Causal inference Flashcards
Study designs for causal inference
Randomised controlled trials
Natural or quasi experimental studies
Longitudinal studies
Analysis methods for causal inference
Confounder adjustment/stratification
Propensity Scores
RCT:
Manipulation: The scientist actively interacts with the environment by modifying certain aspects (X) (according to F. bacon)
Randomization: Subjects are assigned to active (X=1) or control condition (X=0) at random, i.e., regardless of their characteristics. After successful randomization, samples assigned to active, or control condition are equivalent in all aspects (Z) but the exposure (X).
Issues with RCT’s
Lack of external validity/generalizability
Both groups balanced for cofounders
Pyramid of evidence
Level 1: Systematic review of RCT
Level 2: Single RCT
Level 3: Systematic review of observational studies
Level 4: Single observational study
Level 5: Qualitative studies
Level 6: Expert opinion/case studies
Pros RCT
Treatment and control groups can be matched
Strong evidence for cause-effect relationships
Statistical methods are relatively straightforward
Cons of RCT
Expensive, take a long time
Potentially unethical in some circumstances
Prone to selection bias
It might not be generalizable to the real world (too artificial)
Natural or Quasi-experimental designs
Not everything can be an RCT, not possible or not ethical
Can use longitudinal prospective samples
Chronology used to parse out causality, but you are looking at how t0 affects t1, but you cannot see this in reverse to determine the direction of the effect
Twin studies
People love because matched for genes and home-enviro, almost like natural RCT
Monozygotic twins are naturally “matched” for many common confounders
Grew up in the same family at the same time, and share genetic risk factors
Differences in outcomes associated with discordant exposures within twin pairs are often described as causal
Discordant twin design (twins with different in utero outcomes)
Naturally only a twin sample, which may be a specific experience and cannot be easily generalized
Instrumental Variable design
No manipulation or randomization
Although there is no manipulation or randomization of the exposure variable (X), there is manipulation and/or randomization of an instrumental variable (I).
An instrumental variable (I) must:
be correlated with an exposure X (ideally explaining much of the variance in X),
be NOT correlated with the error Z,
be correlated with an outcome Y only through X
Counterfactual
If there are no twins, instruments or policies
No exposure is a causal factor in itself, in isolation.
In this context, we are thinking about causality as a difference between two groups that are otherwise identical, only exists as contrast
Causality may only be derived as part of a well-defined contrast between one condition (e.g., exposure) and an alternative condition (e.g., no exposure), while holding everything else constant.
Causal contrasts can be estimated by using substitutes for the counterfactual condition.
To the extent that substitutes are equivalent to the factual condition in all aspects but the exposure (i.e., they are exchangeable with the counterfactual condition), substitutes can be used to infer causality.
In epidemiology, substitutes are generally either a population other than the target population during the same etiological period or the target population observed at a time other than the etiological period
Cholera counterfactual case
In 1854, John Snow mapped cholera cases in Soho and found that most people who had died from cholera had drunk the water from the Broad Street Pump.
Snow argued to close the pump and removed its handle and the cholera outbreak ended.
Cannot actual be sure this is the cause because not a formal manipulation, but…
Observed outcome (Y), cholera deaths
Exposure (X), Water pump
Two conditions:
0. Pump is closed (X=0), no water is coming out, the neighbourhood is unexposed to the potentially contaminated water
1. Pump is left open (X=1), water is coming out the pump, the neighbourhood is exposed to the potentially contaminated water.
0 is what happened
Observed outcome, cholera deaths (Y), of what happened when exposure (X) was “closed” (X=0).
Y|X=closed = YX=0 = Y0
Unknown potential outcome (Y) that would have happened if the exposure (X) had been – counter to the fact – left “open” (X=1).
Y|X=Open = YX=1 = Y1
Potential outcome: To identify the causal effect of closing the pump on mortality, we would need to compare:
Y0 :The number of deaths (Y) when the pump was closed (X=0)
Y1: The number of deaths (Y) when the pump was left open (X=1)
FUNDAMENTAL PROBLEM OF CAUSAL INFERENCE
We can never know the potential outcome for a counterfactual exposure!
For each ‘unit of analysis’ (condition) we can only observe one potential outcome
Exchangeability
Causal contrasts can be estimated by using substitutes for the counterfactual condition.
To the extent that substitutes are equivalent to the factual condition in all aspects but the exposure (i.e., they are exchangeable with the counterfactual condition), substitutes can be used to infer causality.
Different statistical approaches can be taken to improve equivalence/exchangeability.
