IRAT 4 Study Guide PDF

Detailed Notes on Video 4.1: Inferring What We Want from What We Get – Counterfactuals and Their Proxies Course: Design & Conduct of Observational Studies in Epidemiology (P8438) 1. What We Want: Understanding Causality in Epidemiology Epidemiologists aim to determine causal relationships between...

Detailed Notes on Video 4.1: Inferring What We Want from What We Get – Counterfactuals and Their Proxies Course: Design & Conduct of Observational Studies in Epidemiology (P8438) 1. What We Want: Understanding Causality in Epidemiology Epidemiologists aim to determine causal relationships between exposures (e.g., smoking) and outcomes (e.g., lung cancer). However, since we cannot directly observe causality, we rely on frameworks like: Key Concepts for Causal Inference ​ Directed Acyclic Graphs (DAGs): Graphical models that help visualize causal relationships and confounding structures. ​ Counterfactuals: Hypothetical scenarios representing what would have happened if exposure had not occurred. ​ Causal Theories: Theoretical approaches to infer cause-effect relationships, often relying on assumptions about how the world operates. 2. Inferring Causes in Observational Studies Observational studies do not control exposure assignment, making it necessary to account for potential biases and distortions. 2.1 Identifying Causes To estimate causal effects, we need to address factors that introduce bias: 1.​ Confounding ○​ Occurs when a third variable (confounder) is associated with both the exposure and outcome. ○​ Example: In a study on alcohol consumption and lung cancer, smoking could confound the association since it is related to both. ○​ Solutions: ​ Randomization (in experimental studies) ​ Stratification or adjustment in statistical models ​ Instrumental variable approaches  2.​ Confounder Control ○​ Restriction: Limiting the study to a subset of participants (e.g., only non-smokers). ○​ Matching: Selecting exposed and unexposed participants with similar characteristics. ○​ Multivariable adjustment: Using statistical models to control for confounders (e.g., regression models). 3.​ Selection Bias ○​ Arises when the way participants enter or leave the study is related to both exposure and outcome. ○​ Example: If healthier individuals are more likely to participate in a study on diet and heart disease, results may be skewed. ○​ Mitigation: Careful study design, weighting methods, and sensitivity analysis. 4.​ Cohort Studies ○​ Follow participants over time, but loss to follow-up can create bias if those lost are different from those who remain. ○​ Example: If sicker individuals drop out of a study on workplace stress and heart disease, the study may underestimate the effect of stress. 5.​ Case-Control Studies ○​ Compare cases (those with disease) to controls (without disease), but can suffer from: ​ Recall Bias: Cases may recall exposures differently than controls. ​ Selection Bias: If controls are not representative of the population that produced the cases. 6.​ Measurement Issues ○​ Misclassification Bias: Errors in measuring exposure or outcome can distort results. ○​ Chance Variation: Random fluctuations in data may create spurious associations. ○​ Statistical Significance vs. Real-World Impact: Even small, significant effects may not be meaningful in practice. 3. Explaining Causes in Epidemiology Once a causal effect is identified, we aim to understand the mechanisms behind it. 1.​ Mediation ○​ Identifies pathways through which an exposure affects an outcome. ○​ Example: Smoking → Lung inflammation (Mediator) → Lung cancer. ○​ Statistical Methods: ​ Baron & Kenny method ​ Structural Equation Models (SEM) 2.​ Interaction (Effect Modification)  ○​ Examines whether the effect of an exposure varies across different subgroups. ○​ Example: Air pollution → Asthma risk may be stronger in children than in adults. ○​ Approach: Stratified analysis or inclusion of interaction terms in models. 4. Causal Contrast: How We Compare Disease Risk To infer causality, we compare: ​ Disease experience of an exposed person (observable fact) ​ Disease experience of the same person at the same moment in time had they not been exposed (unobservable counterfactual) Problem: ​ We cannot observe the same person in both exposed and unexposed states simultaneously. ​ Solution: We approximate the counterfactual using a proxy group. 5. Proxies for the Counterfactual Since we cannot observe a single individual in both states, we instead compare: ​ Disease experience of an exposed person (fact) ​ Disease experience of a different, unexposed person (proxy for counterfactual) This comparison is valid only if the unexposed person accurately represents what the exposed person would have been like if unexposed. Exchangeability: The Key Assumption For the proxy comparison to be valid, the unexposed group must be exchangeable with the exposed group. ​ If exchangeability holds: The observed disease risk in the unexposed group equals the counterfactual disease risk in the exposed group. ​ If exchangeability fails: Bias is introduced, leading to incorrect causal estimates. 