HCM Advanced Research Methods part 1: Quantitative methods (lectures/working groups)
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Course
Advanced Research Methods (GW4003MV)
Institution
Erasmus Universiteit Rotterdam (EUR)
Notes of the lectures and working groups from the first part of the course: advanced research methods. In this part the quantitative methods are discussed.
My exam grade: 7.8
Master Healthcare Management.
Quantitative methods – Advanced Research Methods – Joyce Rommens
Lecture 1: What is statistical adjustment and methods for statistical adjustment
Objectives segment 2:
- Introduction to causal inference
- Explain the potential outcomes approach in causal inference and apply it in thinking about causal effect
estimation
- Define causal effects
- Apply the concepts of consistency, positivity, and exchangeability in randomized and non-randomized settings
Causal inference: drawing conclusions about causation or estimating causal relationships. Statistical
inference uses data to address important questions; it tells what is likely and what is unlikely.
Statistical inference is the process by which the data speak to us, enabling us to draw meaningful
conclusions.
Terms used are from epidemiology. Epidemiology does not represent a body of knowledge. It is a
philosophy and methodology that can be applied to a very broad range of health problems. The art of
epidemiology is knowing when and how to apply the various strategies creatively to answer specific
health questions (how we can study what makes you ill) – may be applied to problems outside the
healthcare sector as well.
Common problems with causal effects (A leads to B):
1. Small sample size – whether this is a problem depends on the effect you are proving; when the
effect is very strong a small sample is enough (all study participants die after treatment), when the
effect is small a larger sample is desirable to have some certainty about what is going on. The data
sample needs to be representative of a larger group or population to have accurate estimates.
Easiest to do this to randomly select a subset of the population (every individual should have the
same chance to be in the sample).
2. Study performed or financed by a commercial company – not a problem when agreements exist
on what and how the results are published
3. No control group – for causal estimates you need to know what happened with the treatment,
and what would have happened without the treatment to predict what will happen (regression to
the mean problem; when having severe pain on day 1, it will probably be better on day 10). You need
the outcome of the treatment group and control group that are broadly similar (only differ in
treatment) and compare the two ® try to isolate the impact of one specific intervention.
We are not interested in the outcome per se, but in the role of the treatment
in achieving that outcome. When two outcomes differ and the only
difference between two groups is the treatment, the treatment has a causal
effect (causative or preventive) on the outcome.
Causation (Hernan/Robins): in and individual, a treatment has a causal effect
if the outcome under treatment 1 would be different from the outcome
under treatment 2.
Individual treatment effect is the difference in effects for one individual comparing the treatment
and not having the treatment when having both potential outcomes. Average treatment effect is
calculated from the individual treatment effects in the population.
For individuals, a causal inference cannot be observed as we only observe one potential outcome,
the counterfactual (what would have happened) cannot be observed ® missing data problem,
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, Quantitative methods – Advanced Research Methods – Joyce Rommens
observe only half of the outcomes ® fundamental problem in causal inference. The definition is
therefore not practically useful for individual causal effects.
Examples of causal language: affect, driver, interplay, impact, achieve, enhance, guarantee,
contribute. An author can warn against a causal interpretation, but that does not mean that their
actual goal is not causal.
Counterfactual outcome: potential outcome that is not observed because the subject did not
experience the treatment (‘counter the fact’).
Potential outcome Ya=1 is factual for some subject, and counterfactual for others.
Fundamental problem:
- Individual causal effect cannot be observed except under extremely strong (and generally
unreasonable) 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
Average causal effects can still be determined under three identifiability conditions to observe the
counterfactual:
1. Positivity (about the sample and the way it was composed; ‘positive probability’ of being assigned
to each of the treatment levels) ® what would have happened if.
® Observe what would have happened if, so you need to observe patients being assigned to all
relevant treatments; have a control group. Within these treatment groups patients should be
included for each confounder (for example smokers and non-smokers in treatment group and control
group) ® results for all treatment groups in all strata of the adjustment variable need to be available
to make the analysis possible.
- People with a lighter could also not have had a lighter and vice versa
- L’Oréal: 100% was assigned to the moisturizer, users could not not have used it
2. Consistency (define ‘if’ in what would have happened if: clear definition of treatments).
® The treatments (exposure) must be defined very clearly; clearly define the if. What is the
treatment and what is the without treatment ® precise enough until no meaningful vagueness
remains (need to specify the start and end of the intervention and the implementation of its
different components over time). This condition is crucial as causal effects can only be calculated for
very specified situations and research questions, but often overlooked.
- Hernan: does water kill? ® what do you mean by water? ® being specific!
- ‘How healthy is broccoli’ does not have an answer; what are you comparing it to? How much
broccoli?
