Tutorials : assumption of propensity scores
The hypothesis of positivity, similar to the ambivalence clause in clinical trials (each exposed individual could have been unexposed, and vice versa for ATE), can be evaluated graphically (the distributions of the two propensity scores should overlap). In case of violation, a restriction of the studied population may be necessary to ensure that all included patients could be exposed and not exposed.
The positivity
Comparability of the exposed and non-exposed patients
In the pseudo-sample obtained after weighting, the standardized differences of the baseline characteristics of the two groups should be small. A commonly accepted threshold is 10% (Austin & Stuart 2015).
It is necessary that all the levels of confounders are represented in the exposure and non-exposure groups.
It can be checked by the absence of extreme weights, i.e. values close to 0 or more than 5. Moreover, the mean of weights must be close to 1.
Complementary, in ATE, one can verify that the sum of the weights is approximately equal to the size of the initial sample.
The possible exposition or non-exposition for all included individuals
