Using Biomarkers in Vaccine Development and Evaluation - PowerPoint PPT Presentation

1 / 61
About This Presentation
Title:

Using Biomarkers in Vaccine Development and Evaluation

Description:

An immunologic measurement in response to vaccination that is 'correlated with protection' ... Only antibody responses have been identified as correlates of protection ... – PowerPoint PPT presentation

Number of Views:85
Avg rating:3.0/5.0
Slides: 62
Provided by: Steve667
Category:

less

Transcript and Presenter's Notes

Title: Using Biomarkers in Vaccine Development and Evaluation


1
Using Biomarkers in Vaccine Development and
Evaluation
  • Biostat 578A
  • Lecture 10
  • Contributor Steve Self

2
Immunological Correlates of Protection
  • Key concept in vaccine development/evaluation
  • An immunologic measurement in response to
    vaccination that is correlated with protection
  • Uses
  • Guide for vaccine development
  • Bridging studies in vaccine production
  • Guide refinements of vaccine formulation
  • Basis for regulatory decisions
  • Guides for vaccination policy
  • Precise meaning often confused- needs
    clarification and new terminology

3
Many Licensed Vaccines do not have a Known
Correlate of Protection List of FDA Licensed
Vaccines (from FDA Website)


Product Name Trade Name Sponsor Immunological Correlate of Protection Known?
Anthrax Vaccine Adsorbed Biothrax BioPort Corp Partial, Antibodies
BCG (Bacille Calmette-Guérin) Live TICE BCG Organon Teknika Corp No
BCG Live Mycobax Aventis Pasteur, Ltd
Diphtheria Tetanus Toxoids Adsorbed No Trade Name Aventis Pasteur, Inc Yes, Antibodies
Diphtheria Tetanus Toxoids Adsorbed No Trade Name Aventis Pasteur, Ltd
Diphtheria Tetanus Toxoids Acellular Pertussis Vaccine Adsorbed Tripedia Aventis Pasteur, Inc
Diphtheria Tetanus Toxoids Acellular Pertussis Vaccine Adsorbed Infanrix GlaxoSmithKline
Diphtheria Tetanus Toxoids Acellular Pertussis Vaccine Adsorbed DAPTACEL Aventis Pasteur, Ltd
Diphtheria Tetanus Toxoids Acellular Pertussis Vaccine Adsorbed, Hepatitis B (recombinant) and Inactivated Poliovirus Vaccine Combined Pediarix SmithKline Beecham Biologicals
Haemophilus b Conjugate Vaccine (Diphtheria CRM197 Protein Conjugate) HibTITER Lederle Lab Div, American Cyanamid Co Yes, Antibodies
Haemophilus b Conjugate Vaccine (Meningococcal Protein Conjugate) PedvaxHIB Merck Co, Inc
Haemophilus b Conjugate Vaccine (Tetanus Toxoid Conjugate) ActHIB Aventis Pasteur, SA
Haemophilus b Conjugate Vaccine (Meningococcal Protein Conjugate) Hepatitis B Vaccine (Recombinant) Comvax Merck Co, Inc



