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

FA model

S

D

Cb Ca S ’

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

Aspects of Immunity Modeled

• Susceptibility

• Contagiousness

• Pathogenicity

• Duration

• 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

Immunity acquiring & waning in vaccinated population: SIP vaccine

Vac

cin

atio

n

Vaccination strategy

All children at age of 6 months vaccinated

% 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

ICC & Vaccine effect

Change in Variance with Daycare Size & Sample Size

Preliminary results (1): variance & immunity

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

Empirical power calculation

Empirical power & the number of the pairs of daycare centers

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

Thank You