UE3 Flashcards
Causal analysis
1) Calculate the mean well-being score in the exposed (alcohol use) and in the unexposed group. Is this a causal estimate? Explain your answer
When comparing mean scores between groups, especially in an experimental or observational study where exposure to a particular variable is controlled or observed, a significant difference could suggest a causal relationship. However, several factors need consideration:
1. Confounding Variables: Other factors beyond the exposed variable might influence the outcome. Without proper controls, these factors could confound the results, making it challenging to attribute causation solely to the exposure.
2. Correlation vs. Causation: Just because two variables are associated or show a difference in mean scores doesn’t mean one causes the other. There might be a hidden factor or reverse causality involved.
3. Random Chance: Sometimes, differences in mean scores could occur purely by chance, especially in small sample sizes.
4. Study Design: The study’s design and methodology play a crucial role. Randomized controlled trials (RCTs) provide stronger evidence for causation compared to observational studies due to their ability to control for confounding factors.
To establish a causal relationship more conclusively, researchers often employ additional methods like:
* Randomization: In RCTs, participants are randomly assigned to exposed and unexposed groups, minimizing bias and confounding variables.
* Control Groups: Comparing the exposed group to a similar unexposed group helps isolate the effect of the exposure.
* Longitudinal Studies: Observing changes over time can help establish temporal sequence, a crucial factor in causation.
In summary, while a difference in mean scores between exposed and unexposed groups can suggest a causal relationship, it’s not definitive proof. Additional evidence through rigorous study design, consideration of confounding factors, and replicability of results are necessary to establish a solid causal estimate.
a) What model will you use (logistic regression, linear regression)?
eciding between logistic regression and linear regression for a causal analysis depends on several factors related to the nature of your data, outcome variable, and research question:
Nature of the Outcome Variable:
Binary Outcome: If your outcome variable is binary (e.g., yes/no, 0/1), logistic regression is more suitable. Logistic regression models the probability of the outcome occurrence given the predictor variables.
Continuous Outcome: Linear regression is appropriate for continuous outcome variables. If the outcome is not binary, linear regression might be a better choice.
Linearity Assumption:
Linear regression assumes a linear relationship between predictors and the outcome. If this assumption holds and the outcome variable is continuous, linear regression could be appropriate.
Nature of the Data:
Logistic regression is robust for binary outcomes even when other assumptions (like normality of residuals) are not met. It’s also suitable for dealing with multicollinearity among predictors.
Causal Inference:
For causal analysis, both logistic and linear regressions can provide insights. However, if establishing causation is the primary goal, logistic regression might be preferred for binary outcomes because it models the probability of an event occurring based on the predictor variables, allowing for a clearer interpretation of causal effects.
Understanding Odds Ratios vs. Coefficients:
Logistic regression provides odds ratios, which represent the change in odds of the outcome given a one-unit change in the predictor. Linear regression provides coefficients that represent the change in the outcome for a one-unit change in the predictor.
Consideration of Other Techniques:
For causal inference, other techniques like propensity score matching, instrumental variable analysis, or structural equation modeling might be more suitable depending on the complexity of the causal relationships you aim to explore.
Ultimately, consider the nature of your outcome variable, the assumptions of each regression model, and the specific goals of your causal analysis. If your outcome is binary and you’re interested in estimating probabilities or making predictions, logistic regression tends to be more appropriate. If your outcome is continuous and the relationship with predictors is linear, linear regression could be more suitable. However, both regression types have their strengths and limitations in causal analysis, so it’s crucial to choose based on the characteristics of your data and research question.
c) What assumption(s) do you need before it can be a causal effect estimator?
Establishing a causal effect involves several key assumptions, some of which are:
Covariate Balance: The groups being compared (e.g., treatment vs. control) should be balanced concerning relevant covariates. This balance helps ensure that differences in the outcome can be attributed to the treatment rather than pre-existing differences in characteristics.
Temporal Order: The cause must precede the effect in time. This temporal sequence is crucial for inferring causality.
No Confounding: This assumes there are no unmeasured variables or confounders that influence both the treatment and the outcome. Controlling for confounding variables or using randomization (in experimental studies) helps mitigate this issue.
