Symmetric Vaccine Efficacy from Relative Effect Measures

Computes the symmetric vaccine efficacy (SVE) and associated confidence intervals from a relative effect measure (e.g., relative risk, hazard ratio, odds ratio) obtained from a regression model.

Usage

sve_from_effect(
  theta,
  var_log_theta,
  level = 0.95,
  method = c("profile", "tanh-wald", "wald")
)

Arguments

theta

Numeric. The relative effect measure (e.g., relative risk from Poisson regression, hazard ratio from Cox model, etc.). Can be a vector.

var_log_theta

Numeric. The estimated variance of log(theta), typically obtained from model output (e.g., vcov(model) or the squared standard error). Must have the same length as theta.

level

Confidence level for the interval (default is 0.95).

method

Method used to construct the confidence interval.

One of:

"profile" (default): Profile likelihood-based confidence interval using a normal approximation for log(theta). The interval inverts the likelihood ratio test after transforming to the SVE scale. To use the exact likelihood from a fitted regression model instead of the normal approximation, see sve_from_model().
"tanh-wald": Applies a hyperbolic arctangent transform before forming the Wald interval, then transforms back. Improves coverage when the estimate is near +/- 1.
"wald": Standard Wald interval on the untransformed scale.

Value

A data frame with the following columns:

estimate: The symmetric vaccine efficacy estimate.
lower: Lower bound of the confidence interval.
upper: Upper bound of the confidence interval.
level: Confidence interval level.
method: Indicates the method used for the confidence interval.

Details

The symmetric vaccine efficacy (SVE) from a relative effect measure is: $$ \text{SVE} = \frac{1 - \theta}{\max(1, \theta)} $$ where $\theta$ is the relative effect measure. When $\theta < 1$, this simplifies to $\text{SVE} = 1 - \theta$ (protective). When $\theta > 1$, it becomes $\text{SVE} = (1 - \theta)/\theta$ (harmful).

Examples

# Example with a hazard ratio from a Cox model
# Suppose: HR = 0.7, SE(log(HR)) = 0.15
hr <- 0.7
se_log_hr <- 0.15
var_log_hr <- se_log_hr^2
sve_from_effect(theta = hr, var_log_theta = var_log_hr)
#>   estimate      lower     upper level  method
#> 1      0.3 0.06075634 0.4783036  0.95 Profile

# With tanh-Wald method
sve_from_effect(theta = hr, var_log_theta = var_log_hr, method = "tanh-wald")
#>   estimate      lower     upper level    method
#> 1      0.3 0.08317729 0.4897028  0.95 tanh-Wald

# Example with multiple effect estimates (e.g., from subgroups)
hrs <- c(0.5, 0.8, 1.2)
var_log_hrs <- c(0.04, 0.025, 0.036)
sve_from_effect(theta = hrs, var_log_theta = var_log_hrs)
#>     estimate       lower     upper level  method
#> 1  0.5000000  0.26003647 0.6621455  0.95 Profile
#> 2  0.2000000 -0.08309734 0.4131823  0.95 Profile
#> 3 -0.1666667 -0.42546748 0.1726732  0.95 Profile

# Using output directly from a Cox model
if (FALSE) { # \dontrun{
library(survival)
fit <- coxph(Surv(time, status) ~ vaccination + age + baseline_risk,
             data = sim_trial_data)
hr <- exp(coef(fit)["vaccination"])
var_log_hr <- vcov(fit)["vaccination", "vaccination"]
sve_from_effect(theta = hr, var_log_theta = var_log_hr)
} # }