4
Many Licensed Vaccines do not have a Known
Correlate of Protection List of FDA Licensed
Vaccines (from FDA Website)




Product Name Trade Name Sponsor Immunological Correlate of Protection Known?
Hepatitis A Vaccine, Inactivated Havrix GlaxoSmithKline No
Hepatitis A Vaccine, Inactivated VAQTA Merck Co, Inc
Hepatitis A Inactivated and Hepatitis B (Recombinant) Vaccine Twinrix GlaxoSmithKline
Hepatitis B Vaccine (Recombinant) Recombivax HB Merck Co, Inc Partial, Antibodies
Hepatitis B Vaccine (Recombinant) Engerix-B GlaxoSmithKline
Influenza Virus Vaccine, Live, Intranasal FluMist MedImmune Vaccines, Inc Partial, Antibodies, CTLs suspected
Influenza Virus Vaccine, Trivalent, Types A and B Fluarix GlaxoSmithKline Biologicals
Influenza Virus Vaccine, Trivalent, Types A and B Fluvirin Evans Vaccines
Influenza Virus Vaccine, Trivalent, Types A and B Fluzone Aventis Pasteur, Inc
Japanese Encephalitis Virus Vaccine Inactivated JE-Vax Research Foundation for Microbial Diseases of Osaka University No
Measles Virus Vaccine, Live Attenuvax Merck Co, Inc Partial, Antibodies, CTLS and CD4s suspected
Measles and Mumps Virus Vaccine, Live M-M-Vax Merck Co, Inc (not available) Partial, Antibodies
Measles, Mumps, and Rubella Virus Vaccine, Live M-M-R II Merck Co, Inc
Measles, Mumps, Rubella and Varicella Virus Vaccine Live ProQuad Merck Co, Inc
5
Many Licensed Vaccines do not have a Known
Correlate of Protection List of FDA Licensed
Vaccines (from FDA Website)



Product Name Trade Name Sponsor Immunological Correlate of Protection Known?
Meningococcal Polysaccharide (Serogroups A, C, Y and W-135) Diphtheria Toxoid Conjugate Vaccine Menactra Aventis Pasteur, Inc Yes for some serotypes, Antibodies, no for other serotypes
Meningococcal Polysaccharide Vaccine, Groups A, C, Y and W-135 Combined Menomune-A/C/Y/W-135 Aventis Pasteur, Inc
Mumps Virus Vaccine Live Mumpsvax Merck Co, Inc Partial, Antibodies
Pneumococcal Vaccine, Polyvalent Pneumovax 23 Merck Co, Inc Partial, Serotype-Specific Antibodies
Pneumococcal 7-valent Conjugate Vaccine (Diphtheria CRM197 Protein) Prevnar Lederle Lab Div, American Cyanamid Co
Poliovirus Vaccine Inactivated (Human Diploid Cell) Poliovax Aventis Pasteur, Ltd (not available) No
Poliovirus Vaccine Inactivated (Monkey Kidney Cell) IPOL Aventis Pasteur, SA
Rabies Vaccine Imovax Aventis Pasteur, SA Yes, Antibodies
Rabies Vaccine RabAvert Chiron Behring GmbH Co
Rabies Vaccine Adsorbed No Trade Name BioPort Corp1 (not available)
Rubella Virus Vaccine Live Meruvax II Merck Co, Inc No
Smallpox Vaccine, Dried, Calf Lymph Type Dryvax Wyeth Laboratories, Inc(available only thru CDC or DoD programs) Partial, Antibodies

6
Many Licensed Vaccines do not have a Known
Correlate of Protection List of FDA Licensed
Vaccines (from FDA Website)



Product Name Trade Name Sponsor Immunological Correlate of Protection Known?
Tetanus Diphtheria Toxoids Adsorbed for Adult Use No Trade Name Massachusetts Public Health Biologic Lab Yes, Antibodies
Tetanus Diphtheria Toxoids Adsorbed for Adult Use DECAVAC Aventis Pasteur, Inc
Tetanus Diphtheria Toxoids Adsorbed for Adult Use No Trade Name Aventis Pasteur, Ltd(not available)
Tetanus Toxoid No Trade Name Aventis Pasteur, Inc
Tetanus Toxoid Adsorbed No Trade Name Massachusetts Public Health Biologic Lab
Tetanus Toxoid Adsorbed No Trade Name Aventis Pasteur, Inc
Tetanus Toxoid, Reduced Diphtheria Toxoid and Acellular Pertussis Vaccine, Adsorbed Adacel Aventis Pasteur, Ltd No for Acellular Pertussis
Tetanus Toxoid, Reduced Diphtheria Toxoid and Acellular Pertussis Vaccine, Adsorbed Boostrix GlaxoSmithKline Biologicals
Typhoid Vaccine Live Oral Ty21a Vivotif Berna Biotech, Ltd No
Typhoid Vi Polysaccharide Vaccine TYPHIM Vi Aventis Pasteur, SA
Varicella Virus Vaccine Live Varivax Merck Co, Inc No
Yellow Fever Vaccine YF-Vax Aventis Pasteur, Inc No

