Session 9: Introduction to Sieve Analysis of Pathogen Sequences, for - PowerPoint PPT Presentation

Session 9: Introduction to Sieve Analysis of Pathogen Sequences, for Assessing How VE Depends on Pathogen Genomics– Part I Peter B Gilbert Vaccine and Infectious Disease Division, Fred Hutchinson Cancer Research Center and Department of Biostatistics, University of Washington July 8, 2017 PBG (VIDD FHCRC) Sieve Analysis Methods July 8, 2017 1 / 37

Outline of Module 16: Evaluating Vaccine Efficacy Session 1 ( Gabriel ) Introduction to Study Designs for Evaluating VE Session 2 (Follmann) Introduction to Vaccinology Assays and Immune Response Session 3 (Gilbert) Introduction to Frameworks for Assessing Surrogate Endpoints/Immunological Correlates of VE Session 4 (Follmann) Additional Study Designs for Evaluating VE Session 5 (Gilbert) Methods for Assessing Immunological Correlates of Risk and Optimal Surrogate Endpoints Session 6 (Gilbert) Effect Modifier Methods for Assessing Immunological Correlates of VE (Part I) Session 7 (Gabriel) Effect Modifier Methods for Assessing Immunological Correlates of VE (Part II) Session 8 (Sachs) Tutorial for the R Package pseval for Effect Modifier Methods for Assessing Immunological Correlates of VE Session 9 (Gilbert) Introduction to Sieve Analysis of Pathogen Sequences, for Assessing How VE Depends on Pathogen Genomics Session 10 (Follmann) Methods for VE and Sieve Analysis Accounting for Multiple Founders ‐ PBG (VIDD FHCRC) Sieve Analysis Methods July 8, 2017 2 / 37

Circulating HIV Strains In the setting of the vaccine trial 0, 1, 2, 3, 4 … Placebo Group Vaccine Group Natural Barrier to HIV Infection Vaccine Barrier To HIV Infection 5 5 4 # Isolates 4 # Isolates 3 3 2 2 1 1 0 1 2 3 … 0 1 2 3 … Distribution of Distribution of Infecting Strain Infecting Strain Figure 1 from Gilbert, Self, Ashby (1998, Biometrics ) PBG (VIDD FHCRC) Sieve Analysis Methods July 8, 2017 3 / 37

Outline of Session 9 1 Sieve Analysis Via Cumulative and Instantaneous VE Parameters 2 Cumulative VE Approach: NPMLE and TMLE 3 Mark-Specific Proportional Hazards Model 4 Example 1: RV144 HIV-1 Vaccine Efficacy Trial 5 Example 2: RTS,S Malaria Vaccine Efficacy Trial PBG (VIDD FHCRC) Sieve Analysis Methods July 8, 2017 4 / 37

Cumulative Genotype-Specific VE • T = time from study entry (or post immunization series) until study endpoint through to time τ 1 (e.g., HIV-1 infection) • t = fixed time point of interest t < τ 1 • Discrete genotype-specific cumulative VE � � 1 − P ( T ≤ t , J = j | Vaccine) VE cml/disc ( t , j ) = × 100% , t ∈ [0 , τ 1 ] P ( T ≤ t , J = j | Placebo) • Continuous genetic distance-specific cumulative VE � � 1 − P ( T ≤ t , V = v | Vaccine) VE cml/cont ( t , v ) = × 100% , t ∈ [0 , τ 1 ] P ( T ≤ t , V = v | Placebo) • J = discrete genotype subgroup such as binary, unordered categorical, ordered categorical • V = (approximately) continuous genetic distance to a vaccine sequence PBG (VIDD FHCRC) Sieve Analysis Methods July 8, 2017 5 / 37

Cumulative VE Sieve Effect Tests Fix t at the primary time point of interest • VE cml/disc ( t , j ): H 0 : VE cml/disc ( t , j ) constant in j H mon : VE cml/disc ( t , j ) decreases in j 1 H any : VE cml/disc ( t , j ) has some differences in j 1 • VE cml/cont ( t , v ): H 0 : VE cml/cont ( t , v ) constant in v : VE cml/cont ( t , v ) decreases in v H mon 1 H any : VE cml/cont ( t , v ) has some differences in v 1 or H any A “sieve effect” is defined by H mon being true (i.e., differential VE by 1 1 pathogen genotype) PBG (VIDD FHCRC) Sieve Analysis Methods July 8, 2017 6 / 37

Illustration: Cumulative VE cml / disc ( t = 14 , j ) for 3-Level J ∗ Discrete Genotype−Specific Cumulative VE at t = 14 Months p=0.021 p=0.027 Genotype−Specific Cumulative VE 100% 0.78 75% 0.76 0.71 0.68 ● 0.58 0.56 ● 50% 0.43 ● 0.44 ● 0.41 0.42 25% 0.14 0.10 p=0.029 p=0.033 0% ● −0.04 −0.06 ● −0.12 −0.13 p=0.10 p=0.10 −25% −50% −75% −0.89 p=0.75 −100% −1.01 p=0.87 No. Cases (V:P): 11:25 No. Cases (V:P): 13:23 No. Cases (V:P): 19:18 Unadjusted Adjusted Unadjusted Adjusted Unadjusted Adjusted Full Match Near Distant ∗ Aalen-Johansen (1978, Scand J Stat ) nonparametric MLE (Aalen, 1978, Ann Stat ; Johansen, 1978, SJS ); test for differential VE by Neafsey, Juraska et al. (2015, NEJM ) PBG (VIDD FHCRC) Sieve Analysis Methods July 8, 2017 7 / 37

