CausalMGM expects a tabular dataset with continuous and categorical variables. It then proceeds in three steps to produce a graphical model of this data: 1) (Optional) Feature selection, 2) Learning an undirected model (a model of associations), 3) (Optional) Learning a directed model (model of cause/effect). Feature Selection - PrefDiv

For a graphical model to be an effective visualization tool, it is necessary to query variables of interest, but this can be difficult on large datasets. PrefDiv is a feature selection method that chooses variables that are 1) associated with a target variable of interest but are 2) independent from one another. This reduces the size of the dataset without losing important predictors of a target.

Pref-Div will retain all categorical variables automatically and will only filter continuous variables. The user can return redundant variables as 1) clusters or 2) as a single variable representing the entire cluster. For more information, please refer to: http://home.biokdd.org/biokdd19/camera_ready/sample-sigconf_pvb.pdf.

Undirected Graphical Modeling - Mixed Graphical Models

An undirected graphical model consists of nodes (variables) and edges between variables. An edge between variables A and B in this type of model mean that A and B are conditionally dependent given the rest of the variables in the data. This method assumes that continuous variables are normally distributed, and categorical variables are distributed multinomially. Further the method assumes linear relationships between continuous variables.

For more information, please refer to:
Sedgewick, AJ, Shi, I, Donovan, RM, and Benos, PV. 2016. Learning mixed graphical models with separate sparsity parameters and stability-based model selection. BMC Bioinformatics. 17(S5). p. S175

Directed Graphical Modeling - PC Stable

A directed graphical model depicts cause and effect relationships between variables. We use PC-Stable to convert the undirected graphical model into a directed (causal) model. PC-Stable performs conditional independence tests between variables that have an edge connecting them, until no more edges can be removed this way. Then the method orients these edges using a set of rules.

For more information, please refer to:
Sedgewick, AJ, Buschur, K, Shi, I, Ramsey, JD, Raghu, VK, Manatakis, DV, Zhang, Y, Bon, J, Chandra, D, Karoleski, C, Sciurba, FC, Spirtes, P, Glymour, C, and Benos, PV. 2019. Mixed graphical models for integrative causal analysis with application to chronic lung disease diagnosis and prognosis. Bioinformatics. 35(7), pp. 1204-1212.

Step 1. Upload the dataset

Some requirements for the dataset are:

• Must be in tabular format with variable names in the first row.
• Must have no missing data.
• Must contain only continuous and categorical variables (no censoring).
• Ordinal variables will be treated as continuous if there are more than 5 categories.
  • To treat these as categorical, combine categories to reduce the number to 5.
  • To treat these as continuous, use real numbered values (e.g. 2.0, 3.0, etc.).
• You can use the Check my Data button to confirm proper format

Step 2. Configure the experiment

The meaning of each parameter is as follows:

Pref-Div parameters

Number of variables to be selected - This is the number of continuous features to be selected.
hese selected features, the target variable, and all of the categorical variables will be used for graphical modeling. A higher number enables a more accurate graphical model, but will take longer to run and will be more difficult to visualize/interpret.

Name of target variable - Which variable should be treated as the target variable?

Variables to Keep - Comma-separated list of continuous variables that should be automatically included in the final graphical model. (Not counted towards the "number of variables to be selected")

Automatic clustering - Redundant features will be represented as a cluster variable using Principal Component Analysis instead of a single representative of the entire cluster.

Graphical Modeling Parameters

Lambda parameters determine the sparsity level of the mixed graphical model. A higher lambda value results in fewer (but higher confidence) edges in the output graph. There are separate lambda parameters for each edge type.

Lambda 1 - Controls sparsity for edges between two continuous variables.
Lambda 2 - Controls sparsity for edges between continuous and categorical variables.
Lambda 3 - Controls sparsity for edges between two categorical variables.

Lambda values can be automatically chosen based on stability using the "Find Lambdas" button. Note that this operation can be time consuming for large datasets.

Alpha - PC-Stable requires an alpha value. This is the p-value threshold for the conditional independence tests. A lower alpha value means a sparser graph because fewer tests will meet the threshold for significance.

The sample dataset comes from a population with two lung conditions: 1) Idiopathic Pulmonary Fibrosis (IPF) and 2) Chronic Obstructive Pulmonary Disorder (COPD). The goal was to identify factors that distinguish IPF from COPD.

Undirected model

For the undirected model below, gender is connected to only height and weight. This means that 1) the best variables to predict gender in this dataset are height and weight and 2) gender is conditionally dependent on height (and weight) given the rest of the variables in the graph. In an undirected model, an edge between A and B could arise because of any of the four conditions:

1. A causes B
2. B causes A
3. A and B are both controlled by a confounder
4. A and B are associated because of selection bias for the data sample

Directed model

The directed model below gives cause and effect relationships between variables. In this example, we focus on the "diag" variable which gives the diagnosis for a patient (IPF or COPD). The model suggests that FEV1 and FVC (two clinical measures of lung function) "cause" diagnosis. Cause, in this case, means that an intervention on FEV1 (changing its value for an individual holding everything else in the data constant) would change the likelihood of diagnosis as IPF/COPD. The undirected edge between diag and DIO2 means the algorithm was unable to identify the causal direction. The same interpretation as an undirected graphical model applies to this edge as well.

• Datasets larger than 1000 variables should use feature selection prior to running, otherwise computations may take a very long time.
• Censored data and data with missing values will not work.
• Interactions between continuous variables are assumed to be linear and these variables must be close to normally distributed.
• Interpreting directed edges as causal requires additional assumptions including: no cycles in the graph, no latent confounders.