7
Summary of Licensed Vaccines and Correlates of
Protection
  • The immune responses responsible for protection
    of most licensed vaccines are unknown
  • Correlates known 5 vaccine types
  • Correlates partially known 7 vaccine types
  • Correlates unknown 9 vaccine types
  • Only antibody responses have been identified as
    correlates of protection
  • For many licensed vaccines T cell responses are
    suspected to play a role in protection, but T
    cells have not yet been documented as correlates
    of protection

8
Utility of Biomarkers Prediction
  • Correlates are useful only to the extent that
    they build bridges predicting effects in a new
    setting based on effects observed in another
    setting
  • Different types and sizes of bridges
  • Across vaccine lots, across different vaccine
    formulations, across human populations, across
    viral populations, across species
  • One correlate can be useful in building one type
    of bridge but not another
  • Propose using the term predictor of protection
    (POP) to clarify and specify two essential
    elements
  • What measurement(s) are used as basis for
    prediction?
  • What target for prediction?
  • Need typology for empirical basis of prediction

9
Surrogates of Protection (SOPs)
vs Correlates of Risk (CORs)
  • Correlates of risk
  • Individual-level predictors of risk
  • Estimable from cohort, nested case-control or
    nested case-cohort) studies of different types of
    individuals
  • CORs among vaccinees
  • CORs among non-vaccinees
  • Natural history studies (general high-risk
    cohorts, highly exposed seronegative cohorts)
  • Control groups in randomized vaccine trials
  • Surrogates of protection
  • Individual- or group-level predictors of vaccine
    efficacy (i.e., individual- or group-level
    surrogate endpoints)
  • An immune response identified to be a COR may be
    studied further to see if it is also a SOP and/or
    a POP

10
How Find a COR?
  • Examine immune responses of individuals who
    recover naturally from disease
  • Traditional approach to vaccine development
  • Immune responses preferentially present in those
    who recover are CORs
  • In HIV, very few individuals naturally recover
  • The Center for HIV/AIDS Vaccine Immunology
    (CHAVI) is initiating a large study of Highly
    Exposed Seronegatives to identify CORs
  • Animal challenge models
  • Challenge animals with a pathogen
  • Just prior to challenge, measure the immune
    response to vaccination
  • Compare immune response levels in protected and
    unprotected animals
  • The Gates Foundation may be funding large monkey
    challenge studies to facilitate discovery of
    CORs

11
Direct Assessment of a POP by Meta- Analysis
  • N pairs of immunologic and clinical endpoint
    assessments among vaccinees and non-vaccinees
  • Pairs chosen to reflect specific target of
    prediction
  • Examples
  • 1. Predict efficacy of vaccine to new viral
    strain N strain-specific assessments of
    immunogenicity and efficacy
  • 2. Predict efficacy of new vaccine formulation N
    vaccine efficacy trials of comparable vaccines
    but with different formulations
  • Plot of vaccinee/non-vaccinee contrast in
    endpoint rates (VE) vs contrast in immunologic
    response
  • Prediction for target based on observed
    immunologic response
  • Prediction error read directly from scatter in
    plot
  • Data intensive approach often infeasible

