert Will,2
series analysis where they were 1-s averages. The
day-night light cycle for all rats ran from 2:00 a.m.
(lights on) to 2:00 p.m. (lights off ) throughout the
study. BP1 (High Salt Day 1): Baseline measurements
of systolic, diastolic, and mean arterial pressure and
The size of the variant Creutzfeldt-Jakob Disease (vCJD) epidemic in the United
heart rate were measured from 9:00 a.m. to noon.
Kingdom is a major public health concern and a subject of speculation. The cases
BP2 (High Salt Day 2 – inactive versus active): Repeat
are young (mean age ϭ 28). Assuming that the risk of developing the disease
morning recording (“inactive phase,” lights on), and
record 4 hours during the dark cycle (2:00 p.m. to
in susceptible exposed subjects decreases exponentially with age after age 15,
6:00 p.m. “active phase”). Urine was collected for 24
that all infections occurred between 1980 and 1989, and that the distribution
hours for measurement of volume, sodium, potassi-
of the incubation period is lognormal, we estimate that the mean duration of
um, protein, and creatinine. All BP data this day was
collected for time-series analysis. BP3 (High Salt Day
the incubation period is 16.7 years [95% confidence interval (CI): 12.4 to 23.2]
3): Repeat morning recording. Following the record-
and that the total number of cases will be 205 (upper limit of the 95% CI: 403).
ing period, a blood sample (500 l) was drawn for
determination of creatinine, plasma renin activity,
plasma protein, and hematocrit. Furosemide chal-
be extremely high (4). Therefore, one could
lenge: Following blood draw, an ip injection of furo-
definite (n ϭ 86) or probable (n ϭ 11) variant
pessimistically assume that virtually everybody
semide (10 mg/kg) was given to salt deplete the
Creutzfeldt-Jakob Disease (vCJD) in the United
in the population has been in contact with food,
animals, and the diet switched to a 0.4% low salt.
Kingdom. These patients probably contracted
or bovine products, originating from BSE-in-
BP4 (Stress test): Following a control period, an alert-
ing stimulus (2 mA for 0.3 s) was delivered twice with
the disease by oral ingestion of food contami-
fected animals. The public health response in
a 5-min interval during pressure recording. Change in
nated by the agent of bovine spongiform en-
Europe has been to develop procedures and
mean arterial pressure, the time to peak, and the time
cephalopathy (BSE), before the UK bovine-
diagnostic tests that avoid, as far as possible, the
to 90% recovery were determined. BP5 (Low Salt):
Repeat 3- hour morning recording of blood pressure
specified risk materials (SRM) ban in 1989 (1).
entry of any infected animal into the food chain.
in the salt depleted state. Following the recording
The number of BSE-infected animals is estimat-
The consequences of the BSE epidemic in terms
period, a 1.0- ml blood sample was taken for the
ed to have been in the range of 900,000 to
of human disease are not yet known: With dif-
measurement of plasma renin activity, triglycerides,
total cholesterol, HDL, creatinine, hematocrit, and
1,130,000, with between 460,000 and 482,000
ferent assumptions for risk analysis, in 1997, the
white blood cell count. (Phenotyping protocol, anes-
slaughtered for consumption before the intro-
cumulative cases of vCJD in the United King-
thesitized): Rats were anesthetized with ketamine (30
duction of the November 1989 specified offal
dom were estimated from as few as 75 to as
mg/kg; intramuscular) and Inactin (50 mg/kg; intra-
peritoneal). Catheters were implanted in the femoral
ban (2). The epidemic may have started as early
many as 80,000 (5) and more recently from 70
artery and vein and an electromagnetic flow probe
as 1980 (3), and the number of people exposed
to 136,000 cases (6). These estimates are mark-
was placed on the left renal artery via a midline
to potentially infective doses through food may
edly dependent on assumptions made about the
incision. An iv infusion (50 l/min) of isotonic saline
containing 1% bovine serum albumin replaced fluid
mean duration of the incubation period. Unfor-
losses. After a 45-min equilibration, arterial blood
tunately, no studies in animals or of other hu-
pressure and renal blood flow were measured during
Epidemiology and Information Sciences, INSERM
man spongiform encephalopathies provide pre-
a 15-min control period. Renal and peripheral vascu-
U444, CHU Saint-Antoine, Universite´ Pierre et Marie
cise data for the incubation period. In addition,
lar responses to 5-min iv infusions of angiotensin II
Curie et Assistance Publique–Hoˆpitaux de Paris, 27
(20, 100, 200 ng/kg/min) and norepinephrine (0.5, 1,
