Full papers:Nishiura H, Schwehm M, Eichner M. Epidemiology 2006; 17(5): 576-81
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Full papers: Nishiura H, Schwehm M, Eichner M. Epidemiology 2006; 17(5): 576-81 Nishiura H, Eichner M. Infection 2006; 34: in press. Learning about long-term vaccination effects from outbreak data Martin Eichner, Markus Schwehm & Hiroshi Nishiura 19 September 2006 14
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Learning about long-term vaccination effects from outbreak data. Martin Eichner, Markus Schwehm & Hiroshi Nishiura 19 September 2006. Full papers:Nishiura H, Schwehm M, Eichner M. Epidemiology 2006; 17(5): 576-81 Nishiura H, Eichner M. Infection 2006; 34: in press. 14. Background. - PowerPoint PPT Presentation
Transcript of Full papers:Nishiura H, Schwehm M, Eichner M. Epidemiology 2006; 17(5): 576-81
Full papers: Nishiura H, Schwehm M, Eichner M. Epidemiology 2006; 17(5): 576-81
Nishiura H, Eichner M. Infection 2006; 34: in press.
Learning about long-term vaccination effects from outbreak data
Martin Eichner, Markus Schwehm & Hiroshi Nishiura
19 September 2006
14
Background
CDSR, WHO. WHO Fact Sheet on Smallpox. 2001CDC. Smallpox Response Program & Guidelines. 2003
Since World Health Organization announced the total eradication of smallpox in 1979, routine vaccination was ceased worldwide
The potential for bioterrorism has led to intensive discussions on the durability of vaccine-induced immunity
Mass vaccination prior to an attack is currently not recommended
CDC suggests vaccine-induced immunity lasts more or less for 3-5 years
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Epidemiologic evidence: vaccinated cases tended to be much older than unvaccinated ones.
Text book statements: protection lasts 20 years
Experimental evidence: more than 90% of previously vaccinated individuals hold either cellular or humoral immunity
Are we still protected against smallpox?
Elkington JSC, Outbreak of smallpox in Launceston, 1904Iguchi J. A report on prevention of smallpox, 1929Dixon CW. Smallpox. London, 1962.Eichner M. Am J Epidemiol 2003; 158: 717-723.
Gallwitz S et al. Clin Microbiol 2003;41:4069-70.Hammarlund E et al. Nat Med 2003;9:1131-7.Amara RR et al. J Virol 2004;78:3811-6.Crotty S et al. J Immunol 2003;171:4969-73.12
Unvaccinated
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0-4 5--9 10--19 20--29 30-39 40--Age
Pro
babi
lity
Den
sity
Vaccinated
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0-4 5--9 10--19 20--29 30-39 40--Age
Pro
babi
lity
Den
sity
Elevated age at infection
Suggesting the duration of vaccine-induced immunity
Unvaccinated Vaccinated
Smallpox outbreak in Bombay (1969)
11
Statistical analysis
Historical records on epidemic of smallpox
Criteria for inclusion:(1) Epidemic caused by variola major (not variola minor)(2) Age-specific incidence with vaccination history(3) No revaccination. No post-exposure vaccination (-> UK during the late 19th century)
Key assumptions for a statistical model:(1) Vaccination took place shortly after birth (within 3 months)(2) Primary vaccination failure neglected(3) Booster effects can be adjusted by using age-specific force of infection among unvaccinated(4) Force of infection, probability of case detection, and natural mortality are identical for vaccinated and unvaccinated people
10
Unvaccinated
0
0.1
0.2
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0.4
0.5
0.6
0.7
0.8
0.9
1
0-4 5--9 10--19 20--29 30-39 40--Age
Pro
babi
lity
Den
sity
Vaccinated
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0-4 5--9 10--19 20--29 30-39 40--Age
Pro
babi
lity
Den
sity
Unvaccinatedcases
Vaccinatedcases
)!()())((
)()(
aneamanP
u
amanu
uu
uu
Observed number of unvaccinated cases
in age group a
Poisson probability
Expected number of unvaccinated cases
in age group a
))(( anP uu )(anu )!()())((
)()(
aneamanP
v
amanv
vv
vv
Observed number of vaccinated cases in
age group a
Poisson probability
Expected number of vaccinated cases in
age group a
!)(
kekPk
9
Unvaccinated
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0-4 5--9 10--19 20--29 30-39 40--Age
Pro
babi
lity
Den
sity
Vaccinated
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0-4 5--9 10--19 20--29 30-39 40--Age
Pro
babi
lity
Den
sity
Unvaccinatedcases
Vaccinatedcases
)!()())((
)()(
aneamanP
u
amanu
uu
uu
)!(
)())(()()(
aneamanP
v
amanv
vv
vv
9
Unvaccinated
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0-4 5--9 10--19 20--29 30-39 40--Age
Pro
babi
lity
Den
sity
Vaccinated
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0-4 5--9 10--19 20--29 30-39 40--Age
Pro
babi
lity
Den
sity
Unvaccinatedcases
Vaccinatedcases