12
Schematic Example 1. Plot of Estimated VEs(s)
versus Mean Difference in Antibody Titers to
Strain s 10 strains s Large Phase III Trial
This result would support that strain- specific
antibody titer is a fairly reliable POP for
predicting vaccine efficacy against new viral
strains
13
Indirect Assessment of POPsFrom CORs to SOPs to
POPs
  • Data for direct assessment of POPs are rarely
    available but CORs can often be identified (e.g.,
    Vax004)
  • Two indirect strategies for assessing a COR as a
    SOP/POP
  • Prentice (1989) criterion for a statistical
    surrogate endpoint
  • COR to SOP Can an individual-level regression
    model for risk be identified that is 1)
    consistent across vaccinated and unvaccinated
    individuals and 2) fully explains differences in
    risk between vaccinees and non-vaccinees?
  • SOP to POP Can an individual-level regression
    model with the properties described above be used
    as the basis for prediction of protective effects
    in novel settings?
  • Frangakis and Rubin (2002) criterion for a
    principal surrogate endpoint
  • COR to SOP Do causal vaccine effects on the
    immune response predict causal vaccine effects on
    risk? addressed further in Lecture 12
  • SOP to POP Can the estimated causal effect
    predictiveness of the immune response be used as
    the basis for prediction of protective effects in
    novel settings?

14
Some Examples using the Prentice Criterion
Framework
  • From CORs to SOPs
  • Influenza vaccine Strain-specific Ab titer and
    risk of clinical infection
  • rgp120 HIV-1 vaccine (Vax004) Binding Ab titers
    and risk of infection
  • From SOPs to POPs
  • Influenza vaccine Strain-specific Ab titer and
    strain-specific VEs

15
1943 Influenza Vaccine Field Trial (Salk,
Menke, and Francis)
  • Study subjects
  • 1,776 men in 3651st Service Unit of ASTP at the
    University of Michigan)
  • Age 18-47
  • Housed (mainly) in dormitories and fraternities
  • Dined in 3 mess halls
  • Common daily activities

16
1943 Influenza Vaccine Field Trial(Salk, Menke,
and Francis)
  • Treatment
  • Trivalent vaccine w/ components Weiss Strain A,
    PR8 Strain A, Lee Strain B
  • Placebo control
  • Treatment assignment and delivery
  • Men arranged alphabetically
  • Alternate individuals inoculated with 1 ml of
    vaccine/placebo subcutaneously
  • Subjects blinded to assignment
  • All inoculations completed over 7 day period (Oct
    25-Nov 2)

17
1943 Influenza Vaccine Field Trial(Salk, Menke,
and Francis)
  • Follow-up and serologic assessments
  • Blood for serology at vaccination, 2 weeks and
    at end of study for sample of participants
  • Every 10th vaccinee and every 5th placebo
    recipient included in sample (approx 10 and 20
    of study cohort, respectively)
  • 35 participants lost to follow-up (19 controls,
    16 vaccinees) for retention rate of 98

18
1943 Influenza Vaccine Field Trial
  • Clinical Endpoints
  • Daily sick call, clinic and hospital-based
    surveillance
  • Multiple throat washes for viral culture
  • Blood samples

19
Results
  • Weiss Strain A
  • Case incidence
  • Controls 8.45 / 100
  • Vaccinees 2.25 / 100
  • Estimated VEs 73
  • PR8 Strain A
  • Case incidence
  • Controls 8.22 / 100
  • Vaccinees 2.25 / 100
  • Estimated VEs 73

20
Strain-specific Ab TiterCOR? Also a SOP?
  • COR models
  • Estimate relationship between Ab titer and risk
    within control group (COR among non-vaccinees)
  • Estimate relationship between Ab titer and risk
    within vaccine group (COR among vaccinees)
  • Assess consistency between two COR models
  • Ab titer as SOP?
  • Compute predicted efficacy based on
  • Observed effect of vaccination on Ab titer
  • COR model among non-vaccinees (w/ extrapolation)
  • Observed risk in control group
  • Compare predicted VEs with observed VEs

