respiratory bacteria vaccines: model analyses for vaccine and vaccine trial design jim koopman md...
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Respiratory Bacteria Vaccines: Model Analyses for Vaccine and
Vaccine Trial Design
Jim Koopman MD MPH
Ximin Lin MD MPH
Tom Riggs MD MPH
Dept. of Epidemiology &
Center for Study of Complex Systems
University of Michigan
Questions Addressed
• What role does immunity affecting pathogenicity vs. transmission play in the sharp drop with age in NTHi otitis media?
• What vaccine effects should be sought and measured in trials?
• How should vaccine trials be designed to insure adequate power to detect important effects?
General Issues Regarding NTHi
• Causes 20-40% of acute otitis media• Vaccine market 1 billion $ per year in U.S.• Infection, immunity, and disease data is
meager, non-specific, & highly variable• Knowledge of natural history of infection
and immunity is deficient• Unquestioned assumption that vaccine trials
will be individual based and assess disease outcomes
Aspects of NTHi (& many other bacterial) infections
• Partial immunity, rarely sterilizing– IgA proteases show evolutionary importance of
immunity
• Many variants arise due to transformation competency– No permanent strains yet identified
• Immunity to colonization or infection, disease, & transmission can be distinct
Using NTHi Models for Inference• Models with diverse natural Hx of infection and
immunity, age groupings, and contact patterns were constructed
• Deterministic compartmental (DC) models built first• Gradual acquisition of immunity with each colonization and continuous
loss over time
• All models were fit to the full range of data conformations deemed plausible using least squares
• Projections of vaccine effects made for all fits of all models (about 1000 total)
• Individual event history stochastic models corresponding to the DC models were used for vaccine trial design
Natural history of NTHi colonization
Susceptible with* Susceptibility: θ n (n=0, …, m) Infectiousness: n (n=0, …, m) Pathogenecity: n (n=0, …, m)
Ca Cb
Cc
D
Colonization & Disease
Susceptible with* Susceptibility: θ min(n+1, m) Infectiousness: min(n+1, m) Pathogenecity: min(n+1, m)
Waning of Immunity
Modeling partial immunity
Model agent variation and host response as single process
Assumptions
• equal immunity from each colonization
• multiplicative effects of sequential infections
• immunity limit (m levels)
• immunity waning
Modeling partial immunity:
S1I1S2I2S3I3……Sm-1Im-1SmIm vs. SIR/SIRS/SIS
S1 Ca1 Cb1 D1
Cc1
S2 Ca2
Cb2 D2 Cc2
Sm Cam
Cbm Dm Ccm
m-1 m-1 m-1m-1
m-1 m-1m-1m-1
• Preschool children (0.5-5 years)
1. Day-care + Non-day-care
2. 9 age groups with 6-month interval
• School children (5-15 years)
• Adults
Population structure
Population structure
N1
6-12 Mos daycare
N10
6-12 Mos no daycare
N20
>=15Years
N19 5-15
Years N18
54-60 Mos no daycare
N9
54-60 Mos daycare
Deaths
Deaths Deaths
Deaths
Deaths
Deaths
Aging
Aging
Aging
. . .
. . . Aging
Aging
Births
Births
Contact structure
Daycare N1-N9
Non-Daycare N10-N18
School N19
Adult N20
General Mixing
Daycare Mixing
School Mixing
G G GG
D S
Death rate of individuals less than 1 year 0.00181
Death rate of individuals aged 1-2 years 0.00036
Death rate of individuals aged 3-4 years 0.00036
Death rate of individuals aged 5-15 years 0.00021
Death rate of individuals aged 15 years and over 0.01086
Annual birth rate into 7-12 month age group 0.00938
Rate at which children enter daycare 0.174
Rate at which children leave daycare 0.0358
Day-care attendance at 6 months 0.0785
* The units of all rates are year-1.
Population parameters
Limited & Highly Variable Epidemiologic data
• NTHi prevalence by age & daycare attendance
(diverse methods)
• AOM incidence < age 5 by daycare (combine incidence
studies & fraction with NTHi studies)
• Antibody levels by age (diverse methods)
• Colonization duration (quite limited)
• Daycare risk ratios for AOM
Low Values
High ValuesColonization prevalence values fitted
Colonization prevalence ages 0-5 when in daycare
23% 51%
Colonization prevalence ages 0-5 when not in daycare
9.5% 21%
Colonization prevalence ages 6-15 7% 15%
Colonization prevalence in adults 4% 9%
AOM Incidence values fitted
Annual NTHi AOM incidence age* <1 0.08 0.22
Annual NTHi AOM incidence age 1-2 0.13 0.33
Annual NTHi AOM incidence age 2-3 0.08 0.22
Annual NTHi AOM incidence age 3-4 0.06 0.18
Annual NTHi AOM incidence age 4-5 0.05 0.17
Other Data
• Antibody levels peak during elementary school
• Daycare Risk Ratios from 2 to 3
• Colonization mean of 2 months but many transient episodes and some long (limited data)
• Waning “seems” to be relatively fast
Presumptions Before Our Work
• Very different from Hi Type B
• Colonization is so frequent, even at older ages, that immunity to transmission cannot be important
• Trials should assess effects on AOM, not colonization
General assumptions of our model
• Every colonized individual is infectious
• Acute otitis media (AOM) is the only relevant
disease (Unlike Hi Type B or Strep pneumo)
• Maternal immunity (Children aged 0-6
months totally immune from colonization)
Fitting model to epidemiologic data
• Berkeley Madonna: “boundary value ODE…” & optimize functions
• Empirical identifiability checking
• Extensive robustness assessment for both data conformation and model conformation rather than estimating variance of estimates
Fitting Results
• Most efficient level # is 4
• Needed immunity profile includes– Susceptibility– Contagiousness– Pathogenicity
• Contagiousness and Duration Effects are highly co-linear when fitting equilibrium
Parameter values that fit NTHi prevalence & AOM incidence for models without all immunity effects.