rue Chaligny, 75012 Paris, France. 2National
the observation that only a few cattle, and often
3 g/kg/min) were determined. Following recovery of
Creutzfeldt-Jakob Disease Surveillance Unit, Western
only one, from the same age cohort in a herd
pressure to baseline values, renal vascular and sys-
General Hospital, Edinburgh EH4 2XU, UK. 3Immunite´
have developed BSE suggests that additional
temic arterial responses to two successive doses of
Anti-Infectieuse JE 2236, UFR de Me´decine de
acetylcholine (ACh) (0.1 and 0.2 g/kg/min) were
individual or environmental factors may influ-
Grenoble, Universite´ Joseph Fourier, Domaine de la
measured. L-NAME (5 mg/kg) was then administered
ence the development of the disease. It is be-
23 NOVEMBER 2001 VOL 294 SCIENCE www.sciencemag.org
cause the relation between the risk of the disease
each generation, these s subjects pass through
and the dose, route of infection, host factors, and
We denote by S(t,a) the survival function
the 1980 – 89 “window” at different ages, and
environmental factors is unknown that predic-
from all causes of mortality at date t and age
therefore the final number of persons who will
tions of the possible future of the epidemic rely
a, by (t, a) the force of infection at date t and
ultimately develop the disease varies according-
on mathematical extrapolations based on cur-
age a, and by h the probability density func-
ly. Finally, the probability P(t,a)dadt that a case
tion of the duration of the incubation period.
aged between a and a ϩ da occurs between
One striking epidemiological characteristic
(t, a) is the product of a function f (a) of age
times t and t ϩ dt is expressed mathematical-
of vCJD is the young age distribution of the
and of a function g(t) of calendar time: (t,
ly, then the maximum likelihood approach is
cases (Fig. 1A). The mean age at death of these
a) ϭ f (a)g(t). The choices of functions f and
patients is 28 years. Only 6 of 90 patients who
g express the age-risk relation described
from the available observations, and the fu-
have died were older than 50 years, in compar-
above and the variation of the BSE infectious
ture of the epidemic is assessed with these
ison with 93% of cases of sporadic CJD (7).
risk, respectively (11). The probability distri-
This observation provides a clue to the incuba-
bution of the duration of the incubation peri-
The distribution of the vCJD incubation pe-
tion period in vCJD, i.e., the “age of the patient
od, h(u), was assumed to be lognormal, be-
riod that best fits the data within the framework
at the diagnosis” ϭ “age at infection” ϩ “incu-
of our model has a mean of 16.7 years, with a
bation time.” The ages of the patients with vCJD
infectious diseases (12). A Gamma distribu-
standard deviation of 2.6 years. The 95% upper
at diagnosis and death are collated by the Na-
tion was also used in the sensitivity analysis.
percentile of this distribution is 21.4 years. The
tional Creutzfeldt-Jakob Disease Surveillance
The full statistical formulation necessary to
95% confidence interval (CI) of the estimates of
Unit in the United Kingdom. The causal link
write the likelihood equation implies that a
the mean and standard deviation is relatively
between BSE infection in cattle and human
probabilistic model be chosen to estimate the
narrow: The 95% CI for the estimate of the
vCJD indicates that the age at infection in peo-
population at risk of developing the disease, i.e.,
mean incubation period is 12.4 to 23.2 years,
ple must parallel the course of the BSE epidem-
the exposed/susceptible subjects. According to
and the 95% CI of the standard deviation is
ic. One can therefore compute the distribution of
the formulation we chose, the dates and ages of
0.9 to 8 years (10). The decrease in suscep-
incubation periods by a deconvolution tech-
the observed cases are a realization of a planar
tibility to infection in exposed subjects older
nique taking into account the censorship of cur-
Poisson process (13). In this model, s is the
than 15 years, as estimated from the param-
rent data, as was done successfully with ac-
average number of individuals per generation
eter ␣, was found to be very sharp: 16% per
who can be infected, provided they have been
year of age (CI: 12 to 23%). This means that,
(8). In vCJD, the analysis of the censored data is
exposed to a sufficient dose of infectious agent
under the best fitting hypothesis, an individ-
more complicated because the possible dates of
and have the appropriate individual characteris-
ual aged 20 years in 1981 had 55% less risk
infection range over an extended period of time.