)!()())((
)()(
aneamanP
u
amanu
uu
uu
)!(
)())(()()(
aneamanP
v
amanv
vv
vv
))(1()()( afVamam uv
odds of being vaccinated
probability of still being protected
)()( amam uv Vamam uv )()(
)1/( VVp )1()( aeeaf
model for loss of protection
9
))(1()()( afVamam uv
Unvaccinated
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0-4 5--9 10--19 20--29 30-39 40--Age
Pro
babi
lity
Den
sity
Vaccinated
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0-4 5--9 10--19 20--29 30-39 40--Age
Pro
babi
lity
Den
sity
Unvaccinatedcases
Vaccinatedcases
)!()())((
)()(
aneamanP
u
amanu
uu
uu
)!(
)())(()()(
aneamanP
v
amanv
vv
vv
odds of being vaccinated
probability of still being protected
)1/( VVp )1()( aeeaf
model for loss of protection
a
vvuu anPanPLike ))(())((
searching the parameter values
which maximize the likelihood,,),(),...,( 1 Vamam nuu
9 maximum likelihood estimation
a
e
e
a
a
)5.0ln(1ln
)5.0ln(1
)1()5.0ln(
Estimated duration of vaccine-induced immunity against smallpox
Duration of protection against smallpox [years] Outbreak Year
Median 95 % CI†
London 1870s 11.7 10.6, 12.6
Sheffield 1887-8 15.1 13.7, 17.3
London 1893 17.2 15.4, 19.7 Liverpool 1902-3 23.4 18.6, 32.2 Dewsbury 1904 28.4 24.9, 33.7
London‡ 1929-30 46.0 42.7, 50.6
Gompertz curve)1()(
aeeaf
Median
)1(5.0 aee
CI based on the profile likelihood
8
Conclusions
Variola majorA. London 1870s n = 9 761B. Sheffield 1887-8 n = 6 088C. London 1893 n = 2 101D. Liverpool 1902-3 n = 1 163E. Dewsbury 1904 n = 625
Variola minorF. London 1929-30 n = 3 023
Result: Protection against smallpox lasts for 15 to 35 years Conclusion: Our present population may not hold residual protection
against smallpox infection
6
)()()()( ))(1()())!()(()!(
)!())(( anananu
anu
usuus
uusus
usuusus ababananan
ananP
)()()()( ))(1()())!()(()!(
)!())(( anananv
anv
vsvvs
vvsvs
vsvvsvs ababananan
ananP
Are we protected against severe disease?
Observed number of unvaccinated severe cases in age group
abinomial
probability
Probability that an unvaccinated
develops severe disease
binomial probability
))(( anP usus )(anus
knk ppknk
nkP
)1()!(!
!)(
5
Observed total number of
unvaccinated cases in age group a
Observed number of unvaccinated severe cases in age group
a
Probability that an vaccinated develops
severe disease
Observed total number of vaccinated cases in age group a
)()()()( ))(1()())!()(()!(
)!())(( anananu
anu
usuus
uusus
usuusus ababananan
ananP
)()()()( ))(1()())!()(()!(
)!())(( anananv
anv
vsvvs
vvsvs
vsvvsvs ababananan
ananP
Are we protected against severe disease?
5
)()()()( ))(1()())!()(()!(
)!())(( anananu
anu
usuus
uusus
usuusus ababananan
ananP
)()()()( ))(1()())!()(()!(
)!())(( anananv
anv
vsvvs
vvsvs
vsvvsvs ababananan
ananP
Are we protected against severe disease?
5
)()()()( ))(1()())!()(()!(
)!())(( anananu
anu
usuus
uusus
usuusus ababananan
ananP
)()()()( ))(1()())!()(()!(
)!())(( anananv
anv
vsvvs
vvsvs
vsvvsvs ababananan
ananP
)1()()( auv eabab )()( abab uv
probability of still being protected
model for loss of protection
Are we protected against severe disease?
5
)()()()( ))(1()())!()(()!(
)!())(( anananu
anu
usuus
uusus
usuusus ababananan
ananP
)()()()( ))(1()())!()(()!(
)!())(( anananv
anv
vsvvs
vvsvs
vsvvsvs ababananan
ananP
)1()()( auv eabab )()( abab uv
probability of still being protected
model for loss of protection
a
vsvsusus anPanPLike ))(())((
searching the parameter values
which maximize the likelihood),(),...,( 1 nuu abab
Are we protected against severe disease?
5 maximum likelihood estimation
Variola majorC. London 1893 n = 2101D. Liverpool1902-3 n = 1163E. Dewsbury1904 n = 625
Partial protection against fatality decays very slowly(sometimes lifelong protection)
The majority of vaccinees may still retain partial protection against severe and fatal smallpox
Combining both probabilitiesaeafafaProtect ))(1()()(
Protection against severe disease
4
VdtdV )( 1
vv SVdtdS
1
1
11 u
u SdtdS
2
22 u
u SdtdS
Heterogeneous populations
3
Heterogeneous populations
Vaccination coverage 80%
Heterogeneity parameter q =0.3
Forces of infection1=0.02/year, 2=0.08/year (R01=1.4; R02=5.6 for L=70 years)
3
For small q, our estimates appropriately reflect the true duration of immunity and the true vaccination coverage. For larger values of q, we slightly overestimate tm and p.
Heterogeneous populations
2
Final conclusionsAre we still protected against smallpox?
Bad news: protection against infection and disease should mostly be lost by now
Good news: infected individuals may still be protected against life-threatening disease
Bad news: mild disease may allow higher mobility, may not be easily recognized and, therefore, may increase spread
2
Outlook: simulation studies
1