Immune Effects In The Model(Path effects in all models)
SuscS &
InfectS &
Durat D & I
Goodness of Fit (Root Mean Square Error)
0.01 0.02 0.03 0.37
Duration of immunity (years) 84.7 9.8 4.0 5.1
Relative susceptibility after each colonization 0.55 0.519 0.535 1
Relative contagiousness when re-infected 1 0.76 1 0.301
Relative duration of colonization when re-infected 1 1 0.839 0.599
Colonization prevalence and AOM incidence data fit*
H colH AOM
H colL AOM
L col H AOM
L col L AOM
Goodness of fit (root mean square error) 0.07 0.05 0.05 0.02
Duration of each level of immunity (years), 3.7 4.7 3.4 9.8
Duration / stage colonization | lowest immunity 0.104 0.107 0.0613 0.0549
P(AOM | colonization at the lowest immunity) 0.343 0.127 0.374 0.136
% decrease in AOM probability per immunity level (pathogenicity effect), 0.334 0.301 0.294 0.279
% decrease in susceptibility per immunity level, 0.597 0.594 0.732 0.481
% decrease in contagiousness / immunity level, 0.582 0.237 0.116 0.24
Effective contact rate per year at general site, 173 80.1 50.3 94.4
Effective contact rate per year at daycare site, 655 218 359 113
Effective contact rate per year at school site, 301 68 217 61
Data Conformation
Fitted AOM Incidence Decrease
Colon-ization Prev-alence
AOM Inci-dence
Immunity Type
Decreased0-1
year1-2
years2-3
years3-4
years4-5
years
High High Pathogenicity 1.6% 3.9% 7.9% 10.9% 12.5%
Transmission 12.0% 9.5% 11.8% 17.8% 23.4%
High Low Pathogenicity 1.6% 3.8% 7.6% 10.2% 13.2%
Transmission 23.4% 14.6% 15.3% 23.6% 32.8%
Low High Pathogenicity 1.4% 2.9% 5.1% 6.8% 8.1%
Transmission 15.9% 19.2% 32.6% 48.7% 62.7%
Low Low Pathogenicity 1.8% 3.7% 6.7% 9.0% 10.4%
Transmission 59.7% 34.1% 33.5% 53.2% 70.3%
Sensitivity Analysis to 10% Change In Pathogenicity or Transmission Immunity
Base analysis from previous Table 16.5 5.5 3.7 4.2 4.8
Only susceptibility effects on transmission
15.6 6.0 3.9 4.3 4.7
Susceptibility and duration effects on transmission
8.4 2.6 1.4 1.5 1.8
Susceptibility, contagiousness, & duration effects on transmission
10.2 3.3 2.1 2.5 2.8
Eight levels of immunity 4.6 5.1 2.0 1.5 1.7
Alternate ratios of contact rates by age at the general mixing site
39.5 11.0 5.9 6.7 7.6
Prevalence and incidence fall more steeply with age
19.2 4.7 0.6 0.6 1.2
Prevalence and incidence fall less steeply with age
9.5 3.3 2.0 2.0 2.0
Simpler pattern of compartments for the natural history of infection and immunity
36.3 6.4 3.2 3.4 3.9
Further Sensitivity AnalysisAge 0-1
Age 1-2
Age 2-3
Age 3-4
Age 4-5
Immunity acquisition & waning for P vaccine (Vaccine effects don’t exceed
natural immunity effects)
Vac
cin
atio
n
% reduction in AOM incidence among all preschool children as the result of vaccination at birth
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
4_LL 8_LL 4_HH 8_HH
P IP SP SIP
Models
% R
educ
tion
of A
OM
Inci
denc
e
% reduction in AOM incidence among preschool children due to vaccination at birth.
