petedodd mathematical modelling approach to estimating tb ...€¦ · results china all countries...
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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
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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!
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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!
![Page 4: PeteDodd Mathematical modelling approach to estimating TB ...€¦ · Results China All countries LTBI Comparison Discussion Limitations Advantages 11 Beta-binomialdistributions (Method/conclusion)](https://reader034.vdocuments.us/reader034/viewer/2022042403/5f16ed674f0d9b2f121be4eb/html5/thumbnails/4.jpg)
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.
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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.
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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.
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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.
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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
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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.)
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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
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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%
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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
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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
10−1415−1920−2425−2930−3435−3940−4445−4950−5455−5960−6465−6970−7475−7980−8485−8990−9495−99
100−
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
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
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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
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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
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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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●
●
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
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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
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Pete Dodd
Introduction
Data
Model
Structure
Inference
Results
China
All countries
LTBI
Comparison
Discussion
Limitations
Advantages
17
MCMC chains
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Pete Dodd
Introduction
Data
Model
Structure
Inference
Results
China
All countries
LTBI
Comparison
Discussion
Limitations
Advantages
18
Correlations in parameter samples
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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.
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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.
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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
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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
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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.