Helper Functions to Calculate Proportion Difference

Usage

prop_diff_wald(rsp, grp, conf_level = 0.95, correct = FALSE)

prop_diff_ha(rsp, grp, conf_level)

prop_diff_nc(rsp, grp, conf_level, correct = FALSE)

prop_diff_cmh(rsp, grp, strata, conf_level = 0.95)

prop_diff_strat_nc(
  rsp,
  grp,
  strata,
  weights_method = c("cmh", "wilson_h"),
  conf_level = 0.95,
  correct = FALSE
)

Arguments

rsp: (logical)
whether each subject is a responder or not.
grp: (factor)
vector assigning observations to one out of two groups (e.g. reference and treatment group).
conf_level: (proportion)
confidence level of the interval.
correct: (logical)
whether to include the continuity correction. For further information, see stats::prop.test().
strata: (factor)
variable with one level per stratum and same length as rsp.
weights_method: (string)
weights method. Can be either "cmh" or "heuristic" and directs the way weights are estimated.

Value

A named list of elements diff (proportion difference) and diff_ci

(proportion difference confidence interval).

Functions

prop_diff_wald(): The Wald interval follows the usual textbook definition for a single proportion confidence interval using the normal approximation. It is possible to include a continuity correction for Wald's interval.
prop_diff_ha(): Anderson-Hauck confidence interval.
prop_diff_nc(): Newcombe confidence interval. It is based on the Wilson score confidence interval for a single binomial proportion.
prop_diff_cmh(): Calculates the weighted difference. This is defined as the difference in response rates between the experimental treatment group and the control treatment group, adjusted for stratification factors by applying Cochran-Mantel-Haenszel (CMH) weights. For the CMH chi-squared test, use stats::mantelhaen.test().
prop_diff_strat_nc(): Calculates the stratified Newcombe confidence interval and difference in response rates between the experimental treatment group and the control treatment group, adjusted for stratification factors. This implementation follows closely the one proposed by Yan and Su (2010) . Weights can be estimated from the heuristic proposed in prop_strat_wilson() or from CMH-derived weights (see prop_diff_cmh()).

References

Yan X, Su XG (2010). “Stratified Wilson and Newcombe Confidence Intervals for Multiple Binomial Proportions.” Stat. Biopharm. Res., 2(3), 329--335.

Examples

# Wald confidence interval
set.seed(2)
rsp <- sample(c(TRUE, FALSE), replace = TRUE, size = 20)
grp <- factor(c(rep("A", 10), rep("B", 10)))
prop_diff_wald(rsp = rsp, grp = grp, conf_level = 0.95, correct = FALSE)
#> $diff
#> [1] 0
#> 
#> $diff_ci
#> [1] -0.4382613  0.4382613
#> 

# Anderson-Hauck confidence interval
## "Mid" case: 3/4 respond in group A, 1/2 respond in group B.
rsp <- c(TRUE, FALSE, FALSE, TRUE, TRUE, TRUE)
grp <- factor(c("A", "B", "A", "B", "A", "A"), levels = c("B", "A"))
prop_diff_ha(rsp = rsp, grp = grp, conf_level = 0.90)
#> $diff
#> [1] 0.25
#> 
#> $diff_ci
#> [1] -0.9195011  1.0000000
#> 

## Edge case: Same proportion of response in A and B.
rsp <- c(TRUE, FALSE, TRUE, FALSE)
grp <- factor(c("A", "A", "B", "B"), levels = c("A", "B"))
prop_diff_ha(rsp = rsp, grp = grp, conf_level = 0.6)
#> $diff
#> [1] 0
#> 
#> $diff_ci
#> [1] -0.8451161  0.8451161
#> 

# Newcombe confidence interval

set.seed(1)
rsp <- c(
  sample(c(TRUE, FALSE), size = 40, prob = c(3 / 4, 1 / 4), replace = TRUE),
  sample(c(TRUE, FALSE), size = 40, prob = c(1 / 2, 1 / 2), replace = TRUE)
)
grp <- factor(rep(c("A", "B"), each = 40), levels = c("B", "A"))
table(rsp, grp)
#>        grp
#> rsp      B  A
#>   FALSE 20 10
#>   TRUE  20 30
prop_diff_nc(rsp = rsp, grp = grp, conf_level = 0.9)
#> $diff
#> [1] 0.25
#> 
#> $diff_ci
#> [1] 0.07193388 0.40725819
#> 

# Cochran-Mantel-Haenszel confidence interval

set.seed(2)
rsp <- sample(c(TRUE, FALSE), 100, TRUE)
grp <- sample(c("Placebo", "Treatment"), 100, TRUE)
grp <- factor(grp, levels = c("Placebo", "Treatment"))
strata_data <- data.frame(
  "f1" = sample(c("a", "b"), 100, TRUE),
  "f2" = sample(c("x", "y", "z"), 100, TRUE),
  stringsAsFactors = TRUE
)

prop_diff_cmh(
  rsp = rsp, grp = grp, strata = interaction(strata_data),
  conf_level = 0.90
)
#> $prop
#>   Placebo Treatment 
#> 0.5331117 0.3954251 
#> 
#> $prop_ci
#> $prop_ci$Placebo
#> [1] 0.4306536 0.6355698
#> 
#> $prop_ci$Treatment
#> [1] 0.2890735 0.5017768
#> 
#> 
#> $diff
#> [1] -0.1376866
#> 
#> $diff_ci
#> [1] -0.285363076  0.009989872
#> 
#> $weights
#>       a.x       b.x       a.y       b.y       a.z       b.z 
#> 0.1148388 0.2131696 0.1148388 0.2131696 0.1767914 0.1671918 
#> 
#> $n1
#> a.x b.x a.y b.y a.z b.z 
#>   4  11   8  11  13  11 
#> 
#> $n2
#> a.x b.x a.y b.y a.z b.z 
#>   8   9   4   9   6   6 
#> 

# Stratified Newcombe confidence interval

set.seed(2)
data_set <- data.frame(
  "rsp" = sample(c(TRUE, FALSE), 100, TRUE),
  "f1" = sample(c("a", "b"), 100, TRUE),
  "f2" = sample(c("x", "y", "z"), 100, TRUE),
  "grp" = sample(c("Placebo", "Treatment"), 100, TRUE),
  stringsAsFactors = TRUE
)

prop_diff_strat_nc(
  rsp = data_set$rsp, grp = data_set$grp, strata = interaction(data_set[2:3]),
  weights_method = "cmh",
  conf_level = 0.90
)
#> $diff
#> [1] -0.05777672
#> 
#> $diff_ci
#>      lower      upper 
#> -0.2236537  0.1119331 
#> 

prop_diff_strat_nc(
  rsp = data_set$rsp, grp = data_set$grp, strata = interaction(data_set[2:3]),
  weights_method = "wilson_h",
  conf_level = 0.90
)
#> $diff
#> [1] -0.07771884
#> 
#> $diff_ci
#>      lower      upper 
#> -0.2540844  0.1027720 
#>