Title: Using Biomarkers in Vaccine Development and Evaluation
1Using Biomarkers in Vaccine Development and
Evaluation
- Biostat 578A
- Lecture 10
- Contributor Steve Self
2Immunological 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
3Many 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
4Many 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
5Many 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
6Many 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
7Summary 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
12Schematic 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
13Indirect 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
161943 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)
171943 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
181943 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
20Strain-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
21Estimated Incidence as a Function of Log Antibody
Titer (from logistic regression)
Observed Risk
Expected Risk
22Logistic 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)
23Model-Fit is good, based on Observed and Expected
Incidence
24Estimated 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
25Estimated Incidence as a Function of Log Antibody
Titer, Weiss PR8 Strains A
26Logistic 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)
27Estimated 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
28Discussion
- 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)
29Weiss Strain A
Control
Risk
Vaccine
Ab Titer
30PR8 Strain A
Control
Explained by COR model
Risk
Not explained by COR model
Vaccine
Ab Titer
31Discussion
- 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?
32PR8 Strain A
Control
De-attenuated COR models to accommodate
measurement error Adjusted model consistent w/
SOP
Risk
Vaccine
Ab Titer
33Discussion
- 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
34POP 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
36Problems 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)
37Introduction 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)
38Causal 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
39Causal 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
40Simplification 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
41Interpretation 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
42Interpretation 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)!
43Fundamental 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
44Causal 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
45Causal 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
46Causal 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
47VaxGen 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)
48VaxGen 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)
49VaxGen 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
50Illustration 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
51Imputed 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
52Imputed 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)
54Estimation 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)
56Interpretation
- 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
57Interpretation, 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
58Predicted 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
59Discussion 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
60Implication 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
61From 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