BFpower.props: Sample Size Determination for the Bayesian test of two proportions

Description

Perform sample size determination or calculate probabilities of compelling and misleading evidence for a Bayesian comparison of two proportions.

Usage

BFpower.props(
  threshold,
  true_rate,
  a0,
  b0,
  a1,
  b1,
  a2,
  b2,
  prior_design_1 = "same",
  a1d,
  b1d,
  dp1,
  prior_design_2 = "same",
  a2d,
  b2d,
  dp2,
  n1 = NULL,
  n2 = NULL,
  type_rate = "positive",
  plot_power = FALSE,
  plot_rel = FALSE
)

Value

An object of class BFpower_2p (a list) containing:

type: Character, always "Two-proportions".
analysis_h0: List of analysis prior parameters under the null, containing a and b.
analysis_h1_theta_1: List of analysis prior parameters for group 1 under the alternative, containing a and b.
analysis_h1_theta_2: List of analysis prior parameters for group 2 under the alternative, containing a and b.
design_h1_theta_1: List of design prior parameters for group 1 under the alternative, containing prior, a, b, and p.
design_h1_theta_2: List of design prior parameters for group 2 under the alternative, containing prior, a, b, and p.
results: Data frame of probabilities of compelling and misleading evidence.
grid: Grid used for computation.
threshold: Threshold of compelling evidence.
mode_bf: Character string specifying the mode (sample size determination or power calculation).
plot_power: Logical; whether the power curve is plotted.
plot_rel: Logical; whether the relationship between the Bayes factor and observed proportion differences is plotted.

Arguments

threshold: Numeric scalar. Threshold of compelling evidence.
true_rate: Numeric scalar. Targeted true positive rate (if positive = "positive") or true negative rate (if positive = "negative").
a0: Numeric scalar. Alpha parameter of the Beta prior under the null hypothesis.
b0: Numeric scalar. Beta parameter of the Beta prior under the null hypothesis.
a1: Numeric scalar. Alpha parameter of the Beta analysis prior for group 1 under the alternative hypothesis.
b1: Numeric scalar. Beta parameter of the Beta analysis prior for group 1 under the alternative hypothesis.
a2: Numeric scalar. Alpha parameter of the Beta analysis prior for group 2 under the alternative hypothesis.
b2: Numeric scalar. Beta parameter of the Beta analysis prior for group 2 under the alternative hypothesis.
prior_design_1: Character. The design prior of group 1: "beta", "Point", or "same" (if "same", the design prior is identical to the analysis prior).
a1d: Numeric scalar. Alpha parameter of the design prior for group 1 (used if model1 = "beta").
b1d: Numeric scalar. Beta parameter of the design prior for group 1 (used if model1 = "beta").
dp1: Numeric scalar. True proportion for group 1 in the design prior (used if model1 = "Point").
prior_design_2: Character. The design prior of group 2: "beta", "Point", or "same" (if "same", the design prior is identical to the analysis prior).
a2d: Numeric scalar. Alpha parameter of the design prior for group 2 (used if model2 = "beta").
b2d: Numeric scalar. Beta parameter of the design prior for group 2 (used if model2 = "beta").
dp2: Numeric scalar. True proportion for group 2 in the design prior (used if model2 = "Point").
n1: Numeric integer. Sample size for group 1.
n2: Numeric integer. Sample size for group 2.
type_rate: Character. Choose "positive" to control true/false positive rates or "negative" to control true/false negative rates.
plot_power: Logical; if TRUE, plot the power curve.
plot_rel: Logical; if TRUE, plot the grid for the values of BF across all possible combination of x1 and x2.

Details

1. Sample size determination mode (when n1 = NULL and n2 = NULL):

If no sample sizes are provided for the two groups, the function calculates the minimum sample sizes needed to achieve the desired configuration. The user must provide:

type_rate - either "positive" to control true/false positive rates or "negative" to control true/false negative rates.
true_rate - the targeted true positive or true negative rate (between 0.6 and 0.999).
threshold - the Bayes factor threshold for compelling evidence (must be > 1).

The function iteratively finds the smallest sample sizes for which the probability of obtaining compelling evidence meets or exceeds true_rate.

2. Fixed-sample analysis mode (when n1 and n2 are supplied):

If positive numeric sample sizes n1 and n2 are provided, the function computes the probabilities of obtaining compelling or misleading evidence for these fixed sample sizes. In this mode, type_rate and true_rate are ignored; only the Bayes factor threshold threshold is used.

Model specification:

The user must specify the analysis priors under the null and alternative hypotheses using Beta parameters:

a0, b0 - Beta parameters for the null hypothesis prior.
a1, b1 - Beta parameters for the analysis prior of group 1 under the alternative hypothesis.
a2, b2 - Beta parameters for the analysis prior of group 2 under the alternative hypothesis.

Design priors for the alternative hypothesis can optionally be specified:

prior_design_1, a1d, b1d, dp1 - design prior for group 1 ("same" uses the analysis prior, "beta" requires Beta parameters, "Point" uses a fixed proportion).
prior_design_2, a2d, b2d, dp2 - design prior for group 2.

Plotting:

If plot_power = TRUE, a power curve is plotted showing the probability of compelling evidence as a function of sample sizes. If plot_rel = TRUE, a grid of Bayes factors across possible outcomes is plotted.

Examples

Run this code

BFpower.props(
threshold = 3,
true_rate = 0.8,
a0 = 1,
b0 = 1,
a1 = 156,
b1 = 339,
a2 = 151,
b2 = 339,
plot_power = TRUE,
plot_rel = TRUE)

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