tics (genetic, environmental, and so forth). In
of becoming infected than a child aged 15
Thus, additional statistical modeling was neces-sary. The model we propose provides estimatesof the incubation period and the future burden of
To explain that most of the cases are young,
two (nonexclusive) hypotheses have to bemade: (i) the incubation period is shorter in the
young than in the old, and (ii) the young aremore susceptible to infection. We do not pre-
judge the underlying determinants to these hy-potheses that may be related to differences in
Number of cases
susceptibility or other unknown factors. If thefirst assumption was true, older cases with long-
er incubation periods have a greater chance ofbeing identified later than younger cases. Be-
cause there is no statistically significant relation
between the date of diagnosis and age (Fig. 1B),
we discarded this first assumption. We there-
fore chose the second assumption, namely that
the probability per year that a susceptible sub-
ject becomes infected [the “force of infection”
(9)] decreases with age a. For the calculation,
we assumed that all susceptible children aged
between 0.5 and 15 years, exposed to the infec-
tious agent on year t, experience the same forceof infection. After 15 years of age, we assume
that the force of infection decreases exponen-
tially (10). This hypothesis is in line with the
epidemiological data, which show that vCJD
rarely occurs in older subjects. The age cutoff
Age class
of 15 years was an arbitrary choice. However,
Fig. 1. (A) Age distribution of vCJD cases. Data are as of 1 May 2001, including 97 patients. (B) The
this parameter has been further studied in a
distribution of the date of onset of vCJD by age class. Diamonds indicate observed values; a line is
sensitivity analysis. We assume that the whole
drawn at the median date. There is no apparent relation between age and date of diagnosis
population may have been exposed to the in-
(correlation coefficient ϭ 0.03, P ϭ 0.8), as would have been expected if the incubation time was
fectious agent, with the exception of infants
strongly age dependent, causing older cases to be detected later than younger cases.
www.sciencemag.org SCIENCE VOL 294 23 NOVEMBER 2001
3. C. H. Cohen, A. J. Valleron, Int. J. Epidemiol. 28, 526
4. “Opinion of the scientific steering committee on the
human exposure risk (HER) via food with respect to
BSE” (European Union Scientific Steering Committee,
5. S. N. Cousens, E. Vynnycky, M. Zeidler, R. G. Will, P. G.
Smith, Nature 385, 197 (1997).
6. A. C. Ghani, N. M. Ferguson, C. A. Donnelly, R. M.
Anderson, Nature 406, 583 (2000).
7. Surveillance data collected by the UK Creutzfeldt-
Jakob Disease Surveillance Unit are available at
8. S. Chevret, D. Costagliola, J. J. Lefrere, A. J. Valleron, J.Calendar year Epidemiol. Community Health 46, 582 (1992). Fig. 2. Observed cumulated incidence of vCJD
9. The “force of infection” is defined in mathematical
Fig. 3. Risk function for onset of vCJD as a
epidemiology to quantify the risk per unit of time
(dots) and incidence predicted by the model
function of age and time. Red dots indicate the
(usually, the year) that a susceptible individual has to
acquire the disease after being exposed to the infectious
agent. For a complete review of the concept of force of
infection, see R. M. Anderson and R. May [Infectious
years (99.9% for an individual aged 70). Diseases of Humans: Dynamics and Control (Oxford
The model predictions fit the past cumulat-
The results presented here are based on a
Science Publications, Oxford, 1991), chaps. 3 and 8].
ed incidences, as shown in Fig. 2. Similarly,
lognormal distribution of the incubation period,
10. Supplemental materials are available at Science On-
line at www.sciencemag.org/cgi/content/full/294/
there is a good fit to the observed age distribu-
which is commonly used in the epidemiology
tion (10), as the model predicts that 22 out of
of infectious diseases. However, we repeated
11. The function f(a) was taken in the form f(a) ϭ 0 if
the first 97 diagnosed cases should be less than
the estimation process assuming that the incu-
a Ͻ 0.5, as infants younger than 0.5 year were
20 years of age (19 in the surveillance data set)
assumed to not be exposed to the BSE agent; f(a) ϭ
if 0.5 Ͻ a Ͻ15, which corresponds to the constant
and 82 should be less than 40 years of age (87
found almost identical values for the incubation
risk assumed in children before 15; and f (a) ϭ 0
parameters, the future epidemic size of the ep-
e Ϫ␣(aϪ0.5) if a Ͼ 15. The function g(t ) was chosen to
Details of the variation in the risk function
idemic, and the occurrence of a bimodal age
reflect the increasing probability of the presence of
contaminated meat products in the human diet, in
(14) with age and time up to 2012 are shown in
distribution in the future (10).