21
Estimated Incidence as a Function of Log Antibody
Titer (from logistic regression)
Observed Risk
Expected Risk
22
Logistic Regression ModelsEstimated
Coefficients (SE)
Weiss Strain A
Control Gp Only
Control and Vaccine Gps
Model 1 Model 2
Model 3 Model 4 Intercept
1.80 (0.54) -2.38 (0.12) 1.62
(0.45) 1.80 (0.54) log(Titer) -1.03
(0.14) - -0.98 (0.12)
-1.03 (0.14) Tmt -
-1.39 (0.25) 0.33 (0.32)
-0.43 (1.28) Tmtlog(Titer) -
- -
0.16 (0.25)
23
Model-Fit is good, based on Observed and Expected
Incidence
24
Estimated and Predicted VEsWeiss Strain A
  • Direct estimates of VEs (w/o use of Ab titer)
  • Est-VEsCrude 73
  • Predicted VEs
  • Based on Risk Ab, Controls plus Ab
    Vaccine
  • Pred-VEs 82
  • Prentice Criterion for a surrogate endpoint
  • Vaccine effect on surrogate completely explains
    effect on clinical endpoint
  • Log(Ab titer) satisfies criterion as a surrogate
    of protection

25
Estimated Incidence as a Function of Log Antibody
Titer, Weiss PR8 Strains A
26
Logistic Regression ModelsEstimated
Coefficients (SE)
PR8 Strain A
Control Gp Only
Control and Vaccine Gps
Model 1 Model 2
Model 3 Model 4 Intercept
-1.37 (0.59) -2.41 (0.12) -1.27
(0.53) -1.37 (0.59) log(Titer) -0.27
(0.15) - -0.29 (0.14)
-0.27 (0.15) Tmt -
-1.36 (0.26) -0.89 (0.34)
-0.22 (1.79) Tmtlog(Titer) -
- -
-0.13 (0.34)
27
Estimated and Predicted VEPR8 Strain A
  • Direct estimate of VEs (w/o use of Ab titer)
  • Est-VEsCrude 73
  • Predicted VE
  • Based on Risk Ab, Controls plus Ab
    Vaccine
  • Pred-VEs 33
  • Prentice Criterion for a surrogate endpoint
  • Log(Ab titer) does not satisfy criterion as a
    surrogate of protection
  • Only ½ of overall protective effect is predicted
    from effect on Ab titer

28
Discussion
  • Protection from PR8 Strain A only partly
    described by PR8 Ab titer
  • A (Prentice) surrogate of protection will have
  • The same association between immune response and
    risk in vaccinees and in non-vaccinees
  • Consistency of the within-group association and
    the between-group association (VEs)

29
Weiss Strain A
Control
Risk
Vaccine
Ab Titer
30
PR8 Strain A
Control
Explained by COR model
Risk
Not explained by COR model
Vaccine
Ab Titer
31
Discussion
  • Protection from PR8 Strain A only partly
    described by PR8 Ab titer
  • A possible explanation is that antibodies are
    protective, but the measurements reflect
    something else besides protective responses
    (i.e., measurement error)
  • Measurement error attenuates within-group
    association
  • Q. How to accommodate measurement errors in
    assessment of COR as a SOP?

32
PR8 Strain A
Control
De-attenuated COR models to accommodate
measurement error Adjusted model consistent w/
SOP
Risk
Vaccine
Ab Titer
33
Discussion
  • Protection from PR8 Strain A only partly
    described by PR8 Ab titer
  • Another possible explanation is that there are
    other protective immune responses that were not
    measured
  • E.g., cell-mediated immune responses
  • Another possible explanation is that PR8 Strain A
    has different protective determinants than Weiss
    Strain A

34
POP for Strain-specific VEsDirect Assessment
  • Strain-specific Ab titer as a POP for emerging
    viral strains?
  • Basis of prediction from SMF study
  • N 2 (2 pairs of strain-specific Ab responses
    and estimated VEs)
  • Plot observed strain-specific VEs vs
  • D mean Ab titer (Vaccine vs Control)
  • Predicted VE based on Ab titer distributions
    (Vaccine vs Control) and COR model among
    non-vaccinees

35
Prediction interval of efficacy for new viral
strain??
P-VE for emergent viral strain
36
Problems with Prentice Framework
  • COR models in non-vaccinees may not be estimable
  • If the COR is response to vaccine then cohort
    study relating COR to risk in non-vaccinees is
    impossible
  • If no variation in putative COR among
    non-vaccinees
  • In these cases the causal inference approach
    (based on Frangakis and Rubin) may be more useful
  • Statistical surrogates (satisfying the Prentice
    criteria for a surrogate endpoint) are based on
    net effects, not causal effects, implying this
    criterion may mislead
  • See Frangakis and Rubin (2002)

