# Stochastic Interventional Vaccine Efficacy and Principal Surrogate Analyses of Antibody Markers as Correlates of Protection against Symptomatic COVID-19 in the COVE mRNA-1273 Trial

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. COVE Trial and Study Endpoint

#### 2.2. Ethics Statement

#### 2.3. Case-Cohort Sets Included in the Correlates Analyses

#### 2.4. Pseudovirus Neutralizing Antibody Assay

#### 2.5. Binding Antibody Assay

#### 2.6. Stochastic Interventional VE

_{10}scale such that −1.0 represents a 10-fold decrease in geometric mean and 1.0 represents a 10-fold increase in geometric mean. For each shift, the average risk of COVID-19 in per-protocol baseline negative vaccine recipients was estimated via the method of Hejazi et al. [10]. Downward (negative) shifts that would result in more than 10% of participants having counterfactual values of the marker below the assay’s LOD were omitted. The zero-shift value corresponds to the observed log

_{10}geometric mean marker level. As described in the SAP, these average risk estimates can be translated to the VE scale by also estimating the average risk of per-protocol baseline negative placebo recipients, which are the results that are presented. The analyses were implemented with the txshift and sl3 packages [15,16,17] for the R language and environment for statistical computing [18,19].

#### 2.7. Binary Principal Surrogate Evaluation

_{2}, β

_{3}, and β

_{4,}to construct IGI and EUI bounds. These parameters reflect different types and degrees of post-randomization selection bias, all with a log-odds ratio scale, with details in the Supplementary Text and in Gilbert et al. [20]. For data analysis, first, each sensitivity parameter was set to zero, such that the VE parameters were point-identified, and point estimates and 95% CIs were calculated. Then, each of the sensitivity parameters were set to vary from log(0.75) to −log(0.75) (medium robustness) and from log(0.5) to −log(0.5) (high robustness), such that the estimands were partially identifiable, and IGIs and 95% EUIs were calculated.

#### 2.8. Continuous Marker Principal Surrogate Evaluation

## 3. Results

#### 3.1. Stochastic Interventional VE Analysis Supports Each of the Four Antibody Markers as a Correlate of Protection

_{10}(to a geometric mean of 274 BAU/mL), and increased to 97.6% (97.4%, 97.7%) when shifting D57 Spike IgG marker values up one log

_{10}(to a geometric mean of 27,368 BAU/mL) (Figure 1A). Results were similar for each of the other three D57 markers.

#### 3.2. Binary Principal Surrogate Analysis Supports Each of the Four Antibody Markers as a Correlate of Protection

_{2}= β

_{3}= β

_{4}that are defined in Section 5.4 of Gilbert et al. [20]: [log(1.0), −log(1.0) = 0, 0], [log(0.75), −log(0.75)], or [log(0.50), −log(0.50)], which specify different types and degrees of post-randomization selection bias (see Methods and Supplementary Text for definitions of the sensitivity parameters). For each of the four immune markers at D57, VE point estimates were greater for the High D57 marker subgroup compared to the Low D57 marker subgroup (Table 2, Figure 2). In the special case of setting β

_{2}= β

_{3}= β

_{4}= 0, IGIs collapse to point estimates and EUIs collapse to CIs, in which case estimated VE (95% CI) for Low vs. High D57 Spike IgG was 88% (81, 92%) vs. 95% (92, 97%), and results for the other three immune markers were similar. To assess whether VE differed between the Low and High subgroups, we also estimated ratios (1 − VE(Low))/(1 − VE(High)). For example, when setting β

_{2}= β

_{3}= β

_{4}= 0, the point estimate (95% CI) for D57 Spike IgG was 2.54 (1.31, 4.93), supporting higher VE for the High marker subgroup. This inference is robust to a moderate amount of allowed uncertainty (95% EUI 1.11, 5.83 when each sensitivity parameter is specified to range over [log(0.75), −log(0.75)]), but not robust to the higher amount of allowed uncertainty (95% EUI 0.72, 9.69 for each sensitivity parameter specified to range over [log(0.50), −log(0.50)]). Similar results were obtained for the four D29 markers (Table S1, Figure S4), with the lower limit of the IGI for the (1 − VE(Low))/(1 − VE(High)) ratio exceeding one under a moderate amount of allowed uncertainty for all four markers.

