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Pete Dodd
Introduction
Data
Model
Structure
Inference
Results
China
All countries
LTBI
Comparison
Discussion
Limitations
Advantages
1
Mathematical modelling approach toestimating TB incidencePete Dodd (University of Sheffield)
Tuesday, 31 March 2015
Health Economics & Decision ScienceSchool of Health & Related ResearchUniversity of Sheffield
Pete Dodd
Introduction
Data
Model
Structure
Inference
Results
China
All countries
LTBI
Comparison
Discussion
Limitations
Advantages
2
Overview
Goal:
Can a simple transmission model be used in a statisticallyrigorous manner to obtain consistent estimates of TB burdenusing:
• notification• prevalence• mortality
data?
Other criteria:
• Must be scalable & automated• Must include age structure• Must fairly account for all uncertainty
Motivation:using different data types requires modelling assumptions!
Pete Dodd
Introduction
Data
Model
Structure
Inference
Results
China
All countries
LTBI
Comparison
Discussion
Limitations
Advantages
2
Overview
Goal:
Can a simple transmission model be used in a statisticallyrigorous manner to obtain consistent estimates of TB burdenusing:
• notification• prevalence• mortality
data?
Other criteria:
• Must be scalable & automated• Must include age structure• Must fairly account for all uncertainty
Motivation:using different data types requires modelling assumptions!
Pete Dodd
Introduction
Data
Model
Structure
Inference
Results
China
All countries
LTBI
Comparison
Discussion
Limitations
Advantages
3
Countries considered
country WHO TB incidence(per 100Ky)
population(millions)
Cambodia 400 (366 - 444) 15China 70 (66 - 77) 1,386Indonesia 183 (164 - 207) 250Myanmar 373 (340 - 413) 53Nigeria 338 (194 - 506) 174Pakistan 275 (205 - 357) 182Philippines 292 (261 - 331) 98Thailand 119 (106 - 134) 67Viet Nam 114 (121 - 174) 92
Table: The 9 countries considered, together their WHO estimate of TBincidence for 2013 and their population in 2013.
Pete Dodd
Introduction
Data
Model
Structure
Inference
Results
China
All countries
LTBI
Comparison
Discussion
Limitations
Advantages
4
Prevalence data
country prevalence survey yearsCambodia 2002, 2011China 1990, 2000, 2010Indonesia 2004Myanmar 1994, 2009Nigeria 2012Pakistan 2011Philippines 1997, 2007Thailand 1991, 2012Viet Nam 2007
Table: Years of available prevalence survey data for the 9 countriesconsidered.
• Not available in age-structured n/N form for this work.• Approach to different reporting documented in report.
Pete Dodd
Introduction
Data
Model
Structure
Inference
Results
China
All countries
LTBI
Comparison
Discussion
Limitations
Advantages
5
Mortality data
country iso3 VR data points mortality sourceCambodia 0 CFRChina 22 VRIndonesia 0 CFRMyanmar 0 CFRNigeria 0 CFRPakistan 0 CFRPhilippines 13 VRThailand 15 VRViet Nam 2 VR
Table: Approaches to mortality, and sources in the 2013 GTB report.CFR=approach from CFR; VR=from vital registration data.
• By age (0-14, 15-24, 25-34, 35-44, 45-54, 55-64, 65+),sex and calendar year.
• TB death in HIV -ve individuals.• Used B02 for ICD-9 COD coding; A15-A19 for ICD-10 coding.
Pete Dodd
Introduction
Data
Model
Structure
Inference
Results
China
All countries
LTBI
Comparison
Discussion
Limitations
Advantages
6
Other data
Notifications
• By age (0-14, 15-24, 25-34, 35-44, 45-54, 55-64, 65+),sex and calendar year.
• Available for most years
Demography
• UN ESA Population division modelled population size by5-year age group, sex, and calendar year.
• UN ESA estimated birth rates.
