sve

The goal of sve is to facilitate the calculation of symmetric vaccine efficacy (SVE) and corresponding variance and confidence intervals.

Installation

You can install the development version of sve like so:

devtools::install_github("LucyMcGowan/sve")

Example

library(sve)

The core function, est_sve(), computes the symmetric vaccine efficacy and its confidence interval given the event proportions and sample sizes for the vaccinated and unvaccinated groups.

Example:

• unvaccinated 10% infection rate
  
• vaccinated 5% infection rate
  
• $n_0=n_1=1,000$

est_sve(x0 = 10, 
        x1 = 5, 
        n0 = 1000, 
        n1 = 1000)
#>   estimate      lower     upper level  method
#> 1      0.5 -0.2865842 0.8437684  0.95 Profile

By default, confidence intervals are calculated using the profile likelihood method. To calculate Wald-type intervals on a transformed scale and then back-transformed in order to ensure that they remain between -1 and 1 use method = "tanh-wald":

est_sve(x0 = 10, 
        x1 = 5, 
        n0 = 1000, 
        n1 = 1000,
        method = "tanh-wald")
#>   estimate      lower     upper level    method
#> 1      0.5 -0.1625277 0.8517777  0.95 tanh-Wald

If you would like Wald-type intervals and do not want to use this transformation, you can set the option method = "wald".

Using relative effect measures

The sve_from_model() function computes SVE from relative effect measures (e.g., hazard ratios from Cox models, relative risks from Poisson regression) extracted from model objects. Below is an example using a Cox proportional hazards model and a simulated data set provided in this package (sim_trial_data).

library(survival)

fit <- coxph(Surv(time, status) ~ vaccination + age + baseline_risk, 
             data = sim_trial_data)

sve_from_model(model = fit, data = sim_trial_data, effect_name = "vaccination")
#>              estimate     lower     upper level  method
#> vaccination 0.6776701 0.5907393 0.7472103  0.95 Profile

Methods overview

The symmetric vaccine efficacy (SVE) is defined as

$$\text{SVE}=\frac{(p_0-p_1)}{\max(p_0, p_1)},$$

where:

• $p_0$ = event proportion in the unvaccinated group
  
• $p_1$ = event proportion in the vaccinated group

This formulation ensures the estimator is bounded between -1 and 1. Equivalently, it can be written in terms of a relative effect measure, $\theta$ (such as a relative risk or hazard ratio):

$$\text{SVE} = \frac{(1 - \theta)}{\max(1,\theta)}.$$