#### 3.3. Continuous Principal Surrogate Analysis Supports Each of the Four Antibody Markers as a Correlate of Protection

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Stochastic interventional vaccine efficacy (SVE) estimates against COVID-19 with hypothetical shifts in geometric mean D57 antibody marker level. SVE, with 95% confidence intervals, for D57 (

**A**) Spike IgG, (

**B**) RBD IgG, (

**C**) nAb-ID50, or (

**D**) nAb-ID80, estimated using the method of Hejazi et al. [10]. The y-axis plots the estimated vaccine efficacy (VE) for a vaccine that elicits hypothetical D57 geometric mean value indicated on the x-axis. The vertical red line corresponds to the geometric mean concentration or titer in the COVE study population (baseline negative per-protocol vaccine recipients in the immunogenicity subcohort) and the horizontal red line corresponds to the estimated VE in COVE (follow-up time period from 7 to 100 days post-D57) at a shift of 0, i.e., the observed marker level. BAU, binding antibody units; ID50, 50% inhibitory dilution; ID80, 80% inhibitory dilution; IU, international units; LLOD, lower limit of detection; nAb, neutralizing antibody.

**Figure 2.**Binary principal surrogate vaccine efficacy (VE) against COVID-19 by D57 antibody marker greater than vs. less than or equal to the designated cut-point (median value). The black dot in each panel corresponds to the VE estimate for the relevant D57 antibody marker subgroup (Low or High) for (

**A**) Spike IgG, (

**B**) RBD IgG, (

**C**) nAb-ID50, or (

**D**) nAb-ID80 when β sensitivity parameters are set to zero. The vertical black line denotes the ignorance interval (IGI) when β sensitivity parameters range from log(0.75) to −log(0.75), the vertical red dashed line denotes the 95% confidence interval (CI) when β sensitivity parameters are set to zero, and the vertical blue dashed line denotes the 95% estimated uncertainty interval (EUI) when β sensitivity parameters range from log(0.75) to −log(0.75). The green histogram on each lower panel denotes the distribution of the D57 antibody marker, with the vertical black dashed line placed at the cut-point separating a Low D57 antibody marker response from a High D57 antibody marker response. This cut-point was the median marker value in baseline negative per-protocol vaccine recipients in the immunogenicity subcohort. (

**E**) For each antibody marker, cut-point, relative risk (RR) ratio point estimate, IGI, 95% CI, and 95% EUI. RR ratio = (1 − VE(0))/(1 − VE(1)). BAU, binding antibody units; ID50, 50% inhibitory dilution; ID80, 80% inhibitory dilution; IU, international units; nAb, neutralizing antibody.

**Figure 3.**Continuous principal surrogate vaccine efficacy (VE) against COVID-19 by D57 marker level, with ignorance intervals (dark blue) and 95% estimated uncertainty intervals (light blue) under the No Early Harm (NEH) assumption shown for the sensitivity parameter β assumed to fall in the range [−log(4), 0]. Results are shown for (

**A**) Spike IgG, (

**B**) RBD IgG, (

**C**) nAb-ID50, or (

**D**) nAb-ID80. In each panel, the solid and dashed lines are the estimated VE curve and 95% perturbation confidence intervals with the Equal Early Clinical Risk (EECR) assumption. The curves are plotted over the marker range of the 2.5th to 97.5th percentile (Spike IgG: 519 to 9263 BAU/mL, RBD IgG: 638 to 13,794 BAU/mL, nAb-ID50: 33 to 1321 IU50/mL, nAb-ID80: 95 to 2385 IU80/mL). BAU, binding antibody units; ID50, 50% inhibitory dilution; ID80, 80% inhibitory dilution; IU, international units; nAb, neutralizing antibody.

**Table 1.**Four statistical frameworks for assessing an immune marker measured at a post-vaccination time point as an immune correlate of protection (CoP) against a clinical outcome from a vaccine efficacy trial, all of which were applied to the COVE trial.

Statistical Framework for Assessing a CoP | Objective of the CoP Analysis Applied to an Immune Marker in COVE |
---|---|

Controlled vaccine efficacy (VE) [7] | To assess the vaccine efficacy that would be observed under a hypothetical intervention that assigns all participants to the vaccine arm and to a specific value of the marker, as opposed to assigning all participants to placebo * |

Mediation of VE [8] | To assess the proportion of the overall VE against COVID-19 that is mediated through the marker, through assessment of the natural direct effect (NDE) of vaccine assignment on COVID-19 (NDE = the component of VE that remains after setting (deactivating) the marker to the level it would have if assigned to the placebo arm) |

Stochastic interventional VE [10] | To assess how overall VE would change under user-specified shifts of marker values of vaccine recipients from their observed values |

Principal surrogate VE [11] | To assess how VE varies over subgroups defined by the marker value if assigned to the vaccine arm |

**Table 2.**Principal surrogate correlates of vaccine efficacy (VE) results by Gilbert et al. method [20] for High (above median) vs. Low (below median) D57 antibody marker vaccinated subgroups under the No Early Harm (NEH) assumption with sensitivity analysis scenarios.

VE(0) | VE(1) | (1 − VE(0))/(1 − VE(1)) | |||||
---|---|---|---|---|---|---|---|

Low Marker Vaccine Subgroup | High Marker Vaccine Subgroup | Relative Risk Ratio | |||||

Marker | Sens. * | Ignorance Interval | 95% Estimated Uncertainty Interval | Ignorance Interval | 95% Estimated Uncertainty Interval | Ignorance Interval | 95% Estimated Uncertainty Interval |

D57 Spike IgG | None | (0.88, 0.88) | (0.81, 0.92) | (0.95, 0.95) | (0.92, 0.97) | (2.54, 2.54) | (1.31, 4.93) |

D57 Spike IgG | Med | (0.85, 0.90) | (0.78, 0.93) | (0.95, 0.96) | (0.92, 0.97) | (1.93, 3.35) | (1.11, 5.83) |

D57 Spike IgG | High | (0.80, 0.92) | (0.70, 0.95) | (0.94, 0.96) | (0.91, 0.98) | (1.30, 5.08) | (0.72, 9.69) |

D57 RBD IgG | None | (0.89, 0.89) | (0.81, 0.93) | (0.95, 0.95) | (0.92, 0.97) | (2.26, 2.26) | (1.17, 4.37) |

D57 RBD IgG | Med | (0.86, 0.90) | (0.79, 0.94) | (0.94, 0.95) | (0.92, 0.97) | (1.72, 2.97) | (0.99, 5.17) |

D57 RBD IgG | High | (0.81, 0.93) | (0.72, 0.95) | (0.93, 0.96) | (0.90, 0.98) | (1.15, 4.50) | (0.64, 8.48) |

D57 nAb-ID50 | None | (0.90, 0.90) | (0.84, 0.93) | (0.95, 0.95) | (0.92, 0.97) | (2.25, 2.25) | (1.14, 4.46) |

D57 nAb-ID50 | Med | (0.88, 0.91) | (0.83, 0.94) | (0.95, 0.96) | (0.92, 0.97) | (1.71, 2.97) | (0.97, 5.26) |

D57 nAb-ID50 | High | (0.84, 0.93) | (0.78, 0.95) | (0.94, 0.97) | (0.90, 0.98) | (1.15, 4.50) | (0.63, 8.95) |

D57 nAb-ID80 | None | (0.91, 0.91) | (0.86, 0.95) | (0.94, 0.94) | (0.91, 0.96) | (1.46, 1.46) | (0.76, 2.82) |

D57 nAb-ID80 | Med | (0.90, 0.93) | (0.85, 0.95) | (0.93, 0.95) | (0.90, 0.97) | (1.11, 1.92) | (0.64, 3.34) |

D57 nAb-ID80 | High | (0.87, 0.94) | (0.80, 0.96) | (0.92, 0.95) | (0.88, 0.97) | (0.74, 2.90) | (0.41, 5.37) |

_{2}, β

_{3}, β

_{4}set to zero; Med, β sensitivity parameters β

_{2}, β

_{3}, β

_{4}ranging from log(0.75) to −log(0.75); High, β sensitivity parameters β

_{2}, β

_{3}, β

_{4}ranging from log(0.5) to −log(0.5).

**Table 3.**Principal surrogate correlates of vaccine efficacy results by the Huang, Zhuang, and Gilbert method [22] for D57 antibody marker at various levels under the No Early Harm (NEH) or Equal Early Clinical Risk (EECR) assumption.

Vaccine Efficacy (S_alpha) | |||||||||
---|---|---|---|---|---|---|---|---|---|

Marker | Assumption | Alpha = 0.025 | 0.05 | 0.1 | 0.5 | 0.9 | 0.95 | 0.975 | |

D57 Spike IgG | Concentration (BAU/mL) | 519.4 | 862.1 | 1224 | 2926.2 | 6169.4 | 7724.8 | 9262.9 | |

EECR | Estimate (%) | 91.7 | 92.5 | 93 | 94.2 | 95.0 | 95.1 | 95.2 | |

CI (%) | (86.7, 94.8) | (88.8, 95) | (90.1, 95.1) | (91.5, 96) | (91.9, 96.9) | (91.6, 97.1) | (91.2, 97.4) | ||

NEH | IGI (%) | [92.6, 93.4] | [93, 93.7] | [93.3, 93.9] | [93.9, 94.3] | [94.2, 94.5] | [94.2, 94.6] | [94.3, 94.6] | |

EUI (%) | (89.2, 95.7) | (90.1, 95.7) | (90.5, 95.7) | (91, 96.1) | (90.7, 96.6) | (90.3, 96.8) | (89.7, 97) | ||

D57 RBD IgG | Concentration (BAU/mL) | 637.9 | 1093.5 | 1670.9 | 4423.3 | 9361.8 | 11,560.8 | 13,793.5 | |

EECR | Estimate (%) | 90.6 | 91.8 | 92.6 | 94.1 | 95 | 95.2 | 95.4 | |

CI (%) | (84.4, 94.4) | (87.4, 94.7) | (89.4, 94.8) | (91.4, 95.9) | (91.7, 97) | (91.8, 97.2) | (91.8, 97.5) | ||

NEH | IGI (%) | [92.6, 93.2] | [93.2, 93.6] | [93.5, 93.9] | [93.9, 94.7] | [94.2, 95.2] | [94.3, 95.4] | [94.3, 95.5] | |

EUI (%) | (89.3, 95.5) | (90.4, 95.6) | (90.9, 95.6) | (91.1, 96.4) | (90.7, 97) | (90.5, 97.2) | (90.1, 97.3) | ||

D57 nAb-ID50 | Titer (IU50/mL) | 33 | 60.8 | 88.7 | 248.1 | 786.5 | 1100.8 | 1320.8 | |

EECR | Estimate (%) | 91.5 | 92.3 | 92.9 | 94.2 | 95.2 | 95.5 | 95.6 | |

CI (%) | (84.6, 95.3) | (88, 95.1) | (89.5, 95.1) | (91.6, 96) | (91.2, 97.4) | (90.7, 97.8) | (90.3, 98) | ||

NEH | IGI (%) | [90.9, 91.7] | [92, 92.7] | [92.6, 93.2] | [94.2, 94.7] | [95.2, 95.7] | [95.5, 96] | [95.6, 96.2] | |

EUI (%) | (87, 94.2) | (88.7, 94.8) | (89.6, 95.2) | (91.3, 96.4) | (91.6, 97.5) | (91.6, 97.8) | (91.6, 98) | ||

D57 nAb-ID80 | Titer (IU80/mL) | 94.7 | 130.6 | 161.7 | 544.9 | 1248.9 | 1871.8 | 2385 | |

EECR | Estimate (%) | 90.8 | 91.5 | 92 | 94.3 | 95.2 | 95.6 | 95.9 | |

CI (%) | (84.4, 94.6) | (86.7, 94.6) | (88, 94.6) | (91.4, 96.2) | (91, 97.4) | (90.7, 97.9) | (90.3, 98.2) | ||

NEH | IGI (%) | [90.9, 92.1] | [91.5, 92.7] | [91.9, 93] | [94, 94.9] | [94.6, 95.8] | [94.9, 96.2] | [95.1, 96.4] | |

EUI (%) | (86.9, 94.5) | (87.8, 94.8) | (88.4, 95.1) | (91, 96.6) | (90.9, 97.5) | (90.6, 97.9) | (90.4, 98.1) |

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**MDPI and ACS Style**

Huang, Y.; Hejazi, N.S.; Blette, B.; Carpp, L.N.; Benkeser, D.; Montefiori, D.C.; McDermott, A.B.; Fong, Y.; Janes, H.E.; Deng, W.;
et al. Stochastic Interventional Vaccine Efficacy and Principal Surrogate Analyses of Antibody Markers as Correlates of Protection against Symptomatic COVID-19 in the COVE mRNA-1273 Trial. *Viruses* **2023**, *15*, 2029.
https://doi.org/10.3390/v15102029

**AMA Style**

Huang Y, Hejazi NS, Blette B, Carpp LN, Benkeser D, Montefiori DC, McDermott AB, Fong Y, Janes HE, Deng W,
et al. Stochastic Interventional Vaccine Efficacy and Principal Surrogate Analyses of Antibody Markers as Correlates of Protection against Symptomatic COVID-19 in the COVE mRNA-1273 Trial. *Viruses*. 2023; 15(10):2029.
https://doi.org/10.3390/v15102029

**Chicago/Turabian Style**

Huang, Ying, Nima S. Hejazi, Bryan Blette, Lindsay N. Carpp, David Benkeser, David C. Montefiori, Adrian B. McDermott, Youyi Fong, Holly E. Janes, Weiping Deng,
and et al. 2023. "Stochastic Interventional Vaccine Efficacy and Principal Surrogate Analyses of Antibody Markers as Correlates of Protection against Symptomatic COVID-19 in the COVE mRNA-1273 Trial" *Viruses* 15, no. 10: 2029.
https://doi.org/10.3390/v15102029