HIV Vaccine Trials. 1. Does vaccine prevent HIV infection? Vaccine Efficacy (VE) = 1 P(infected vaccine) P(infected placebo)

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1 HIV Vaccine Trials 1. Does vaccine prevent HIV infection? Vaccine Efficacy (VE) = 1 P(infected vaccine) P(infected placebo) 2. What is vaccine s impact on post-infection outcomes? Viral load, CD4 count, genetic distance, time from infection diagnosis to AIDS, time from infection diagnosis to secondary transmission,... Vaccines being designed to ameliorate post-infection variables. Merck/HVTN trial 502

2 Recent HIV Vaccine Trial RV144: ALVAC + AIDSVAX subjects randomized to vaccine or placebo. 51/8197 infected in vaccine arm. 74/8198 infected in placebo arm. VE = = This vaccine did not lower the viral loads of people who were vaccinated but caught the virus anyway. -New York Times (For First Time, AIDS Vaccine Shows Some Success, Sept 25, 2009)

3 The Problem Placebo Arm Vaccine Arm Infected Infected

4 The Problem (continued) Example: Let Y =log 10 -transformed viral load. Immune System Strong Weak Vaccine Y = 5 Y = 5 Placebo Y = 3 Y = 5 Y = 4

5 Observational Study: Other Variables Treatment Outcome Our Situation: Other Variables Treatment Infection Outcome

6 The Problem Placebo Arm Vaccine Arm Infected Infected

7 Observed { Data 0 if subject i = 1,,N randomized to placebo Z i = 1 if randomized to vaccine { 0 if not infected S i = 1 if infected Y i = outcome Potential Outcomes / Counterfactuals S i (z) = infection status indicator if subject i is assigned treatment z. Y i (z) = outcome if assigned treatment z. Average Causal Effect ACE = E[Y (1) Y (0) (S(0),S(1)) = (1,1)] Does the vaccine affect post-infection outcomes for those who would have been infected regardless of treatment assignment?

8 Assumptions 1. Stable Unit Treatment Value Assumption (SUTVA) The potential outcomes for each trial participant are unrelated to the treatment assignment of other subjects. 2. Ignorable Treatment Assignment (S (0),S (1), Y (0),Y (1)) Z 3. Monotonicity: S i (1) S i (0). Everyone infected in the vaccine arm would have been infected if randomized to placebo.

9 Vaccine viral loads: f ai v (y) = f v (y) Placebo viral loads: f ai p (y) is not identifiable. f p (y) = (1 VE)fp ai (y) + VEfp prot (y)

10 Bounds (Hudgens, Hoering, Self 2003): Vaccine viral loads: Placebo viral loads:

11 Selection bias model (Gilbert, Bosch, Hudgens 2003): Define w(y) P(S(1) = 1 S(0) = 1,Y(0) = y). Perform sensitivity analyses: fp ai (y) = w(y) 1 VE f p(y) where w(y)f p (y)dy = 1 VE. Let w(y) = exp(α + βy) 1 + exp(α + βy) where β is unidentifiable sensitivity parameter. Odds Ratio (OR): Given infection in the placebo arm, for a 1-unit increase in viral load, the odds of being infected if randomized to the vaccine arm multiplicatively increase by OR = exp(β).

12 OR=0 OR= OR= 0.01 OR= 0.02 OR= 0.05 OR= 0.1 OR= 0.2 OR= OR= 0.5 OR= OR= 0.8 OR= OR= 1 OR= 1.1 OR= 1.25 OR= 1.5 OR= 2 OR= 3 OR= 5 OR= 10 OR= 20 OR= 50 OR= 100 OR= 1000 OR =

13 Sensitivity Analysis of ACE (mean vaccine viral load minus mean placebo viral load given infected regardless of treatment assignment) ACE β

14 VaxGen s trial of AIDSVAX B/B Conducted between 1998 and subjects 61 sites throughout North America and the Netherlands 2:1 vaccine:placebo assignment Vaccine was not found to protect against infection ( VE = 0.048) Among non-whites VE = /604 (5.0%) infected in vaccine arm 29/310 (9.4%) infected in placebo arm

