mr_cML: Constrained maximum likelihood (cML) method

In MendelianRandomization: Mendelian Randomization Package

Constrained maximum likelihood (cML) method

Description

Constrained maximum likelihood (cML) based Mendelian Randomization method robust to both correlated and uncorrelated pleiotropy.

Usage

mr_cML(
  object,
  MA = TRUE,
  DP = TRUE,
  K_vec = 0:(length(object@betaX) - 2),
  random_start = 0,
  num_pert = 200,
  random_start_pert = 0,
  maxit = 100,
  random_seed = 314,
  n,
  Alpha = 0.05
)

## S4 method for signature 'MRInput'
mr_cML(
  object,
  MA = TRUE,
  DP = TRUE,
  K_vec = 0:(length(object@betaX) - 2),
  random_start = 0,
  num_pert = 200,
  random_start_pert = 0,
  maxit = 100,
  random_seed = 314,
  n,
  Alpha = 0.05
)

Arguments

object	An MRInput object.
MA	Whether model average is applied or not. Default is TRUE.
DP	Whether data perturbation is applied or not. Default is TRUE.
K_vec	Set of candidate K's, the constraint parameter representing number of invalid IVs. Default is from 0 to (#IV - 2).
random_start	Number of random starting points for cML, default is 0.
num_pert	Number of perturbation when DP is TRUE, default is 200.
random_start_pert	Number of random start points for cML with data perturbation, default is 0.
maxit	Maximum number of iterations for each optimization. Default is 100.
random_seed	Random seed, default is 314. When random_seed=NULL, no random seed will be used and the results may not be reproducible.
n	Sample size. When sample sizes of GWAS for exposure and outcome are different, and/or when sample sizes of different SNPs are different, the smallest sample size is recommended to get conservative result and avoid type-I error. See reference for more discussions.
Alpha	Significance level for the confidence interval for estimate, default is 0.05.

Details

The MRcML method selects invalid IVs with correlated and/or uncorrelated peliotropic effects using constrained maximum likelihood. cML-BIC gives results of the selected model with original data, while cML-MA-BIC averages over all candidate models. cML-BIC-DP and cML-MA-BIC-DP are the versions with data-perturbation to account for selection uncertainty when many invalid IVs have weak pleiotropic effects.

When DP is performed, two goodness-of-fit (GOF) tests are developed to check whether the model-based and DP- based variance estimates converge to the same estimate. Small p-values of GOF tests indicate selection uncertainty is not ignorable, and results from DP is more reliable. See reference for more details.

As the constrained maximum likelihood function is non-convex, multiple random starting points could be used to find a global minimum. For some starting points the algorithm may not converge and a warning message will be prompted, typically this will not affect the results.

Value

The output from the function is an MRcML object containing:

Exposure	A character string giving the name given to the exposure.
Outcome	A character string giving the name given to the outcome.
Estimate	Estimate of theta.
StdError	Standard error of estimate.
Pvalue	p-value of estimate.
BIC_invalid	Set of selected invalid IVs if cML-BIC is performed, i.e. without MA or DP.
GOF1_p	p-value of the first goodness-of-fit test.
GOF2_p	p-value of the second goodness-of-fit test.
SNPs	The number of SNPs that were used in the calculation.
Alpha	Significance level for the confidence interval for estimate, default is 0.05.
CILower	Lower bound of the confidence interval for estimate.
CIUpper	Upper bound of the confidence interval for estimate.
MA	Indicator of whether model average is applied.
DP	Indicator of whether data perturbation is applied.

References

Xue, H., Shen, X., & Pan, W. (2021). Constrained maximum likelihood-based Mendelian randomization robust to both correlated and uncorrelated pleiotropic effects. The American Journal of Human Genetics, 108(7), 1251-1269.

Examples

# Perform cML-MA-BIC-DP:
mr_cML(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds,
byse = chdloddsse), num_pert=5, MA = TRUE, DP = TRUE, n = 17723)
# num_pert is set to 5 to reduce computational time
# the default value of 200 is recommended in practice

# Perform cML-BIC-DP:
mr_cML(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds,
byse = chdloddsse), MA = TRUE, DP = FALSE,, n = 17723)
   

MendelianRandomization documentation built on Aug. 9, 2023, 1:05 a.m.