Nonparametric Bounds for the Average Causal Effect due to Balke and Pearl.

Usage

bpbounds(p, t = NULL, fmt = "trivariate")

Arguments

p

Object of class "table" containing either cell counts or conditional probabilities. For trivariate data these are for the phenotype/treatment-outcome association given Z, i.e. P(X, Y | Z).

Cell counts could be generated from xtabs(~ x + y + z, data = data). And then conditional probabilities obatained by calling prop.table(..., margins = 3) on your object from xtabs().

If you only know the conditional probabilities you can enter these, e.g. for the Balke and Pearl Vitamin A example:

cp   <- c(.0064, 0, .9936, 0, .0028, .001, .1972, .799)
tabp <- as.table(array(
  cp,
  dim = c(2, 2, 2),
  dimnames = list(
    x = c(0, 1),
    y = c(0, 1),
    z = c(0, 1)
  )
))

And then call bpbounds() using this object.

For bivariate data this object contains cell conditional probabilities for the outcome-instrument (Y|Z) association.

t

Specified for bivariate data. Object with treatment/phenotype-instrument cell counts or conditional probabilities, i.e. (X|Z).

fmt

A character string which sould be either "bivariate" (i.e. X, Z in one dataset and Y, Z in another dataset) or "trivariate" (X, Y, Z in the same dataset).

Value

List with the following elements:

fmt: whether the data is bivariate or trivariate
nzcats: 2 or 3, the no. instrument categories
inequality: Logical, indicating whether the IV inquality is satisfied
bplb: Lower bound of ACE
bpub: Upper bound of ACE
bplower: Vector of lower bound probabilities
bpupper: Vector of upper bound probabilities
p11low: Lower bound of P(Y=1|do(X=1))
p11upp: Upper bound of P(Y=1|do(X=1))
p10low: Lower bound of P(Y=1|do(X=0))
p10upp: Upper bound of P(Y=1|do(X=0))
p11lower: Vector of probabilities for lower bound of P(Y=1|do(X=1))
p11upper: Vector of probabilities for upper bound of P(Y=1|do(X=1))
p10lower: Vector of probabilities for lower bound of P(Y=1|do(X=0))
p10upper: Vector of probabilities for upper bound of P(Y=1|do(X=0))
crrlb: Lower bound of CRR
crrub: Upper bound of CRR
monoinequality: Logical, indicating whether the monoticity inequality is satisfied
monobplb: Lower bound of ACE assuming monotonicity
monobpub: Upper bound of ACE assuming monotonicity
monobplower: Vector of probabilities for lower bound of ACE assuming monotonicity
monobpupper: Vector of probabilities for upper bound of ACE assuming monotonicity
monop11low: Lower bound of P(Y=1|do(X=1)) assuming monotonicity
monop11upp: Upper bound of P(Y=1|do(X=1)) assuming monotonicity
monop10low: Lower bound of P(Y=1|do(X=0)) assuming monotonicity
monop10upp: Upper bound of P(Y=1|do(X=0)) assuming monotonicity
monop11lower: Vector for corresponding bound above
monop11upper: Vector for corresponding bound above
monop10lower: Vector for corresponding bound above
monop10upper: Vector for corresponding bound above
monocrrlb: Lower bound of CRR assuming monotonicity
monocrrub: Upper bound of CRR assuming monotonicity

Examples

# \donttest{
# Vitamin A example, using cell counts

require(tidyr)
#> Loading required package: tidyr
require(bpbounds)

tab1dat <- data.frame(
  z = c(0, 0, 1, 1, 1, 1, 0, 0),
  x = c(0, 0, 0, 0, 1, 1, 1, 1),
  y = c(0, 1, 0, 1, 0, 1, 0, 1),
  freq = c(74, 11514, 34, 2385, 12, 9663, 0, 0)
)
tab1inddat <- uncount(tab1dat, freq)
xt         <- xtabs(~ x + y + z, data = tab1inddat)
p          <- prop.table(xt, margin = 3)
bpres      <- bpbounds(p)
sbpres     <- summary(bpres)
print(sbpres)
#> 
#> Data:                    trivariate
#> Instrument categories:   2
#> 
#> Instrumental inequality: TRUE 
#>  Causal parameter Lower bound Upper bound
#>               ACE  -0.1946228 0.005393689
#>      P(Y|do(X=0))   0.9936141 0.993614084
#>      P(Y|do(X=1))   0.7989912 0.999007772
#>               CRR   0.8041263 1.005428354
#> 
#> Monotonicity inequality: TRUE 
#>  Causal parameter Lower bound Upper bound
#>               ACE  -0.1946228 0.005393689
#>      P(Y|do(X=0))   0.9936141 0.993614084
#>      P(Y|do(X=1))   0.7989912 0.999007772
#>               CRR   0.8041263 1.005428354
#> 
# }

# \donttest{
# Vitamin A example, using conditional probabilities

require(bpbounds)
cp = c(.0064, 0, .9936, 0, .0028, .001, .1972, .799)
tabp = as.table(array(
  cp,
  dim = c(2, 2, 2),
  dimnames = list(
    x = c(0, 1),
    y = c(0, 1),
    z = c(0, 1)
  )
))
bpbounds(tabp)
#> 
#> Data:                    trivariate
#> Instrument categories:   2
#> 
#> Instrumental inequality: TRUE 
#>  Causal parameter Lower bound Upper bound
#>               ACE  -0.1946000    0.005400
#>      P(Y|do(X=0))   0.9936000    0.993600
#>      P(Y|do(X=1))   0.7990000    0.999000
#>               CRR   0.8041465    1.005435
#> 
#> Monotonicity inequality: TRUE 
#>  Causal parameter Lower bound Upper bound
#>               ACE  -0.1946000    0.005400
#>      P(Y|do(X=0))   0.9936000    0.993600
#>      P(Y|do(X=1))   0.7990000    0.999000
#>               CRR   0.8041465    1.005435
#> 
# }