Package 'ebdm'

Example Data: Binary Variables

Description

Simulated dataset for testing the cor_bin() function.

Usage

data(bin_example)

Format

A data frame with 3 columns:

ni

Sample size per study

xi

Count of first binary variable

yi

Count of second binary variable

---

Example Data: Continuous Variables

Description

Simulated dataset for testing the cor_cont() function.

Usage

data(cont_example)

Format

A data frame with 5 columns:

Sample_Size

Sample size for each study.

Mean_X

Sample mean of variable X.

Mean_Y

Sample mean of variable Y.

Variance_X

Sample variance of variable X.

Variance_Y

Sample variance of variable Y.

---

Estimate the Joint Distribution of Two Binary Variables from Marginal Summaries

Description

Performs maximum likelihood estimation (MLE) of the joint distribution of two binary variables using only marginal summary data from multiple studies.

Usage

cor_bin(ni, xi, yi, ci_method = c("none", "normal", "lr"))

Arguments

ni	Numeric vector. Sample sizes for each dataset.
xi	Numeric vector. Count of observations where variable 1 equals 1.
yi	Numeric vector. Count of observations where variable 2 equals 1.
ci_method	Character string. Method for confidence interval computation. Options are "none" (default), "normal", or "lr" (likelihood ratio).

Value

A named list with point estimates, variance, standard error, and confidence interval (if requested).

p1_hat

Estimated marginal probability for variable 1.

p2_hat

Estimated marginal probability for variable 2.

p11_hat

Estimated joint probability.

var_hat

Estimated variance of p11_hat.

sd_hat

Standard error of p11_hat.

ci

Confidence interval for p11_hat, if requested.

Examples

data(bin_example)
cor_bin(bin_example$ni, bin_example$xi, bin_example$yi, ci_method = "lr")

---

Estimate the Bivariate Normal Distribution from Marginal Summaries

Description

Estimate the correlation coefficient $\rho$ (and marginal means / SDs) of two normally-distributed variables using summary-level data from multiple independent studies.

Usage

cor_cont(
  n,
  xbar,
  ybar,
  s2x = NULL,
  s2y = NULL,
  method = c("proposed", "weighted"),
  ci_method = c("none", "normal", "lr")
)

Arguments

n	Numeric vector. Sample size of each study.
xbar, ybar	Numeric vectors. Sample means of the two variables.
s2x, s2y	Numeric vectors. Sample variances; required for method = "proposed".
method	Character. "proposed" uses the proposed MLE method in the paper; "weighted" replicates the weighted mean based method (Baseline) when no variances are available.
ci_method	Confidence interval type: "none", "normal", or "lr" (likelihood ratio). Only implemented when method = "proposed".

Value

A list with elements

• mu_x, mu_y : estimated marginal means

• sigma_x, sigma_y : estimated SDs

• rho : estimated correlation

• se : standard error of rho (proposed only)

• ci : confidence interval for rho (if requested)

Examples

data(cont_example)
# Example with full summaries
cor_cont(cont_example$Sample_Size, cont_example$Mean_X, cont_example$Mean_Y,
 cont_example$Variance_X, cont_example$Variance_Y, method = "proposed", ci_method = "lr")

# Only means + n, weighted mean method
cor_cont(cont_example$Sample_Size, cont_example$Mean_X, cont_example$Mean_Y, method = "weighted")

---

Estimate Parameters in a Two-Component Gaussian Mixture Using Study-Level Summaries

Description

Estimates group-specific means and standard deviations $(\mu_1, \mu_0, \sigma_1, \sigma_0)$ in a two-component normal mixture model based on aggregate data across multiple studies. The continuous variable $X$ is assumed to follow a Gaussian mixture conditional on a binary group indicator $Y \in \{0,1\}$, with each study reporting only summary-level statistics.

Usage

est_mixture(ni, xbar, mi, s2 = NULL, method = c("gmm", "naive"))

Arguments

ni	Integer vector of sample sizes per study.
xbar	Numeric vector of sample means per study.
mi	Integer vector of group 1 counts per study.
s2	Numeric vector of sample variances per study. Required if method = "gmm".
method	Estimation method to use. One of "naive" or "gmm". Default is "gmm".

Details

#' Two estimation methods are available:

• "naive": Likelihood-based estimator using only sample means.

• "gmm": Generalized method of moments (GMM) estimator using sample means and variances.

Value

A named list containing:

mu1_hat, mu0_hat

Estimated means of the two groups.

sigma1_hat, sigma0_hat

Estimated standard deviations.

se

Standard errors of the parameter estimates (NA if method = "naive").

ci

List of 95% confidence intervals for each parameter (NULL if method = "naive").

method

A character string indicating the method used.

Examples

# Load example dataset included in the package
data(mixture_example)

# Estimate using GMM (recommended) with full summary statistics
est_mixture(
  ni = mixture_example$ni,
  xbar = mixture_example$xbar,
  s2 = mixture_example$s2,
  mi = mixture_example$mi,
  method = "gmm"
)

# Estimate using naive likelihood method (only means used)
est_mixture(
  ni = mixture_example$ni,
  xbar = mixture_example$xbar,
  mi = mixture_example$mi,
  method = "naive"
)

---

Example Data: Mixture Model Summaries

Description

Simulated dataset for testing the est_mixture() function. Each row corresponds to one study providing summary-level data from a two-component normal mixture.

Usage

data(mixture_example)

Format

A data frame with 4 columns:

ni

Sample size for each study.

mi

Count of group 1 individuals in each study.

xbar

Sample mean of the outcome variable.

s2

Sample variance of the outcome variable.

---