15 Sensitivity Analysis of ACE (mean vaccine viral load minus mean placebo viral load given infected regardless of treatment assignment) for non-white cohort in VaxGen s Phase III Trial of AIDSVAX B/B. ACE Odds Ratio

16 Our Elicitation Experience Elicited sensitivity parameters from 10 HIV vaccine experts for STEP trial. Consider the Merck/HVTN trial. Given two participants assigned placebo who become infected during the course of the trial: who do you believe would be more likely infected if, contrary to fact, they were assigned vaccine? the person with the higher set-point viral load the person with the lower set-point viral load We would like you to translate your belief into a range of possible odds ratios. Consider two people infected in the placebo arm with set-point viral loads of 4.0 and 5.0 log10 copies/ml (approximately corresponding to the 25th and 75th percentiles of the MACS cohort). Suppose these two people had instead been assigned vaccine. Then the odds of infection in the vaccine arm for the individual with the set-point viral load of 5.0 is times the odds of infection for the individual with the set-point viral load of 4.0. Please fill in this blank, giving us both a plausible lower and upper limit for this odds ratio. lower limit for the odds ratio upper limit for the odds ratio

17 Non-white cohort of VaxGen Trial ACE Odds Ratio

18 Eliciting a Counterfactual Sensitivity Parameter Mentally Challenging Friendly revenge After heavily concentrating [for a couple of hours] on your abstract questions I am getting back at you, who navigate in the abstract for a living, with the attached puzzle [a Sudoku]. Biases What if they re all wrong? At one level direct elicitation of experts opinions seems a bad idea likely to perpetuate the errors of the past. On the other hand elicitation of experts knowledge and analytical processes is crucial. -Cox (1998)

19 Appendages to the Method Conditioning on Baseline Covariates Time-to-event outcomes Relaxing monotonicity

20 Monotonicity Assumption?

21 Monotonicity S(0) p 01 = 0 p 11 = p 1 log( p00p 11 p 10p 01 ) = Pr(S(0) = 1 S(1) = 1) = 1. S(1) p 00 p 01 1 p 0 1 p 10 p 11 p 0 1 p 1 p 1 Placebo Vaccine

22 Relaxing Monotonicity S(0) p 01 > 0 p 11 < p 1 log( p00p 11 p 10p 01 ) < Pr(S(0) = 1 S(1) = 1) < 1. S(1) p 00 p 01 1 p 0 1 p 10 p 11 p 0 1 p 1 p 1 Placebo Vaccine

23 Relaxing Monotonicity (Jemiai and Rotnitzky, 2005) S(1) p S(0) 00 p 01 1 p 0 1 p 10 p 11 p 0 1 p 1 p 1 ψ log p00 p 11 p 10 p 01 p 11 φ Pr(S(0) = 1 S(1) = 1). Specify ψ, β 0, and β 1; perform analysis; repeat over plausible range. Placebo Vaccine β 0 β 1

24 Bounds Zhang and Rubin, 2003 Jemiai and Rotnitzky, 2005 S(0) S(1) p 00 p 01 1 p 0 1 p 10 p 11 p 0 1 p 1 p 1 If p 0 + p 1 < 1 then bounds are uninformative. p 11 very small Placebo Vaccine

25 Sensitivity Analysis of SCE(t) (probability of starting antiretrovirals by t=2 years in placebo minus probability of starting in vaccine given infected regardless of treatment assignment) for non-white cohort in VaxGen s Phase III Trial of AIDSVAX B/B. Estimated SCE(t=2 years) OR = exp(β)

26 Sensitivity analysis of SCE(t=2 years) for VaxGen s non-white cohort. φ=pr(infected in placebo infected in vaccine) OR 1 = exp(β 1 ) OR 1 = exp(β 1 ) φ = OR 0 = exp(β 0 ) φ = OR 0 = exp(β 0 ) OR 1 = exp(β 1 ) OR 1 = exp(β 1 ) φ = OR 0 = exp(β 0 ) φ = OR 0 = exp(β 0 ) OR 1 = exp(β 1 ) OR 1 = exp(β 1 ) φ = OR 0 = exp(β 0 ) φ = OR 0 = exp(β 0 )

