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

13

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

babili

ty D

ensity

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

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

babili

ty D

ensity

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

)!(

)())((

)()(

an

eamanP

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 )!(

)())((

)()(

an

eamanP

v

amanv

vv

vv

Observed number of vaccinated cases in

age group a

Poisson probability

Expected number of vaccinated cases in

age group a

!)(

k

ekP

k

9

Unvaccinated

0

0.1

0.2

0.3

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0.5

0.6

0.7

0.8

0.9

1

0-4 5--9 10--19 20--29 30-39 40--Age

Pro

babili

ty D

ensity

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

)!(

)())((

)()(

an

eamanP

u

amanu

uu

uu

)!(

)())((

)()(

an

eamanP

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

babili

ty D

ensity

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

)!(

)())((

)()(

an

eamanP

u

amanu

uu

uu

)!(

)())((

)()(

an

eamanP

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

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0.7

0.8

0.9

1

0-4 5--9 10--19 20--29 30-39 40--Age

Pro

babili

ty D

ensity

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

)!(

)())((

)()(

an

eamanP

u

amanu

uu

uu

)!(

)())((

)()(

an

eamanP

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()())!()(()!(

)!())(( ananan

uan

uusuus

uusus

usuusus ababananan

ananP

)()()()( ))(1()())!()(()!(

)!())(( ananan

van

vvsvvs

vvsvs

vsvvsvs ababananan

ananP

Are we protected against severe disease?

Observed number of unvaccinated severe cases in age group

a

binomial 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()())!()(()!(

)!())(( ananan

uan

uusuus

uusus

usuusus ababananan

ananP

)()()()( ))(1()())!()(()!(

)!())(( ananan

van

vvsvvs

vvsvs

vsvvsvs ababananan

ananP

Are we protected against severe disease?

5

)()()()( ))(1()())!()(()!(

)!())(( ananan

uan

uusuus

uusus

usuusus ababananan

ananP

)()()()( ))(1()())!()(()!(

)!())(( ananan

van

vvsvvs

vvsvs

vsvvsvs ababananan

ananP

Are we protected against severe disease?

5

)()()()( ))(1()())!()(()!(

)!())(( ananan

uan

uusuus

uusus

usuusus ababananan

ananP

)()()()( ))(1()())!()(()!(

)!())(( ananan

van

vvsvvs

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()())!()(()!(

)!())(( ananan

uan

uusuus

uusus

usuusus ababananan

ananP

)()()()( ))(1()())!()(()!(

)!())(( ananan

van

vvsvvs

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 probabilities

aeafafaProtect ))(1()()(

Protection against severe disease

4

Vdt

dV)( 1

vv SVdt

dS1

1

1

1 uu Sdt

dS

2

2

2 uu Sdt

dS

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