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
6-12 12-18 18-24 24-30 30-36 36-42 42-48 48-54 54-60
Age (months)
% R
edu
ctio
n o
f AO
M In
cid
ence
P_Daycare
SIP_Daycare
P_Non-daycare
SIP_Non-daycare
Absolute reduction of AOM incidence by age and daycare attendance among preschool children due to
vaccination at birth.
0
5
10
15
20
25
30
6-12 12-18 18-24 24-30 30-36 36-42 42-48 48-54 54-60
Age (months)
AO
M C
ases
per
100
Per
son
-yea
rs
P_Daycare
SIP_Daycare
P_Non-daycare
SIP_Non-daycare
AOM cases among daycare and non-daycare children from a population of 1,000,000 before and after
vaccination at birth with SIP vaccines.
0
100
200
300
400
500
600
700
6-12 12-18 18-24 24-30 30-36 36-42 42-48 48-54 54-60
Age (months)
No
. of A
OM
Cases
Before vaccination_daycare
After vaccination_daycare
Before vaccination_non-daycare
After vaccination_non-daycare
Summary of Deterministic Model Findings
• Wide range of feasible models fit to a wide range of feasible data
• Over this entire huge range, the intuition that immune effects on pathogenicity are the major determinants of AOM incidence proves to be wrong
• Trials must assess transmission
Model Refinements Desirable
• Model agent strains with different degrees of cross reacting immunity
• Incorporate evolution of agent into vaccine effect assessment
• Make maternal immunity and acquisition time for vaccine immunity more realistic
Additional Practical Need for Indirect Effects
• Very young age of highest risk means little time to get all the booster effects needed
Using NTHi Models for Inference About Vaccine Trial Design
• Convert deterministic compartmental model to individual event history model
• Add distinct daycare units and families• Construct vaccine trials assessing
colonization in the IEH models with varying randomization schemes, vaccine effects exceeding natural immunity, sample collection periods, serology & typing results
• Hundreds of thousands of vaccine trial simulations performed
Conclusions from Vaccine Trial Simulations
• Most efficient randomization unit is daycare– Individual randomized trials run too much risk of
missing important vaccine effects
• Standard power calculation methods for Group Randomized Trials are far off because they are based on individual effect
• Role of inside vs. outside transmission in daycare significantly affects power
• Molecular assessment of transmission worthwhile
Standard variance calculation in Group Randomized Trials (GRTs)
• variance:
• ICC: intraclass correlation
• Assumes objective is measurement of
individual effects
))1(1()1(
ICCNN
PP
Simple Model For Insight
S
S*
I
Equilibrium distribution of states solved theoretically for daycare with 12 children
Vaccine effect decreases susceptibility by 50%
Unvacc mostly within trans 30%Prev
Vacc mostly within trans
Unvacc mostly outside trans
Vacc mostly outside trans
SIS* cum prob distn (UNVAC)
0
0.2
0.4
0.6
0.8
1
1 2 3 4 5 6 7 8 9 10 11 12 13
# infected
Pro
b.
dis
tn
S
I
S*
SIS* cum prob distn (VAC)
0
0.2
0.4
0.6
0.8
1
1 2 3 4 5 6 7 8 9 10 11 12 13
# infected
Pro
b. d
istn
S_vac
I_vac
S*_vac
SIS* cum prob distn (UNVAC)
0
0.2
0.4
0.6
0.8
1
1 2 3 4 5 6 7 8 9 10 11 12 13
# infected
Pro
b.
dis
tn
S
I
S*
SIS* cum prob distn (VAC)
0
0.2
0.4
0.6
0.8
1
1 2 3 4 5 6 7 8 9 10 11 12 13
# infected
Pro
b. d
istn
S_vac
I_vac
S*_vac
SIS* cum prob distn (UNVAC)
0
0.2
0.4
0.6
0.8
1
1 2 3 4 5 6 7 8 9 10 11 12 13
# infected
Pro
b.
dis
tn
S
I
S*
SIS* cum prob distn (VAC)
0
0.2
0.4
0.6
0.8
1
1 2 3 4 5 6 7 8 9 10 11 12 13
# infected
Pro
b. d
istn
S_vac
I_vac
S*_vac
SIS* cum prob distn (UNVAC)
0
0.2
0.4
0.6
0.8
1
1 2 3 4 5 6 7 8 9 10 11 12 13
# infected
Pro
b.
dis
tn
S
I
S*
SIS* cum prob distn (VAC)
0
0.2
0.4
0.6
0.8
1
1 2 3 4 5 6 7 8 9 10 11 12 13
# infected
Pro
b. d
istn
S_vac
I_vac
S*_vac
Unvacc mostly within trans 50%Prev
Vacc mostly within trans
Unvacc mostly outside trans
Vacc mostly outside trans
Significance of S & S* Contribution to Power Calculation
• Serological ability to assess cumulative infection level would contribute considerably to power
Why standard power calculations for GRTs are way off
• ICC is determined by transmission dynamics
• Effect is determined by transmission dynamics
• Power is not just determined a single outcome state but by correlated infection and immunity states