27 Prostate Cancer Prevention Trial 18,882 randomized to daily finasteride or placebo for 7 years 17% on finasteride had detectable cancer 23% on placebo had detectable cancer 36% of cancers on finasteride were severe 22% of cancers on placebo were severe Z randomized treatment assignment (1=finasteride) S(z) indicator of cancer detected if assigned to treatment z Y (z) cancer severity if assigned to treatment z Estimand: E(Y (1) Y (0) S(0) = S(1) = 1)

28 Three parameters to elicit: Elicitation Experience 1. Consider those in the finasteride arm who got prostate cancer. What percentage of them do you believe would have gotten cancer if, contrary to fact, they were randomized to the placebo arm? What are plausible lower and upper values for this percentage? lower upper Optimist: 100% ( %) Pessimist: 90% (80 95%)

29 2. Given two men assigned placebo who got cancer during the course of the trial: who do you believe would be more likely to have gotten cancer if, contrary to fact, they were assigned finasteride? the person with the higher Gleason score the person with the lower Gleason score the two are equally likely We would like you to translate your belief into a range of possible odds ratios. Consider two people who got cancer in the placebo arm, one with a Gleason score of >=7 and the other <7. Suppose these two people had instead been assigned finasteride. Then the odds of cancer in the finasteride arm for the man with the high Gleason score is times the odds of cancer for the man with the low Gleason score. Please fill in this blank, giving us both a plausible lower and upper limit for this odds ratio. lower limit for the odds ratio upper limit for the odds ratio Optimist: 1.2 ( ) Pessimist: 3.0 ( )

30 3. Given two men assigned finasteride who got cancer during the course of the trial: who do you believe would be more likely to have gotten cancer if, contrary to fact, they were assigned placebo? the person with the higher Gleason score the person with the lower Gleason score the two are equally likely Again, we would like you to translate your belief into a range of possible odds ratios. Consider two people who got cancer in the finasteride arm with Gleason scores of >=7 and <7. Suppose these two people had instead been assigned placebo. Then the odds of cancer in the placebo arm for the man with the high Gleason score is times the odds of cancer for the man with the low Gleason score. Please fill in this blank, giving us both a plausible lower and upper limit for this odds ratio. lower limit for the odds ratio upper limit for the odds ratio Optimist: 1.2 ( ) Pessimist: 0.33 ( )

31 Optimist Pessimist Pr(S(0) = 1 S(1) = 1) 1.0 ( ) 0.90 ( ) OR ( ) 3.0 ( ) OR ( ) 0.33 ( )

32 Sensitivity Analysis of ACE (Proportion with severe cancer in finasteride minus proportion with severe cancer in placebo given cancer regardless of treatment assignment) for Prostate Cancer Prevention Trial. ACE Estimated ACE 95% C.I. ACE at β 0 = + 95% C.I. at β 0 = + β 0 OR

33 φ = 0.99 φ = 0.95 φ = 0.9 OR 1 = exp(β1) OR 1 = exp(β1) OR 1 = exp(β1) OR 0 = exp(β 0) OR 0 = exp(β 0) OR 0 = exp(β 0) φ = 0.8 φ = 0.5 S(0),S(1) Independent, φ = 0.24 OR 1 = exp(β1) OR 1 = exp(β1) OR 1 = exp(β1) OR 0 = exp(β 0) OR 0 = exp(β 0) OR 0 = exp(β 0)

34 Discussion 1. Showing over wide range 2. Is there a need to elicit? 3. A priori versus post-hoc 4. Interpretation of sensitivity parameters 5. Range of selected parameter incompatible with data

35 References Hudgens, Hoering, Self (2003), Statistics in Medicine, 22: Gilbert, Bosch, Hudgens (2003), Biometrics, 59: Jemiai (2005), PhD Dissertation w/ Rotnitzky at Harvard Biostatistics. Shepherd, Gilbert, Jemiai, Rotnitzky (2006), Biometrics, 62: Jemiai, Rotnitzky, Shepherd, Gilbert (2007), JRSS-B, 69: Shepherd, Gilbert, Mehrotra (2007), TAS, 61: Shepherd, Gilbert, Lumley (2007), JASA, 102: Shepherd, Redman, Ankerst (2008), JASA, 484: