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Week 1-4 lectures and workgroups ARM
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Week 1-4 lectures and workgroups ARM
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Advanced Research MethodsWeek 1
Lecture
Causal inference
Causation: in an individual, a treatment has a causal effect if the outcome
under treatment 1 would be different from the outcome under treatment 2.
Average treatment effect: average of individual effects in a population.
Counterfactual outcome: potential outcome that is not observed because
the subject did not experience the treatment. Potential outcome Ya=1 is
factual for some subjects and counterfactual for others.
Individual causal effect cannot be observed. Except under extremely strong assumptions. Average causal
effect cannot be inferred from individual estimates. Causal inference as a missing data problem. We
need a different approach to causal effects.
Identifiability conditions: average causal effects can still be determined under certain conditions.
‘Observing’ the counterfactual: what would have happened? Based on population averages, causal
effects can be estimated if 3 identifiability conditions hold: positivity, consistency, exchangeability. If the
conditions are met, then association of exposure and outcome is unbiased estimate of causal effect.
Positivity: about the sample and the way it was composed. ‘Positive probability’ of being assigned to
each of the treatments. People in one group could also have been in the other group. Control group.
Units are assigned to all relevant treatments within levels of adjustment factors.
Consistency: what would have happened if? If. Is it consistent? Specific formulated? Comparison to?
Exchangeability: what would have happened if? Treatment groups are exchangeable: it does not matter
who gets treatment A and who gets treatment B. Potential outcomes are independent of the
treatment that was actually received. It may be necessary to take other factors into account
(adjustment). Association can be ascribed to treatment effect.
Stratification (statistical adjustment)
,Meeting the conditions: RCT. Random -> exchangeability and positivity. Defining interventions ->
consistency.
Directed acyclic graph (DAG)
Association: statistical relationship. Association does not equal causation.
Causation: difference between potential outcomes
This association equals this difference if identifiability conditions hold
Adjustment to improve exchangeability: small number of factors? Stratification is possible. Matching.
Weighting. Regression analysis. Complete and correct adjustment leads to exchangeability. Adjust in
your analysis for
Traditional selection strategies:
- Correlation matrix: select variables with significant association with outcome
- Stepwise backward selection: start with all variables in regression model, remove the variable
that is the least statistically significant, repeat steps. Or retain variable if removal leads to
substantial change in effect estimate
- Adjust for confounders which are defined as being associated with the exposure and
conditionally associated with the outcome given the exposure is not in the causal pathway
between exposure and outcome
Problem with these strategies: they rely on observed
data rather than any theory, important variables may
be missed, choices must be made before data is
collected, strategy may increase bias rather than
reduce it, stepwise methods lead to underestimation
of statistical uncertainty.
Solution: DAG (directed, acyclic graph). Graphical
representation of underlying causal structures. DAGs
encode a priori causal knowledge. Data is not enough.
Simple rules can be used to determine what variables
to adjust for.
DAG terminology: paths, causal paths and backdoor paths, open and closed paths, blocking open paths,
collider, confounding, confounder.
- A path is a route between exposure X and outcome Y. it does not have to follow the direction of
the arrows.
, - A causal path follows the direction of the arrows. A backdoor path does not.
- All paths are open unless arrows collide somewhere along the path. A collider blocks a path. This
is a backdoor path. Path does not contribute to association of exposure and outcome. Adjusting
for a collider opens the path, but you want it to stay a backdoor path. Otherwise, you would
open the backdoor path and generate an association.
- Open paths transmit association: the association of X and Y is the combination of all open paths
between them. An open path is blocked when we adjust for a variable along the path.
- Confounding: bias caused by a common cause of exposure and outcome
- Confounder: variable that can be used to remove confounding
Collider bias: it is not a problem until you adjust for the collider. Do not adjust.
Selection bias: collider bias?
Confounding bias: if you do not adjust for the confounder
Literature
Hernan Miguel: causal inference from observational data requires prior causal assumptions or beliefs, which must be derived
from subject-matter knowledge, not from statistical associations detected in the data. We have used causal diagrams to
describe three possible sources of statistical association between two variables: cause and effect, sharing of common causes,
and calculation of the association within levels of a common effect. There is confounding when the association between
exposure and disease includes a noncausal component attributable to their having an uncontrolled common cause. There is
selection bias when the association between exposure and disease includes a noncausal component attributable to restricting
the analysis to certain level(s) of a common effect of expo-sure and disease or, more generally, to conditioning on a common
effect of variables correlated with exposure and disease. In either case, the exposed and the unexposed in the study are not
comparable, or exchangeable, which is the ultimate source of the bias. Statistical criteria are insufficient to characterize either
confounding or selection bias
Hernan Miguel: The potential outcomes approach, a quantitative counterfactual theory, describes conditions under which the
question can be answered affirmatively. This article reviews one of those conditions, known as consistency, and its implications
for real world decisions. Components of consistency: sufficiently well-defined interventions, linkage between interventions and
the data.
Julia Rohrer: Correlation does not imply causation; but often, observational data are the only option, even though the research
question at hand involves causality. To summarize, the practice of making causal inferences on the basis of observational data
depends crucially on awareness of potential confounders and meaningful statistical control (or noncontrol) that takes into
account estimation issues such as nonlinear confounding and measurement error. Back-door paths must be considered before
data are collected to make sure that all relevant variables are measured. In addition, variables that should not be controlled for
(i.e., colliders and media-tors) need to be considered. Causal inferences based on observational data require researchers to
make very strong assumptions. Researchers who attempt to answer a causal research question with observational data should
not only be aware that such an endeavor is challenging, but also understand the assumptions implied by their models and
communicate them transparently. In addition, instead of reporting a single model and championing it as “the truth,”
researchers should consider multiple potentially plausible sets of assumptions and see how assuming any of these scenarios
would affect their conclusions. Thus, causal inference based on observational data is not a lost cause per se—indeed, in
combination with additional knowledge from the relevant domain, highly convincing causal arguments can be made.
Wheelan Chapter 13 Program evaluation
Welcome to program evaluation, which is the process by which we seek to measure the causal
effect of some intervention – anything from a new cancer drug to a job placement program for
high school dropouts.
RCT – natural experiment (longer lives – education) - nonequivalent control (nonrandomized
treatment and control groups)
Wheelan Chapter 6 Problems with probability
A certain outcome makes a similar outcome in the future more likely
Assuming events are independent when they are not, not understanding when events ARE
independent, clusters happen (rare cancer among teenagers), reversion/regression to the mean,
, statistical discrimination (men pay more for auto insurance), the prosecutor's fallacy (there is a
darn good chance that he could be that random someone else, the one in a million guy whose
DNA just happens to be similar to the real killer's by chance. Because the chance of finding a
coincidental one in a million match are relatively high if you run the sample through a database
with samples from a million people)
Probability tells us what is more likely and what is less likely
Wheelan Chapter 7 The importance of data
We ask data to do one of three things: we may demand a sample that is representative of a
population, provide some source of comparison,
Publication bias: positive findings are more likely to be published than negative findings
Recall bias: patients recall more (diet, sports) than non-patients
Survivorship bias: you have a room of people with varying heights, forcing the short people to
leave will raise the average height, but it doesn't make anyone taller
Healthy user bias: people who take vitamins are not per se healthier because of the vitamins,
but because they are more occupied with their health
Workgroup
Case 1 The costs of COPD treatment. COPD (chronic obstructive pulmonary disease) is a progressive lung disease, which is
characterized by breathlessness, loss of energy, coughing, wheezing and sputum production. From time to time, many patients
experience a temporary worsening of their disease, which is called an exacerbation. A study investigates whether it is less
expensive to treat these exacerbations in the patient’s home instead of in the hospital. In the context of their study, patients and
their doctors decide where the treatment will take place. Some patients prefer the hospital, while others like to be treated at
home. Doctors do not find all patients equally suitable for home treatment. Several elements may play a role in the decision,
such as the patient’s age and sex, the severity of their lung problems at the start of treatment. The researchers record all those
elements for their patients. Furthermore, they determine their healthcare costs in the six weeks after the start of treatment.
These costs include contacts with homecare nurses, the general practitioner and the hospital, and the costs of medication. Given
that the study is not randomised, the researchers realise that they have to adjust their analysis to get unbiased estimates of the
cost difference between the two treatment options.
1. Re-visit the DAG language from lecture 1 and the literature. What is the meaning of the following
terms: path, backdoor path, causal path, confounding, collider, blocking and unblocking?
- A path is a route between exposure X and outcome Y. it does not have to follow the direction of
the arrows.
- A causal path follows the direction of the arrows. A backdoor path does not. X leads to Y.
- Backdoor path does not follow the arrows and is not causal.
- All paths are open unless arrows collide somewhere along the path. A collider blocks a path. This
is a backdoor path. Path does not contribute to association of exposure and outcome. Adjusting
for a collider opens the path, but you want it to stay a backdoor path. Otherwise, you would
open the backdoor path and generate an association.
- Open paths transmit association: the association of X and Y is the combination of all open paths
between them. An open path is blocked when we adjust for a variable along the path.
- Confounding: bias caused by a common cause of exposure and outcome
- Blocking: if you adjust for a confounder
- Unblock: if you adjust for a collider
2. In what circumstances do you draw an arrow in a DAG?
Draw an arrow in case of a causal relation. Draw an arrow if you are not sure it should not be there.
3. Explain the difference between selection bias (collider bias) and confounding.
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