Consistency: The treatment effect should be consistent across different populations, settings, and time frames. In other words, if the treatment causes a certain effect, this effect should be observable consistently.
No Selection Bias: Selection bias occurs when there’s a systematic difference between the treatment and control groups that isn’t due to the treatment itself. Randomization helps mitigate selection bias in experimental studies.
Sufficient Overlap: There should be overlap in the distributions of covariates between treated and untreated groups. This ensures that the effects observed in one group can be reasonably compared to the other.
No Interference: This assumes that the treatment given to one individual does not affect the outcomes of others (no spillover effects).
Ignorability or Unconfoundedness: This is a fundamental assumption in causal inference that implies that, conditional on the observed variables, the treatment assignment is independent of potential outcomes. In other words, given the measured covariates, the treatment is as good as randomly assigned.
Stable Unit Treatment Value Assumption (SUTVA): This assumption posits that there is no variation in the treatment effect for different units, and there is no interaction between units due to treatment.
These assumptions form the backbone of many causal inference methods, such as randomized control trials, propensity score matching, instrumental variable analysis, and others. However, in real-world scenarios, it’s challenging to meet all assumptions perfectly. Researchers use various statistical techniques and study designs to minimize violations of these assumptions and strengthen the case for inferring causality.
Define propensity score
The propensity score is the probability of receiving a particular treatment (or exposure) given a set of observed covariates. In causal inference, especially when dealing with observational data, the propensity score is a crucial component in attempting to balance or control for confounding variables.
For example, in a study where individuals self-select into treatment or control groups (non-random assignment), the propensity score helps create a pseudo-randomization effect. It summarizes the characteristics of individuals that predict their likelihood of receiving the treatment, allowing researchers to balance these characteristics across treatment groups.
In simpler terms, the propensity score estimates the likelihood of receiving the treatment based on observed characteristics. Once the propensity scores are calculated for each individual, various methods such as matching, stratification, or weighting based on propensity scores can be used to create more balanced comparison groups and help control for confounding when estimating causal effects in observational studies.
4) You plan to estimate the effect of surgery on the disability score using propensity score matching
a) Indicate how you would estimate the effect of surgery on the disability score using such an approach (you do not have to perform it).
Calculate Propensity Scores:
Use logistic regression to estimate the propensity scores for each individual, representing the likelihood of receiving surgery based on observed covariates.
Match Participants:
Match individuals who underwent surgery (treatment group) with similar individuals who did not have surgery (control group) based on their propensity scores. Common matching methods include nearest-neighbor matching, exact matching, or kernel matching.
Assess Balance:
Evaluate the balance of covariates between the treatment and control groups after matching to ensure that they are comparable in terms of observed characteristics.
Estimate Treatment Effect:
Finally, estimate the effect of surgery on the disability score by comparing the average disability score between the matched treatment and control groups.
b) Indicate whether the estimate would be an average treatment effect (ATE), an average treatment effect in the treated (ATT), or a complier average treatment effect.
Average Treatment Effect (ATE):
ATE estimates the average effect of the treatment on the entire study population, regardless of whether they received the treatment.
Average Treatment Effect in the Treated (ATT):
ATT estimates the average effect of the treatment specifically for those individuals who actually received the treatment.
Complier Average Treatment Effect (CATE):
CATE estimates the effect of treatment for individuals who comply with treatment if assigned to receive it.
Indicators to Determine the Type of Estimate from Propensity Score Matching:
Matching Strategy:
One-to-One Matching:
ATE: If the analysis compares outcomes between all treated and untreated individuals after matching.
ATT: If the analysis focuses only on the treated individuals’ outcomes after matching.
Many-to-One or One-to-Many Matching:
ATE: If the analysis compares outcomes between all treated and untreated individuals after matching.
ATT: If the analysis compares outcomes only among the treated individuals within the matched groups.
Focus of Analysis:
If the analysis compares outcomes between all treated and untreated individuals after matching, it indicates an estimate of ATE.
If the analysis compares outcomes only among the treated individuals within the matched groups, it indicates an estimate of ATT.
