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