1. 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

2. 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?

3. 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

4. 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

5. 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

6. Natural history of NTHi colonization

7. FA model

8. 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

9. Modeling partial immunity: S 1 I 1 S 2 I 2 S 3 I 3 ……S m-1 I m-1 S m I m vs. SIR/SIRS/SIS

10. Aspects of Immunity Modeled Susceptibility Contagiousness Pathogenicity Duration

11. 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

13. Contact structure

14. 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

15. 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

16. Low Values High Values Colonization 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 6-157%15% Colonization prevalence in adults4%9% AOM Incidence values fitted Annual NTHi AOM incidence age* <10.080.22 Annual NTHi AOM incidence age 1-20.130.33 Annual NTHi AOM incidence age 2-30.080.22 Annual NTHi AOM incidence age 3-40.060.18 Annual NTHi AOM incidence age 4-50.050.17

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

18. 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

19. 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)

20. 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

21. 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

22. Parameter values that fit NTHi prevalence & AOM incidence for models without all immunity effects. Immune Effects In The Model (Path effects in all models) Susc S & Infect S & DuratD & I Goodness of Fit (Root Mean Square Error) 0.010.020.030.37 Duration of immunity (years)  84.79.84.05.1 Relative susceptibility after each colonization  0.550.5190.5351 Relative contagiousness when re-infected  10.7610.301 Relative duration of colonization when re-infected  110.8390.599

23. Colonization prevalence and AOM incidence data fit* H col H AOM H col L AOM L col H AOM L col L AOM Goodness of fit (root mean square error) 0.070.05 0.02 Duration of each level of immunity (years), 3.74.73.49.8 Duration / stage colonization | lowest immunity 0.1040.1070.06130.0549 P(AOM | colonization at the lowest immunity) 0.3430.1270.3740.136 % decrease in AOM probability per immunity level (pathogenicity effect), 0.3340.3010.2940.279 % decrease in susceptibility per immunity level, 0.5970.5940.7320.481 % decrease in contagiousness / immunity level, 0.5820.2370.1160.24 Effective contact rate per year at general site, 17380.150.394.4 Effective contact rate per year at daycare site, 655218359113 Effective contact rate per year at school site, 3016821761

24. Data Conformation Fitted AOM Incidence Decrease Colon- ization Prev- alence AOM Inci- dence Immunity Type Decreased 0-1 year 1-2 years 2-3 years 3-4 years 4-5 years High Pathogenicity1.6%3.9%7.9%10.9%12.5% Transmission12.0%9.5%11.8%17.8%23.4% HighLow Pathogenicity1.6%3.8%7.6%10.2%13.2% Transmission23.4%14.6%15.3%23.6%32.8% LowHigh Pathogenicity1.4%2.9%5.1%6.8%8.1% Transmission15.9%19.2%32.6%48.7%62.7% Low Pathogenicity1.8%3.7%6.7%9.0%10.4% Transmission59.7%34.1%33.5%53.2%70.3% Sensitivity Analysis to 10% Change In Pathogenicity or Transmission Immunity

25. Base analysis from previous Table 16.55.53.74.24.8 Only susceptibility effects on transmission 15.66.03.94.34.7 Susceptibility and duration effects on transmission 8.42.61.41.51.8 Susceptibility, contagiousness, & duration effects on transmission 10.23.32.12.52.8 Eight levels of immunity 4.65.12.01.51.7 Alternate ratios of contact rates by age at the general mixing site 39.511.05.96.77.6 Prevalence and incidence fall more steeply with age 19.24.70.6 1.2 Prevalence and incidence fall less steeply with age 9.53.32.0 Simpler pattern of compartments for the natural history of infection and immunity 36.36.43.23.43.9 Further Sensitivity Analysis Age 0-1 Age 1-2 Age 2-3 Age 3-4 Age 4-5

26. Immunity acquisition & waning for P vaccine (Vaccine effects don’t exceed natural immunity effects) Vaccination

27. Immunity acquiring & waning in vaccinated population: SIP vaccine Vaccination

28. Vaccination strategy All children at age of 6 months vaccinated

29. % reduction in AOM incidence among all preschool children as the result of vaccination at birth

30. % reduction in AOM incidence among preschool children due to vaccination at birth.

31. Absolute reduction of AOM incidence by age and daycare attendance among preschool children due to vaccination at birth.

32. AOM cases among daycare and non-daycare children from a population of 1,000,000 before and after vaccination at birth with SIP vaccines.

33. 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

34. 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

35. Additional Practical Need for Indirect Effects Very young age of highest risk means little time to get all the booster effects needed

36. 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

37. 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

38. Standard variance calculation in Group Randomized Trials (GRTs) variance: ICC: intraclass correlation Assumes objective is measurement of individual effects

39. ICC & Vaccine effect

40. Change in Variance with Daycare Size & Sample Size

41. Preliminary results (1): variance & immunity

42. Simple Model For Insight S S* I Equilibrium distribution of states solved theoretically for daycare with 12 children Vaccine effect decreases susceptibility by 50%

43. Unvacc mostly within trans 30%Prev Vacc mostly within trans Unvacc mostly outside trans Vacc mostly outside trans

44. Unvacc mostly within trans 50%Prev Vacc mostly within trans Unvacc mostly outside trans Vacc mostly outside trans

45. Significance of S & S* Contribution to Power Calculation Serological ability to assess cumulative infection level would contribute considerably to power

46. Empirical power calculation

47. Empirical power & the number of the pairs of daycare centers

48. 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

49. Thank You