Pete Dodd
Introduction
Data
Model
Structure
Inference
Results
China
All countries
LTBI
Comparison
Discussion
Limitations
Advantages
7
Model overview
It
nt
mt
Xt
notified un-notified
mt
death deathsurvival survival
VR process
ut
ptn,pt
u
pt
survey
1 2
3 4
5
6
8
7
9
Pete Dodd
Introduction
Data
Model
Structure
Inference
Results
China
All countries
LTBI
Comparison
Discussion
Limitations
Advantages
8
Summary table of parameter values and priors
..
name meaning distributionλ0 initial FOI Γ(0.01, 2.5).1[0.01,0.04]β transmission coefficient Γ(1,6).1[1.5,9]πA primary progression B(2, 20).1[0.075,0.125]πK primary progression (age 0-14)∗ Γ(4.2, 50.4).1[πA, 1]v partial protection B(3, 5).1[0.6,0.9]ϵ endogenous progression Γ(10−3, 5).1[5.10−4, 1.10−2]
CFRu un-notified case fatality B(3, 2).1[0.4,0.6]CFRn notified case fatality B(1, 20).1[0.05,0.1]Tu un-notified disease duration ℓN (log 3, .1).1[1.5, 5.5]Tn notified disease duration ℓN (log 0.5, .4).1[0.1, 1.3]VR probability TB death in register B(3, 1).1[0.01,0.9]CDR final case detection probability B(3, 1).1[0.4,0.9]dCDR rate change in CDR 1[0.01,0.3]
Table: First half represents additional transmission modelparameters; second half are the parameters in current use in WHOestimation processes (with the exception of dCDR). Γ(s, r) denotes aGamma distribution with shape s and rate r; B(a, b) denotes a Betadistribution with shape parameters a, b; ℓN (L,S) denotes a log-normaldistribution with parameters L and S; and 1[a, b] denotes an indicatorfor belonging to the interval [a, b].(∗Not involved in inference.)
Pete Dodd
Introduction
Data
Model
Structure
Inference
Results
China
All countries
LTBI
Comparison
Discussion
Limitations
Advantages
9
Inference overview
Philosophy
Bayesian approach =⇒ uncertainty in all model parameterssampled, consistent with the data.
• many unobserved states to be summed over• some parameters don't effect fit (nuisance parameters)• some parameters correlated given data
(Don't really care about parameter values)
Details
• Affine invariant MCMC sampler• many chains started near MAP• simple to tune & parellizable• handles correlations well
• Average log-likelihood from 10 runs used for each step• 500 steps with 1,000 chains
Pete Dodd
Introduction
Data
Model
Structure
Inference
Results
China
All countries
LTBI
Comparison
Discussion
Limitations
Advantages
10
Likelihood approximation
0.000
0.025
0.050
0.075
0.100
−1060 −1050 −1040 −1030 −1020LL
dens
ity
Figure: ℓ− Eℓ ∼ N(0, σ)
|logELik− E log(Lik)| = log(Eeℓ−Eℓ) ≈ σ2
2≲ 1%
Pete Dodd
Introduction
Data
Model
Structure
Inference
Results
China
All countries
LTBI
Comparison
Discussion
Limitations
Advantages
11
Beta-binomial distributions(Method/conclusion)
0 200 400 600 800 1000
0.000
0.002
0.004
0.006
0.008
0.010
1:1000
dbet
abin
om(1
:100
0, s
ize
= 10
00, t
heta
= 2
00, p
= 0
.7)
Figure: Beta-binomial has 2-levels: p ∼ Beta, n ∼ Binom(N, p)
• Binomial representations of processes like detection aretightly weighted for moderate N
• Unrealistic representation of certainty• Leads to an extremely peaked likelihood, that undervalues
prevalence surveys and under-represents uncertainty
Pete Dodd
Introduction
Data
Model
Structure
Inference
Results
China
All countries
LTBI
Comparison
Discussion
Limitations
Advantages
12
Demography
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1991 1992 1993 1994 1995
1996 1997 1998 1999 2000
2001 2002 2003 2004 2005
2006 2007 2008 2009 2010
0−45−9
10−1415−1920−2425−2930−3435−3940−4445−4950−5455−5960−6465−6970−7475−7980−8485−8990−9495−99
100−
0−45−9
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100−