parallel to the increasing incidence of BSE in animals
Fig. 3: The model predicts that the peak of the
over the period 1980–89. Possible exposures after
epidemic will be in 2000/2001 and that the
longer than in human growth hormone–related
1989 were not considered in this analysis. Mimicking
the incidence profile observed in the BSE epidemic
annual number of cases should gradually de-
CJD, which is between 9 and 10 years (15) in
during the same period, we set g(t ) ϭ
crease after this date. The total number of ex-
the sensitive homozygous genotypes. It is short-
␥ e Ϫ␥(t Ϫ1989). From the knowledge of the doubling
pected vCJD cases is, according to our model,
er than the one estimated in Kuru (16), which
time observed in the BSE epidemic (14 months)
during the 1980–88 period (2), we extrapolate ␥ ϭ
low at 205 cases (upper limit of the 95% CI:
may exceed three decades, although, a priori,
ln(2)/(14/12) ϭ 0.596. As only the product
403). One prediction from the model is that in
one would have expected a longer value because
identifiable, because of the form for the force of
the next few years, the age distribution will
in Kuru, there is no species barrier and the
become bimodal and that the proportion of older
disease was transmitted orally as in vCJD. The
12. P. E. Sartwell, Am. J. Hyg. 51, 310 (1950).
13. D. R. Brillinger, Biometrics 42, 693 (1986). PRNP 129 genotype has a crucial importance in
determining the risk of developing CJD. Yet to
P͑t,a͒dtda ϭ S͑t,a͒͵ ͭexpͫϪ ͵ ͑t Ϫ u,u͒duͬ
infections occurring between 1980 and 1989, as
date, all tested vCJD patients have been ho-
we assume that the likelihood of new human
mozygous for methionine at codon 129, as are
infection with BSE after the bovine SRM ban in
about 40% of the total UK population. If there
͑t Ϫ v,v͒h͑a Ϫ v͒dvͮdtda
1989 should have been considerably reduced.
are two subpopulations of vCJD patients, one
with “short” incubation times and methionine
The log-likelihood of the observed cases is
report is that it is focused on the most striking
homozygosity, the other with “long” incubation
sP͑t,a͒dadt,
epidemiological characteristic of vCJD, name-
times and valine homozygosity or heterozygos-
ly, the age distribution of the cases. In contrast
ity, our method would not identify the second
where the first sum is over all observed cases and the
to other models, which are based primarily on
distribution parameters, because cases of vCJD
integration is made in the domain D corresponding to
scenarios related to dietary exposures to BSE in
with genotypes other than methionine homozy-
ages between 0.5 and 100 years and to years be-
gosity have not yet been identified.
tween 1980 and 2000. s is the intensity of the
Poisson birth process. Numerical maximization of the
make any assumptions about this parameter that
Our age-risk model allows an estimate of the
likelihood was done with a modified Levenberg Mar-
future size of the epidemic. If we independently
quardt algorithm (SLATEC) after reparameterization
introduce our estimates of the incubation period
of the model A logarithmic transformation was used
tween age and force of infection, we made one
in the Ghani or Cousens models, we find similar
for all variables but incubation mean time. The max-
imization was independently performed with a New-
of the most parsimonious choices possible, i.e.,
“low” predictions: 80 to 630 cases with the
ton-Raphson method (NAG), and all presented re-
a function beginning with a plateau during
Ghani model and 801 with the Cousens model
sults were in agreement in the two methods, with
childhood, followed by an exponential decrease.
(17). In conclusion, our prediction of the epi-
differences between estimates of less than 10Ϫ2.
Numerical integrations were carried out to a preci-
The sensitivity analysis in which all possible
demic of vCJD lies in the “optimistic” end of the
alternatives to the 15-year age limit were tested
ranges of previously published figures, and this
15. J. Huillard d’Aignaux et al., Neurology 53, 1197
ruled out an even simpler model with only one
low value is in favor of a large species barrier
16. R. L. Klitzman, M. P. Alpers, D. C. Gajdusek, Neuro-
exponential function (age limit ϭ 0) and found
epidemiology 3, 20 (1984).
as the optimal value an age limit of 16. We
17. The figure obtained from the Cousens model when an
have no clear physiological explanation for
References and Notes
incubation period of mean 15 years and 95th percen-
this age limit: Although a relation with puber-
1. M. E. Bruce et al., Nature 389, 498 (1997).
2. N. M. Ferguson, C. A. Donnelly, M. E. J. Woolhouse,
18. We thank J. Gagnon for helpful discussions.
ty may be hypothesized, experimental evi-
R. M. Anderson, Philos. Trans. R. Soc. London Ser. BBiol. Sci. 352, 803 (1997).
23 NOVEMBER 2001 VOL 294 SCIENCE www.sciencemag.org

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