MRcML

R package for Mendelian randomization with constraind maximum likelihood (MRcML) methods. Here is the reference: Constrained maximum likelihood-based Mendelian randomization robust to both correlated and uncorrelated pleiotropic effects.

Installation

Install the package from GitHub with:

# install.packages("devtools")
devtools::install_github("xue-hr/MRcML")

Example

Here is an example which shows how to apply MRcML methods to make inference about the causal effect from Fast Glucose (FG) to Type-2 Diabetes (T2D).

library(MRcML)
summary(T2D_FG)
#>        Length Class  Mode   
#> b_exp  17     -none- numeric
#> b_out  17     -none- numeric
#> se_exp 17     -none- numeric
#> se_out 17     -none- numeric

Example data T2D_FG is a list which contains estimated effects sizes and standard errors of 17 SNPs on T2D and FG. Now we perfrom the main function with sample size of FG which is 46186, and using 100 random start points. We set the random seed random_seed = 1 to make sure results are replicable.

cML_result = mr_cML(T2D_FG$b_exp,
                    T2D_FG$b_out,
                    T2D_FG$se_exp,
                    T2D_FG$se_out,
                    n = 46186,
                    random_start = 100,
                    random_seed = 1)
#> Warning in cML_estimate_random(b_exp = b_exp, b_out = b_out, se_exp = se_exp, :
#> May not converge to minimums with some given start points and maximum number of
#> iteration, lead to Fisher Information matrices not positive definite. Could try
#> increasing number of iterations (maxit) or try different start points. Note:
#> If multiple random start points are used, this warning does not likely affect
#> result.

We get a warning message from the function cML_estimate_random(). The reason is: here we use 100 random starting points to minimize the non-convex loss function, some of them may not converge to a local minimum and result in Fisher Information matrices that are not positive definite. It is not likely affecting the optimization result, since in the end we only use the start point gives the minimum loss and discard all other start points including those do not converge. Now lets take a look at the results:

cML_result
#> $MA_BIC_theta
#> [1] 2.110808
#> 
#> $MA_BIC_se
#> [1] 0.2455809
#> 
#> $MA_BIC_p
#> [1] 8.314666e-18
#> 
#> $BIC_theta
#> [1] 2.236579
#> 
#> $BIC_se
#> [1] 0.2061844
#> 
#> $BIC_p
#> [1] 2.050249e-27
#> 
#> $BIC_invalid
#> [1]  8 12 13 15 17
#> 
#> $BIC_vec
#>  [1] 316.27016 114.79456  89.17168  83.95043  80.85419  78.09146  78.74102
#>  [8]  85.62170  93.12957 101.96266 110.79080 120.24385 130.04801 140.13491
#> [15] 150.51854 161.10701
#> 
#> $MA_AIC_theta
#> [1] 2.09175
#> 
#> $MA_AIC_se
#> [1] 0.3012363
#> 
#> $MA_AIC_p
#> [1] 3.814609e-12
#> 
#> $AIC_theta
#> [1] 1.996619
#> 
#> $AIC_se
#> [1] 0.2194686
#> 
#> $AIC_p
#> [1] 9.242142e-20
#> 
#> $AIC_invalid
#> [1]  1  5  8 12 13 14 15 17

BIC selected model gives us indices of invalid IVs: 8, 12, 13, 15, 17. Now lets draw the scatter plot, invalid IVs are marked with blue:

Now let us perform cML with data perturbation. The default number of perturbations is 200, and we use 10 random start points. In real application, we recommend use more random start points to get reliable results even it takes more time, like 10 or even 100; in simulations the number of random start points could be set to 0 (i.e. do not use random start) to speed up.

cML_result_DP = mr_cML_DP(T2D_FG$b_exp,
                          T2D_FG$b_out,
                          T2D_FG$se_exp,
                          T2D_FG$se_out,
                          n = 46186,
                          random_start = 10,
                          random_start_pert = 10,
                          random_seed = 1,
                          num_pert = 200)

Results with data perturbation:

cML_result_DP
#> $MA_BIC_theta
#> [1] 2.110809
#> 
#> $MA_BIC_se
#> [1] 0.2455808
#> 
#> $MA_BIC_p
#> [1] 8.313889e-18
#> 
#> $BIC_theta
#> [1] 2.236579
#> 
#> $BIC_se
#> [1] 0.2061844
#> 
#> $BIC_p
#> [1] 2.050249e-27
#> 
#> $BIC_invalid
#> [1]  8 12 13 15 17
#> 
#> $MA_BIC_DP_theta
#> [1] 1.895029
#> 
#> $MA_BIC_DP_se
#> [1] 0.5151985
#> 
#> $MA_BIC_DP_p
#> [1] 0.0002348404
#> 
#> $BIC_DP_theta
#> [1] 1.884913
#> 
#> $BIC_DP_se
#> [1] 0.5313405
#> 
#> $BIC_DP_p
#> [1] 0.0003889549
#> 
#> $GOF1_p
#> [1] 4.046025e-12
#> 
#> $GOF2_p
#> [1] 2.204418e-16