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100−
0−45−9
10−1415−1920−2425−2930−3435−3940−4445−4950−5455−5960−6465−6970−7475−7980−8485−8990−9495−99
100−
−40000 0 40000 −40000 0 40000 −40000 0 40000 −40000 0 40000 −40000 0 40000Number (thousands)
Age
sex
●●
●●
female
male
China
Pete Dodd
Introduction
Data
Model
Structure
Inference
Results
China
All countries
LTBI
Comparison
Discussion
Limitations
Advantages
13
Overview of other outputs
●● ● ● ● ● ● ●
●
●
● ● ● ●
● ● ● ● ●
0
50
100
150
1990 1995 2000 2005 2010year
rate
per
100
,000
per
yea
r
variable
●
●
●
●
●
●
e_inc_100k
e_mort_exc_tbhiv_100k
incidence
mortality
notifications
VR
●● ● ● ● ● ● ●
●
●
● ● ● ●
● ● ● ● ●
0
500,000
1,000,000
1,500,000
2,000,000
1990 1995 2000 2005 2010year
num
bers
per
yea
r
variable
●
●
●
●
●
●
e_inc_num
e_mort_exc_tbhiv_num
incidence
mortality
notifications
VR
0
1,000,000
2,000,000
3,000,000
1990 1995 2000 2005 2010year
num
bers variable
e_prev_num
prevalence
●
●●
●
●
● ●
●
●
●●
●●
●●
●
●
●
●●
● ●
●
●
1990 2000 2010
0
100
200
300
400
0−15
15−
25
25−
35
35−
45
45−
55
55−
65
65+
0−15
15−
25
25−
35
35−
45
45−
55
55−
65
65+
0−15
15−
25
25−
35
35−
45
45−
55
55−
65
65+
age
TB
pre
vale
nce
per
100,
000
Pete Dodd
Introduction
Data
Model
Structure
Inference
Results
China
All countries
LTBI
Comparison
Discussion
Limitations
Advantages
14
Notifications, incidence, mortality
●
●●
● ● ● ●●
●
●
● ● ● ●
●● ● ●
●
0
50
100
150
1990 1995 2000 2005 2010year
rate
per
100
,000
per
yea
r
variable
●
●
●
●
●
●
e_inc_100k
e_mort_exc_tbhiv_100k
incidence
mortality
notifications
VR
Pete Dodd
Introduction
Data
Model
Structure
Inference
Results
China
All countries
LTBI
Comparison
Discussion
Limitations
Advantages
15
Prevalence by age in survey years
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●
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●
●
●
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●
●
●
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●
●
●
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●
●
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1990 2000 2010
0
100
200
300
400
0−15
15−
25
25−
35
35−
45
45−
55
55−
65
65+
0−15
15−
25
25−
35
35−
45
45−
55
55−
65
65+
0−15
15−
25
25−
35
35−
45
45−
55
55−
65
65+
age
TB
pre
vale
nce
per
100,
000
Pete Dodd
Introduction
Data
Model
Structure
Inference
Results
China
All countries
LTBI
Comparison
Discussion
Limitations
Advantages
16
Prevalence through time
●● ● ● ● ● ● ●
●
●
● ● ● ●
● ● ● ● ●
0
50
100
150
1990 1995 2000 2005 2010year
rate
per
100
,000
per
yea
r
variable●
●
●
●
●
●
e_inc_100ke_mort_exc_tbhiv_100kincidencemortalitynotificationsVR
●● ● ● ● ● ● ●
●
●
● ● ● ●
● ● ● ● ●
0
500,000
1,000,000
1,500,000
2,000,000
1990 1995 2000 2005 2010year
num
bers
per
yea
r variable●
●
●
●
●
●
e_inc_nume_mort_exc_tbhiv_numincidencemortalitynotificationsVR
0
1,000,000
2,000,000
3,000,000
1990 1995 2000 2005 2010year
num
bers variable
e_prev_numprevalence
●
●●
●
●
● ●
●
●
●●
●●
●●
●
●
●
●●
● ●
●
●
1990 2000 2010
0
100
200
300
400
0−15
15−2
5
25−3
5
35−4
5
45−5
5
55−6
5
65+
0−15
15−2
5
25−3
5
35−4
5
45−5
5
55−6
5
65+
0−15
15−2
5
25−3
5
35−4
5
45−5
5
55−6
5
65+
age
TB p
reva
lenc
e pe
r 100
,000
Pete Dodd
Introduction
Data
Model
Structure
Inference
Results
China
All countries
LTBI
Comparison
Discussion
Limitations
Advantages
17
MCMC chains
Pete Dodd
Introduction
Data
Model
Structure
Inference
Results
China
All countries
LTBI
Comparison
Discussion
Limitations
Advantages
18
Correlations in parameter samples
Pete Dodd
Introduction
Data
Model
Structure
Inference
Results
China
All countries
LTBI
Comparison
Discussion
Limitations
Advantages
19
Summary table of estimates
..
