Pre-requisites

• Basic knowledge of R syntax
• Familiarity with regression

Workshop Participation

Students will have the opportunity to solve toy problems and execute example code in R.

R / Bioconductor packages used

if (!requireNamespace("BiocManager", quietly = TRUE))
    install.packages("BiocManager")
## Bioconductor 3.9 Stable Release
BiocManager::install(version = "3.9")

• dagitty
• DESeq2
• edgeR
• limma

library(dagitty)
library(DESeq2)
library(edgeR)
library(limma)

Time outline

Learning goals

• Describe the differences in common experimental and observational study designs
• Apply concepts of study design to common analyses in bioinformatics such as GWAS and survival analysis
• Understand key concepts of epidemiology such as causal inference, confounders, collidors, mediators, counterfactuals, and study designs
• Develop a structural causal diagram/directed acyclic graph (DAG) of causal relationships and assess pathways of interest
• Recognize the limitations and assumptions of multivariable regression in observational studies, and how this affects common analyses such as DESeq2, edgeR, and limma

Learning objectives

• Assess a study design in terms of causal inference
• Learn about path blocking to prevent confounding
• Create a DAG in R using daggity
• Identify situations when multivariate adjustment for variables is inappropriate
• Select the correct model formula/matrix in DESeq2, edgeR, or limma to deconfound

Example: A dog and an ambulance

An ambulance drives by a house with its sirens on. A dog in the house barks. We can ask the causal question in a straightforward way: Did the ambulance driving by the house cause the dog to bark?

Alternatively, we can rephrase the question in terms of a counterfactual: Would the dog have barked if the ambulance had not driven by the house? We can visualize the relationship using a causal diagram also called a directed acyclic graph (DAG).

This diagram depicts the cause or exposure (the ambulance) and the effect or the outcome (the dog barking) with an arrow indicating the direction of the causal relationship. In contrast to a diagram showing a statistical relationship, causal diagrams must state a directional relationship.

This is the simplest form of a causal diagram. If we were to statistically model the effect for this relationship using regression, a simple two-variable model containing the exposure and the outcome would give us a correct, unbiased estimate of the actual strength of the cause on the effect. However, we are rarely that lucky. A common source of bias is confounding.

Confounding

Confounding arises when a third variable is present in the relationship between cause-and-effect. A confounder is present when:

1. The confounder causes the outcome
2. The confounder causes the exposure
3. The confounder is not a mediator (i.e. it is not present on the causal pathway between the exposure and the outcome)

Returning to our example, the relationship between the ambulance and the barking dog could be confounded by a third variable: a nearby car crash. Perhaps this car crash is what started the dog barking before the ambulance even arrived, but the ambulance caused the dog to bark even more.

We can “deconfound” the effect of interest by controlling for the confounder. The old-fashioned way of doing this is to manually stratify your data by levels of the confounder. Then you calculate an effect size for each stratum. In a modern regression model, we can include the confounder in our model and it is controlled for. We are effectively stratifying the effect across different levels of the confounder then averaging across strata to get an effect size.

Colliders

Taken at face value, colliders are similar to confounders. However, colliders are not common causes of the exposure and outcome. Instead:

1. The outcome causes the collider
2. The exposure causes the collider
3. The collider is not a mediator

Adjusting for a collider as one would for a confounder can create bias. In effect by adjusting for a collider, a backdoor pathway is created between the exposure and the outcome. So what’s the proper way of dealing with colliders? Ignoring them! Hypothesized colliders should not be adjusted for or included in models.

Selection bias

A final major issue of causal inference is selection bias. This arises when selection is dependent on the outcome in the study:

As can be seen from the DAG above, selection bias is a collider. In this case, the study is conditioned on the collider by the act of selection for the study. As a result, the study is biased. Another way to think of selection bias is the “already dead” problem. People who have already died of the outcome are not alive to be in the study. These people may have a more aggressive or serious form of the outcome and not including them masks some of the causal relationship.