6. Illustrative Scenarios of Causal Comparisons Scenario 1: Ideal Counterfactual (Theoretical Perfect Case) ​ John is exposed. ​ Nhoj is John’s counterfactual self if he had not been exposed. ​ If John develops disease (1), but Nhoj does not (0), the causal effect is:1−0=11−0=1 (Strong evidence for causality) Scenario 2: Good Proxy Comparison ​ John is exposed. ​ Eddie is unexposed and is a valid proxy for John’s counterfactual. ​ If John develops disease (1) and Eddie does not (0), the causal effect is:1−0=11−0=1 (Exchangeability holds; valid estimate) Scenario 3: Poor Proxy Comparison ​ John is exposed. ​ Brian is unexposed but is NOT a valid proxy. ​ If John and Brian both develop disease (1), the causal effect appears as:1−1=01−1=0 (Suggests no effect, but result is misleading due to non-exchangeability.) 7. Implications for Epidemiology ​ Observational studies approximate counterfactual comparisons using proxy groups. ​ Validity depends on exchangeability—failure to meet this condition leads to bias. ​ Randomized controlled trials (RCTs) ensure exchangeability, but in observational studies, we must rely on study design and statistical techniques to mitigate bias. Best Practices to Improve Causal Inference ​ Better Study Design: Use longitudinal designs, match groups carefully, and apply sensitivity analyses. ​ Statistical Techniques: ○​ Propensity score matching ○​ Instrumental variables ○​ Inverse probability weighting ​ Critical Thinking: Always question whether observed differences reflect real causal effects or biases. Final Takeaways ​ Epidemiology seeks to answer causal questions but faces challenges in approximating counterfactuals. ​ Proxy comparisons work only if exchangeability is met. ​ Bias, confounding, and selection issues can distort causal estimates. ​ Advanced statistical methods help improve causal inference but require careful interpretation. Detailed Notes on Video 4.2: Inferring What We Want from What We Get – Response Types Course: Design & Conduct of Observational Studies in Epidemiology (P8438) 1. Introduction: The Problem of Non-Exchangeability This lecture builds on the previous discussion on counterfactuals and proxies, focusing on the role of response types in determining exchangeability between exposed and unexposed groups. Key Question: Why was Brian a poor proxy for John’s counterfactual (Nhoj) in the previous lecture? ​ Answer: ○​ Individuals respond differently to exposure due to underlying biological or environmental factors. ○​ John and Brian may have belonged to different response types, making Brian a poor proxy for John’s counterfactual self (Nhoj). ○​ If Brian and John do not share the same potential disease risk in the absence of exposure, using Brian as John’s counterfactual leads to biased estimates of causal effects. Objective of This Lecture: ​ Introduce response types as a framework for understanding why people react differently to exposure. ​ Explain how response types affect potential outcomes and exchangeability. ​ Discuss the Greenland and Robins Schema for causal inference. 2. The Concept of Response Types in Epidemiology When studying causality, we are interested in comparing what happens when an individual is exposed vs. what would have happened had they not been exposed. ​ The gold standard for causal inference is a randomized controlled trial (RCT), where groups are balanced through randomization. ​ In observational studies, we approximate counterfactuals using a proxy (an unexposed group), which only works if the groups are exchangeable. Exchangeability Fails When Response Types Differ Different individuals have different biological predispositions or environmental conditions that make them react differently to exposure. ​ If the proxy group (unexposed) is systematically different from the exposed group, bias is introduced. ​ Response types help us understand why exchangeability breaks down. 3. The Sufficient Causes Model A sufficient cause is a set of multiple contributing factors that together cause disease. ​ Exposure alone is rarely sufficient to cause disease—other risk factors must be present. ​ Different people carry different combinations of sufficient causes, leading to different responses to exposure. How Response Types Relate to Sufficient Causes ​ Individuals are classified into response types based on which sufficient causes they carry. ​ This classification determines whether they will develop disease with or without exposure. ​ Key Idea: The presence or absence of additional risk factors (B, S, T, G) determines response type. 4. Classification of Response Types A person’s response type determines their disease risk under exposure and non-exposure conditions. Respons Effect of Potential Potential