RRlsi: RR likelihood support interval.

In ABS-dev/PF: Prevented fraction

RR likelihood support interval.

Description

likelihood support interval for the risk ratio or prevented fraction by the likelihood profile.

Usage

RRlsi(
  y = NULL,
  formula = NULL,
  data = NULL,
  compare = c("vac", "con"),
  alpha = 0.05,
  k = 8,
  use.alpha = FALSE,
  pf = TRUE,
  iter.max = 50,
  converge = 1e-06,
  rnd = 3,
  start = NULL,
  track = FALSE,
  full.track = FALSE
)

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 group).
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 formula.
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 (see details).
k	Likelihood ratio criterion.
use.alpha	Base choice of k on its relationship to alpha?
pf	Estimate RR or its complement PF?
iter.max	Maximum number of iterations
converge	Convergence criterion
rnd	Number of digits for rounding. Affects display onlyRR, not estimates.
start	Optional starting value.
track	Verbose tracking of the iterations?
full.track	Verbose tracking of the iterations?

Details

Estimates a likelihood support interval for RR or PF by the profile likelihood method using the DUD algorithm.

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. RRlsi() will make the conversion from \alpha to k if use.alpha = TRUE.

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

An object of class rrsi with the following fields:

estimate	matrix of point and interval estimates - see details
estimator	either "PF" or "RR"
y	data.frame with "y1", "n1", "y2", "n2" values.
rnd	how many digits to round the display
k	likelihood ratio criterion
alpha	complement of confidence level

Author(s)

PF-package

References

Royall R. Statistical Evidence: A Likelihood Paradigm. Chapman & Hall, Boca Raton, 1997. Section 7.6
Ralston ML, Jennrich RI, 1978. DUD, A Derivative-Free Algorithm for Nonlinear Least Squares. Technometrics 20:7-14.

Examples

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

y_vector <- c(4, 24, 12, 28)
RRlsi(y_vector)

# 1/8 likelihood support interval for PF

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

# PF
#     PF     LL     UL
# 0.6111 0.0168 0.8859

y_matrix <- matrix(c(4, 20, 12, 16), 2, 2, byrow = TRUE)
y_matrix
#      [, 1] [, 2]
# [1, ]    4   20
# [2, ]   12   16

RRlsi(y_matrix)

# 1/8 likelihood support interval for PF

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

# PF
#     PF     LL     UL
# 0.6111 0.0168 0.8859

require(dplyr)
data1 <- data.frame(group = rep(c("treated", "control"), each = 2),
  y = c(1, 3, 7, 5),
  n = c(12, 12, 14, 14),
  cage = rep(paste('cage', 1:2), 2))

data2 <- data1 |>
  group_by(group) |>
  summarize(sum_y = sum(y),
    sum_n = sum(n))
RRlsi(data = data2, formula =  cbind(sum_y, sum_n) ~ group,
   compare = c("treated", "control"))

# 1/8 likelihood support interval for PF
#
# corresponds to 95.858% confidence
# (under certain assumptions)
#
# PF
# PF     LL     UL
# 0.6111 0.0168 0.8859

ABS-dev/PF documentation built on April 26, 2024, 3:29 p.m.