Design and estimation for evaluating principal surrogate markers in vaccine trials

Abstract

In vaccine research, immune biomarkers that can reliably predict a vaccine's effect on the clinical endpoint (i.e., surrogate markers) are important tools for guiding vaccine development. This article addresses issues on optimizing two-phase sampling study design for evaluating surrogate markers in a principal surrogate framework, motivated by the design of a future HIV vaccine trial. To address the problem of missing potential outcomes in a standard trial design, novel trial designs have been proposed that utilize baseline predictors of the immune response biomarker(s) and/or augment the trial by vaccinating uninfected placebo recipients at the end of the trial and measuring their immune biomarkers. However, inefficient use of the augmented information can lead to counter-intuitive results on the precision of estimation. To remedy this problem, we propose a pseudo-score type estimator suitable for the augmented design and characterize its asymptotic properties. This estimator has superior performance compared with existing estimators and allows calculation of analytical variances useful for guiding study design. Based on the new estimator we investigate in detail the problem of optimizing the sampling scheme of a biomarker in a vaccine efficacy trial for efficiently estimating its surrogate effect, as characterized by the vaccine efficacy curve (a causal effect predictiveness curve) and by the predicted overall vaccine efficacy using the biomarker.

Figure 1

(a) Vaccine efficacy curves: VE{S(1)} versus S(1). The grey horizontal line is the vaccine efficacy in the population defined as 1 − P(Y = 1|Z = 1)/P(Y = 1|Z = 0). (b) Plot of VE^new(Δ) versus Δ (the location shift in immune response for the refined vaccine versus original vaccine), under the assumption that P [Y = 1|Z = z, S(1) = s] = Φ(β₀ + β₁z + β₂s + β₃sz) and P[Y = 1|Z^new = z, S(1) = s] = Φ {β₀ + β₁ + β₂s + β₃(s + Δ)}.

Figure 2

Efficiency of estimators for various designs as γ_V varies from 1 to Cost − 1 relative to the design with γ_V = γ_P, given fixed Cost = γ_V + γ_P, for (a) Cost = 5 and (b) Cost = 10, given ρ = 0.5. Relative Efficiency presented is equal to (variance at γ_V = γ_P = Cost/2)/(variance at various γ_V and γ_P = Cost − γ_V).

Figure 3

Efficiency of estimators for various designs as γ_V varies from 1 to Cost−1 relative to the design with γ_V = γ_P, given fixed Cost = γ_V + γ_P = 5 for different linear correlations ρ, for estimating (a) VE{S(1)} and (b) VE^New(Δ). Relative Efficiency presented is equal to (variance at γ_V = γ_P = Cost/2)/(variance at various γ_V and γ_P = Cost − γ_V ).