RR likelihood support interval.

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?

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

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

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

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.

Author

PF-package

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 
#> 

# 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
#      [, 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 
#> 

# 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 
#> 

# 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