Example e Type Exposure Outcome if Outcome if Exposed Unexposed Type 1 – No effect Disease Disease Genetic disorder that causes Doomed disease regardless of exposure Type 2 – Exposure Disease No Disease Air pollution triggering Causal causes asthma in a susceptible disease individual Type 3 – Exposure No Disease Disease Vitamin D preventing rickets Protectiv prevents e disease Type 4 – No effect No Disease No Disease Person with genetic Immune immunity to malaria 5. Why Response Types Matter for Exchangeability In observational studies, we compare the exposed group to the unexposed group as a proxy for the counterfactual. ​ For this comparison to be valid, the unexposed group must be exchangeable with the exposed group. ​ If the distribution of response types differs between groups, bias is introduced. Examples of Exchangeability Failures ​ If the unexposed group has a higher proportion of immune individuals, disease rates will be underestimated, making exposure appear more harmful than it really is. ​ If the unexposed group has a higher proportion of doomed individuals, disease rates will be overestimated, making exposure appear less harmful than it really is. Implications for Study Design ​ When designing observational studies, matching, stratification, and statistical adjustments are necessary to ensure exchangeability. ​ Instrumental variables and propensity score methods help mitigate exchangeability problems by matching on response type likelihoods. 6. Greenland and Robins Schema for Understanding Causal Effects The Greenland and Robins framework is used to classify individuals based on their response to exposure. Response Effect of Potential Potential Interpretation Type Exposure Outcome if Outcome if Exposed Unexposed Type 1 – No effect Disease Disease Exposure makes Doomed no difference Type 2 – Exposure Disease No Disease Exposure is Causal increases harmful disease risk Type 3 – Exposure No Disease Disease Exposure is Protective prevents disease beneficial Type 4 – No effect No Disease No Disease Exposure makes Immune no difference How This Schema Helps in Epidemiology ​ It provides a structured way to understand causal effects and exchangeability. ​ It highlights how different individuals react differently to the same exposure, explaining why some studies find conflicting results. ​ It emphasizes the need for stratified analysis based on susceptibility, immunity, and other modifying factors. 7. Real-World Example: Causes of Schizophrenia Hypothesis: Micronutrient (MN) deficiency contributes to schizophrenia. Effect of Exposure Potential Potential Example (MN Deficiency) Outcome if Outcome if Exposed Unexposed  Type 1 – Doomed Disease Disease Person with CAT Virus Type 2 – Causal Disease No Disease Person with genotype sensitive to MN deficiency Type 3 – Protective No Disease Disease Person with a genotype that requires MN Type 4 – Immune No Disease No Disease Person without genetic susceptibility Key Insights from This Example ​ Genetic and environmental factors modify how exposure affects individuals. ​ One-size-fits-all conclusions may be misleading—some people develop disease because of MN deficiency, while others remain unaffected. ​ Stratified analyses are essential to detect true causal effects. 8. Key Takeaways ​ Response types explain why individuals react differently to exposure. ​ Observational studies assume exchangeability, but this assumption often fails due to differences in response types. ​ Greenland and Robins schema helps in structuring causal inference. ​ Statistical methods (matching, stratification, instrumental variables) are needed to adjust for response type differences. ​ Real-world applications include investigating gene-environment interactions in disease risk. Final Thoughts This lecture refines our understanding of why causal inference is difficult in observational studies. ​ Understanding response types allows us to interpret results more accurately. ​ The failure to account for response types can lead to biased conclusions about exposure effects. ​ Future epidemiological research should stratify individuals based on response types to improve causal inference. Detailed Notes on Video 4.3: Inferring What We Want from What We Get – Response Types: Take 2 Course: Design & Conduct of Observational Studies in Epidemiology (P8438) 1. Introduction: Refining Response Types and Causal Inference This lecture builds upon Video 4.2, further exploring how response types impact causal inference and exchangeability. Key Questions Explored in This Lecture: 1.​ How do response types affect our ability to estimate causal effects? 2.​ What is the difference between a causal contrast and an observed association? 3.​ Under what conditions does an observed risk ratio (RR₍proxy₎) approximate the true causal effect (RR₍causal₎)? 4.