Transcript The Challenges of Analysing Outbreaks of Infectious

The Challenges of Analysing
Outbreaks of Infectious Diseases
Christl Donnelly
Department of Infectious Disease Epidemiology
Imperial College London
Context
• Revolution in data availability for public health
planning:
 Population/demography
 Disease surveillance
 Molecular/genetic (for disease and people)
120
• Dual role for modelling and analysis:
 Disease control (e.g. FMD, Influenza, SARS,
Polio, bovine TB, HIV…).
 Basic science – increasing understanding.
SARS
80
Hong Kong 2003
60
40
20
7-May
23-Apr
9-Apr
26-Mar
12-Mar
0
26-Feb
 Interpret pattern
 Understand mechanisms
 Predict trends
Daily incidence
• Models integrate data into conceptual
framework to:
100
Why are infectious diseases different?
The risk of my getting infected depends on the
risk (and thus the risk behaviour) of others!
For example, a person can become HIV-infected
from a single sexual contact with a single
lifetime partner.
Whereas an IV drug user who shares needles
within a closed user community will not become
infected if all members of that community remain
uninfected.
3
International coordination is key
4
Epidemiological modelling
The spread of infectious diseases is typically
modelled as a function of potential transmission links
between individual people / animals / cells or groups
such as households or farms.
The disease system is described using precisely
defined equations. These equations are then used to
obtain predictions that can be compared with
observed data.
0.35
corrected for
censoring
model
0.3
0.25
probability
0.2
0.15
0.1
0.05
12
10
8
6
4
2
0
0
Both biological
• infectiousness
• duration of symptoms
and non-biological
• time from symptoms until treatment
• number of individuals in a typical family
components of the disease system are
incorporated into a model.
days
from report of FMD until farm slaughter
Insights into transmission:
Opportunities for control
Epidemiological models can be used to
identify risk factors of disease such as
• injecting drug use for HIV,
• use of cattle feed containing meat
and bonemeal for BSE, and
• highly fragmented farm structure
for FMD.
These results can be used to identify
high-risk populations and points in the
infection-transmission cycle that might
be targeted by intervention measures.
Relative transmission risk for farms,
averaged over 5-km squares,
incorporating farm fragmentation data.
(Ferguson, Donnelly & Anderson, Nature 2001)
By modelling possible intervention
measures, predictions can also be
obtained for the effects of different
control options prior to implementation.
6
Science and evidence-based policy
Despite growing acceptance of evidence-based medicine/healthcare
paradigm, basing public policy on firm scientific evidence is still
relatively uncommon.
Need to promote public understanding and acceptance that scientific
evidence as critical to:
 informing policy makers and stakeholders,
 demonstrating the potential benefits/risks of policy changes,
 highlighting uncertainties in the potential policy impacts
Key to gaining public trust are openness and promotion of public
understanding of science.
7
What does a simple outbreak model show
about contact tracing and quarantining?
Example mini-outbreak
Asymptomatic
Increasing infectiousness
Symptomatic
2
8
What does a simple outbreak model show
about contact tracing and quarantining?
Example mini-outbreak
Asymptomatic
Symptomatic
Increasing infectiousness
5
3
4
9
What does a simple outbreak model show
about contact tracing and quarantining?
Example mini-outbreak
Asymptomatic
Increasing infectiousness
Symptomatic
2
1
3
4
10
3
Impact of self isolation augmented by
0contact tracing (and quarantine)
B
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Insufficient
control to
prevent epidemic
15
12
12
Influenza
3
3
C
00
0%
SARS
6
6
Smallpox
9
9
HIV
90% SI
90% SI + 100% CT
Outbreak
controlled
Outbreak controlled
20%
40%
60%
80%
100%
 = proportion of infections that occur prior to symptoms or
by asymptomatic infection
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Real-time analysis: tools and priorities
 Much more data are available immediate for analysis
• For example, considerable demographic data are available
• Increasingly systematic approaches to data collection reduce
biases and missing values
Real-time requirements:
• To identify the few simplifying assumptions that may considerably
speed-up inference;
• To reduce the dimension of the data as much as possible (reduction
in computational time);
• To design fast and efficient algorithms;
• To address biases arising from censoring.
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Real-time data capture in Hong Kong
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SARS Timeline
• 16 Nov 02 – The first case of an atypical pneumonia is reported in
the Guangdong province in southern China.
• 26 Feb 03 – First cases of unusual pneumonia reported in Hanoi,
Vietnam.
