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Symmetric Vaccine Efficacy

est_sve.Rd

Computes the symmetric vaccine efficacy (SVE) and associated confidence intervals based on observed proportions of events in vaccinated and unvaccinated groups.

Usage

est_sve(
  x0,
  x1,
  n0,
  n1,
  level = 0.95,
  method = c("profile", "tanh-wald", "wald", "exact"),
  correction = FALSE
)

Arguments

x0

Numeric. Number of events in the unvaccinated group.

x1

Numeric. Number of events in the vaccinated group.

n0

Integer. Sample size of the unvaccinated group.

n1

Integer. Sample size of the vaccinated group.

level

Numeric. Confidence level for the interval (default is 0.95).

method

Character. Method used to construct the confidence interval.

One of:

  • "profile" (default): Profile likelihood confidence interval using likelihood ratio test inversion. More accurate than Wald-based methods, especially for small samples or extreme efficacy values.

  • "tanh-wald": Applies a hyperbolic arctangent transform before forming the Wald interval, then transforms back. Keeps the interval bounded in (-1,1).

  • "wald": Standard Wald interval on the untransformed scale.

  • "exact": Uses exact conditional inference by conditioning on total cases and inverting the conditional binomial distribution (Clopper-Pearson limits for the conditional parameter). Conservative due to discreteness, but reliable for small samples or boundary cases.

correction

Logical. Whether to perform a bias correction, default: FALSE.

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.

Details

By default, confidence intervals are constructed using the profile likelihood. Two Wald-based intervals are available, one that uses the hyperbolic arctangent (tanh-Wald) to keep the bounds within (-1, 1), and the original-scale Wald. An exact method based on the Clopper-Pearson intervals is also available.

The symmetric vaccine efficacy (SVE) is defined as: $$ \text{SVE} = 2 \times \frac{p_0 - p_1}{p_0 + p_1 + |p_0 - p_1|} $$

The profile likelihood method constructs confidence intervals by inverting the likelihood ratio test. For a given SVE value, it finds the maximum likelihood estimates of p0 and p1 subject to the constraint that their SVE equals the specified value, then compares this constrained likelihood to the unconstrained MLE.

Examples

# Example: unvaccinated 10% infection rate, vaccinated 5%, equal group sizes

# Profile likelihood method
est_sve(x0 = 10, x1 = 5, n0 = 100, n1 = 100, method = "profile")
#>   estimate      lower     upper level  method
#> 1      0.5 -0.2614476 0.8394814  0.95 Profile

# Wald (tanh-Wald)
est_sve(x0 = 100, x1 = 50, n0 = 1000, n1 = 1000, method = "tanh-wald")
#>   estimate     lower     upper level    method
#> 1      0.5 0.3191164 0.6457354  0.95 tanh-Wald

# Without transform (uses Wald interval)
est_sve(x0 = 100, x1 = 50, n0 = 1000, n1 = 1000, method = "wald")
#>   estimate     lower     upper level method
#> 1      0.5 0.3360176 0.6639824  0.95   Wald

# Exact method for small samples
est_sve(x0 = 10, x1 = 5, n0 = 100, n1 = 100, method = "exact")
#>   estimate      lower     upper level method
#> 1      0.5 -0.3771404 0.8659031  0.95  Exact