The Positivity Assumption

Categories → Study Design , Data , Causal Inference , Validation

The validity of Causal Inference results depends on an assumption about the data, known as Positivity.

What is Positivity?

The positivity assumption, also known as the "positivity condition" or "common support assumption," is an important concept in causal inference. Remember, Causal inference is the process of drawing conclusions about the causal relationships between variables based on observed data.

Why is it important?

The positivity assumption is a fundamental assumption that is necessary for causal inference methods to produce unbiased and meaningful results. It states that, in the observed data, there must be a non-zero probability of every individual or unit receiving any level of the treatment or exposure variable. In other words, there should be some diversity in the treatment assignment across the study population.

This assumption ensures that there are individuals in the study with different characteristics who both receive and do not receive the treatment. If the positivity assumption is violated, meaning that certain groups have no chance of receiving the treatment, it can lead to issues such as model instability, biased estimates, or difficulty in generalizing the study findings to a broader population.

How can I check Positivity?

Researchers often check for positivity during the study design phase and may need to make adjustments or choose different statistical methods if the assumption is not met. Common methods for assessing positivity include examining the distribution of covariates across treatment groups and using propensity score models to ensure that there is overlap in the propensity scores between treated and untreated groups (propensity distribution analysis). Causal Wizard provides both these checks when you choose a Propensity Score method for your analysis.

Here is an example of a propensity score distribution plot from CausalWizard, broken down by Treated and Control groups so that you can verify both groups are present for all propensity values:

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