Multivariable inverse-variance weighted method with measurement error

The mr_mvivwme function performs multivariable Mendelian randomization via the inverse-variance method with measurement error.

Usage

mr_mvivwme(
  object,
  model = "default",
  correl = FALSE,
  correl.x = NULL,
  distribution = "normal",
  alpha = 0.05,
  max_iter = 100,
  no_ini = 1,
  seed = 20201201,
  ...
)

# S4 method for MRMVInput
mr_mvivwme(
  object,
  model = "default",
  correl = FALSE,
  correl.x = NULL,
  distribution = "normal",
  alpha = 0.05,
  max_iter = 100,
  no_ini = 1,
  seed = 20201201,
  ...
)

Arguments

object: An MRMVInput object.
model: What type of model should be used: "default", "random" or "fixed". The random-effects model ("random") is a multiplicative random-effects model, allowing overdispersion in the weighted linear regression (the residual standard error is not fixed to be 1, but is not allowed to take values below 1). The fixed-effect model ("fixed") sets the residual standard error to be 1. The "default" setting is to use a fixed-effect model with 3 genetic variants or fewer, and otherwise to use a random-effects model.
correl: If the genetic variants are correlated, then this correlation can be accounted for.
correl.x: Correlation matrix for exposures. Default is to assume the exposures are uncorrelated.
distribution: The type of distribution used to calculate the confidence intervals. Options are "normal" (default) or "t-dist".
alpha: The significance level used to calculate the confidence interval. The default value is 0.05.
max_iter: The maximum number of iterations in the optimisation procedure.
no_ini: The number of initial values for the optimisation procedure.
seed: The random seed to use for the optimisation procedure. The default value is 20201201. If set to NA, the random seed will not be set (for example, if the function is used as part of a larger simulation).
...: Additional arguments to be passed to the regression method.

Value

The output from the function is an MVIVWME object containing:

Model: A character string giving the type of model used ("fixed", "random", or "default").
Exposure: A character vector with the names given to the exposure.
Outcome: A character string with the names given to the outcome.
Estimate: A vector of causal estimates.
StdError: A vector of standard errors of the causal estimates.
CILower: The lower bounds of the causal estimates based on the estimated standard errors and the significance level provided.
CIUpper: The upper bounds of the causal estimates based on the estimated standard errors and the significance level provided.
Alpha: The significance level used when calculating the confidence intervals.
Pvalue: The p-values associated with the estimates (calculated as Estimate/StdError as per Wald test) using a normal or t-distribution (as specified in distribution).
Correlation: The matrix of genetic correlations.
SNPs: The number of genetic variants (SNPs) included in the analysis.
RSE: The estimated residual standard error from the regression model.
Heter.Stat: Heterogeneity statistic (Cochran's Q statistic) and associated p-value: the null hypothesis is that all genetic variants estimate the same causal parameter; rejection of the null is an indication that one or more variants may be pleiotropic.

Details

The extension of multivariable Mendelian randomization to account for measurement error in the genetic associations with the exposure traits.

References

Zhu, Jiazheng, Stephen Burgess, and Andrew J. Grant. Bias in Multivariable Mendelian Randomization Studies Due to Measurement Error on Exposures, 2022. https://doi.org/10.48550/arXiv.2203.08668.

Examples

mr_mvivwme(mr_mvinput(bx = cbind(ldlc, hdlc, trig), bxse = cbind(ldlcse, hdlcse, trigse),
   by = chdlodds, byse = chdloddsse))
#> 
#> Multivariable inverse-variance weighted method accounting for measurement error
#> (variants uncorrelated, random-effect model)
#> 
#> Number of Variants : 28 
#> ------------------------------------------------------------------
#>    Exposure Estimate Std Error  95% CI       p-value
#>  exposure_1    2.025     0.504  1.038, 3.012   0.000
#>  exposure_2   -0.561     0.676 -1.886, 0.765   0.407
#>  exposure_3    0.738     0.281  0.188, 1.288   0.009
#> ------------------------------------------------------------------
#> Residual standard error =  1.436 
#> Heterogeneity test statistic = 51.5230 on 25 degrees of freedom, (p-value = 0.0014)