Transcript Some problems with pandemic influenza R0 estimates

Pandemic Influenza Forecasting: Does Past
Performance Indicate Future Performance?
Institute for Mathematical Sciences
(IMS), Singapore
Workshop on Mathematical models for the Study of the
Infection Dynamics of Emergent and Re-emergent
Diseases in Humans
22-26 October 2007
Julian W Tang
Department of Microbiology
The Chinese University of Hong Kong
Different types of mathematical
models:
Biofluiddynamics
Different types of mathematical
models:
Biofluiddynamics
Different types of mathematical
models:
Biofluiddynamics
Different types of
mathematical models:
Cosmological
Different types of
mathematical models:
Cosmological
Different types of
mathematical models:
Cosmological
Summary

Previous influenza pandemic R0 estimates:

have been based on behaviour of past influenza
pandemics (1918, 1957, 1968).
Summary

Previous influenza pandemic R0 estimates:

have been based on behaviour of past influenza
pandemics (1918, 1957, 1968).

And for the next pandemic:
the world’s population has increased several times
 rapid, frequent travel is the norm
 the next pandemic strain is unknown

Summary (cont)

However:
previous outbreak reports may be unreliable
 asymptomatic cases probably were not recorded
 not all symptomatic cases were laboratory confirmed

Summary (cont)

However:
previous outbreak reports may be unreliable
 asymptomatic cases probably were not recorded
 not all symptomatic cases were laboratory confirmed,


Even if they were confirmed as influenza A, no sequencing
was available to confirm the no. of true secondary cases
from the same index case – they could have been sick from
another viral infection
Summary (cont)

However:
previous outbreak reports may be unreliable
 asymptomatic cases probably were not recorded
 not all symptomatic cases were laboratory confirmed,


Even if they were confirmed as influenza A, no sequencing was
available to confirm the no. of true secondary cases from the
same index case – they could have been sick from another viral
infection

