Propensity Score Matching (PSM)

 

The multivariable scoring system is based on the value of the predictor variables to construct a PSM value.

On the other hand, it is the probability that subject with given characteristics will receive treatment or not.

To describe the propensity score, let the dichotomous (0,1) variable Z indicate treatment, and let X be the vector of available pretreatment covariates. The propensity score e(X) for an individual is defined as the conditional probability of being treated given his or her covariates X: e(X) = Pr(Z=1|X).

The propensity score is a one-dimensional variable that summarizes the multidimensional pretreatment covariates X. Among persons with a given propensity score, the distribution of the covariates X is on average the same among the treated and untreated.

v  Method:

Identify candidate predictors of the two treatments, perform a logistic regression where outcome will be two treatment, obtain a predicted probability of two treatments, this probability for each subject is the “PS” for each subject. Then we can use this score in few ways

Ø  Match A treatment patients to B treatment patients based on their PS (most often used) (we may do stratification of covariates based on PS)

o   Covariate balancing followed by table 1

o   Inefficient when large proportion of the samples cannot be matched

o   Rational same as Case-control studies

o   Remove confounding by matching factors

o   Matched cohort- match participants based on a close range of the PS, run unconditional regression instead of conditional one

 

Ø  Include PS as covariate in the model

o   May gain more power compared to including all the potential confounders in the model

o   But association between PS and outcome variable may modeled inappropriately

Ø  Standardize/weighting using PS

Weighting- weights the inverse of the PS,

▪ 1/ê(X), in treated patients

▪ 1/(1- ê(X)), in untreated patients

also known as inverse-probability-of-treatment weighted (IPTW) estimator

v  Main purpose of PSM:

Ø  Remove confounding by components of the score

Ø  Only fit 1 variable in the model instead of all the predictors of treatment separately

 

v  Use of PSM:

Ø  Stratification

In a sufficiently large sample, stratification on the PS alone balances the distribution of all the covariates in each stratum

 

Ø  Matching

Low PS= no treatment based on covariate history

High PS= get treatment based on covariate history

Limitation:

o   May loose too many subjects during the process

o   It’s difficult to match individual from the tails of the distribution because of lacking overlap of the PS between treated and untreated

Ø  Regression adjustment with the propensity score

Ø  Weighted regression adjustments

Ø  Restriction (less used)

Conclusion

Ø  In most studies that use “traditional” and propensity-score methods to control for confounding indicate very similar results- reassuring approach to control for confounding is different

Ø  Use of the propensity score to adjust for multiple confounders is “just” another tool, and not a universal remedy to adjust for confounding by indication

Ø  The interpretation of propensity score analyses depends on the underlying assumptions with respect to

o   residual confounding

o   effect modification

o   overlap in propensity score distributions between exposed and unexposed

note:

Confounding by Indication:

Confounding by indication is a special type of confounding that can occur in observational (non-experimental) pharmaco-epidemiologic studies of the effects and side effects of drugs. 

This type of confounding arises from the fact that individuals who are prescribed a medication or who take a given medication are inherently different from those who do not take the drug, because they are taking the drug for a reason. 

In medical terminology, such individuals have an "indication" for use of the drug. Even if the study population consists of subjects with the same disease, e.g., osteoarthritis, they may differ in the severity of their disease and may therefore differ in the need for medication. 

Aschengrau and Seage give the example of studies of the association between antidepressant drug use and infertility. The use of antidepressant medications may appear to be associated with an increased risk of infertility. However, depression itself is a known risk factor for infertility. As a result, there would appear to be an association between antidepressants and infertility. 

One way of dealing with this is to study the association in subjects who are receiving different treatments for the same underlying disease condition.

(Ref)

Further study

1. Kurth T, Walker AM, Glynn RJ, Chan KA, Gaziano JM, Berger K, Robins JM. Results of multivariable logistic regression, propensity matching, propensity adjustment, and propensity-based weighting under conditions of nonuniform effect. Am J Epidemiol. 2006 Feb 1;163(3):262-70. doi: 10.1093/aje/kwj047. Epub 2005 Dec 21. PMID: 16371515.

Summary of the above article:

Evaluate the effect of tissue plasminogen activator (t-PA) on death among 6,269 ischemic stroke patient (2000-2001) registered in German stroke registry (used 5 methods)

• 1      multivariable logistic regression
• 2      propensity score- based analysis
• 3      regression adjustment with PS
• 4      Two PS based weighted methods- TE on entire study population IPTW,
•           
• weighting methods estimates the treatment effect in a population whose distribution of risk factors is equal to that found in all study subjects.
• 5.       Another-SMR weights on treated population

Weighting method estimates the treatment effect in a population whose distribution of risk factors is equal to that found in the treated study subjects only.

 

Treatment (n=212, total= 6,269)

Crude= 3.35, Lowest- 1.11 (SMR weights), highest- 10.77 (IPTW)

Low PS= Risks of dying were high

Probable #question you may ask during the #exam:

I am interested in studying the treatment effect of a Watchman in patients with atrial fibrillation, and examining whether it protects against the risk of stroke in a population of patients 65 – 85 years of age. Information on the watchman is provided below. However, I am concerned about confounding by clinical and demographic factors including age, sex, prior stroke, prior transient ischemic attack, history of major bleed, high fall risk score (higher score associated with a higher risk of falling), and thromboembolic risk score (higher score associated with a higher risk of thromboembolism).

 

Please design a study that will use propensity score methods to control for these confounding factors. Please describe the source population; your study design; the study population you will use; the method by which you will use the propensity score to control for confounding; the analytic model you will use including the independent variable, dependent variable, and covariate(s) in the model; and your hypothesis about the association between the Watchman and stroke.

 

 

The Watchman is a small, permanent device that can be used to treat atrial fibrillation (AFib) by reducing the risk of blood clots and stroke: 

• What it does - The Watchman is implanted in the left atrial appendage (LAA), a small pouch in the heart's upper left chamber, to prevent blood clots from forming. 
• How it's used - A doctor inserts a catheter through a vein in the leg and guides the Watchman into the LAA. The device then gently expands to close off the LAA. 
• Who it's for - The Watchman is an alternative to blood thinners for patients with AFib who can't tolerate them or who have trouble taking them consistently. 
• Procedure - The Watchman procedure is minimally invasive and usually performed under general anesthesia. Patients typically stay overnight in the hospital. 
• Recovery -After the procedure, patients may need to take blood thinners for a period of time. They should also avoid strenuous activity and monitor the incision site for signs of infection. 

#Epidemiology #propensityscorematching #PSM