Skip to contents

IDR confidence interval.

IDRsc.Rd

Estimates confidence interval for the incidence density ratio or prevented fraction based on it.

Usage

IDRsc(
  y = NULL,
  data = NULL,
  formula = NULL,
  compare = c("con", "vac"),
  alpha = 0.05,
  pf = TRUE,
  rnd = 3
)

Arguments

y

Data vector c(y1, n1, y2, n2) where y are the positives, n are the total, and group 1 is compared to group 2 (control or reference).

data

data.frame containing variables of formula.

formula

Formula of the form cbind(y, n) ~ x, where y is the number positive, n is the group size, x is a factor with two levels of treatment.

compare

Text vector stating the factor levels: compare[1] is the vaccinate group to which compare[2] (control or reference) is compared.

alpha

Complement of the confidence level.

pf

Estimate IDR, or its complement PF?

rnd

Number of digits for rounding. Affects display only, not estimates.

Value

A rr1 object with the following elements.

  • estimate: vector with point and interval estimate

  • estimator: either PF or IDR

  • y: data vector

  • rnd: how many digits to round the display

  • alpha: complement of confidence level

Details

The incidence density is the number of cases per subject-time; its distribution is assumed Poisson. IDRsc estimates a confidence interval for the incidence density ratio using Siev's formula based on the Poisson score statistic. \( IDR = \widehat{IDR}\left\{ 1 + \left( \frac{1}{{{y}_{1}}} + \frac{1}{{{y}_{2}}} \right)\frac{z_{\alpha / 2}^{2}}{2}\ \ \pm \ \ \frac{z_{\alpha / 2}^{2}}{2{{y}_{1}}{{y}_{2}}}\sqrt{{{y}_{\bullet }}\left( {{y}_{\bullet }}z_{\alpha / 2}^{2} + 4{{y}_{1}}{{y}_{2}} \right)} \right\} \)

The data may also be a matrix. In that case y would be entered as

matrix(c(y1, n1 - y1, y2, n2 - y2), 2, 2, byrow = TRUE).

References

Siev D, 1994. Estimating vaccine efficacy in prospective studies. Preventive Veterinary Medicine 20:279-296, Appendix 1.

Graham PL, Mengersen K, Morton AP, 2003. Confidence limits for the ratio of two rates based on likelihood scores:non-iterative method Statistics in Medicine 22:2071-2083.

Siev D, 2004. Letter to the editor. Statistics in Medicine 23:693. (Typographical error in formula: replace the two final minus signs with subscript dots.)

See also

IDRlsi

Author

PF-package

Examples

# All examples represent the same observation, with data entry by vector,
# matrix, and formula+data notation.

y_vector <- c(26, 204, 10, 205)
IDRsc(y_vector, pf = FALSE)
#> 
#> IDR 
#> 95% interval estimates
#> 
#>  IDR   LL   UL 
#> 2.61 1.28 5.34 
#> 

# IDR
# 95% interval estimates

#  IDR   LL   UL
# 2.61 1.28 5.34

y_matrix <- matrix(c(26, 178, 10, 195), 2, 2, byrow = TRUE)
y_matrix
#>      [,1] [,2]
#> [1,]   26  178
#> [2,]   10  195
#      [, 1] [, 2]
# [1, ]   26  178
# [2, ]   10  195

IDRsc(y_matrix, pf = FALSE)
#> 
#> IDR 
#> 95% interval estimates
#> 
#>  IDR   LL   UL 
#> 2.61 1.28 5.34 
#> 

# IDR
# 95% interval estimates

#  IDR   LL   UL
# 2.61 1.28 5.34

require(dplyr)
data1 <- data.frame(group = rep(c("treated", "control"), each = 5),
            n = c(rep(41, 4), 40, rep(41, 5)),
            y = c(4, 5, 7, 6, 4, 1, 3, 3, 2, 1),
            cage = rep(paste("cage", 1:5), 2))
data2 <- data1 |>
  group_by(group) |>
  summarize(sum_y = sum(y),
  sum_n = sum(n))
IDRsc(data = data2, formula =  cbind(sum_y, sum_n) ~ group,
    compare = c("treated", "control"), pf = FALSE)
#> 
#> IDR 
#> 95% interval estimates
#> 
#>  IDR   LL   UL 
#> 2.61 1.28 5.34 
#> 

# IDR
# 95% interval estimates

#  IDR   LL   UL
# 2.61 1.28 5.34