37
Introduction to Causal Inference Approach from
CORs to CSOPs (Expanded on in Lecture 12)
  • In the causal inference paradigm, causal vaccine
    efficacy is based on comparing risk within the
    same individual if he/she were assigned vaccine
    versus if assigned control
  • A difference within the same individual is
    directly attributable to vaccine, and thus is a
    causal effect
  • A CSOP, i.e., a Causal Surrogate of Protection,
    is defined in this framework (defined below)

38
Causal Inference Approach from CORs to CSOPs
  • VEcausal 1 PrY(1) 1/PrY(0)1
  • Y(1) indicator of outcome if assigned vaccine
  • Y(0) indicator of outcome if assigned placebo
  • Interpretation of VEcausal Percent reduction in
    risk for a subject assigned vaccine versus
    assigned control
  • In randomized, blinded trial, VEcausal can be
    estimated by comparing event rates in vaccine and
    control groups

39
Causal Inference Approach From CORs to CSOPs
  • Approach to assessing whether a COR is a CSOP
    Study how causal vaccine efficacy varies over
    groups defined by fixed values of both the immune
    response if assigned vaccine, X(1), and the
    immune response if assigned control, X(0)
  • VEcausal(x1,x0) 1- PrY(1)1X(1)x1,X(0)x0
  • PrY(0)1X(1)x1,X(0)x0
  • Compares risk for the same individual who would
    have immune responses x1 under vaccine and x0
    under control

40
Simplification of Causal Vaccine Efficacy
Parameter
  • For many immunological measurements, X(0) is
    constant (e.g., 0) for all subjects, because
    placebo does not induce responses
  • Causal VE can be rewritten as
  • VEcausal(x1,x0c) VEcausal(x1)
  • 1-PrY(1)1X(1)x1/PrY(0)1X(1)x1
  • Simplified interpretation Percent reduction in
    risk for a vaccinated individual with response x1
    compared to if he/she had not been vaccinated
  • E.g., VEcausal(x1high response) 0.5 an
    individual with high immune response to vaccine
    has halved risk compared to if he/she had not
    been vaccinated

41
Interpretation of VEcausal(x1)
  • VEcausal(0)0 implies the immune response is
    causally necessary as defined by Frangakis and
    Rubin (FR) (2002) the vaccine can only have
    efficacy in a person if it stimulates x1 gt 0
  • VEcausal(x1) increasing with x1 implies a higher
    immune response to vaccine directly causes lower
    risk- implies a COR is a CSOP
  • Motivates terminology Causal Surrogate of
    Protection (CSOP)
  • The slope of increase of VEcausal(x1) with x1
    measures the strength of the causal correlation
    of x1 with protection
  • This slope is a measure of the associative effect
    in the terminology of FR
  • VEcausal(x1) constant in x1 implies that this
    immune response has no causal effect on risk,
    i.e., x1 is a COR but not a CSOP

42
Interpretation of VEcausal(x1)
  • Note that there must be some protection in order
    for a COR to be a CSOP
  • VEcausal 0 and no enhancement of risk at any
    immune response level implies VEcausal(x1) 0
    for all x1- not a CSOP
  • Causal surrogate of protection is only
    meaningful when there is some protection
    (VEcausal gt 0)!