• 10 Mar 03 – Dr Carlo Urbani reports an unusual outbreak of the
illness he calls sudden acute respiratory syndrome (SARS) to the
main office of the WHO. He notes that the disease has infected an
usually high number of healthcare workers (22) at the hospital.
• 11 Mar 03 – A similar outbreak of a mysterious respiratory disease
is reported among healthcare workers in Hong Kong.
• 12 Mar 03 – WHO issues a global alert about a new infectious
disease of unknown origin in both Vietnam and Hong Kong.
• 15 Mar 03 – WHO issues a heightened global health alert about the
mysterious pneumonia with a case definition of SARS as after cases
in Singapore and Canada are also identified.
International travel advisories issued by WHO and CDC.
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Probable SARS Cases in Hong Kong: 2003
120
8096 cases – 774 deaths
China
5327 cases – 349 deaths
Hong Kong
1755 cases – 299 deaths
80
60
40
20
28-May
21-May
14-May
07-May
30-Apr
23-Apr
16-Apr
09-Apr
02-Apr
26-Mar
19-Mar
12-Mar
05-Mar
26-Feb
0
19-Feb
Daily incidence
100
Worldwide
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Censoring – A key statistical challenge
If not corrected for…
• Case fatality rate could be underestimated (because cases with longer
times from infection to death won’t have died yet)
• The incubation period could be underestimated (because cases with
longer times from infection to diagnosis/recording in the database are less
likely to have been recorded).
• Onward transmission could be underestimated
Today
Primary case
Detected secondary cases
Secondary cases not yet detected
Time
Infectiousness period
Considerable pressure for clear, definitive results immediately!
16
Time from symptoms to identification / hospital admission
mean days from onset to admission
10
9
8
7
6
5
Important to minimise this interval since
symptomatic individuals may be
transmitting infection on to close
contacts
Significant shortening of mean duration
observed over the course of the
epidemic
4
3
2
1
0
19- 26- 5- 12- 19- 26- 2- 9- 16- 23- 30- 7- 14- 21Feb Feb Mar Mar Mar Mar Apr Apr Apr Apr Apr May May May
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Real-time Estimation of the Case Fatality Rate
• Patients may remain in hospital for several weeks
• Outcome (death / survival) not known for many patients
• Therefore early in the epidemic a large proportion of
observations are censored
• Method 1:
• Method 2:
D
CFR 
C
D = Number of deaths
D
CFR 
( D  R)
D = Number of deaths
C = Total number of cases
R = Number recovered
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Adapted Kaplan-Meier Method
Two terminal states with hazard functions h0(t) and h1(t) and associated
(incomplete) survivor functions:
 t

Si (t )  exp  hi ( x)dx 
 0

The estimate of the case fatality rate is then:ˆ
ˆi   (t )hi (t )dt
 i   (t )hi (t )dt
where
(t )  S0 (t ) S1 (t )
(t )  S (t ) S (t )
0
1 in discrete time (days) using the simple
Estimate the hazard function
estimator:
hˆij  dij / n j
where dij is the number of events of type i on day j and nj is the number
remaining at risk at time j
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Adapted Kaplan-Meier Method
To extrapolate
incomplete survivor
functions, assume that
death/discharge rate at
the tail occurs at the
same rate as previously:
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0 

ˆ0
ˆ0  ˆ1
0.2
0.1

0
0
20
40
Non-parametric
probability
days from
admission of survival
Non-parametric probability of discharge
K-M like estimate
60
20
Impact on WHO methods
Donnelly CA, Ghani AC, Leung GM, et al. Epidemiological determinants
of the spread of the causal agent of severe acute respiratory
syndrome in Hong Kong. Lancet 361: 1761-6, 2003. Online 7 May 03.
“WHO Update 49 - SARS case fatality ratio, incubation period 7 May 03
Case fatality ratio
WHO has today revised its initial estimates of the case fatality ratio of
SARS. …
On the basis of more detailed and complete data, and more reliable
methods, WHO now estimates that the case fatality ratio of SARS ranges
from 0% to 50% depending on the age group affected, with an overall
estimate of case fatality of 14% to 15%. …
A more accurate and unbiased estimation of case fatality for SARS can
be obtained with a third method, survival analysis. This method relies on
detailed individual data on the time from illness onset to death or full
recovery, or time since illness onset for current cases. Using this method,
WHO estimates that the case fatality ratio is 14% in Singapore and 15%
in Hong Kong.”