Statistical approaches for exchangeability
Stratification in regression
Propensity scores
Directed Acrylic Graphs (DAGs)
Use DAGs to visualise your theoretical causal model, between exposure and outcome of interest, including all Confounders (C) and Mediators (M)
X – Smoking
Y – Lung cancer
Must also consider other possible factors that cause x and y, known as confounders
These are unfortunately also associated with eachother
Must also consider mediaators
Confounders
other possible factors that cause x and y
possible factors the cause x and y
X <- C -> Y
Mediators
anything caused by X that in turn causes Y
X -> M -> Y
Moderators
a third variable that affects the strength of the relationship between a dependent and independent variable
Stratification in regression models
Stratifying is sorting data or people into distinct layers, for example, male and female
Allows adjustment for confounders
Mediators are already included in the model
Propensity scores
Attempts to use confounders to split process into two stages
Looking at everything that is related to X
Looking at everything that is related to Y
Can use this to create a propensity score, to see how likely a person is to have an exposure, and use that score as a covariate
It is a balancing score to allow comparisons between subjects with similar prior probabilities of experiencing a certain exposure.
Exchangeability is limited to the variables included in the model.
Exchangeability should be examined by testing if the distribution of confounding variables is similar between exposed and non-exposed with similar propensity scores (e.g., standardized mean difference).
Two ways to do propensity scores
Stratification of Propensity Score
Propensity score matching
Both basically uses all confounders to create a risk score to compare with outcome, instead of one causal factor
Stratification of Propensity Score
Subjects are stratified into subsets based on previously defined thresholds of the estimated propensity score (e.g., quintiles).
Within each propensity score stratum, treated and untreated subjects will have roughly similar values of the propensity score.
The average treatment effect is computed first within each stratum then pooled across strata.
Propensity score matching
It consists in forming matched sets of exposed and non-exposed subjects with similar values of propensity score.
Matching is generally 1:1 with nearest neighbor, without or with replacement (non-exposed subject used once or more).
Compute average treatment effect (‘unbiased’ effect of exposure) as average of effect in matched pairs.
Why is Missing Data a problem
Missing data is a threat to causal inference, regardless of study design.
Like confounders, specific patterns of missingness may generate artificial associations between exposure and outcome.
Missing data can introduce significant bias in the analysis by influencing the exchangeability/balance of the causal contrast
Types of missing data
Missing completely at random (MCAR)
Missing at random (MAR)
Missing not at random (MNR)
Missing completely at random (MCAR)
Missingness is completely unrelated to all other variables in the dataset
ex. all participants have the same likelihood of having missing data (a researcher lost some interview booklets)
Missing at random (MAR)
Missingness is related to exposure X (or, more generally, to an observed variable)
Given X, missingness does not depend on Y (or, more generally, unobserved data).
Because missingness is related to X, exposed and unexposed groups are not balanced.
Analysis of complete observations would give a biased estimate of the effect of exposure.
However, it is possible to achieve balance by using information in X.
ex. victims of maltreatment are more likely to have missing data (drop out of the study).
Missing not at random (MNR)
Missingness is related to outcome Y (or, more generally, to an unobserved variable).
Missingness depends on Y (or, more generally, unobserved data).
Because missingness is related to Y, we do not know if exposed and unexposed groups are balanced.
Analysis of complete observations would give a biased estimate of the effect of exposure.
It is not possible to achieve balance by using information in X.
ex. individuals with depression are more likely to have missing data
Methods to deal with missing data
Naive methods
List-wise deletion
Pair-wise deletion
Single imputation
Modern methods
Multiple imputation (explicit)
Maximum likelihood estimation (implicit).
We can only identify mechanisms of missingness based on X (observed data), that is, we can only discriminate between MCAR and MAR.
Multiple imputation and Maximum likelihood estimation assume MAR – they generate imputed values by considering how patterns of missingness relate to exposure X and other observed variables.
Neither method deals effectively with MNAR conditions, which is dealt with through structural equation modeling (maximum likelihood estimations) and sensitivity analysis of different assumptions.
Pair-wise deletion
eliminates cases with missing values on an analysis-by-analysis basis [assumes MCAR].
List-wise deletion
eliminates cases with missing values from all analyses [assumes MCAR].
Single imputation
replaces all missing values with a single set of values, such as
(1)the arithmetic mean [assumes MCAR],
(2)a score at a prior assessment,
(3)a score from another individual with a similar set of background characteristics, or
(4)a predicted scores from regression analysis [assume MAR, does not include a measure of uncertainty for the imputed value, with unrealistically small SE].
Multiple imputation (explicit)
It generates multiple filled-in datasets from different imputation algorhythms and produces average imputed values. assume MAR
Maximum likelihood estimation (implicit)
It maximizes the likelihood of observed multivariate data, and uses the resulting distribution to produce imputed values. It includes error by MLE function.
