iscb vaccines subcommittee web seminar series november 7 , 2012
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Assessing Immune Correlates of Protection Via Estimation of the Vaccine Efficacy Curve Peter Gilbert Fred Hutchinson Cancer Research Center and University of Washington, Department of Biostatistics. ISCB Vaccines SubCommittee Web Seminar Series November 7 , 2012. Outline .  PowerPoint PPT PresentationTRANSCRIPT
ISCB Vaccines SubCommittee Web Seminar SeriesNovember 7, 2012
Assessing Immune Correlates of
Protection Via Estimation of the Vaccine Efficacy Curve
Peter Gilbert
Fred Hutchinson Cancer Research Center and University of Washington, Department of Biostatistics
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Outline
1. Introduction: Concepts and definitions of immune correlates/surrogate endpoints
2. Evaluating an immune correlate of protection via the vaccine efficacy curve
3. Statistical methods
Context: Preventive Vaccine Efficacy Trial
• Primary Objective– Assess VE: Vaccine Efficacy to
prevent pathogenspecific disease
• Secondary Objective– Assess vaccineinduced
immune responses as correlates of protection
Randomize
Vaccine
Measure immune response
Follow for clinical endpoint (pathogenspecific disease)
Receive inoculations
Placebo
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Importance of an Immune Correlate• Finding an immune correlate is a central goal of vaccine research
– One of the 14 ‘Grand Challenges of Global Health’ of the NIH & Gates Foundation (for HIV, TB, Malaria)
• Immune correlates useful for:– Shortening trials and reducing costs– Guiding iterative development of vaccines between basic and clinical
research– Guiding regulatory decisions– Guiding immunization policy– Bridging efficacy of a vaccine observed in a trial to a new setting
• Pearl (2011, International Journal of Biostatistics) suggests that bridging is the reason for a surrogate endpoint
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Two Major Concepts/Paradigms for Surrogate Endpoints
Causal agent paradigm (e.g., Plotkin, 2008, Clin Infect Dis)Causal agent of protection = marker that mechanistically causes vaccine efficacy against the clinical endpoint
Prediction paradigm (e.g., Qin et al., 2007, J Infect Dis)Predictor of protection = marker that reliably predicts the level of vaccine efficacy against the clinical endpoint
Both are extremely useful for vaccine development, but are assessed using different approaches
For the goal of statistical assessment of surrogate endpoint validity in an efficacy trial, the prediction paradigm is used
As in the statistical literature, a good surrogate endpoint allows predicting VE from the vaccine effect on the surrogate
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Immune Correlates Terminology: Contradictions
Qin et al. (2007)• Correlate (of risk) = measured
immune response that predicts infection in the vaccine group
• Surrogate = measured immune response that can be used to reliably predict VE (may or may not be a mechanism of protection)
Plotkin (2008)• Correlate (of protection) =
measured immune response that actually causes protection (mechanism of protection)
• Surrogate = measured immune response that can be used to reliably predict VE (is definitely not a mechanism of protection)
Qin et al. correlate Plotkin correlate [very different]
Qin et al. surrogate Plotkin surrogate
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Reconciliation of Terminology: Plotkin and Gilbert (2012, Clin Inf Dis)
Term Synonyms DefinitionCoP Correlate of
ProtectionPredictor of Protection;Good Surrogate Endpoint
An immune marker statistically correlated with vaccine efficacy (equivalently predictive of vaccine efficacy)* that may or may not be a mechanistic causal agent of protection
mCoP Mechanistic Correlate of Protection
Causal Agent of Protection; Protective Immune Function
A CoP that is mechanistically causally responsible for protection
nCoP NonMechanistic Correlate of Protection
Correlate of Protection Not Causal; Predictor of Protection Not Causal
A CoP that is not a mechanistic causal agent of protection
*A CoP can be used to accurately predict the level of vaccine efficacy conferred to vaccine recipients (individuals or subgroups defined by the immune marker level). Thus a CoP is a surrogate endpoint in the statistical literature, and may be assessed with the Prentice framework or the principal stratification framework.
