IDRsc: IDR confidence interval.

In ABS-dev/PF: Prevented fraction

IDR confidence interval.

Description

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.

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).

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

Author(s)

PF-package

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

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

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

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

ABS-dev/PF documentation built on Sept. 19, 2024, 10:31 a.m.