The goal of NetCoupler is to estimate causal links between a set of -omic (e.g. metabolomics, lipidomics) or other high-dimensional data and an external variable, such as a disease outcome, an exposure, or both. The NetCoupler-algorithm, initially formulated during Clemens’ PhD thesis (Wittenbecher 2017), links a conditional dependency network with an external variable (i.e. an outcome or exposure) to identify network-independent associations between the network variables and the external variable, classified as direct effects.
A typical use case we have in mind would be if a researcher might be interested in exploring potential pathways that exist between a health exposure like red meat consumption, its impact on the metabolic profile, and the subsequent impact on an outcome like type 2 diabetes incidence. So for instance, you want to ask questions to get answers that look like the figure below.
The input for NetCoupler includes:
lm()), including confounders to adjust for.
The final output is the modeling results along with the results from NetCoupler’s classification. Results can then be displayed as a joint network model in graphical format.
There are a few key assumptions to consider before using NetCoupler for your own research purposes.
NetCoupler has several frameworks in mind:
%>%or base R
The general workflow for using NetCoupler revolves around several main functions, listed below as well as visualized in the figure below:
nc_standardize(): The algorithm in general, but especially the network estimation method, is sensitive to the values and distribution of the variables. Scaling the variables by standardizing, mean-centering, and natural log transforming them are important to obtaining more accurate estimations.
nc_estimate_network(): Estimate the connections between metabolic variables as a undirected graph based on dependencies between variables. This network is used to identify metabolic variables that are connected to each other as neighbours.
nc_estimate_outcome_links(): Uses the standardized data and the estimated network to classify the conditionally independent relationship between each metabolic variable and an external variable (e.g. an outcome or an exposure) as either being a direct, ambiguous, or no effect relationship.
classify_option_list. See the help documentation of the estimating functions for more details. For larger datasets, with more sample size and variables included in the network, we strongly recommend lowering the threshold used to reduce the risk of false positives.
nc_join_links(): Not implemented yet. Join together the exposure- and outcome-side estimated links.
nc_plot_network(): Not implemented yet. Visualize the connections estimated from
nc_plot_links(): Not implemented yet. Plots the output results from either
The below is an example using a simulated dataset for demonstrating NetCoupler. For more examples, particularly on how to use with different models, check out the
For estimating the network, it’s (basically) required to standardize the metabolic variables before inputting into
nc_estimate_network(). This function also log-transforms and scales (mean-center and z-score normalize) the values of the metabolic variables. We do this because the network estimation algorithm can sometimes be finicky about differences in variable numerical scale (mean of 1 vs mean of 1000).
library(NetCoupler) std_metabolic_data <- simulated_data %>% nc_standardize(starts_with("metabolite"))
If you have potential confounders that you need to adjust for during the estimating links phase of NetCoupler, you’ll need to include these confounding variables when standardizing the metabolic variables. You do this by regressing the confounding variables on the metabolic variables by using the
regressed_on argument of
nc_standardize(). This will automatically first standardize the variables, run models on the metabolic variables that includes the confounding variables, and then extract the residuals from the model which are then used to construct the network. Here’s an example:
std_metabolic_data <- simulated_data %>% nc_standardize(starts_with("metabolite"), regressed_on = "age")
After that, you can estimate the network. The network is by default estimated using the PC-algorithm. You can read more about it in the help page of the
pc_estimate_undirected_graph() internal function.
# Make partial independence network from metabolite data metabolite_network <- std_metabolic_data %>% nc_estimate_network(starts_with("metabolite"))
For the exposure and outcome side, you should standardize the metabolic variables, but this time, we don’t regress on the confounders since they will be included in the models.
standardized_data <- simulated_data %>% nc_standardize(starts_with("metabolite"))
Now you can estimate the outcome or exposure and identify direct effects for either the exposure side (
exposure -> metabolite) or the outcome side (
metabolite -> outcome). For the exposure side, the function identifies whether a link between the exposure and an index node (one metabolic variable in the network) exists, independent of potential confounders and from neighbouring nodes (other metabolic variables linked to the index variable). Depending on how consistent and strong the link is, the effect is classified as “direct”, “ambiguous”, or “none”.
