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Bayesian Multivariate Bernoulli Test

Source: R/main_functions.R
bmvb.Rd

Perform a Bayesian test for differences between two groups on multiple binary outcomes using a Multivariate Bernoulli distribution, as described in Kavelaars et al. (2020) .

Usage

bmvb(
  data,
  grp,
  grp_a,
  grp_b,
  y_vars,
  test = c("right_sided", "left_sided"),
  rule = c("All", "Any", "Comp"),
  w = NULL,
  prior_a = 0.5,
  prior_b = 0.5,
  n_it = 10000,
  return_samples = FALSE
)

Arguments

data

Data frame containing the data.

grp

Character string. Name of the grouping variable.

grp_a

Value of grp indicating first group.

grp_b

Value of grp indicating second group.

y_vars

Character vector. Names of outcome variables (currently supports 2 outcomes).

test

Character. Direction of test: "left_sided" for P(A>B) or "right_sided" for P(B>A). Default is "right_sided".

rule

Character. Decision rule: "All" (all outcomes favor hypothesis), "Any" (at least one outcome favors hypothesis), or "Comp" (weighted combination). Default is "All".

w

Numeric vector. Weights for compensatory rule. Only used if rule = "Comp". If NULL and rule = "Comp", equal weights are used. Default is NULL.

prior_a

Numeric. Prior hyperparameter (Dirichlet) for group A. Default is 0.5 (Jeffreys' prior)

prior_b

Numeric. Prior hyperparameter (Dirichlet) for group B. Default is 0.5 (Jeffreys' prior).

n_it

Integer. Number of MCMC iterations. Default is 10000.

return_samples

Logical. Should posterior samples be returned? Default is FALSE.

Value

An object of class bmvb, a list containing:

estimates

A list with posterior means (mean_a, mean_b) and standard deviations (sd_a, sd_b) of the category probabilities for both groups.

sample_sizes

A list with group sample sizes (n_a, n_b).

delta

A list with posterior mean differences (mean_delta), posterior standard errors (se_delta), posterior probability of the hypothesis (pop), and, if rule = "Comp", the weighted difference (w_delta).

info

A list with test specifications, including the decision rule, test direction, group labels, and weights (if applicable).

samples

If return_samples = TRUE, a list containing posterior draws of theta_a, theta_b, and delta.

References

Kavelaars X, Mulder J, Kaptein M (2020). “Decision-making with multiple correlated binary outcomes in clinical trials.” Statistical Methods in Medical Research, 29(11), 3265–3277. doi:10.1177/0962280220922256 .

Examples

# \donttest{
# Example with simulated data
# Generate data
set.seed(123)
data <- data.frame(
treatment = rep(c("control", "drug"), each = 50),
 outcome1 = rbinom(100, 1, 0.5),
 outcome2 = rbinom(100, 1, 0.5)
)

# Analyze
result <- bmvb(
 data = data,
 grp = "treatment",
 grp_a = "control",
 grp_b = "drug",
 y_vars = c("outcome1", "outcome2"),
 n_it = 10000
)

print(result)
#> 
#> Multivariate Bernoulli Analysis
#> =================================
#> 
#>    Group mean y1 mean y2
#>  control   0.501   0.501
#>     drug   0.442   0.501
#>   n(control) = 50    n(drug) = 50
#> 
#> Posterior probability P(drug > control) [All rule]: 0.129
#> 
#> Use summary() for credible intervals and ESS.
#> 
# }