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A Predictive Surrogate/CoP May or May Not be a Mechanism of Protection*
Definition of a CoP: An endpoint that can be used to reliably predict the vaccine effect on the clinical endpoint
Plotkin and Gilbert (2012, Clin Inf Dis) Figure 1. A correlate of protection (CoP) may either be a mechanism of protection, termed mCoP, or a nonmechanism
of protection, termed nCoP, which predicts vaccine efficacy through its (partial) correlation with another immune response(s) that mechanistically protects.
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Many Ways for a CoR to Fail to be a CoP “A Correlate Does Not a Surrogate Make” –Tom Fleming
1. The biomarker is not in the pathway of the intervention's effect, or is insensitive to its effect– E.g., the immunological assay is noisy
2. The biomarker is not in the causal pathway of the exposure/infection/disease process– E.g., the antibody response neutralizes serotypes of the
pathogen that rarely expose trial participants but fails to predominantly exposing serotypes
3. The intervention has mechanisms of action independent of the disease process– E.g., other immunological functions not measured by the assay
are needed for protection
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Catastrophic Failure of a CoR to be a CoP: the ‘Surrogate Paradox’
• Surrogate Paradox: The vaccine induces an immune response, the immune response is inversely correlated with disease risk in vaccinees, but VE < 0%
Three Causes of the Surrogate Paradox*1. Confounding of the association between the potential
surrogate and the clinical endpoint 2. The vaccine positively affects both the surrogate and the
clinical endpoint, but for different sets of subjects 3. The vaccine may have a negative clinical effect in ways not
involving the potential surrogate
*From Tyler VanderWeele
“There is a plague on Man, the opinion that he knows something.”
− Michel de Montaigne (1580, Essays)
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Outline
1. Introduction: Concepts and definitions of immune correlates/surrogate endpoints
2. Evaluating an immune correlate of protection via the vaccine efficacy curve*
3. Statistical methods
*Gilbert, Hudgens, Wolfson (2011, J Inter Biostatistics) discussed thescientific value of the vaccine efficacy curve for vaccine development
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Two Frameworks for Assessing a CoP from a Single Vaccine Efficacy Trial: Prentice & Principal Stratification (PS)
Key Issue: Do trial participants have prior exposure to the pathogen under study?
If Yes, immune responses vary for both vaccine and placebo recipients In this case, the Prentice and PS frameworks both apply
If No, immune responses vary for vaccinees only, and the Prentice framework does not apply (Chan et al., 2002, Stats Med) In this case, only the PS framework applies
In this talk we consider the PS approach in both settings
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Concept of PS Framework: Assess Association of IndividualLevel Vaccine Effects on the Surrogate and Clinical Endpoint
Vaccine Effect on Immune Response Marker for an Individual
Vacc
ine
Effe
ct o
n C
linic
al E
ndpo
int
Probability an individual is protected
Definition of a Principal Surrogate/Principal CoP
• Define the vaccine efficacy surface as
VE(s1, s0) = 1 –
• Interpretation: Percent reduction in clinical risk for a vaccinated subject with markers (s1, s0) compared to if s/he had not been vaccinated
• Definition: A principal CoP is a marker with large variability of VE(s1, s0) in (s1, s0)
• Another useful property is VE(s1 = s0) = 0– This property is Average Causal Necessity: No vaccine effect on
the marker implies no vaccine efficacy
Risk of clinical endpoint for vaccinees for subgroup with marker effect (s1, s0)
Risk of clinical endpoint for placebos for subgroup with marker effect (s1, s0)
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Marker Useless as a CoP