Illustration: Cumulative VE cml / cont ( t = 14 , v ) for Continuous Distance V ∗ Continuous Genetic Distance−Specific Cumulative VE at t = 14 Months Genetic Distance−Specific Cumulative VE Vaccine ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● Placebo ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 100% 75% 95% pointwise CI 50% 25% 0% −25% −50% H00: p = 0.015 H0: p = 0.10 −75% No. Cases (V:P): 44:66 −100% 0.1 0.2 0.3 0.4 0.5 Genetic Distance to Vaccine Insert Sequence ∗ Aalen-Johansen (1978, Scand J Stat ) nonparametric MLE (Aalen, 1978, Ann Stat ; Johansen, 1978, SJS ); test for differential VE by Neafsey, Juraska et al. (2015, NEJM ) PBG (VIDD FHCRC) Sieve Analysis Methods July 8, 2017 8 / 37

Estimation of Cumulative VE Parameters: Approach Without Covariates • Nonparametric maximum likelihood estimation and testing Assumptions Required for Consistent Inference • No interference: Whether a subject experiences the malaria endpoint does not depend on the treatment assignments of other subjects • A randomized trial • Random dropout: Whether a subject drops out by time t does not depend on observed or unobserved subject characteristics • MCAR genotypes: Endpoint cases with missing pathogen genomes have missingness mechanism Missing Completely at Random (MCAR) PBG (VIDD FHCRC) Sieve Analysis Methods July 8, 2017 9 / 37

Estimation of Cumulative VE Parameters: With Covariates • Targeted minimum loss-based estimation (tMLE) and testing Assumptions Required for Consistent Inference • No interference • A randomized trial • Correct modeling of dropout • Missing at Random genotypes Advantages of approach with covariates • Correct for bias due to covariate-dependent dropout • Increase precision via covariates predicting the endpoint and/or dropout • Correct for bias from covariate-dependent missing genotypes (e.g., pathogen load-dependent) • Increase precision by predicting missing genotypes (the best predictors would be based on pathogen sequences of later-sampled pathogens) PBG (VIDD FHCRC) Sieve Analysis Methods July 8, 2017 10 / 37

Instantaneous Genotype-Specific VE Parameters • h ( t , j ) = Hazard of the malaria endpoint with discrete genotype j • λ ( t , v ) = Hazard of the malaria endpoint with continuous genetic distance v • Discrete genotype-specific instantaneous vaccine efficacy � � 1 − h ( t , j | Vaccine) VE haz/disc ( t , j ) = × 100% h ( t , j | Placebo) • Continuous genetic distance-specific instantaneous vaccine efficacy � � 1 − λ ( t , v | Vaccine) VE haz/cont ( t , v ) = × 100% λ ( t , v | Placebo) • Proportional hazards assumption: VE haz / disc ( t , j ) = VE haz / disc ( j ) and VE haz / cont ( t , v ) = VE haz / cont ( v ) for all t ∈ [0 , τ 1 ] PBG (VIDD FHCRC) Sieve Analysis Methods July 8, 2017 11 / 37

Illustration: Instantaneous VE haz / disc ( j ) for 3-Level J ∗ Discrete Genotype−Specific Instantaneous VE to 14 Months p=0.023 p=0.03 Genotype−Specific Instantaneous VE 100% 75% 0.76 0.73 0.71 0.69 ● 0.54 0.52 ● 50% 0.45 0.44 ● ● 0.42 0.41 25% 0.12 0.05 p=0.031 ● 0.04 0% p=0.036 −0.05 ● −0.10 −0.11 p=0.11 p=0.10 −25% −50% −75% −0.95 −100% −1.01 p=0.79 p=0.87 No. Cases (V:P): 12:25 No. Cases (V:P): 13:23 No. Cases (V:P): 19:18 Unadjusted Adjusted Unadjusted Adjusted Unadjusted Adjusted Full Match Near Distant ∗ Gilbert (2000, Stat Med ): genotype-specific Cox model PBG (VIDD FHCRC) Sieve Analysis Methods July 8, 2017 12 / 37

Illustration: Instantaneous VE haz / cont ( v ) for Continuous Distance V ∗ Continuous Genetic Distance−Specific Instantaneous VE to 14 Months Genetic Distance−Specific Instantaneous VE Vaccine ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● Placebo ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 100% 75% 95% pointwise CI 50% 25% 0% −25% −50% H00: p = 0.015 H0: p = 0.10 −75% No. Cases (V:P): 44:66 −100% 0.1 0.2 0.3 0.4 0.5 Genetic Distance to Vaccine Insert Sequence ∗ Juraska and Gilbert (2013, Biometrics ): overall endpoint Cox model + semiparametric biased sampling model PBG (VIDD FHCRC) Sieve Analysis Methods July 8, 2017 13 / 37