Hence, estimates of R0 from previous influenza pandemics
are probably inaccurate – but how inaccurate?
“The best
data we
have”
R0=?
coughs
Infected
index case
comes to
school
Enters a
susceptible
population (e.g.
a classroom of
children)
“The best
data we
have”
Exposed, infected, asymptomatic
R0=5?
(As estimated by
contemporary
infection control
team)
R0=11
(As estimated by
God)
Exposed, infected, symptomatic
Exposed, infected, symptomatic, but from index
case on the school bus that morning)
“The best
data we
have”
Exposed, infected, asymptomatic,
not counted as 2o case (e.g. lab
testing only performed for
symptomatic cases)
R0=5?
(As estimated by
contemporary
infection control
team)
R0=10
(As estimated by
God)
Exposed, infected, symptomatic
R0=20
(2003)
R0=20?
(2003)
R0<21?
(2004)
R0=20?
(2003)
R0<21?
(2004)
R0<2-3?
(2004)
Transmissibility of 1918 Pandemic Influenza
(Supplementary Information)
Christina E. Mills (1), James M. Robins (1,2), Marc Lipsitch (1,3)
(1) Department of Epidemiology, Harvard School of Public Health, 677 Huntington Avenue, Boston,
Massachusetts 02115, USA
(2) Department of Biostatistics, Harvard School of Public Health, 677 Huntington Avenue, Boston,
Massachusetts 02115, USA
(3) Department of Immunology and Infectious Diseases, Harvard School of Public Health, 677 Huntington
Avenue, Boston, Massachusetts 02115, USA
Mills CE, Robins JM, Lipsitch M. Nature. 2004 Dec 16;432(7019):904-6.
Supplementary Discussion
“Two recent papers have used estimates of the basic reproductive number much higher than
those reported here, up to 20 (ref. 25) or 21 (ref. 26).
We have endeavoured to understand the reasons for this major divergence in estimates. This
effort has been hampered by ambiguities in the original reports from which the data underlying
the estimates of Gog (25) and Fraser (26) are derived.”
Supplementary Material. Mills CE, Robins JM, Lipsitch M. Transmissibility of 1918
pandemic influenza. Nature. 2004 Dec 16;432(7019):904-6.
Supplementary Discussion
“One source of data is an outbreak of influenza A/H1N1 in January-February 1978
in a British boarding school (27). The report of this outbreak gives the number of
children “confined to bed” on each day of the epidemic. If one interpreted “confined
to bed” as a measure of prevalence of infectiousness”
Supplementary Material. Mills CE, Robins JM, Lipsitch M. Transmissibility of 1918
pandemic influenza. Nature. 2004 Dec 16;432(7019):904-6.
Supplementary Discussion
“One source of data is an outbreak of influenza A/H1N1 in January-February 1978
in a British boarding school (27). The report of this outbreak gives the number of
children “confined to bed” on each day of the epidemic. If one interpreted “confined
to bed” as a measure of prevalence of infectiousness”
- Presumably meaning - being infected? Assuming bed-bound as soon as
symptomatic for “illness” rather than “infection control” reasons?
Supplementary Material. Mills CE, Robins JM, Lipsitch M. Transmissibility of 1918
pandemic influenza. Nature. 2004 Dec 16;432(7019):904-6.
Supplementary Discussion
“and if one used latent and infectious periods of the sort assumed in our study, then
one would indeed infer a very large R (on the order of 20) from these data, because
the growth in the number “confined to bed” has an initial doubling time of less than 1
day (vs. ~3 days in our data sets). Under these assumptions, one would have to infer
that the transmissibility of influenza A/H1N1 in this boarding school (the year of the
subtype’s reintroduction) was much higher than the estimates we report.”
Supplementary Material. Mills CE, Robins JM, Lipsitch M. Transmissibility of 1918
pandemic influenza. Nature. 2004 Dec 16;432(7019):904-6.
Supplementary Discussion
“and if one used latent and infectious periods of the sort assumed in our study, then
one would indeed infer a very large R (on the order of 20) from these data, because
the growth in the number “confined to bed” has an initial doubling time of less than 1
day (vs. ~3 days in our data sets). Under these assumptions, one would have to infer
that the transmissibility of influenza A/H1N1 in this boarding school (the year of the
subtype’s reintroduction) was much higher than the estimates we report.”
- How do you judge whether one set of assumptions is better than another?
From a biological, or mathematical viewpoint?
Supplementary Material. Mills CE, Robins JM, Lipsitch M. Transmissibility of 1918
pandemic influenza. Nature. 2004 Dec 16;432(7019):904-6.
Supplementary Discussion
“We suspect, however, that a better explanation for the extremely rapid increase in
the number of children “confined to bed” is the timing of ascertainment, since
confinement to bed is not in fact equivalent to biological infectiousness (viral
shedding).”
Supplementary Material. Mills CE, Robins JM, Lipsitch M. Transmissibility of 1918
pandemic influenza. Nature. 2004 Dec 16;432(7019):904-6.
Supplementary Discussion
“We suspect, however, that a better explanation for the extremely rapid increase in
the number of children “confined to bed” is the timing of ascertainment, since
confinement to bed is not in fact equivalent to biological infectiousness (viral
shedding).”
- Confinement to bed (for symptomatic reasons) implies a symptomatic state
(or are some students malingering – not unusual nowadays?). This can be
variable in severity and in degree of tolerance for each individual, thus the