CEPR(v1, v0)VE(s1, s0)
Marker if vaccinated s1 Mar
ker i
f pla
cebo
s0
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CEPR(v1, v0)VE(s1, s0)
Marker if vaccinated s1 Mar
ker i
f pla
cebo
s0
Marker that is an Excellent CoP
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Simplest Way to Think About the PS Framework for Assessing a CoP: It’s Simply Subgroup Analysis
• Conceptually the analysis assesses VE in subgroups defined by the vaccine effect on the marker– Evaluate if and how VE varies with ‘baseline’ subgroups defined
by (S1, S0)– Principal stratification makes (S1, S0) equivalent to a baseline
covariate
• A useful CoP will have strong effect modification, i.e., VE(s1, s0) varies widely in (s1, s0)
• It would be even more valuable to identify actual baseline covariates that wellpredict VE, but it’s much more likely that a response to vaccination wellpredicts VE
Simplified Definition of a Principal Surrogate/Principal CoP: Ignore the Immune Response under Placebo, S0
• Define the vaccine efficacy curve as
VE(s1) = 1 –
• Interpretation: Percent reduction in clinical risk for a vaccinated subject with markers s1 compared to if s/he had not been vaccinated
• Definition: A principal CoP is a marker with large variability of VE(s1) in s1• The vaccine efficacy curve is useful in both settings that participants have prior
exposure to the pathogen or not• If no prior exposure, then VE(s1, s0) = VE(s1), such that the vaccine efficacy
surface simplifies to the vaccine efficacy curve
Risk of clinical endpoint for vaccinees for subgroup with marker s1
Risk of clinical endpoint for placebos for subgroup with marker s1
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Vaccine Efficacy Curve: Assess How VE Varies in the Marker Under Vaccination
Marker level s1
VE(s1)
Black marker: worthlessas surrogate
Green and blue markers satisfy causal necessity
Blue marker: very goodsurrogate
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Excellent CoP: Sets the Target for Improving the Vaccine
Marker level s1
Black marker: worthlessas surrogate
Green and blue markers satisfy causal necessity
Blue marker: very goodsurrogate
VE(s1)
Target: Improve the vaccine regimen by increasing the percentage of vaccinees with high immune responses
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Knowledge of a CoP Guides Future Research to Develop Improved Vaccines
Identification of a good CoP in an efficacy trial is the ideal primary endpoint in followup Phase I/II trials of refined vaccines
It also generates a bridging hypothesis: If a future vaccine is identified that generates higher marker levels in more vaccinated subjects, then it will have improved overall VE
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Using the CoP for Improving the Vaccine Regimen
Original Vaccine New Vaccine 1 New Vaccine 2
Marker levels
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Using the CoP for Improving the Vaccine Regimen
Suppose each new vaccine is tested in an efficacy trial Under the bridging hypothesis we expect the following efficacy
results:
This is the idealized model for using a CoP to iteratively improve a vaccine regimen
Original Vaccine New Vaccine 1 New Vaccine 2
Marker level Marker level Marker level
Est
imat
ed V
E
Overall TE = 75%Overall TE = 50%
Overall TE = 31%
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Outline
1. Introduction: Concepts and definitions of immune correlates/surrogate endpoints
2. Evaluating an immune correlate of protection via the vaccine efficacy curve
3. Statistical methods
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Challenge to Evaluating a Principal CoP: The Immune Responses to Vaccine are Missing for Subjects Assigned Placebo
• Accurately filling in the unknown immune responses is needed to evaluate a principal CoP
• Two approaches to filling in the missing data (Follmann, 2006, Biometrics): – BIP (Baseline immunogenicity predictor): At baseline, measure a