3. Exchangeability ® it does not matter who gets treatment A and who gets
treatment B.
® The potential outcomes must be independent of the treatment that was received (𝑌𝑎 ⊥ A).
It must not matter who of the two treatment groups get treatment A and who get treatment B so
that the association can be ascribed to the treatment effect.
- Potential outcomes are independent of the treatment that was received
- Cigarette lighters (yes/no) is not exchangeable: smoking is involved
‘Observing’ the counterfactual: what would have happened? If the conditions are met, then
association of exposure and outcome is unbiased estimate of causal effect.
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, Quantitative methods – Advanced Research Methods – Joyce Rommens
If the three conditions are met, the association of the exposure and outcome is an unbiased estimate
of causal effect.
The three identifiability conditions are automatically met by using Randomized Controlled Trials
(RCT) (gold standard). As the selected patients are randomly assigned to the different treatment
groups and the treatment is clearly described. Often randomization cannot be used due to practical
or ethical considerations (smoking, having children). Besides, there is limited generalizability
(external validity) due to treatment protocol and different patients in the sample from outside the
sample. Observational studies have real world outcomes (compared to those from the RCT in an
artificial setting). However, the internal validity is threatened as exchangeability is not guaranteed
(incomparability between two groups). Positivity and consistency need the explicit attention in
observational studies. Observational studies are commonly used when it is not possible to randomly
divide the sample into different groups (for example women with children and without children)
Stratification: divide a sample in different groups according to the value of one variable.
Meeting the conditions: RCT
- Select patients
- Randomly assign them to treatment groups
¨ Random: exchangeability
¨ Random: positivity
¨ Defining interventions: consistency
RCT Observational studies
Limited generalizability (external validity) Real-world outcomes
due to treatment protocol and patient
selection
Practical, ethical considerations Availability of data
Internal validity threatened by lack of exchangeability
Positivity and consistency need explicit attention
Tentamentraining:
RCT Observational
Participants randomly assigned to groups Participants not randomized
Similar in groups Effects in real life
Minimizes risk of internal validity Lack of internal validity
because of lack of
exchangeability
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, Quantitative methods – Advanced Research Methods – Joyce Rommens
Limited generalizability (external validity) Overall ‘good’ generalizability
® If you have poor internal validity, you mostly have good external validity.
® With RCT you minimize the risk of ‘random noise’ that influences the experience (internal validity).
However, this is a risk for the generalizability. You don’t know if people do/react the same outside of
the laboratory.
Objectives segment 3:
- Using graph theory to achieve exchangeability
- Using directed acyclic graphs in the design and evaluation of an analysis
- Rules and terms of DAG
- Applying the concepts of confounder, confounding (traditional and structural)
Association does not equal causation.
- Association: statistical relationship
- Causation: difference between potential outcomes
We need: theory/subject knowledge and causal structure. We design the analysis accordingly.
To meet the exchangeability condition, statistical adjustments can be made. Statistical adjustments
remove the effect of a variable by adjusting for it (including it in the regression model etc.) making an
estimation of the causal effect of the exposure on the outcome in the absence of confounding effects
possible (called conditioning for DAG). In case no effect is found in the adjusted association while it is
in the unadjusted, the effect runs via other variables.
Stratification/selection – dividing members of the population into homogeneous subgroups (strata)
before sampling (only analyze smokers with and without a cigarette lighter). Unadjusted results may
imply a relationship that does not exist when stratifying the groups. This is an only possibility when
having a small number of factors (confounders) that are categorized. The advantage is that it is easy
and intuitively interpretable.
- Matching – for every treated patient you find one non- treated patient with similar
observable characteristics against whom the effect of the treatment can be assessed.
- Weighting – reduce the bias in the survey estimates by giving weights to patients in the data
to reflect that patient’s importance relative to the other patients. The number of patients in
the sample that have certain characteristics are decreased so that the sample is more
representative of the target population.
- Regression analysis – adjust for several covariates (confounders) at the same time; you need
to think about what to adjust for. It is relatively easy to use when having access to the
software, but hard to use as well as when making mistakes the results can be biased. More is
not always better in this case. There are different ways to select the variables you adjust for.
- Correlation matrix – look at correlations with all the covariates available in the
dataset.
§ When variables are significantly associated with the outcome, they are
included in the regression model. This is a bad method.
- Stepwise backward selection – start with a regression model that includes all the
covariates and
§ remove the variable that is the least statistically significant and important,
§ then run the model again etc. the variables should be retained if removal
leads to substantial change in the effect estimate as leaving it out leads to
confounding.
- Adjust for confounders – what could be confounders?
§ Confounders are associated with the exposure,
§ conditionally associated with the outcome given the exposure and
§ not in the causal pathway between exposure and outcome.
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