43
Fundamental Problem of Causal Inference
Approach
  • In controls, X(1) is not measured- it is the
    immune response he/she would have had had he/she
    been vaccinated
  • To estimate VEcausal(x1) a technique is needed
    for predicting the X(1)s of controls
  • Approaches suggested by Dean Follmann (Covered in
    Lecture 12)
  • Exploit correlations of X(1) with
    subject-specific characteristics measured in both
    vaccinees and controls
  • Immunological measurements
  • Immune response to a non-HIV vaccine or
    blank-vector
  • Closeout vaccination of uninfected control
    subjects
  • Assume the (unmeasured) X(1) during the trial
    equals the immune response Xc measured after the
    trial

44
Causal Inference Approach
  • This approach most useful when
  • The range of immune responses in controls is very
    narrow e.g., X(0) zero for the VaxGen trials,
    which simplifies VEcausal(x1) to vary only in x1
  • Limited variability of X(0) in controls makes
    difficult assessing whether a COR is a SOP within
    the Prentice framework

45
Causal Inference Approach VaxGen Illustration
U.S. Trial
Risk of Infection by Antibody Quartile
Q1 Q2 Q3 Q4
Vaccine 0.18 0.10 0.10 0.08
Placebo ? ? ? ?
  • ? is the risk for a placebo recipient with Qk
    quartile antibody response that he/she would have
    had had he/she been vaccinated

46
Causal Inference Approach VaxGen Illustration
  • Idea Control/adjust for the antibody response if
    assigned vaccine
  • Decreasing relative risks (vaccine/placebo) with
    increasing antibody levels implies a CSOP- some
    causal effect
  • Constant relative risks (vaccine/placebo) with
    increasing antibody levels implies not a CSOP- no
    causal effect

47
VaxGen Illustration Example 1 COR is a CSOP
Q1 Q2 Q3 Q4
Vaccine 0.18 0.10 0.10 0.08
Placebo 0.18 0.18 0.18 0.18
  • A CSOP- a higher vaccine-induced antibody
    response directly causes a lower risk of
    infection (relative risks 1, 0.56, 0.56, 0.44)

48
VaxGen Illustration Example 2 COR Not a CSOP
Q1 Q2 Q3 Q4
Vaccine 0.18 0.10 0.10 0.08
Placebo 0.36 0.20 0.20 0.16
  • Not a CSOP- the level of vaccine-induced antibody
    response does not causally effect the risk of
    infection (relative risks 0.5, 0.5, 0.5, 0.5)

49
VaxGen Illustration
  • Estimates for Example 1
  • VEcausal(Q1) 1 0.18/0.18 0
  • VEcausal(Q2) 1 0.10/0.18 0.44
  • VEcausal(Q3) 1 0.10/0.18 0.44
  • VEcausal(Q4) 1 0.08/0.18 0.56
  • VEcausal(x1) increasing in antibody quartile
    implies a CSOP
  • Estimates for Example 2
  • VEcausal(Q1) 1 0.18/0.36 0.5
  • VEcausal(Q2) 1 0.10/0.20 0.5
  • VEcausal(Q3) 1 0.10/0.20 0.5
  • VEcausal(Q4) 1 0.08/0.16 0.5
  • VEcausal(x1) constant in antibody quartile
    implies not a CSOP

50
Illustration with 1943 Influenza Trial Much
Variation in X(0)
  • Imputation of X(1) ( log ab titer) for controls
  • Assume any two control subjects with log ab
    titers X1(0) lt X2(0) have X1(1) lt X2(1) i.e., a
    higher response for a control subject implies a
    higher response had he/she received vaccine
  • This equipercentile assumption is X(1)
    Fv-1(Fc(X(0)))
  • Fv empirical distribution of log ab titer in
    vaccine group
  • Fc empirical distribution of log ab titer in
    control group
  • This assumption allows construction of a complete
    dataset of X(1),X(0) for all trial
    participants

51
Imputed X(1)s corresponding to the observed x0s
in controls
exp(x0) observed in controls Imputed exp(X(1))
16 128
32 256
64 512
128 1024
256 2048
512 4096
1024 8192
52
Imputed X(1)s corresponding to the observed X0s
in controls
  • The imputation scheme yields a simple
    relationship
  • Imputed X(1) log(8) x0
  • For vaccinees with lowest observed X(1)log(32),
    X(0) is unknown
  • For these subjects impute X(0)log(16) the
    lowest observed response in controls
  • For Weiss Strain A, the dataset has the following
    principal strata mass points (x1,x0) at which
    VEcausal(x1,x0) can be estimated (on log scale)
  • (32,16),(128,16),(256,32),(512,64),(1024,128), (20
    48,256),(4096,512),(8192,1024)

