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Proportion Difference

Source: R/prop_diff.R
prop_diff.Rd

[Stable]

Usage 

d_proportion_diff(conf_level, method, long = FALSE)

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
)

s_proportion_diff(
  df,
  .var,
  .ref_group,
  .in_ref_col,
  variables = list(strata = NULL),
  conf_level = 0.95,
  method = c("waldcc", "wald", "cmh", "ha", "newcombe", "newcombecc", "strat_newcombe",
    "strat_newcombecc"),
  weights_method = "cmh"
)

a_proportion_diff(
  df,
  .var,
  .ref_group,
  .in_ref_col,
  variables = list(strata = NULL),
  conf_level = 0.95,
  method = c("waldcc", "wald", "cmh", "ha", "newcombe", "newcombecc", "strat_newcombe",
    "strat_newcombecc"),
  weights_method = "cmh"
)

estimate_proportion_diff(
  lyt,
  vars,
  ...,
  var_labels = vars,
  show_labels = "hidden",
  table_names = vars,
  .stats = NULL,
  .formats = NULL,
  .labels = NULL,
  .indent_mods = NULL
)

Arguments

conf_level

(proportion)
confidence level of the interval.

method

(string)
the method used for the confidence interval estimation.

long

(logical)
Whether a long or a short (default) description is required.

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).

correct

logical
include the continuity correction. For further information, see for example stats::prop.test().

strata

(factor)
with one level per stratum and same length as rsp.

weights_method

(string)
it can be one of c("cmh", "heuristic") and directs the way weights are estimated.

df

(data frame)
data set containing all analysis variables.

.var

(string)
single variable name that is passed by rtables when requested by a statistics function.

.ref_group

(data frame or vector)
the data corresponding to the reference group.

.in_ref_col

(logical)
TRUE when working with the reference level, FALSE otherwise.

variables

(named list of string)
list of additional analysis variables.

lyt

(layout)
input layout where analyses will be added to.

vars

(character)
variable names for the primary analysis variable to be iterated over.

...

arguments passed to s_proportion_diff().

var_labels

character for label.

show_labels

label visibility: one of "default", "visible" and "hidden".

table_names

(character)
this can be customized in case that the same vars are analyzed multiple times, to avoid warnings from rtables.

.stats

(character)
statistics to select for the table.

.formats

(named character or list)
formats for the statistics.

.labels

(named character)
labels for the statistics (without indent).

.indent_mods

(named integer)
indent modifiers for the labels.

Value

String describing the analysis.

Functions

  • d_proportion_diff(): This is an auxiliary function that describes the analysis in s_proportion_diff.

  • 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()).

  • s_proportion_diff(): Statistics function estimating the difference in terms of responder proportion.

  • a_proportion_diff(): Formatted Analysis function which can be further customized by calling rtables::make_afun() on it. It is used as afun in rtables::analyze().

  • estimate_proportion_diff(): Adds a descriptive analyze layer to rtables pipelines. The analysis is applied to a dataframe and return the estimations, in rcells. The ellipsis (...) conveys arguments to s_proportion_diff(), for instance na.rm = FALSE if missing data should be accounted for.

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 
#> 

# Summary

## "Mid" case: 4/4 respond in group A, 1/2 respond in group B.
nex <- 100 # Number of example rows
dta <- data.frame(
  "rsp" = sample(c(TRUE, FALSE), nex, TRUE),
  "grp" = sample(c("A", "B"), nex, TRUE),
  "f1" = sample(c("a1", "a2"), nex, TRUE),
  "f2" = sample(c("x", "y", "z"), nex, TRUE),
  stringsAsFactors = TRUE
)

s_proportion_diff(
  df = subset(dta, grp == "A"),
  .var = "rsp",
  .ref_group = subset(dta, grp == "B"),
  .in_ref_col = FALSE,
  conf_level = 0.90,
  method = "ha"
)
#> $diff
#> [1] -0.1204336
#> attr(,"label")
#> [1] "Difference in Response rate (%)"
#> 
#> $diff_ci
#> [1] -17.82763  17.58677
#> attr(,"label")
#> [1] "90% CI (Anderson-Hauck)"
#> 

# CMH example with strata
s_proportion_diff(
  df = subset(dta, grp == "A"),
  .var = "rsp",
  .ref_group = subset(dta, grp == "B"),
  .in_ref_col = FALSE,
  variables = list(strata = c("f1", "f2")),
  conf_level = 0.90,
  method = "cmh"
)
#> $diff
#> [1] -0.1045856
#> attr(,"label")
#> [1] "Difference in Response rate (%)"
#> 
#> $diff_ci
#> [1] -15.98426  15.77509
#> attr(,"label")
#> [1] "90% CI (CMH, without correction)"
#> 

a_proportion_diff(
  df = subset(dta, grp == "A"),
  .var = "rsp",
  .ref_group = subset(dta, grp == "B"),
  .in_ref_col = FALSE,
  conf_level = 0.90,
  method = "ha"
)
#> RowsVerticalSection (in_rows) object print method:
#> ----------------------------
#>   row_name formatted_cell indent_mod                       row_label
#> 1     diff           -0.1          0 Difference in Response rate (%)
#> 2  diff_ci  (-17.8, 17.6)          1         90% CI (Anderson-Hauck)

l <- basic_table() %>%
  split_cols_by(var = "grp", ref_group = "B") %>%
  estimate_proportion_diff(
    vars = "rsp",
    conf_level = 0.90,
    method = "ha"
  )

build_table(l, df = dta)
#>                                   B         A      
#> ———————————————————————————————————————————————————
#> Difference in Response rate (%)           -0.1     
#>   90% CI (Anderson-Hauck)             (-17.8, 17.6)