time spent mobile whilst symptomatic and infectious, is variable for each
person.
Supplementary Material. Mills CE, Robins JM, Lipsitch M. Transmissibility of 1918
pandemic influenza. Nature. 2004 Dec 16;432(7019):904-6.
Supplementary Discussion
“We suspect, however, that a better explanation for the extremely rapid increase in
the number of children “confined to bed” is the timing of ascertainment, since
confinement to bed is not in fact equivalent to biological infectiousness (viral
shedding).”
- Confinement to bed (for symptomatic reasons) implies a symptomatic state. This can
be variable in severity and in degree of tolerance for each individual, thus the time
spent mobile whilst symptomatic and infectious, is variable for each person.
- Also, for all respiratory viruses, they certainly appear to be infectious during
their symptomatic period, but also, possibly, for 12-24 hours before symptom
onset (Fraser et al. 2004; Wu et a. 2006?)
Supplementary Material. Mills CE, Robins JM, Lipsitch M. Transmissibility of 1918
pandemic influenza. Nature. 2004 Dec 16;432(7019):904-6.
Supplementary Discussion
“Moreover, confinement to bed may reduce or increase an individual’s opportunities
for transmission, depending on living conditions and hygiene.”
Supplementary Material. Mills CE, Robins JM, Lipsitch M. Transmissibility of 1918
pandemic influenza. Nature. 2004 Dec 16;432(7019):904-6.
Supplementary Discussion
“Moreover, confinement to bed may reduce or increase an individual’s opportunities
for transmission, depending on living conditions and hygiene.”
- Yes! Exactly the point. If friends come to visit (especially in boarding
schools), e.g. room-mates, etc., a degree of secondary infection can continue –
and they still need to visit the bathroom (contact? duration of contact required
to transmit?). Also, most symptomatic patients are not completely prostrate,
and will tend to walk around, talk to people (it is very boring just lying in bed).
Supplementary Material. Mills CE, Robins JM, Lipsitch M. Transmissibility of 1918
pandemic influenza. Nature. 2004 Dec 16;432(7019):904-6.
Supplementary Discussion
“An alternate (not mutually exclusive) hypothesis is that transmission was more intense
in this boarding school than in the general population”
Supplementary Material. Mills CE, Robins JM, Lipsitch M. Transmissibility of 1918
pandemic influenza. Nature. 2004 Dec 16;432(7019):904-6.
Supplementary Discussion
“An alternate (not mutually exclusive) hypothesis is that transmission was more intense
in this boarding school than in the general population”
– Another respiratory virus, adenovirus (see Abstract), is well known to be
more aggressive in high-density military barracks than in the general
population – a boarding school environment is probably very similar. It would
not be surprising if a new pandemic influenza strain behaved in a similar
manner – though we have no idea what virus this will be at the moment.
Supplementary Material. Mills CE, Robins JM, Lipsitch M. Transmissibility of 1918
pandemic influenza. Nature. 2004 Dec 16;432(7019):904-6.
Supplementary Discussion
“or (even more speculatively) that the strain introduced by a single student returning
from Hong Kong was especially transmissible.”
Supplementary Material. Mills CE, Robins JM, Lipsitch M. Transmissibility of 1918
pandemic influenza. Nature. 2004 Dec 16;432(7019):904-6.
Supplementary Discussion
“or (even more speculatively) that the strain introduced by a single student returning
from Hong Kong was especially transmissible.”
– But, all of this is speculation anyway – it is a different interpretation of the
same outbreak. Of course, host factors may play a role in whether an infected
individual becomes a ‘super-spreader’, or even just a ‘great’ or ‘above-average’
-spreader’. Anyway, what is meant by ‘especially transmissible’ anyway? R >20,
or R >3?
Supplementary Material. Mills CE, Robins JM, Lipsitch M. Transmissibility of 1918
pandemic influenza. Nature. 2004 Dec 16;432(7019):904-6.
Supplementary Discussion
“We believe that the estimate of R~20 from these data is unlikely for another reason: 251 of
the 763 children remained uninfected in this outbreak, which is inconsistent with an R in
excess of ~3 (assuming a well-mixed population)”
Supplementary Material. Mills CE, Robins JM, Lipsitch M. Transmissibility of 1918
pandemic influenza. Nature. 2004 Dec 16;432(7019):904-6.
Supplementary Discussion
“We believe that the estimate of R~20 from these data is unlikely for another reason: 251 of
the 763 children remained uninfected in this outbreak, which is inconsistent with an R in
excess of ~3 (assuming a well-mixed population)”
– This is making an assumption about an assumption, i.e. assuming that R is not 20
and then assuming that there must be a reason for this! It is always possible to have
some susceptibles uninfected, even in a major outbreak, perhaps due to social
distancing/ chance/ variability shedding concentration, or unique host immune
responses.
Supplementary Material. Mills CE, Robins JM, Lipsitch M. Transmissibility of 1918
pandemic influenza. Nature. 2004 Dec 16;432(7019):904-6.
Supplementary Discussion
“We believe that the estimate of R~20 from these data is unlikely for another reason: 251 of
the 763 children remained uninfected in this outbreak, which is inconsistent with an R in
excess of ~3 (assuming a well-mixed population)”