Interpretation and Reporting:
The interpretation and conclusions drawn from the analysis will guide whether the estimate is focused on the overall population (ATE) or specifically on those who received treatment (ATT).
Complier Average Treatment Effect (CATE):
Determining CATE typically involves more complex analyses, such as instrumental variable methods or other techniques specifically designed to estimate the effect for individuals who comply with treatment under certain conditions. It’s a more nuanced estimation that considers compliance with treatment assignment, often found in studies with compliance or adherence issues.
User
What are the assumptions that are made when doing propesnuity matched analysis
Propensity score matching is a statistical technique used to reduce bias in observational studies by creating similar groups that have similar probabilities of receiving a treatment. Several assumptions are typically made when conducting propensity score matching:
Strong ignorability or conditional independence: This is the core assumption behind propensity score matching. It assumes that, conditional on the propensity score, the assignment to treatment or control groups is random or as good as random. In other words, given the propensity score, there are no unobserved confounding variables affecting both the treatment assignment and the outcome.
Common support: There should be overlap in the distribution of propensity scores between the treated and control groups. This ensures that it’s possible to find comparable matches between the groups.
Correct model specification: The model used to estimate the propensity score needs to be correctly specified. It should include all relevant confounding variables that influence both treatment assignment and the outcome.
Large enough sample size: Having a sufficiently large sample size ensures that after matching, there are enough observations in each group to make meaningful comparisons and reduce the likelihood of biases.
Similar treatment effect across all levels of propensity score: It assumes that the treatment effect is constant across all levels of the propensity score. This is referred to as the “common treatment effect assumption.”
Lokking at crude and adjusted comaprisosn explain the differences
The Crude OLS estimate indicates a -0.06 risk difference with a 95% confidence interval of -0.08 to -0.03, while the Adjusted OLS estimate shows a 0.03 risk difference with a 95% confidence interval of 0.01 to 0.05.
There’s a notable shift in the association between ICU admission and in-hospital mortality when moving from the crude to the adjusted model. The Crude OLS suggests a negative association, implying that ICU admission is associated with a reduction in mortality. However, the Adjusted OLS estimate, after accounting for additional factors, shows a positive association between ICU admission and mortality.
This shift might occur due to confounding variables not considered in the crude model. The crude model does not control for potential variables that could influence both ICU admission and mortality, leading to a biased estimate. When the model is adjusted to account for these confounding factors (which might include age, comorbidities, severity of illness, etc.), the association changes, suggesting that ICU admission might actually be associated with increased mortality when these factors are taken into consideration.
what is IV analysis and its assumptions
The three key assumptions in instrumental variable (IV) analysis are:
Relevance: The instrument must be correlated with the variable of interest (ICU admission) but should not directly affect the outcome (mortality) except through its impact on the variable of interest.
Independence: The instrument should be independent of any confounders that might influence the outcome, except through its relationship with the variable of interest.
Exclusion Restriction: There should be no other pathways between the instrument and the outcome, except through the variable of interest.
c. The IV estimate was obtained by a 2-stage least squares regression model. Explain what a 2-stage least squares model is.
A two-stage least squares (2SLS) model is a statistical method used in instrumental variable analysis. It involves two stages:
First stage: The instrument is used to predict the endogenous variable (ICU admission). This stage generates predicted values for ICU admission based on the instrument.
Second stage: These predicted values are utilized in a regression analysis to estimate the relationship between the endogenous variable (ICU admission) and the outcome (mortality). This method helps in addressing endogeneity by isolating the variation in the endogenous variable that is determined by the instrument.
d. Look at the propensity matched estimate and the IV analysis estimate with 95% confidence intervals. What do you observe? Could you give an explanation?
The propensity matched estimate shows a 0.04 risk difference (95% CI: 0.01 to 0.08), indicating a positive association between ICU admission and mortality in the matched cohort. However, the IV analysis estimate is 0.01 (95% CI: -2.45 to +2.30), with a wide and imprecise confidence interval that spans zero. This wide interval suggests high uncertainty in the estimate and raises questions about the reliability of the instrument used in the IV analysis or the fulfillment of the assumptions necessary for IV analysis. The propensity matched estimate appears more precise compared to the IV analysis in this study.