In the example below, we specifically generated the simulated data so that the exposure is associated with metabolites 1, 8, and 12. And as we can see, those links have been correctly identified.
outcome_estimates <- standardized_data %>% nc_estimate_outcome_links( edge_tbl = as_edge_tbl(metabolite_network), outcome = "outcome_continuous", model_function = lm ) outcome_estimates #> # A tibble: 12 × 6 #> outcome index_node estimate std_error fdr_p_value effect #> * <chr> <chr> <dbl> <dbl> <dbl> <chr> #> 1 outcome_continuous metabolite_1 0.0466 0.0254 0.124 ambiguous #> 2 outcome_continuous metabolite_10 0.00449 0.0254 0.947 ambiguous #> 3 outcome_continuous metabolite_11 -0.00700 0.0254 0.912 none #> 4 outcome_continuous metabolite_12 0.350 0.0242 0 direct #> 5 outcome_continuous metabolite_2 -0.0280 0.0255 0.424 none #> 6 outcome_continuous metabolite_3 -0.0936 0.0252 0.000620 direct #> 7 outcome_continuous metabolite_4 0.0267 0.0256 0.453 ambiguous #> 8 outcome_continuous metabolite_5 0.103 0.0253 0.000167 ambiguous #> 9 outcome_continuous metabolite_6 0.113 0.0252 0.0000237 ambiguous #> 10 outcome_continuous metabolite_7 0.00171 0.0255 0.956 none #> 11 outcome_continuous metabolite_8 0.0212 0.0253 0.548 none #> 12 outcome_continuous metabolite_9 0.201 0.0250 0 direct exposure_estimates <- standardized_data %>% nc_estimate_exposure_links( edge_tbl = as_edge_tbl(metabolite_network), exposure = "exposure", model_function = lm ) exposure_estimates #> # A tibble: 12 × 6 #> exposure index_node estimate std_error fdr_p_value effect #> * <chr> <chr> <dbl> <dbl> <dbl> <chr> #> 1 exposure metabolite_1 0.173 0.0228 0 direct #> 2 exposure metabolite_10 0.318 0.0219 0 direct #> 3 exposure metabolite_11 0.0543 0.0232 0.0409 ambiguous #> 4 exposure metabolite_12 0.0242 0.0231 0.380 none #> 5 exposure metabolite_2 -0.0430 0.0231 0.106 ambiguous #> 6 exposure metabolite_3 0.0411 0.0231 0.123 ambiguous #> 7 exposure metabolite_4 0.00344 0.0232 0.920 none #> 8 exposure metabolite_5 0.0479 0.0232 0.0717 ambiguous #> 9 exposure metabolite_6 -0.0189 0.0230 0.506 none #> 10 exposure metabolite_7 -0.162 0.0229 0 direct #> 11 exposure metabolite_8 -0.355 0.0216 0 direct #> 12 exposure metabolite_9 0.0571 0.0230 0.0292 ambiguous
If you want to adjust for confounders and have already used
regressed_on in the
nc_standardize() function, add confounders to
nc_estimate_exposure_links() with the
outcome_estimates <- standardized_data %>% nc_estimate_outcome_links( edge_tbl = as_edge_tbl(metabolite_network), outcome = "outcome_continuous", model_function = lm, adjustment_vars = "age" )
If the analysis is taking a while, you can use the future package to speed things up by implementing parallel processing. It’s easy to use parallel processing with NetCoupler since it uses the future package. By setting the “processing plan” with
multisession, NetCoupler will use parallel processing for its computationally intensive component of the algorithm. After you run your code, close up the parallel processing by putting it back to normal with
plan(sequential). Using the future package you can speed up the processing by almost 2.5 times.
# You'll need to have furrr installed for this to work. library(future) plan(multisession) outcome_estimates <- standardized_data %>% nc_estimate_outcome_links( edge_tbl = as_edge_tbl(metabolite_network), outcome = "outcome_continuous", model_function = lm ) plan(sequential)
Colombo, Diego, and Marloes H. Maathuis. 2014. “Order-Independent Constraint-Based Causal Structure Learning.” Journal of Machine Learning Research 15 (1): 3741–82. https://dl.acm.org/doi/10.5555/2627435.2750365.
Wittenbecher, Clemens. 2017. “Linking Whole-Grain Bread, Coffee, and Red Meat to the Risk of Type 2 Diabetes.” Doctoralthesis, Universität Potsdam. https://nbn-resolving.org/urn:nbn:de:kobv:517-opus4-404592.