IDRlsi: IDR likelihood support interval.

In ABS-dev/PF: Prevented fraction

IDR likelihood support interval.

Description

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

Usage

IDRlsi(
  y = NULL,
  formula = NULL,
  data = NULL,
  alpha = 0.05,
  k = 8,
  use.alpha = FALSE,
  pf = TRUE,
  converge = 1e-08,
  rnd = 3,
  start = NULL,
  trace.it = FALSE,
  iter.max = 24,
  compare = c("con", "vac")
)

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).
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.
data	data.frame containing variables of the formula.
alpha	Complement of the confidence level.
k	Likelihood ratio criterion.
use.alpha	Base choice of k on its relationship to alpha?
pf	Estimate IDR or its complement PF?
converge	Convergence criterion
rnd	Number of digits for rounding. Affects display only, not estimates.
start	describe here.
trace.it	Verbose tracking of the iterations?
iter.max	Maximum number of iterations
compare	Text vector stating the factor levels: compare[1] is the vaccinate group to which compare[2] (control or reference) is compared.

Details

Estimates likelihood support interval for the incidence density ratio based on orthogonal factoring of reparameterized likelihood. The incidence density is the number of cases per subject-time; its distribution is assumed Poisson.

Likelihood support intervals are usually formed based on the desired likelihood ratio, often 1 / 8 or 1 / 32. Under some conditions the log likelihood ratio may follow the chi square distribution. If so, then \alpha = 1 - F(2log(k), 1), where F is a chi-square CDF. if ⁠use.alpha = TRUE``RRsc()⁠ will make the conversion from \alpha to k .

The data may also be a matrix, in which case y would be entered as matrix(c(y1, n1 - y1, y2, n2 - y2), 2, 2, byrow = TRUE).

Value

A rrsi object with the following elements.

• estimate: vector with point and interval estimate

• estimator: either PF or IDR

• y: data.frame with "y1", "n1", "y2", "n2" values.

• k: Likelihood ratio criterion

• rnd: how many digits to round the display

• alpha: complement of confidence level

Author(s)

PF-package

References

Royall R. Statistical Evidence: A Likelihood Paradigm. Chapman & Hall, Boca Raton, 1997. Section 7.2.

See Also

IDRsc

Examples

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

y_vector <- c(26, 204, 10, 205)
IDRlsi(y_vector, pf = FALSE)

# 1 / 8 likelihood support interval for IDR

# corresponds to 95.858% confidence
#   (under certain assumptions)

# IDR
#  IDR   LL   UL
# 2.61 1.26 5.88

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

IDRlsi(y_matrix, pf = FALSE)

# 1 / 8 likelihood support interval for IDR

# corresponds to 95.858% confidence
#   (under certain assumptions)

# IDR
#  IDR   LL   UL
# 2.61 1.26 5.88

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))
IDRlsi(data = data1, formula = cbind(y, n) ~ group,
               compare = c("treated", "control"), pf = FALSE)

# 1 / 8 likelihood support interval for IDR

# corresponds to 95.858% confidence
#   (under certain assumptions)

# IDR
#  IDR   LL   UL
# 2.61 1.26 5.88

require(dplyr)
data2 <- data1 |>
  group_by(group) |>
  summarize(sum_y = sum(y),
    sum_n = sum(n))

IDRlsi(data = data2, formula = cbind(sum_y, sum_n) ~ group,
               compare = c("treated", "control"), pf = FALSE)

# 1 / 8 likelihood support interval for IDR

# corresponds to 95.858% confidence
#   (under certain assumptions)

# IDR
#  IDR   LL   UL
# 2.61 1.26 5.88

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