Christl Donnelly

1
The Challenges of Analysing Outbreaks of
Infectious Diseases
Christl Donnelly Department of Infectious Disease
EpidemiologyImperial College London
2
Context

• Revolution in data availability for public
  health planning
• Population/demography
• Disease surveillance
• Molecular/genetic (for disease and people)
• Models integrate data into conceptual framework
  to
• Interpret pattern
• Understand mechanisms
• Predict trends
• Dual role for modelling and analysis
• Disease control (e.g. FMD, Influenza, SARS,
  Polio, bovine TB, HIV).
• Basic science increasing understanding.

3
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
4
International coordination is key
4
5
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.

• 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.

from report of FMD until farm slaughter
6
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-transmissi
  on cycle that might be targeted by intervention
  measures.
• By modelling possible intervention measures,
  predictions can also be obtained for the effects
  of different control options prior to
  implementation.

Relative transmission risk for farms, averaged
over 5-km squares, incorporating farm
fragmentation data. (Ferguson, Donnelly
Anderson, Nature 2001)
6
7
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
8
What does a simple outbreak model show about
contact tracing and quarantining?
Example mini-outbreak
Asymptomatic
Symptomatic
2
Increasing infectiousness
8
9
What does a simple outbreak model show about
contact tracing and quarantining?
Example mini-outbreak
Asymptomatic
Symptomatic
5
3
Increasing infectiousness
4
9
10
What does a simple outbreak model show about
contact tracing and quarantining?
Example mini-outbreak
Asymptomatic
Symptomatic
2
1
3
Increasing infectiousness
4
10
11
Impact of self isolation augmented by contact
tracing (and quarantine)
90 SI
90 SI 100 CT
11
12
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.

12
13
Real-time data capture in Hong Kong
13
14
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.

14
15
Probable SARS Cases in Hong Kong 2003
Worldwide 8096 cases 774 deaths China 5327
cases 349 deaths Hong Kong 1755 cases 299
deaths
15
16
Censoring A key statistical challenge

• If not corrected for
• Case fatality rate could be underestimated
  (because cases with longer times from infection
  to death wont 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
• Considerable pressure for clear, definitive
  results immediately!

16
17
Time from symptoms to identification / hospital
admission
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
17
18
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 Number of deaths C Total number of cases
D Number of deaths R Number recovered
18
19
Adapted Kaplan-Meier Method

• Two terminal states with hazard functions h0(t)
  and h1(t) and associated (incomplete) survivor
  functions
• The estimate of the case fatality rate is then
• 
  where
• Estimate the hazard function in discrete time
  (days) using the simple estimator
• where dij is the number of events of type i on
  day j and nj is the number remaining at risk at
  time j

19
20
Adapted Kaplan-Meier Method
To extrapolate incomplete survivor functions,
assume that death/discharge rate at the tail
occurs at the same rate as previously
20
21
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
ratioWHO 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.
21
22
Post-epidemic Evaluation of Case Fatality Rate
Estimators
Source Ghani et al., American Journal of
Epidemiology 162 479-486, 2005.
22
23
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
4
Y
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 gt1 for an epidemic to take off.

23
24
Transmission Model Reproduced the Observed
Dynamics
Reproductive number in HK
Average of 1000 model simulations
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
25
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).

25
After this some movements to slaughterhouse are
allowed.
26
FMD Geographic spread and daily incidence
BBC
26
27
Farm demography
No. of farmsper 5x5 km
27
28
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.
28
29
Pair correlation transmission model
Equations somewhat tedious, even for simplified
form of model
dS/dt-(tmw)SI-pbSI/N dE/dt
pbSI/N tSI-nE-mEI dI/dtnE-sI-m
II dSS/dt-2(tmw)SSI-2pbSSI/N dSE/
dtt(SSI-ISE)-m(SEIISE)-wISEpb(SS-S
E)I/N dSI/dtnSE-(tmw)(ISISI)-
pbSII/N dEE/dttISE-2mEEI-2nEE
2pbSEI/N dEI/dtnEE-m(EIIEI)-(ns)E
I pbSII/N dII/dt2nEI-2sII-2m(III
II).
29
30
Telegraph April 2001
30
31
Predictions as released by OST
Predictions as made using data up to 29 March.

• 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
32
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
33
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
34
The impact of reactive culling on cattle TB
incidence
The reactive treatment was associated with a 27
increase in the incidence of cattle TB (p0.0145
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.
Donnelly et al. Nature 426, 834-837, 2003.
34
35
Bait marking A standard technique for mapping
badger home ranges
35
36
The first comparison reactive culling
Bait marking data were consistent with hypothesis
that badgers range more widely when densities
are reduced by reactive culling
data from triplets B, D, G H
no culling
36
37
Furthermore
Badger densities were slightly reduced, and
badger movements expanded, on land immediately
outside proactive culling areas
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
38
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)
38
39
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 survey-only areas
(95 CI 5.0 to 58 higher)
39
40
FMD Data What is available now?

• Full data are available to research workers.
• See Defras Animal Health and Welfare FMD Data
  Archive
• https//secure2.csl.gov.uk/fmd/

40
41
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