country incidence per 100K/y mortality per 100K/y prevalence per 100KCambodia 241 (204 - 292) 52 (38 - 78) 525 (397 - 660)China 74 (65 - 86) 15 (11 - 19) 118 (99 - 140)Indonesia 125 (110 - 152) 17 (12 - 25) 203 (168 - 252)Myanmar 117 (89 - 159) 22 (13 - 36) 204 (146 - 311)Nigeria 91 (68 - 137) 30 (21 - 49) 296 (198 - 449)Pakistan 140 (91 - 179) 43 (22 - 58) 322 (195 - 426)Philippines 362 (317 - 441) 112 (81 - 147) 565 (500 - 667)Thailand 88 (75 - 103) 27 (19 - 36) 157 (128 - 194)Viet Nam 56 (51 - 64) 6 (5 - 11) 76 (52 - 101)
Table: Incidence, mortality and prevalence are shown, together with95% credible intervals in brackets, for each country. For 2013.
Pete Dodd
Introduction
Data
Model
Structure
Inference
Results
China
All countries
LTBI
Comparison
Discussion
Limitations
Advantages
20
LTBI estimates
country infections %Cambodia 3,793,000 25China 263,233,000 19Indonesia 35,772,000 14Myanmar 8,829,000 17Nigeria 30,392,000 18Pakistan 41,266,000 23Philippines 31,043,000 32Thailand 13,394,000 20Viet Nam 15,356,000 17
Table: Numbers of individuals latently infected with M.tb according tothe model (to the nearest thousand), and the percentage of thepopulation that this represents. For 2013.
Pete Dodd
Introduction
Data
Model
Structure
Inference
Results
China
All countries
LTBI
Comparison
Discussion
Limitations
Advantages
21
Comparison with WHO estimates
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Cambodia
Cambodia
China
China
China Indonesia
Indonesia
Indonesia
Myanmar
Myanmar
Myanmar
Nigeria
Nigeria
Nigeria
Pakistan
Pakistan
Pakistan
Philippines
Philippines
Philippines
Thailand
Thailand
Thailand
Viet Nam
Viet Nam
Viet Nam
0
200
400
600
0 200 400 600WHO per 100K capita estimate
mod
el p
er 1
00K
cap
ita e
stim
ate
variable
●a
●a
●a
incidence
mortality
prevalence
Pete Dodd
Introduction
Data
Model
Structure
Inference
Results
China
All countries
LTBI
Comparison
Discussion
Limitations
Advantages
22
Limitations
Cons
• Inference was suboptimal• Priors used were rather ad hoc• No HIV/ART• Sex disaggregation not used• Beta-binomial choice• Difficulties defining appropriate n/N• Only single model structure considered
Pete Dodd
Introduction
Data
Model
Structure
Inference
Results
China
All countries
LTBI
Comparison
Discussion
Limitations
Advantages
23
Advantages
Pros
• Parsimonious, well-defined, consistent, automated and fast• Makes statistically rigorous use of notification, prevalence
and mortality data• Propagates uncertainty• Can be extended to consider other evidence
(e.g. LTBI, capture-recapture data)• Other models giving It → It+1 could be used, compared,
averaged• Under-15 age-groups could be subdivided and refined• Predicted outputs can be age-disaggregated• Structured as R package - model together with cleaned
data. Press-and-go.