​ How do we quantify exchangeability using response type proportions? Key Concepts Covered: ​ Greenland and Robins schema for response types and exchangeability ​ Mathematical definitions of causal contrast ​ Causal risk ratio vs. observed association ​ Requirements for valid exchangeability in observational studies 2. Revisiting the Greenland and Robins Schema for Response Types The Greenland and Robins Schema categorizes individuals based on their potential disease outcomes under exposure and non-exposure conditions. Response Effect of Potential Potential Interpretation Type Exposure Outcome if Outcome if Exposed Unexposed Type 1 – No effect Disease Disease Exposure makes Doomed no difference  Type 2 – Exposure Disease No Disease Exposure is Causal increases harmful disease risk Type 3 – Exposure No Disease Disease Exposure is Protective prevents disease beneficial Type 4 – No effect No Disease No Disease Exposure makes Immune no difference Why Are Response Types Important? ​ People in a population belong to different response types. ​ We cannot directly observe an individual’s response type, only their exposure status and outcome. ​ Misalignment of response type proportions in exposed vs. unexposed groups leads to bias in estimating causal effects. 3. Response Types in Populations: A Mathematical Framework Each individual in a study belongs to one of the four response types, but we only observe aggregate proportions within exposed and unexposed groups. Response Disease Status if Disease Status if Proportion in Proportion in Type Exposed (A=1) Unexposed (A=0) Exposed (p) Unexposed (q) Type 1 – 1 (Disease) 1 (Disease) p₁ q₁ Doomed Type 2 – 1 (Disease) 0 (No Disease) p₂ q₂ Causal Type 3 – 0 (No Disease) 1 (Disease) p₃ q₃ Protective Type 4 – 0 (No Disease) 0 (No Disease) p₄ q₄ Immune 4. Causal Contrast: The Theoretical Ideal for Causal Inference To determine the true causal effect of exposure, we compare two risks: (1) Risk in the exposed (observed): Number of exposed individuals who develop diseaseTotal exposed individuals at riskTotal exposed individuals at riskNumber of exposed individuals who develop disease​ (2) Risk in the exposed had they not been exposed (counterfactual, unobserved): Number of exposed individuals who would have had disease if unexposedTotal exposed individuals at riskTotal exposed individuals at riskNumber of exposed individuals who would have had disease if unexposed​ Causal Risk Ratio (RR₍causal₎): RRcausal=Risk in actually exposedCounterfactual risk in exposed if unexposedRRcausal​=Counterfactual risk in exposed if unexposedRisk in actually exposed​ Expanding this in terms of response type proportions: RRcausal=p1+p2p1+p3RRcausal​=p1​+p3​p1​+p2​​ where: ​ p1p1​= Proportion of doomed individuals in the exposed group. ​ p2p2​= Proportion of causal individuals in the exposed group. ​ p3p3​= Proportion of protective individuals in the exposed group. Key Takeaways: ​ Causal risk ratio tells us how much exposure truly increases or decreases risk. ​ Protective individuals in the exposed group decrease the causal effect estimate. ​ Causal individuals in the exposed group increase the causal effect estimate. 5. Observed Association: The Proxy for the Causal Contrast Because we cannot observe the true counterfactual risk in the exposed, we instead compare risk in the unexposed group as a proxy. (1) Observed Risk in the Exposed (A=1) Exposed individuals who develop diseaseTotal exposed individuals at riskTotal exposed individuals at riskExposed individuals who develop disease​ (2) Observed Risk in the Unexposed (A=0) Unexposed individuals who develop diseaseTotal unexposed individuals at riskTotal unexposed individuals at riskUnexposed individuals who develop disease​ The observed risk ratio (RR₍proxy₎) is: RRproxy=Risk in actually exposedRisk in actually unexposedRRproxy​=Risk in actually unexposedRisk in actually exposed​ Expanding in terms of response type proportions: RRproxy=p1+p2q1+q3RRproxy​=q1​+q3​p1​+p2​​ where: ​ q1q1​= Proportion of doomed individuals in the unexposed group. ​ q3q3​= Proportion of protective individuals in the unexposed group. 6. When Does RR₍proxy₎ Accurately Estimate RR₍causal₎? For the observed association (RR₍proxy₎) to be equal to the true causal effect (RR₍causal₎), the following condition must hold: p1+p3=q1+q3p1​+p3​=q1​+q3​ What Does This Mean? ​ The proportion of doomed and protective individuals in the exposed group must equal the proportion of doomed and protective individuals in the unexposed group. ​ If this balance is violated, the observed association (RR₍proxy₎) does not reflect the true causal effect (RR₍causal₎). 7. Exchangeability: Ensuring Valid Comparisons Mathematical Condition for Exchangeability For valid causal inference, the balance of response types must hold: (q1+q3)=(p1+p3)(q1​+q3​)=(p1​+p3​) Implications of Violated Exchangeability ​ If q1+q3>p1+p3q1​+q3​>p1​+p3​: ○​ Unexposed group has more doomed individuals. ○​ Disease risk is overestimated, leading to an underestimated causal effect. ​ If q1+q3