RR exact CI, OTSST method.

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

Usage

RRotsst(
  y = NULL,
  data = NULL,
  formula = 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).
data: data.frame containing variables of the 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 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)

Value

An object of class rr1 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

Details

Estimates confidence intervals based on the score statistic that are 'exact' in the sense of accounting for discreteness. 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).

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.

Author

PF-package

Examples

# All examples represent the same observation, with data entry by multiple
# options.

y_vector <- c(4, 24, 12, 28)
RRotsst(y_vector, rnd = 3)
#> 
#> PF 
#> 95% interval estimates
#> 
#>     PF     LL     UL 
#> 0.6111 0.0148 0.8519 
#> 

# PF
# 95% interval estimates

#    PF     LL     UL
# 0.6111 0.0148 0.8519

y_matrix <- matrix(c(4, 20, 12, 16), 2, 2, byrow = TRUE)
RRotsst(y_matrix, rnd = 3)
#> 
#> PF 
#> 95% interval estimates
#> 
#>     PF     LL     UL 
#> 0.6111 0.0148 0.8519 
#> 

# PF
# 95% interval estimates

#    PF     LL     UL
# 0.6111 0.0148 0.8519

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))
RRotsst(data = data2, formula =  cbind(sum_y, sum_n) ~ group,
   compare = c("treated", "control"))
#> 
#> PF 
#> 95% interval estimates
#> 
#>     PF     LL     UL 
#> 0.6111 0.0148 0.8519 
#> 

# PF
# 95% interval estimates
#
# PF     LL     UL
# 0.6111 0.0148 0.8519