predictor(s) of the immune response in both vaccinees and placebos – CPV (Closeout placebo vaccination): At study closeout, vaccinate
diseasefree placebo recipients and measure the immune response
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Example of a Good BIP: Antibody Responses to Hepatitis A and B Vaccines*
*Czeschinski et al. (2000, Vaccine) 18:10741080
Spearman rankr = .85
No crossReactivity
N=75 subjects
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Baseline Immunogenicity Predictor
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Schematic of Baseline Immunogenicity Predictor (BIP) & Closeout Placebo Vaccination (CPV) Trial Designs*
W
W 

S=S(1)
Sc
*Proposed by Follmann (2006, Biometrics)
1 1 +
1 1 +
S(1)
CPV Approach
BIP Approach
BIP Approach
Vx
Vx
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Literature on Statistical Methods for Estimating the Vaccine Efficacy Curve via BIP and/or CPV
Article Comment1. Follmann (2006, Biometrics)
Binary outcome; BIP&CPV; Estimated likelihood
2. Gilbert and Hudgens (2008, Biometrics)
Binary outcome; BIP; Estimated likelihood; 2phase sampling
3. Qin, Gilbert, Follmann, Li (2008, Ann Appl Stats)
Timetoevent outcome (Cox model); BIP&CPV; Estimated likelihood; 2phase sampling
4. Wolfson and Gilbert (2010, Biometrics)
Binary outcome; BIP&CPV; Estimated likelihood; 2phase sampling; relaxed assumptions
5. Huang and Gilbert (2011, Biometrics)
Binary outcome; BIP&CPV; Estimated likelihood; 2phase sampling; relaxed assumptions; compare markers
6. Huang, Gilbert, Wolfson (2012, under revision)
Binary outcome; BIP&CPV; Pseudolikelihood; 2phase sampling; relaxed assumptions; marker sampling design
7. Miao, Li, Gilbert, Chan (2012, under revision)
Timetoevent outcome (Cox model); BIP; Estimated likelihood with multiple imputation; 2phase sampling
8. Gabriel and Gilbert (2012, submitted)
Timetoevent outcome (Weibull model); BIP+CPV; Estimated likelihood and pseudolikelihood; 2phase sampling; threshold models
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Summary of One of the Principal Stratification Methods: Gilbert and Hudgens (2008, Biometrics) [GH]
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Notation (Observed and Potential Outcomes)
Z = vaccination assignment (0 or 1; placebo or vaccine)
W = baseline immunogenicity predictor of S
S = candidate surrogate endpoint/immune CoP measured at time after randomization
Y = clinical endpoint (0 or 1; 1 = experience event during followup)
S(Z) = potential surrogate endpoint under assignment Z, for Z=0,1
Y(Z) = potential clinical endpoint under assignment Z, for Z=0,1
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Assumptions
A1 Stable Unit Treatment Value Assumption (SUTVA):
(Si(1), Si(0), Yi(1), Yi(0)) is independent of the treatment assignments Zj of other subjects
− A1 implies “consistency”: (Si(Zi), Yi(Zi)) = (Si, Yi)
A2 Ignorable Treatment Assignment:
Zi is independent of (Si(1), Si(0), Yi(1), Yi(0))
− A2 holds for randomized blinded trials
A3 Equal individual clinical risk up to time that S is measured (zero vaccine efficacy for any individual up to time )
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Definition of a Principal Surrogate/Principal CoP(Frangakis and Rubin, 2002; Gilbert and Hudgens, 2008)
• Definerisk(1)(s1, s0) = Pr(Y(1) = 1S(1) = s1, S(0) = s0)
risk(0)(s1, s0) = Pr(Y(0) = 1S(1) = s1, S(0) = s0)
• A contrast in risk(1)(s1, s0) and risk(0)(s1, s0) is a causal effect on Y for the population {S(1) = s1, S(0) = s0}
• VE(s1, s0) = 1  risk(1)(s1, s0) / risk(0)(s1, s0)
• A good CoP has VE(s1, s0) varying widely in (s1, s0) [i.e., a large amount of effect modification]
• Also, with VE(s1) = 1  risk(1)(s1) / risk(0)(s1), a good CoP has VE(s1) varying widely in s1
• These definitions allow for a spectrum of principal CoPs, some more useful than others, depending on the degree of effect modification
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Statistical Methods: Build on TwoPhase Sampling Methods
