Correlation vs. Causation in Clinical Research

Introduction

One of the most important principles in clinical research is also one of the most frequently misunderstood: an observed association does not necessarily mean that one variable causes the other.

Researchers routinely observe relationships between exposures, biomarkers, treatments, patient characteristics, and clinical outcomes.

For example, a study might find that patients with higher inflammatory biomarker concentrations have higher mortality.

That is an important finding. But it does not immediately establish that increasing the biomarker causes mortality.

The observed relationship could arise because the biomarker is itself affected by underlying disease severity, because another variable affects both the biomarker and mortality, because of selection into the study, or because the direction of causality is different from what was initially assumed.

What Does Correlation Mean?

In everyday clinical research, the word correlation is often used broadly to mean that two variables are associated. For two continuous variables, one common measure is the Pearson correlation coefficient.

For paired observations \((X_i,Y_i)\), the Pearson correlation coefficient is:

The value of \(r\) ranges from \(-1\) to \(1\).

However, even a correlation close to \(1\) or \(-1\) does not by itself prove that one variable causes the other.

What Does Causation Mean?

A causal question is fundamentally different from a descriptive association.

Instead of asking:

"Are exposure \(X\) and outcome \(Y\) associated?"

we ask something closer to:

"What would happen to \(Y\) if we intervened and changed \(X\)?"

This is a counterfactual way of thinking about causation.

For a particular patient, imagine two possible worlds:

• A world in which the patient receives the exposure or treatment.
• A world in which the same patient does not receive it.

The individual causal effect would compare the outcome in these two potential worlds.

where \(Y(1)\) is the potential outcome under exposure and \(Y(0)\) is the potential outcome under no exposure.

The fundamental problem is that we generally cannot observe both potential outcomes for the same person at the same time.

Correlation Does Not Imply Causation

Suppose a clinical study finds:

This indicates a substantial positive linear association.

It does not tell us why the association exists.

Several explanations are possible.

Example: Coffee and Cardiovascular Risk

Imagine an observational study reports that coffee consumption is associated with cardiovascular disease.

A simplistic interpretation might be:

"Coffee causes cardiovascular disease."

But suppose smoking is more common among heavy coffee drinkers.

Smoking is itself associated with cardiovascular disease.

The observed relationship between coffee and cardiovascular disease could therefore be partly explained by smoking.

This is an example of confounding.

What Is a Confounder?

A confounder is a variable that creates a misleading or distorted estimate of the relationship between an exposure and an outcome.

A simple causal structure can be represented as:

Here:

• \(X\) = exposure
• \(Y\) = outcome
• \(Z\) = confounding variable

The arrows indicate that \(Z\) influences both the exposure and the outcome.

Consequently, \(X\) and \(Y\) can appear associated even if there is no direct causal pathway from \(X\) to \(Y\).

A Classic Clinical Example of Confounding

Suppose an observational study finds that patients receiving a particular treatment have higher mortality.

Does the treatment cause death?

Not necessarily.

Patients receiving the treatment may have more severe disease.

Disease severity may influence both treatment assignment and mortality.

If severity is not adequately controlled, the crude treatment-mortality association may make an effective treatment appear harmful.

This is particularly important in observational studies of treatments because treatment assignment is often related to patient characteristics.

Confounding by Indication

A particularly important form of confounding in clinical research is confounding by indication.

Suppose a treatment is preferentially prescribed to the sickest patients.

The treated group may consequently have worse outcomes than the untreated group even if the treatment is beneficial.

Without appropriate adjustment, comparing the raw outcomes can produce a misleading estimate of treatment effectiveness.

Reverse Causation

Another major problem is reverse causation.

The researcher may assume:

when the true relationship is:

For example, suppose low physical activity is associated with poor health.

One interpretation is that inactivity causes poor health.

But people with worsening disease may reduce their physical activity.

In that case, the disease is contributing to the observed inactivity.

The relationship may therefore operate in both directions.

Selection Bias

An association can also arise because the individuals included in a study are not representative of the population relevant to the causal question.

Selection bias occurs when study participation, treatment availability, follow-up, or inclusion in the analysis depends on variables related to the exposure and outcome.

For example, suppose a study analyzes only patients who remain enrolled in a long-term observational cohort.

If continued participation depends on both health status and exposure, conditioning on study participation can distort the observed association.

Collider Bias

A particularly important form of selection bias is collider bias.

Suppose two variables independently influence whether a patient enters a study:

where \(S\) represents study selection.

If researchers condition on \(S\), they can induce an association between \(X\) and \(Y\) even when no causal relationship exists between them.

Why Randomization Is So Powerful

Randomized controlled trials are designed to break the systematic relationship between treatment assignment and baseline prognostic factors.

In a randomized trial:

In expectation, randomization balances both measured and unmeasured baseline characteristics across treatment groups.

Therefore, differences in outcomes between randomized groups can be attributed to the treatment, subject to issues such as nonadherence, missing data, post-randomization events, and chance.

Randomization Does Not Make a Study Perfect

Randomization is powerful, but it does not eliminate every problem.

A randomized clinical trial can still experience:

• Loss to follow-up
• Nonadherence
• Treatment switching
• Missing outcome measurements
• Protocol deviations
• Measurement error
• Insufficient sample size
• Chance imbalance in baseline characteristics

The important point is that randomization provides a strong foundation for causal inference by addressing confounding at treatment assignment.

Association vs. Causal Effect

Consider a treatment indicator \(A\) and outcome \(Y\).

An observational comparison might estimate:

This is an observed group difference.

A causal effect asks a different question:

The two quantities are equal only under assumptions that make the observed groups comparable with respect to the causal question.

The Role of Statistical Significance

A common mistake is to assume that a statistically significant association is automatically causal.

