Title: Probabilistic Two Sample Mendelian Randomization
Type: Package
Version: 1.0.1
Description: Efficient statistical inference of two-sample MR (Mendelian Randomization) analysis. It can account for the correlated instruments and the horizontal pleiotropy, and can provide the accurate estimates of both causal effect and horizontal pleiotropy effect as well as the two corresponding p-values. There are two main functions in the 'PPMR' package. One is PMR_individual() for individual level data, the other is PMR_summary() for summary data.
License: GPL-3
Encoding: UTF-8
LazyData: true
Imports: Rcpp (≥ 1.0.0)
LinkingTo: Rcpp, RcppArmadillo
RoxygenNote: 7.3.2
NeedsCompilation: yes
BugReports: https://github.com/umich-biostatistics/PPMR/issues
Packaged: 2025-09-17 19:02:37 UTC; mk
Author: Zhongshang Yuan [aut], Xiang Zhou [aut], Michael Kleinsasser [cre]
Maintainer: Michael Kleinsasser <mkleinsa@umich.edu>
Depends: R (≥ 3.5.0)
Repository: CRAN
Date/Publication: 2025-09-17 19:20:09 UTC

Individual level dataset

Description

A simulated individual level dataset for PMR.

Usage

Exampleindividual

Format

A list contains the following objects:

zx

the standardized genotype matrix for 465 individuals and 50 cis-SNPs in eQTL data.

zy

the standardized genotype matrix for 2000 individuals and 50 cis-SNPs in GWAS data.

x

the standarized gene expression vector for 465 individuals in eQL data.

y

the standarized complex trait vector for 2000 individuals in GWAS data.

Summary level dataset

Description

A simulated summary level dataset for PMR

Usage

Examplesummary

Format

A list contains the following objects:

betax

the cis-SNP effect size vector for one specific gene in eQTL data.

betay

the cis-SNP effect size vector for one specific gene in GWAS data.

Sigma1

the LD matrix in eQTL data.

Sigma2

the LD matrix in GWAS data.

n1

the sample size of eQTL data.

n2

the sample size of GWAS data.

PPMR Individual-level Analysis

Description

PPMR Individual-level Analysis

Usage

PMR_individual(yin, zin, x1in, x2in, gammain, alphain, max_iterin, epsin)

Arguments

yin

Numeric vector of the outcome variable (length n1).

zin

Numeric vector of the mediator variable (length n2).

x1in

Numeric n1 \times p matrix of SNP genotypes for the outcome model.

x2in

Numeric n2 \times p matrix of SNP genotypes for the mediator model. Must have the same number of columns p as x1in.

gammain

Integer flag (0/1). If 1, constrains the gamma parameter to 0.

alphain

Integer flag (0/1). If 1, constrains the alpha parameter to 0.

max_iterin

Integer. Maximum number of EM iterations (default: 50 or more).

epsin

Numeric. Convergence tolerance for the log-likelihood.

Value

A named list with elements:

alpha

Estimated causal effect of the mediator on the outcome.

gamma

Estimated direct effect of the SNPs on the outcome.

sigmaX

Residual variance of the outcome model.

sigmaY

Residual variance of the mediator model.

sigmabeta

Variance of the genetic effects.

loglik_seq

Vector of log-likelihood values across iterations.

loglik

Final log-likelihood value.

iteration

Number of iterations before convergence.

Examples

# ---- Simulate simple example data ----
set.seed(456)
n1 <- 8
n2 <- 10
p  <- 3

# Outcome and mediator vectors
y <- c(0.5, -0.3, 0.1, 0.4, -0.2, 0.0, 0.6, -0.1)
z <- c(0.2, -0.4, 0.3, 0.1, -0.1, 0.5, 0.0, 0.4, -0.3, 0.2)

# Fixed genotype design matrices (n × p) with mild correlations
x1 <- matrix(c(
  1.0, 0.2, 0.1,
  0.2, 1.0, 0.3,
  0.1, 0.3, 1.0,
  0.4, 0.1, 0.2,
  0.2, 0.4, 0.3,
  0.3, 0.2, 0.4,
  0.5, 0.1, 0.3,
  0.1, 0.5, 0.2
), nrow = n1, byrow = TRUE)

x2 <- matrix(c(
  1.0, 0.3, 0.2,
  0.3, 1.0, 0.4,
  0.2, 0.4, 1.0,
  0.5, 0.1, 0.3,
  0.2, 0.5, 0.1,
  0.3, 0.2, 0.4,
  0.4, 0.3, 0.2,
  0.1, 0.4, 0.3,
  0.2, 0.1, 0.5,
  0.3, 0.2, 0.4
), nrow = n2, byrow = TRUE)

# Run PPMR individual-level analysis
PMR_individual(
  yin        = y,
  zin        = z,
  x1in       = x1,
  x2in       = x2,
  gammain    = 0,
  alphain    = 0,
  max_iterin = 50,
  epsin      = 1e-6
)

PPMR Summary-level Analysis

Description

PPMR Summary-level Analysis

Usage

PMR_summary(
  betaxin,
  betayin,
  Sigma1sin,
  Sigma2sin,
  samplen1,
  samplen2,
  gammain,
  alphain,
  max_iterin,
  epsin
)

Arguments

betaxin

Numeric vector of estimated SNP–exposure effects (length 'p').

betayin

Numeric vector of estimated SNP–outcome effects (length 'p').

Sigma1sin

Numeric 'p x p' covariance matrix for the exposure SNP associations (typically an LD matrix).

Sigma2sin

Numeric 'p x p' covariance matrix for the outcome SNP associations.

samplen1

Integer. Sample size used to estimate betaxin.

samplen2

Integer. Sample size used to estimate betayin.

gammain

Integer flag (0/1). If 1, constrains the gamma parameter to 0.

alphain

Integer flag (0/1). If 1, constrains the alpha parameter to 0.

max_iterin

Integer. Maximum number of EM iterations (default: 50 or more).

epsin

Numeric. Convergence tolerance for the log-likelihood.

Value

A named list with elements:

alpha

Estimated causal effect of the mediator on the outcome.

gamma

Estimated direct effect of the SNPs on the outcome.

sigmaX

Residual variance for the exposure model.

sigmaY

Residual variance for the outcome model.

sigmabeta

Variance of the genetic effects.

loglik_seq

Vector of log-likelihood values across iterations.

loglik

Final log-likelihood value.

iteration

Number of iterations used before convergence.

Examples

# ---- Simulate simple example data ----
set.seed(123)
p  <- 3
n1 <- 10
n2 <- 12
betax <- c(0.2, -0.1, 0.3)
betay <- c(0.1,  0.0, 0.2)
Sigma1 <- matrix(c(0.6, 0.2, 0.1,
                   0.2, 0.5, 0.1,
                   0.1, 0.1, 0.4), 3, 3)
Sigma2 <- matrix(c(0.5, 0.1, 0.0,
                   0.1, 0.6, 0.1,
                   0.0, 0.1, 0.5), 3, 3)

PMR_summary(
  betaxin   = betax,
  betayin   = betay,
  Sigma1sin = Sigma1,
  Sigma2sin = Sigma2,
  samplen1  = n1,
  samplen2  = n2,
  gammain   = 0,
  alphain   = 0,
  max_iterin = 50,
  epsin      = 1e-6
)