– This is making an assumption about an assumption, i.e. assuming that R is not 20 and then
assuming that there must be a reason for this! It is always possible to have some susceptibles
uninfected, even in a major outbreak, perhaps due to social distancing/ chance/ variability
shedding concentration, or unique host immune responses.
- E.g. in the case of the Singapore doctor, his pregnant wife and mother-in-law,
quarantined together in the same room for 2.5 weeks (Frankfurt March 2003), the
doctor and his wife seroconverted ad were viraemic for SARS in multiple body
secretions (blood, NPA, urine, stool), but amazingly, the mother-in-law never
seroconverted.
Supplementary Material. Mills CE, Robins JM, Lipsitch M. Transmissibility of 1918
pandemic influenza. Nature. 2004 Dec 16;432(7019):904-6.
Supplementary Discussion
“We believe that the estimate of R~20 from these data is unlikely for another reason: 251 of
the 763 children remained uninfected in this outbreak, which is inconsistent with an R in
excess of ~3 (assuming a well-mixed population)”
- Also, how do they know that these boys were uninfected? No symptoms? Was there
any subtype-specific influenza A laboratory confirmation performed for all ‘infected’
and ‘uninfected’ cases? Perhaps they were just asymptomatic, with good immune
control and less shedding. Also, the diagnostic assays at that time were almost less
sensitive than they are now, thus underestimating the no. of secondary cases.
Modern molecular epidemiology
expectations and level of proof to
demonstrate ‘true’ secondary cases.
However, may still be difficult if similar to
contemporary circulating viral strains
Supplementary Material. Mills CE, Robins JM, Lipsitch M. Transmissibility of 1918 pandemic
influenza. Nature. 2004 Dec 16;432(7019):904-6.
Supplementary Discussion
“However, given the limited description available, these hypotheses must remain
speculative.”
Supplementary Material. Mills CE, Robins JM, Lipsitch M. Transmissibility of 1918 pandemic
influenza. Nature. 2004 Dec 16;432(7019):904-6.
Supplementary Discussion
“However, given the limited description available, these hypotheses must remain
speculative.”
- Just the like reasons given for extracting a lower R value from this outbreak report!
Supplementary Material. Mills CE, Robins JM, Lipsitch M. Transmissibility of 1918 pandemic
influenza. Nature. 2004 Dec 16;432(7019):904-6.
Supplementary Discussion
“In summary, we believe that these higher estimates result from a combination of
ambiguity in the quantities measured (in the case of the boarding school outbreak)
and in the interpretation of parameters in papers reporting earlier analyses.”
Supplementary Material. Mills CE, Robins JM, Lipsitch M. Transmissibility of 1918 pandemic
influenza. Nature. 2004 Dec 16;432(7019):904-6.
Supplementary Discussion
“In summary, we believe that these higher estimates result from a combination of
ambiguity in the quantities measured (in the case of the boarding school outbreak)
and in the interpretation of parameters in papers reporting earlier analyses.”
- But surely this could go either way? We all tend to believe/see what we want
to, yes? This is a consequence of mathematicians trying to interpret clinical
outbreak data, without the practical hand-on experience of the common
pitfalls and limitations inherent in collecting and reporting such data.
Supplementary Material. Mills CE, Robins JM, Lipsitch M. Transmissibility of 1918 pandemic
influenza. Nature. 2004 Dec 16;432(7019):904-6.
Supplementary Discussion
We cannot, however, exclude the possibility that the English boarding school
outbreak actually represented a more rapid spread (and therefore, we infer, higher
value of R) than those we have analyzed for larger populations in the main text. “
Supplementary Material. Mills CE, Robins JM, Lipsitch M. Transmissibility of 1918 pandemic
influenza. Nature. 2004 Dec 16;432(7019):904-6.
Supplementary Discussion
We cannot, however, exclude the possibility that the English boarding school
outbreak actually represented a more rapid spread (and therefore, we infer, higher
value of R) than those we have analyzed for larger populations in the main text. “
-No, of course you cannot! But the lower R value has now been widely
accepted as real! If there is uncertainty. Yet, why go for a very specific lower
estimate, instead of suggesting all possible ranges of R, as Fraser et al. 2004,
did…? Practical, political economic reasons/pressures? Perhaps, but the virus
will not pay any attention to this!
Fig. 2. Parameter estimates. Plausible ranges for the key parameters R0 and (see main text for sources) for four
viral infections of public concern are shown as shaded regions. The size of the shaded area reflects the
uncertainties in the parameter estimates. The areas are color-coded to match the assumed variance values for()
and S() of Fig. 1 appropriate for each disease, for reasons that are apparent in Fig. 3.
Fraser C, Riley S, Anderson RM, Ferguson NM. Factors that make an infectious disease outbreak controllable. Proc Natl Acad Sci
U S A. 2004 Apr 20;101(16):6146-51.
Mills et al. (2004)’s
estimate of R (<3) for
pandemic influenza, a
respiratory virus, is similar
to of HIV – a sexually
transmitted disease
acquired only via intimate
contact.
Fig. 2. Parameter estimates. Plausible ranges for the key parameters R0 and (see main text for sources) for four
viral infections of public concern are shown as shaded regions. The size of the shaded area reflects the
