IDR likelihood support interval.

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.

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

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).

References

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

Author

PF-package

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 
#> 

# 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
#      [, 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 
#> 

# 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)
#> 'y' and 'n' values will be summed by treated and control designation in datacolumn group
#> 
#> 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 
#> 

# 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)
#> Loading required package: dplyr
#> 
#> Attaching package: ‘dplyr’
#> The following object is masked from ‘package:PF’:
#> 
#>     filter
#> The following objects are masked from ‘package:stats’:
#> 
#>     filter, lag
#> The following objects are masked from ‘package:base’:
#> 
#>     intersect, setdiff, setequal, union
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 
#> 

# 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