53
(No Transcript)
54
Estimation of VEcausal(x1,x0)
  • Logistic regression model in vaccine group to
    estimate Pr(Y1X(1)x1,X(0)x0,Zvaccine)
    at each point (x1,x0) specified earlier
  • Logistic regression model in control group to
    estimate Pr(Y1X(1)x1,X(0)x0,Zcontrol)
    at each point (x1,x0)
  • VEcausal(x1,x0) is estimated as one minus the
    ratio of these estimated probabilities

55
(No Transcript)
56
Interpretation
  • Subjects with antibody titers (32,16) under
    (vaccine,control) have causal efficacy 0.38
  • Subjects with antibody titers ? (128,16) under
    (vaccine,control), with X(1) X(0) log(8),
    have causal efficacy 0.75
  • Efficacy approximately constant across the 7
    principal strata of individuals with non-low
    antibody titers
  • Suggests a threshold of efficacy antibody titers
    ? 128 confer 75 protection

57
Interpretation, Continued
  • Ability to assess Ab titer as a CSOP is limited
    because can only study VEcausal(x1,x0) over a
    narrow set of (x1,x0) values
  • Cannot assess FR dissociative effects, because
    X(1) never equals X(0)
  • Limited ability to assess FR associative effects
  • Cannot assess the slope of VE(X(1),X(0)c) with
    X(1) increasing for X(0) fixed at a constant level

58
Predicted VEcausal
  • Can predict the overall vaccine efficacy for a
    population with a certain distribution of
    principal strata (x1,x0) by summing estimated
    stratum-specific VEcausal(x1,x0) estimates
  • E.g., internal to the Salk trial
  • Predicted VEcausal
  • ?(x1,x0) subjects in PS(x1,x0) ?
    Est.VEcausal(x1,x0) 0.75
  • Close to observed VEcausal 0.73
  • Comparing Predicted VEcausal and Observed
    VEcausal is one level of diagnostic for the
    imputation assumption

59
Discussion from the Example
  • Causal estimation sensitive to imputation
    assumption
  • E.g., changing the assumption X(1)log(32)
    implies X(0)log(16) to X(1)log(32) implies
    X(0)log(4) changes the estimated VEcausal for
    lowest titer responders from 0.38 to 0.73
  • Only a small set of principal strata (x1,x0)
    exist with non-negligible probability
  • A strength- focus inference on the
    relevant/meaningful sub-populations
  • A limitation- cannot assess how causal efficacy
    varies over certain regions of the plane (x1,x0)
  • When have a solid basis for imputation, the
    causal approach may be a useful complement to the
    Prentice approach when (X(1),X(0)) both
    substantially vary

60
Implication Causal Approach Best
Motivated when X(0) is Constant
  • FR causal approach attractive when X(0)c for all
    trial participants
  • The range of (X(1),X(0)) collapses from 2
    dimensions to one
  • Often will be able to estimate VEcausal(X(1),X(0)
    c) over a meaningful range for X(1)
  • Plots of Estimated VEcausal(X(1),X(0)c) highly
    interpretable
  • Straightforward to assess FR associative and
    disassociative effects
  • Lighter imputation assumptions than when X(0)
    varies

61
From a Causal Surrogate or of Protection (CSOP)
to a POP
  • Consider the problem of predicting protection
    against a new viral strain
  • Predicted strain-specific VEcausal can be
    computed based on
  • The estimated S-S VEcausal(S-S X(1)) for S-S
    X(1)s spanning the observed range in vaccinees
  • The estimated distribution of S-S X(1)s in
    vaccinees
  • A plot of Observed S-S VEcausal versus Predicted
    S-S VEcausal informs about the value of the CSOP
    as a POP
  • This approach can be taken using data from a
    single (large) trial or across multiple trials
Write a Comment
User Comments (0)
About PowerShow.com