• Casecohort or casecontrol sampling (Ignore S0)− (W, S(1)) measured in
• All infected vaccines • Sample of uninfected vaccines
− W measured ino All infected placeboso Sample of uninfected placebos
• 2Phase designs (E.g., Prentice, 1986, Biometrika; Kulich and and Lin, 2004, JASA; Breslow et al., 2009, AJE, Stat Biosciences)− Phase 1: Measure inexpensive covariates in all subjects− Phase 2: Measure expensive covariates X in a sample of subjects
• Our application
− Vaccine Group: Exactly like 2phase design with X = (W, S(1))− Placebo Group: Like 2phase design with X = (W, S(1)) and S(1)
missing
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IPW CaseCohort Methods Do Not Apply: Hence we use a Full LikelihoodBased Method
• Most of the published 2phase sampling/casecohort failure time methods cannot be extended to estimate the VE curve – This is because they are inverse probability weighted (IPW) methods, using
partial likelihood score equations that sum over subjects with phase2 data only, which assume that every subject has a positive probability that S(1) is observed
– However, all placebo subjects have zeroprobability that S(1) is observed
• To deal with this problem, the published methods all use full likelihood, using score equations that sum over all subjects
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Maximum Estimated Likelihood* with BIP
• Posit models for risk(1)(s1,0; ) and risk(0)(s1,0; )
• Vaccine arm: − (Wi, Si(1)) measured: Likld contribn risk(1)(Si(1), 0;
)− (Wi, Si(1)) not measured: risk(1)(s1, 0; )
dF(s1)
• Placebo arm:− Wi measured: Likld contribn risk(0)(s1, 0; )
dFSW(s1 Wi) − Wi not measured: risk(0)(s1, 0; ) dF(s1)
• L(, FSW, F) = i risk(1)(Si(1),0; )Yi (1  risk(1)(Si(1),0; ))1Yi]Zi }i [Vx subcohort]
risk(0)(si,0; )dFSW(s1Wi)Yi (1  risk(0)(s1,0; )) dFSW(s1Wi)1Yi]1Zi }i [Plc subcohort]
risk(1)(si,0; )dF(s1)Yi (1  risk(1)(s1,0; )) dF(s1)1Yi]Zi }1i [Vx not subcohort]
risk(0)(si,0; )dF(s1)Yi (1  risk(0)(s1,0; )) dF(s1)1Yi]1Zi }1i [Plc not subcohort]
*Pepe and Fleming (1991) an early article on estimated likelihood
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Maximum Estimated Likelihood Estimation(MELE)
• Likelihood L(, FSW, F)− is parameter of interest [VE curve depends only on ]− FSW
and F are nuisance parameters
Step 1: Choose models for FSW and F and estimate them based on
vaccine arm data
Step 2: Plug the consistent estimates of FSW and F into the likelihood,
and maximize it in − e.g., EM algorithm
Step 3: Estimate the variance of the MELE of , accounting for the uncertainty in the estimates of FSW
and F
− Bootstrap
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Example: Nonparametric Categorical Models
• Assume: −S and W categorical with J and K levels; Si(0)=1 for all i
[No prior exposure scenario: category 1 = negative response]−Nonparametric models for P(S(1)=j, W=k)−A4NP: Structural models for risk(z) (for z=0, 1)
risk(z)(j, 1, k; ) = zj + ’k for j=1, …, J; k=1, …, K
Constraint: 0 ≤ zj + ’k ≤ 1 and k ’k = 0 for identifiability
A4NP asserts no interaction: W has the same effect on risk for the 2 study groups (untestable)
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Vaccine Efficacy Curve for Categorical Marker
CEPrisk(j, 1) = log (avgrisk(1)(j, 1) / avgrisk(0)(j, 1))
where avgrisk(z)(j, 1) = (1/K) k risk(z)(j, 1, k; )
VE(j, 1) = 1 – exp{CEPrisk(j, 1)}
The vaccine efficacy curve is VE(j, 1) at each level j of S(1)
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Tests for the Vaccine Efficacy Curve VE(j, 1) Varying in j
• Wald tests for whether a biomarker has any surrogate value
− Under the null, PAE(w) = 0.5 and AS = 0− Z = (Est. PAE(w) – 0.5)/ s.e.(Est. PAE(w))− Z = Est. AS/ s.e.(Est. AS)
o Estimates obtained by MELE; bootstrap standard errors
• For nonparametric case A4NP, test H0: CEPrisk(j, 1) = 0 vs H1: CEPrisk(j, 1) increases in j (like BreslowDay trend test)
T = j>1(j1) {Est. 0j – (Est. 0j + Est. 1j)(Est. z0 /(Est. z0 + Est. z1))} divided by bootstrap s.e.
