RRtosst: RR exact CI, TOSST method.

In ABS-dev/PF: Prevented fraction

RR exact CI, TOSST method.

Description

Estimates confidence interval for the risk ratio or prevented fraction; exact method based on the score statistic (inverts two one-sided tests).

Usage

RRtosst(
  y = NULL,
  formula = NULL,
  data = NULL,
  compare = c("vac", "con"),
  alpha = 0.05,
  pf = TRUE,
  stepstart = 0.1,
  iter.max = 36,
  converge = 1e-06,
  rnd = 3,
  trace.it = FALSE,
  nuisance.points = 120,
  gamma = 1e-06
)

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.
pf	Estimate RR or its complement PF?
stepstart	starting interval for step search
iter.max	Maximum number of iterations
converge	Convergence criterion
rnd	Number of digits for rounding. Affects display only, not estimates.
trace.it	Verbose tracking of the iterations?
nuisance.points	number of points over which to evaluate nuisance parameter
gamma	parameter for Berger-Boos correction (restricts range of nuisance parameter evaluation)

Details

Estimates confidence intervals based on the score statistic that are 'exact' in the sense of accounting for discreteness. Inverts two one-sided score tests. The score statistic is used to select tail area tables, and the binomial probability is estimated over the tail area by taking the maximum over the nuisance parameter. Algorithm is a simple step search.

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 fields.

• estimate: vector with point and interval estimate

• estimator: either "PF" or "RR"

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

• rnd: how many digits to round the display

• alpha: complement of confidence level

Author(s)

PF-package

References

Koopman PAR, 1984. Confidence intervals for the ratio of two binomial proportions. Biometrics 40:513-517.

Agresti A, Min Y, 2001. On small-sample confidence intervals for parameters in discrete distribution. Biometrics 57: 963-971.

Berger RL, Boos DD, 1994. P values maximized over a confidence set for the nuisance parameter. Journal of the American Statistical Association 89:214-220.

See Also

RRotsst, rr1

Examples

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

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

# PF
# 95% interval estimates

#    PF    LL    UL
# 0.611 0.012 0.902

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

RRtosst(y_matrix)

# PF
# 95% interval estimates

#    PF    LL    UL
# 0.611 0.012 0.902

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

# PF
# 95% interval estimates

#    PF    LL    UL
# 0.611 0.012 0.902

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