case_control_b: Case-Control Analysis

In bayesics: Bayesian Analyses for One- and Two-Sample Inference and Regression Methods

Case-Control Analysis

Description

Bayesian analysis of a case-control study (without covariates).

Usage

case_control_b(
  cases,
  controls,
  x,
  large_sample_approx,
  ROPE,
  prior_mean = 0,
  prior_sd = log(10)/1.96,
  plot = TRUE,
  CI_level = 0.95,
  seed = 1,
  mc_error = 0.005
)

Arguments

cases	vector of length 2, giving the numbers at risk and not at risk, respectively, for cases
controls	vector of length 2, giving the numbers at risk and not at risk, respectively, for controls
x	2x2 contingency table. The rows should depict the at risk status (first row is at risk, second row is not at risk), and the columns should depict the case control status (first column is case, second column is control).
large_sample_approx	If all cell counts of x are not too low (\geq 5) then use the approximation that the empirical log odds are normally distributed. (See details for more.) If missing, this will be set to TRUE iff all cell counts are greater than or equal to 5.
ROPE	ROPE for odds ratio. Provide either a single value or a vector of length two. If the former, the ROPE will be taken as (1/ROPE,ROPE). If the latter, these will be the bounds of the ROPE.
prior_mean	numeric. The prior mean on the log odds ratio
prior_sd	numeric. The prior sd on the log odds ratio. See details for default values.
plot	logical. Should a plot be shown?
CI_level	The posterior probability to be contained in the credible interval.
seed	integer. Always set your seed!!! (ignored if large_sample_approx = TRUE.)
mc_error	The relative monte carlo error of the quantiles of the CIs. (ignored if large_sample_approx = TRUE.)

Details

If large_sample_approx = TRUE (the default if left missing and all cell counts are at least 5), then the likelihood is

\log(\hat\omega) \sim N\left(\log(\omega),\frac{1}{n_{11}} + \frac{1}{n_{12}} + \frac{1}{n_{21}} + \frac{1}{n_{22}} \right),

where \omega is the odds ratio, \hat\omega is the empirical odds ratio, n_{ij}, i,j = 1,2 are the cells of the 2x2 contingency table. The prior on \log\omega is

\log\omega \sim N(a,b^2).

If the large sample approximation is not used, then inference is made on the odds ratio by instead putting uniform priors on \Pr(exposure|outcome).

Value

(returned invisible) list including the following:

• data: data

• posterior_mean: posterior mean of the odds ratio (cases vs. controls)

• CI: Credible interval

• Pr_oddsratio_in_ROPE: Probability the odds ratio (cases vs. controls) is in the ROPE

• posterior_draws: posterior draws of the odds ratio (cases vs. controls)

• or_plot: odds ratio (cases vs. controls) posterior plot

Examples

case_control_b(matrix(c(8,47,1,26),2,2))

case_control_b(c(8,47),
               c(1,26))

bayesics documentation built on March 11, 2026, 5:07 p.m.