uncertainties in the parameter estimates. The areas are color-coded to match the assumed variance values for()
and S() of Fig. 1 appropriate for each disease, for reasons that are apparent in Fig. 3.
Fraser C, Riley S, Anderson RM, Ferguson NM. Factors that make an infectious disease outbreak controllable. Proc Natl Acad Sci
U S A. 2004 Apr 20;101(16):6146-51.
Fraser et al. (2004)’s
approach is probably
more realistic (in the
absence of any facts),
taking into account the
possible uncertainties
of the behaviour of a
new virus.
Mills et al. (2004)’s estimate
of R (<3) for pandemic
influenza, a respiratory virus,
is similar to of HIV – a
sexually transmitted disease
acquired only via intimate
contact.
Fig. 2. Parameter estimates. Plausible ranges for the key parameters R0 and (see main text for sources) for four
viral infections of public concern are shown as shaded regions. The size of the shaded area reflects the
uncertainties in the parameter estimates. The areas are color-coded to match the assumed variance values for()
and S() of Fig. 1 appropriate for each disease, for reasons that are apparent in Fig. 3.
Fraser C, Riley S, Anderson RM, Ferguson NM. Factors that make an infectious disease outbreak controllable. Proc Natl Acad Sci
U S A. 2004 Apr 20;101(16):6146-51.
Conclusions
We are all human and often, we see what we want to see.
In ambiguous data, it is even easier to see what we want to see.
Conclusions
We are all human and often, we see what we want to see.
In ambiguous data, it is even easier to see what we want to see.
The fact that this same outbreak report was used in at least
two different papers by 2 different groups of mathematicians,
and was interpreted to give very different R values (1-3 vs >20)
by each group, suggests that the interpretation is still open.
Conclusions
We are all human and often, we see what we want to see.
In ambiguous data, it is even easier to see what we want to see.
The fact that this same outbreak report was used in at least two different papers
by 2 different groups of mathematicians, and was interpreted to give very
different R values (1-3 vs >20) by each group, suggests that the interpretation is
still open.
Is such ambiguous data helpful or misleading? The points
raised in this presentation can be applied to any outbreak
report, and probably none of them will present definitive proof
(by modern standards now) of epidemiological linkage.
Conclusions
We are all human and often, we see what we want to see.
In ambiguous data, it is even easier to see what we want to see.
The fact that this same outbreak report was used in at least two different papers
by 2 different groups of mathematicians, and was interpreted to give very
different R values (1-3 vs >20) by each group, suggests that the interpretation is
still open.
Is such ambiguous data helpful or misleading? The points raised in this
presentation can be applied to any outbreak report, and probably none of them
will present definitive proof (by modern standards now) of epidemiological
linkage.
Of course, a high R will be difficult to deal with in any
optimistic or practical way for the purposes of pandemic
planning.
Conclusions
We are all human and often, we see what we want to see.
In ambiguous data, it is even easier to see what we want to see.
The fact that this same outbreak report was used in at least two different papers
by 2 different groups of mathematicians, and was interpreted to give very
different R values (1-3 vs >20) by each group, suggests that the interpretation is
still open.
Is such ambiguous data helpful or misleading? The points raised in this
presentation can be applied to any outbreak report, and probably none of them
will present definitive proof (by modern standards now) of epidemiological
linkage.
Of course, a high R will be difficult to deal with in any optimistic or practical way
for the purposes of pandemic planning.
So, perhaps a low R was interpreted from this outbreak to keep
everyone happy and in this way, perhaps also, has given us a
false sense of security. Time will tell…
So does past performance indicate future
performance for pandemic influenza?

No, I don’t think so because:

Too many other parameters have changed (world
population/density increase, more rapid, frequent air
travel, etc.)
So does past performance indicate future
performance for pandemic influenza?

No, I don’t think so because:

Too many other parameters have changed (world population/density
increase, more rapid, frequent air travel, etc.)

Another influenza pandemic is not necessarily likely
based on previous pandemic events (why should it be?)
So does past performance indicate future
performance for pandemic influenza?

No, I don’t think so because:



Too many other parameters have changed (world population/density
increase, more rapid, frequent air travel, etc.)
Another influenza pandemic is not necessarily likely based on previous
pandemic events (why should they be?)
If it does occur, it may still not be an H5 virus, but
whatever it is, there is no reason why estimates of R
from previous influenza pandemic viruses should have
any bearing at all on the R for the new influenza
pandemic virus

although the virus will still be influenza A, both the
environment and virus subtype will be different from previous
pandemics
Is another influenza pandemic
imminent/ inevitable/ just a matter of
time?
Not sure!