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Post-epidemic Evaluation of Case Fatality Rate Estimators
Source: Ghani et al., American Journal of Epidemiology 162: 479-486, 2005.
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Reproduction number R of an epidemic
• Epidemics spread through contact (between individuals or farms)
• ‘Chain reaction’ gives exponential growth until epidemic begins to
run out of susceptible individuals/farms to infect.
8
7
6
5
Y 4
Y=1
t=1
Y=2
t=2
Y=4
t=3
Y=8
t=4
3
2
1
0
1
2
3
4
t
• R is the number of secondary infections caused by one primary
case at the start of an epidemic.
• Needs to be >1 for an epidemic to take off.
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Transmission Model Reproduced the Observed Dynamics
Reproductive number in HK
Average of 1000 model simulations
4.00
120
Daily incidence
3.50
3.00
RtXSS
2.50
2.00
1.50
1.00
0.50
100
80
60
40
20
07-May
23-Apr
09-Apr
26-Mar
12-Mar
30-Apr
16-Apr
2-Apr
19-Mar
5-Mar
19-Feb
26-Feb
0
0.00
Day
Riley S, Fraser C, Donnelly CA et al. Transmission dynamics of the etiological
agent of SARS in Hong Kong: Impact of public health interventions. Science
300: 1961-6, 2003. Online 23 May 03.
24
Déirdre
FMD Timeline (2001)
• 19 Feb (1st case) – Veterinarian at Essex abattoir reports suspected
FMD in 27 sows and 1 boar. Livestock movements prohibited within
8km of the infected premises.
• 23 Feb (6 cases) – Case identified in Heddon-on-the-Wall [first
outside Essex]. From 5pm no movements of FMD-susceptible
animals until 2 March*; fairs and markets closed; deer and fox
hunting and hare coursing prohibited.
• 26 Feb – Neil Ferguson emailed John Wilesmith (VLA Epidemiology
Department) regarding epidemiological analysis of FMD epidemic.
• 6 Mar (80 cases) – Meeting chaired by John Krebs re: potential for
epidemiological analysis to inform control and eradication efforts.
Attendees from Imperial College London, Edinburgh, Cambridge
and Warwick. MAFF invited to send representatives to the meeting,
but were unable to do so due to the demands of FMD control.
• 13 March (199 cases) – Epidemiological data emailed by John
Wilesmith (VLA Epidemiology Department).
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*After this some movements to slaughterhouse are allowed.
FMD
Geographic spread
and daily incidence
BBC
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Farm demography
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No. of farms
per 5x5 km
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49 - 145
33 - 48
20 - 32
9 - 19
1-8
Sheep
only
Cows and
sheep
Cows only
27
Report-slaughter delay distribution
The potentially avoidable risks of transmission after infection has been
reported but before the farm has been slaughtered are cause for
concern, but these delays are decreasing.
0.35
5
corrected for
censoring
model
0.2
0.15
0.1
nonCDG
GB
3
2
1
0.05
0
26-30
Mar
21-25
Mar
16-20
Mar
11-15
Mar
1-10
Mar
12
10
19-28
Feb
days
8
6
4
2
0
0
probability
0.25
CDG
4
mean delay (days)
0.3
day of report
28
Pair correlation transmission model
Equations somewhat tedious, even for simplified form of
model: d[S]/dt=-(tmw)[SI]-pb[S][I]/N
d[E]/dt= pb[S][I]/N t[SI]-n[E]-m[EI]
d[I]/dt=n[E]-s[I]-m[II]
d[SS]/dt=-2(tmw)[SSI]-2pb[SS][I]/N
d[SE]/dt=t([SSI]-[ISE])-m([SEI]+[ISE])-w[ISE]+pb[SS]-[SE])[I]/N
d[SI]/dt=n[SE]-(tmw)([ISI]+[SI])- pb[SI][I]/N
d[EE]/dt=t[ISE]-2m[EEI]-2n[EE]+ 2pb[SE][I]/N
d[EI]/dt=n[EE]-m([EI]+[IEI])-(ns)[EI]+ pb[SI][I]/N
d[II]/dt=2n[EI]-2s[II]-2m([II]+[III]).
29
Telegraph – April 2001
30
Predictions as released by OST
450
Model predictions by Dr Neil Ferguson, Dr Christl Donnelly & Prof. Roy Anderson, Imperial College
A: Several Days to Slaughter
Confirmed daily case incidence
400
350
B: Slaughter on infected premises
within 24 hours
300
250
200
A
Predictions as
made using data
up to 29 March.
