Observational Studies, Experiments, and Causality

Observational Studies, Experiments, and Causality

• Ethical constraint on experiments

  • Exposing people to unhealthy conditions to study outcomes is often unethical
  • Example: exposure to smoking to see if it causes lung cancer
  • Therefore, researchers may not assign harmful treatments; they rely on observational data
  • Ethical takeaway: we must protect subjects and avoid unethical manipulations

• Key distinction: Observational studies vs experiments

  • Explanatory variable (X): the factor of interest (e.g., exposure to smoking, darkness during sleep)
  • Response variable (Y): the outcome of interest (e.g., lung cancer, myopia)
  • In experiments, the explanatory variable is assigned by the researchers
  • In observational studies, researchers simply observe and record X and Y without assigning X
  • Observation focus: monitoring what occurs rather than imposing a treatment

• Definitions and terminology

  • Explanatory variable: $X$
  • Response variable: $Y$
  • Observational study: data collection by observing or recording natural behavior or conditions without intervention
  • Experiment: a study design where the explanatory variable is assigned (randomly or otherwise) to subjects
  • Association: a relationship between X and Y observed in data (X and Y vary together)
  • Causation (causal relationship): X causes Y (changing X would change Y under an intervention)
  • Confounding factor (Z): a variable that affects both X and Y, potentially producing a spurious association
  • Reverse causation: the possibility that Y influences X, not vice versa

• Illustrative case: darkness during sleep and myopia (Nature article reference)

  • Observational question: Are infants raised with different levels of darkness during sleep more likely to develop myopia later?
  • Explanatory variable: darkness exposure during sleep (how much the infant is exposed to darkness)
  • Data collection: observational records of infants’ sleep environments and later vision outcomes
  • Study design note: researchers observed whether each child slept with darkness vs. light and then tracked outcomes years later

• Experimental vs observational in this context

  • In this sleep study, researchers did not assign infants to dark vs non-dark sleep conditions
  • Because X was not randomly assigned, this is an observational study, not an experiment
  • Result: the study can show an association between darkness exposure and later myopia, not a proven causal link

• Key lesson: observational studies show association, not necessarily causation

  • There may be a relationship between X (e.g., light exposure) and Y (e.g., myopia), but that relationship may not be causal
  • Other explanations include reverse causation or third variables influencing both X and Y
  • Example from speech: more light exposure at night could be linked to myopia, but it could be that a genetic predisposition influences both sleep environment and vision, or that another factor correlates with both

• Potential causal pathways and confounding factors

  • If a variable could plausibly affect both X and Y, it’s a candidate confounder
  • In observational studies, plausible confounders must be considered to avoid mistaken causal claims
  • The presence of confounders can create or mask associations between X and Y
  • Researchers must seek plausible explanations for how a confounder might influence both the explanatory and the response variables

• Example: sunscreen use and melanoma (skin cancer)

  • Observational study finding: increases in sunscreen use were associated with increased risk of skin cancer
  • Important interpretation: association does not imply causation
  • Plausible confounders: sun exposure (people who spend more time in sun may both use sunscreen more and have higher melanoma risk due to UV exposure)
  • Possible reverse causation or other factors: individuals with higher perceived risk or genetic predispositions toward sun sensitivity
  • Takeaway: even striking associations can be explained by confounding factors or reverse causation in observational data

• Formal concepts and simple notation

  • Let $X$ be the explanatory variable and $Y$ the outcome
  • In observational data, we typically observe the association: $P(Y|X)$
  • Causal effect under intervention (do-notation): $P(Y|do(X))$
  • With a confounder $Z$ that affects both $X$ and $Y$, the observed association can be decomposed as:
  • Observed association accounting for confounding: $P(Y|X) = \sum_z P(Y|X, Z=z)\,P(Z=z|X)$
  • Causal effect adjusting for confounding (if we could intervene and fix $X$ independent of $Z$): $P(Y|do(X)) = \sum_z P(Y|X, Z=z)\,P(Z=z)$
  • These expressions illustrate how confounding can bias observed associations and how adjusting for confounders is essential to approach causal interpretation

• Practical implications for research design

  • When random assignment is unethical or impractical, rely on observational studies but be cautious about causal claims
  • Use methods to address confounding (e.g., statistical adjustment, stratification, matching, instrumental variables) to improve causal inference
  • Consider alternative explanations and reverse causation in interpretation
  • Validate findings with triangulation across multiple studies and designs to assess real-world relevance

• Real-world relevance and takeaways

  • Observational evidence can reveal important associations that warrant further study, policy consideration, or public health action, even if causality isn’t established
  • Ethical constraints remind us why rigorous experimental design is not always feasible, underscoring the value—and limits—of observational data
  • Understanding the difference between association and causation helps prevent misinterpretation of study results

• Summary takeaway

  • If you cannot or should not assign X, you conduct observational studies to observe X and Y
  • You can observe associations, but causality requires careful analysis, consideration of confounders, and possibly different study designs or methods

• Quick reference glossary

  • Explanatory variable: the factor whose effect we want to study, denoted $X$
  • Response variable: the outcome of interest, denoted $Y$
  • Observational study: study that observes data without assignment of $X$
  • Experiment: study where $X$ is assigned by the researchers
  • Confounding factor: a variable that influences both $X$ and $Y$, potentially biasing the observed association
  • Association vs causation: association = a relationship observed in data; causation = changing $X$ would cause a change in $Y$