Est. z = (1/J) j zj
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Simulation Study: Vax004 HIV Vaccine Efficacy Trial*
• Step 1: For all N=5403 subjects, generate (Wi, Si(1)) from a bivariate normal with means (0.41, 0.41), sds (0.55, 0.55), correlation = 0.5, 0.7, or 0.9
sd of 0.55 chosen to achieve the observed 23% rate of leftcensoring
Values of Wi, Si(1) < 0 set to 0; values > 1 set to 1
• Step 2: Bin Wi and Si(1) into quartiles
Under model A4NP generate Yi(Z) from a Bernoulli(zj + ’k) with the parameters set to achieve:
o P(Y(1) = 1) = 0.067 and P(Y(0) = 1) = 0.134 (overall VE = 50%)
o The biomarker has either (i) no or (ii) high surrogate value
*Flynn et al. (2005, JID), Gilbert et al. (2005, JID)
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Simulation Plan
• Scenario (i) (no surrogate value)−CEPrisk(j, 1) = 0.69 for j = 1, 2, 3, 4−i.e., VE(j, 1) = 0.50 for j = 1, 2, 3, 4
• Scenario (ii) (high surrogate value)−CEPrisk(j, 1) = 0.22, 0.51, 0.92, 1.61 for j =
1, 2, 3, 4−i.e., VE(j, 1) = 0.2, 0.4, 0.6, 0.8 for j =
1, 2, 3, 4
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Simulation Plan
• Step 3: Create casecohort sampling (3:1 control: case)
−Vaccine group: (W, S(1)) measured in all infected (n=241) and a random sample of 3 x 241 uninfected
−Placebo group: W measured in all infected (n=127) and a random sample of 3 x 127 uninfected
• The data were simulated to match the real VaxGen trial as closely as possible
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Model A4NP Simulation Results: Bias and Coverage Probabilities [Table 1 of GH]
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Model A4NP Simulation Results: Power to Detect the VE(j,1) curve varying in j [Table 2 of GH]
Trend tests for VE(j, 1) increasing in j: Power 0.83, 0.99, > 0.99 for = 0.5, 0.7, 0.9
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Conclusions of Simulation Study
• The MELE method of Gilbert and Hudgens performs well for realisticallysized Phase 3 vaccine efficacy trials, with accuracy, precision, and power improving sharply with the strength of the BIP (desire high )
• This shows the importance of developing good BIPs
• R code for the nonparametric method available at the Biometrics website and at http://faculty.washington.edu/peterg/SISMID2011.html
• Crossing over more placebo subjects improves power of CPV and BIP + CPV designs
• There is no point of diminishing returns− steady improvement with more crossed over, out to complete crossover
• If the BIP is high quality (e.g., > 0.50), then the BIP design is quite powerful with only modest incremental gain by adding CPV
• However, CPV has additional value beyond efficiency improvement:– Helps in diagnostic tests of structural modeling assumptions (A4)– May help accrual and enhance ethics– May adaptively initiate crossover, e.g., as soon as the lower 95%
confidence limit for VE exceeds 30% • Pseudoscore method superior to estimated likelihood method (Huang,
Gilbert, Wolfson, 2012, under revision); recommend this method in practice– Happy to provide the code for this method (for BIP, CPV, BIP+CPV)
Remarks on Power for Evaluating a Principal Surrogate Endpoint (For All Methods Beyond GH)
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Concluding Remarks
• Opportunity to improve assessment of immune CoPs by increasing research into developing BIPs
– The better the BIP, the greater the accuracy and precision for estimating the vaccine efficacy curve
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Some Avenues for Identifying Good BIPs
• Demographic factors– E.g., age, gender, BMI, immune status
• Host immune genetics– E.g., HLA type and MHC binding prediction machine learning methods for
predicting T cell responses• Add beneficial licensed vaccines to efficacy trials and use known correlates of
protection as BIPs (Follmann’s [2006] original proposal) – The HVTN is exploring this strategy in a Phase 1 trial in preparation for
efficacy trials• Develop ‘pathogen exposure history’ chip• In efficacy trials where participants have prior exposure to the pathogen,
measure the potential CoP at baseline and use it as the baseline predictor– E.g., Varicella Zoster vaccine trials: baseline gpELISA titers strongly predict
postimmunization titers– Miao, Li, Gilbert, Chan (2012, under review) and Gabriel and Gilbert (2012,
in preparation) estimate the Zoster vaccine efficacy curve using this excellent BIP (will constitute an excellent example when published)