A common source of selection bias is loss to follow-up. In survival analysis in particular this can be important as the people who are lost may differ in important ways from those who completed the study. Unfortunately because these people were lost, it is often difficult to assess how they differed from those who were not lost.

Randomized Control Trials (RCTs)

• Exposure of interest is assigned at random
• Because exposure is assigned at random, there are no possible confounders of the relationship between exposure and outcome
• Considered the gold standard for causal inference
• Selection bias is still possible

Question: How can selection bias occur in an RCT?

Cohort Studies

• Participants are chosen on a common characteristic (such as occupation, location, or history of a particular disease)
• They are then followed over time and exposures and outcomes can be assessed
• Selection bias and confounding can occur

Case-Control Studies

• Participants are chosen based on having an outcome of interest (cases)
• Then controls are selected that are similar to the cases (often matched on age, sex, and other demographic variables)
• Selection bias and confounding can occur

Genome-Wide Association Study (GWAS)

• Observational study of phenotypes

• Often participants are chosen based on a specific phenotype or disease

• Can be a case-control or a cohort study

Question: What are some possible sources of confounding or bias in a GWAS?

Dagitty

Dagitty allows for creating causal diagrams, but also gives you more information including what variables to adjust for in complicated causal models.

g1 <- dagitty( "dag {
    W1 -> Z1 -> X -> Y
    Z1 <- V -> Z2
    W2 -> Z2 -> Y
    X <- W1 -> W2 -> Y
}")
plot(graphLayout(g1))

for( n in names(g1) ){
    for( m in setdiff( descendants( g1, n ), n ) ){
        a <- adjustmentSets( g1, n, m )
        if( length(a) > 0 ){
            cat("The total effect of ",n," on ",m,
                " is identifiable controlling for:\n",sep="")
            print( a, prefix=" * " )
        }
    }
}

## The total effect of V on Z2 is identifiable controlling for:
##  *  {}
## The total effect of V on Y is identifiable controlling for:
##  *  {}
## The total effect of V on Z1 is identifiable controlling for:
##  *  {}
## The total effect of V on X is identifiable controlling for:
##  *  {}
## The total effect of W1 on Z1 is identifiable controlling for:
##  *  {}
## The total effect of W1 on X is identifiable controlling for:
##  *  {}
## The total effect of W1 on Y is identifiable controlling for:
##  *  {}
## The total effect of W1 on W2 is identifiable controlling for:
##  *  {}
## The total effect of W1 on Z2 is identifiable controlling for:
##  *  {}
## The total effect of W2 on Z2 is identifiable controlling for:
##  *  {}
## The total effect of W2 on Y is identifiable controlling for:
##  *  { V, X }
##  *  { W1 }
## The total effect of X on Y is identifiable controlling for:
##  *  { W2, Z2 }
##  *  { V, W2 }
##  *  { V, W1 }
##  *  { W1, Z1 }
## The total effect of Z1 on X is identifiable controlling for:
##  *  { W1 }
## The total effect of Z1 on Y is identifiable controlling for:
##  *  { W1, W2, Z2 }
##  *  { V, W1 }
## The total effect of Z2 on Y is identifiable controlling for:
##  *  { W2, X }
##  *  { W1, W2, Z1 }
##  *  { V, W2 }

DESeq2

DESeq2 uses negative binomial regression. As such, it allows you to deconfound by including the confounder as a variable in the design statement:

ddsSE <- DESeqDataSet(se, design = ~ exposure + confounder1 + confounder2)
ddsSE

edgeR and limma

You can use model.matrix() to specify the exposure and confounders:

batch <- factor(ds$Batch)
treat <- factor(ds$tx)
y <- factor(ds$surv)
design <- model.matrix(~treat + batch)

Then fit the model either in edgeR:

fit <- glmQLFit(y, design)

Or in limma:

fit <- lmFit(y, design)

As mentioned in the confounding section, estimates obtained for the relationship between the exposure and the outcome have been adjusted for the included confounders (deconfounded). This means that the observed estimate is an averaged effect size across strata of the confounder(s).