Suppose:

for the association between an exposure and outcome.

This provides evidence against a specified null statistical hypothesis.

It does not establish that the exposure causes the outcome.

A highly precise estimate of a biased association is still biased.

A Large Sample Does Not Guarantee Causality

Increasing the sample size reduces random error.

It does not automatically remove systematic bias.

For example, suppose a study has:

participants but treatment assignment is strongly confounded.

The resulting estimate may have an extremely narrow confidence interval while still being substantially biased.

This leads to an important distinction:

Regression Adjustment

Regression models are frequently used to adjust for measured confounding variables.

For a continuous outcome, a simple model might be:

where:

• \(Y\) = outcome
• \(X\) = exposure of interest
• \(Z_1,\ldots,Z_k\) = measured covariates
• \(\beta_1\) = exposure coefficient conditional on the included covariates

Adjustment can reduce confounding if the relevant confounders are correctly measured and appropriately modeled.

However, regression adjustment does not automatically make an observational study causal.

Why "Adjust for Everything" Is Not a Good Strategy

A common misconception is that researchers should simply put every available variable into a regression model.

This can be harmful.

Some variables may be:

• Mediators of the treatment effect
• Colliders
• Consequences of the exposure
• Strongly affected by selection
• Measured with substantial error

Adjusting for these variables can introduce bias rather than remove it.

Confounder vs. Mediator

Consider:

Here \(M\) is a mediator.

For example:

If the research question is the total treatment effect, adjusting for blood pressure reduction would block part of the pathway through which treatment operates.

The correct adjustment therefore depends on the causal estimand being sought.

Total Effect vs. Direct Effect

Suppose:

There are potentially two different causal questions.

Total Effect

What is the overall effect of changing \(X\), including effects operating through \(M\)?

Direct Effect

What is the effect of changing \(X\) while holding the mediator pathway fixed according to a specified causal definition?

These are different estimands.

Directed Acyclic Graphs

Directed acyclic graphs, or DAGs, provide a visual language for representing causal assumptions.

For example:

This structure indicates that \(Z\) is a common cause of both \(X\) and \(Y\).

The graphical structure helps researchers identify variables that may need to be controlled to block noncausal backdoor pathways.

The Backdoor Path

Suppose:

The path from \(X\) to \(Y\) through \(Z\) is a noncausal pathway.

If \(Z\) is a sufficient confounder, conditioning on \(Z\) can block this pathway.

The goal is not to mechanically adjust for every variable. The goal is to identify an appropriate adjustment set based on the assumed causal structure.

Clinical Example: Cholesterol and Cardiovascular Events

Suppose an observational study finds that higher LDL cholesterol is associated with a higher risk of cardiovascular events.

This association is biologically plausible and supported by extensive evidence.

But even here, the causal question is distinct from the observational association.

Researchers may need to consider:

• Age
• Smoking
• Diabetes
• Blood pressure
• Other cardiovascular risk factors
• Medication use
• Prior cardiovascular disease

A randomized trial of an intervention that lowers LDL provides a particularly strong way to evaluate whether changing LDL-related treatment changes clinical outcomes.

Clinical Example: Biomarker and Survival

Suppose a biomarker \(B\) is strongly associated with mortality.

Researchers might initially conclude:

"The biomarker causes mortality."

But the biomarker could instead be a marker of underlying disease severity.

In this situation, the biomarker may be highly useful for prediction without being a causal driver of mortality.

Prediction Does Not Equal Causation

This distinction is especially important in modern clinical machine learning.

Suppose a model predicts mortality accurately using a laboratory measurement.

That does not imply that changing the laboratory measurement will reduce mortality.

Predictive importance asks:

Causal inference asks a different question, conceptually closer to:

The \(do(X=x)\) notation represents an intervention that sets \(X\) to a specified value.

The Importance of the Intervention

Causal inference is fundamentally connected to intervention.

Compare these questions:

The final questions require an intervention or a credible strategy for emulating the intervention using observational data.

Observational Studies Can Still Support Causal Inference

It would be incorrect to conclude that only randomized trials can ever provide causal information.

Well-designed observational studies can contribute important causal evidence when investigators have:

• A clearly defined target population
• A clearly defined exposure or treatment
• Appropriate temporal ordering
• Careful measurement of relevant confounders
• A defensible causal model
• Appropriate statistical adjustment
• Sufficient follow-up
• Sensitivity analyses for important assumptions

However, causal interpretation requires assumptions that are generally stronger than simply observing an association.

The Exchangeability Assumption

A central concept in causal inference is exchangeability.

Informally, after accounting for the relevant measured covariates, the treated and untreated groups should be comparable with respect to their potential outcomes.

Symbolically, one common formulation is:

where:

• \(A\) = treatment or exposure
• \(Z\) = measured covariates
• \(Y(1)\) = potential outcome under treatment
• \(Y(0)\) = potential outcome under no treatment

If important confounders are unmeasured, this assumption may fail.

Positivity

Another important assumption is positivity.

For individuals with relevant covariate patterns, there must be a nonzero probability of receiving each treatment level being compared.

Conceptually:

cor(
  clinical_data$biomarker,
  clinical_data$survival_time,
  method = "pearson"
)

cor(
  clinical_data$biomarker,
  clinical_data$survival_time,
  method = "spearman"
)

model <- lm(
  outcome ~ treatment + age + sex + disease_severity,
  data = clinical_data
)

summary(model)

model <- glm(
  stroke ~ treatment + age + sex + hypertension_severity,
  data = clinical_data,
  family = binomial()
)

summary(model)

model <- glm(
  outcome ~ treatment * age_group + sex + disease_severity,
  data = clinical_data,
  family = binomial()
)

summary(model)