C: Slaughter on infected and
neighbouring farms within 24 and 48
hours, respectively
Data up to 29 March
150
100
50
B
Data from 30 March
C
0
18-Feb 4-Mar 18-Mar 1-Apr 15-Apr 29-Apr 13-May 27-May 10-Jun 24-Jun
8-Jul
Date
Ferguson NM, Donnelly CA and Anderson RM. The foot-and-mouth epidemic in Great Britain:
Pattern of spread and impact of interventions. Science 292: 1155-60, 2001. Online 12 Apr 01.
31
Choices of statistical methods
 Very sophisticated (e.g. data augmentation methods)…
• Can estimate sophisticated transmission models (space, relative
susceptibility/infectivity according to the type of farm, number of animals…);
• Can deal with most of the uncertainties to be found in field data
• Main limitation: difficult to implement/update, computational time;
 … or relatively simple (e.g. back-calculation type methods):
• Easy to implement /fast;
• Principle:
• To reconstruct the transmission tree;
• Then, estimating R is just a matter of counting secondary cases in the tree;
• Main limitation: only provide estimates of R (nothing on space, susceptibility
and infectiousness variation according to type…)
 We developed an EM algorithm:
• Model the daily probability of transmission between 2 farms;
• EM algorithm: inference based on the comparison of
• Number of transmission events predicted by the model;
• Number of transmission events occurring in the epidemic;
Ferguson NM, Donnelly CA and Anderson RM. Nature 413: 542-8, [4 Oct] 2001.
32
Randomised Badger Culling Trial (RBCT)
Three treatments:
Proactive culling
Reactive culling
Survey-only
Trial areas were recruited in sets of three, known as
triplets.
The ten triplets have been denoted A through J.
The first triplet to be proactively culled was Triplet B
(Dec 1998). The last triplet to begin proactive culling was
Triplet D (Dec 2002).
Thereafter proactive culls happened roughly annually.
33
The impact of reactive culling on cattle TB incidence
Donnelly et al. Nature 426, 834-837, 2003.
The reactive treatment
was associated with
a 27% increase in the
incidence of cattle TB
(p=0.0145; standard
95% CI of 4.8-53%
increase) when
compared with no
culling areas. After
adjustment for
overdispersion, the CI
expands to: 2.4%
decrease to 65%
increase.
34
Bait marking
A standard technique for mapping badger home ranges
colour
marked bait
matching bait returns to setts 35
The first comparison: reactive culling
Bait marking data were consistent with hypothesis that badgers
range more widely when densities are reduced by reactive culling
Triplet D
30
reactive
culling
400
bait returns per sett
no
culling
450
25
350
20
300
250
15
200
10
150
100
5
50
0
0
reactive
median bait return distance
data from triplets B, D, G & H
survey
only
no culling
36
Furthermore…
Badger densities were slightly reduced, and badger movements
expanded, on land immediately outside proactive culling areas
badger
density
badger
movement
data from triplets B, C, D, G & H
This means that, if disruption
of badger spatial organization
caused the increased cattle
TB incidence in reactive
culling areas, we should see
the same effect on farms
neighbouring proactive
culling areas
37
Results
from inside
proactive
culling
areas
Proactive
Survey-only
The incidence
of cattle TB
inside proactive
culling areas
was 19% lower
than that inside
survey-only
areas
(95% CI:
6.2 to 30% lower)
0
100km
38
Results from
just outside
proactive
culling areas
Proactive
Survey-only
The incidence
of cattle TB up
to 2km outside
proactive culling
areas was
29% higher
than that on
farms up to 2km
outside surveyonly areas
0
100km
(95% CI:
5.0 to 58% higher)
39
FMD Data – What is available now?
Full data are available to research workers.
See: Defra’s Animal Health and Welfare: FMD Data Archive
https://secure2.csl.gov.uk/fmd/
40
MRC Centre for Outbreak Analysis and Modelling
Founded in March 2007 with Prof Neil Ferguson as Director.
Its mission is to be an international resource and centre of excellence
for research on the epidemiological analysis and modelling of novel
infectious disease outbreaks.
The centre will undertake applied collaborative work with national and
international agencies in support of policy planning and response
operations against emerging infectious disease threats.
Based at Imperial College London, the Centre also involves staff at the
UK Health Protection Agency.
41