{"id":9576,"date":"2023-01-03T13:54:55","date_gmt":"2023-01-03T12:54:55","guid":{"rendered":"https:\/\/www.iese.fraunhofer.de\/blog\/?p=9576"},"modified":"2024-02-26T10:56:55","modified_gmt":"2024-02-26T09:56:55","slug":"causal-inference","status":"publish","type":"post","link":"https:\/\/www.iese.fraunhofer.de\/blog\/causal-inference\/","title":{"rendered":"Causal inference: An introduction on how to separate causal effects from spurious correlations in data"},"content":{"rendered":"

What is causal inference in statistics data science? While „correlation does not imply causation“, it is possible to identify causal effects even in data that does not come from randomized controlled trials. Our AI expert, Dr. Julien Siebert, just published a paper on the applications of statistical causal inference in software engineering<\/a>. In this Fraunhofer IESE blog post, he gives an introduction to the topic of causal inference, its benefits, its limitations, and other pointers to deepen our readers‘ knowledge of this topic.<\/p>\n

In general, the best way to measure the causal effect of an action („a treatment“) on a system of interest („the outcome“) is to perform a randomized controlled trial.<\/p>\n

However, in many cases, performing such a controlled experiment is not possible (for practical or ethical reasons). In such cases, analysts are then left with so-called „observational data“; i.e., data that has been gathered in an uncontrolled setting.<\/p>\n

The problem with such data is that the observed effect might be due to different factors: some truly causal ones, and some others due to unrelated correlation (a.k.a. spurious correlation).<\/p>\n

\"An
An example of (easily detectable) spurious correlation. Source https:\/\/www.tylervigen.com\/spurious-correlations<\/a><\/figcaption><\/figure>\n

Finding methods for separating the wheat (causal effects) from the chaff (spurious correlations), that is, identifying causal effects from the nets of spurious correlations, has been the focus of researchers in the field of causal inference such as Judea Pearl and colleagues (Pearl & Mackenzie 2018; Pearl, Glymour & Jewell 2016).<\/p>\n

In this blog post, I will present a short introduction to the topic of causal inference.<\/p>\n

Example: Simpson’s paradox<\/h2>\n

One important thing to realize is that, contrary to widespread belief in data science, data cannot speak for itself. Or at least, in some cases known as statistical paradoxes, data can be interpreted in completely opposite directions, especially if the underlying assumptions about how the data was generated are not explicit.<\/p>\n

The typical example, often used in many textbooks on causal inference, is Simpson’s paradox (Pearl 2013), illustrated in the figure below.<\/p>\n

\"Causal<\/a>
An illustration of Simpson’s paradox (source Wikipedia<\/a>). Analyzing the whole population (black) or the different groups (colors) separately leads to opposite interpretations. The whole population shows a negative effect of X on Y, whereas for each group, the effect of X on Y is positive.<\/figcaption><\/figure>\n

Modeling causal assumptions<\/h2>\n

In order to solve the paradox, it is necessary to make some assumptions explicit. In our example, if gender influences treatment uptake (e.g., if men are more likely to take the drug) and if gender also influences recovery (e.g., if women have lower blood pressure), then gender is a so-called confounder. In this case, it is necessary to analyze the data separately for the different genders.<\/p>\n

Modeling these causal hypotheses is the first step in causal inference. Typically, these assumptions take the form of a causal graph, where nodes represent variables, links represent potential direct causal effects, and no link represents the strong hypothesis that there is no direct effect between the variables.<\/p>\n

\"A
An example of a causal graph made up of three nodes: gender, treatment (drug), outcome (healthy). The gender node (red) has an influence on both the treatment and the outcome. It is a confounder. Graph and colors from DAGitty<\/a>.<\/figcaption><\/figure>\n

One of the good things about having such a representation (apart from making causal hypotheses explicit) is that it is technically possible to try to falsify it by assessing which variables have to be independent in the data.<\/p>\n

\"a
In this graph, blood pressure and gender are statistically independent given a specific treatment. This can be directly measured in the data in order to check whether the model is valid. Graph and colors from DAGitty<\/a>. Note that the model also implies a second conditional independence: Treatment and outcome are statistically independent given a specific pair of blood pressure and gender.<\/figcaption><\/figure>\n
<\/div>\n

\u00a0Identifying whether causal effect can be computed from data<\/h2>\n

The graphical structure helps to disentangle correlations from causality. Through the application of a causal identification method called the do-calculus (Pearl, 2012), it is possible to decide whether we can measure causal effect from observational data and how the data needs to be analyzed. Going back to Simpson’s paradox, the application of the do-calculus can tell us whether we should analyze the data separately for each gender or whether we should analyze it for the whole population. Technically, the do-calculus involves the concepts of d-separation as well as backdoor and frontdoor criteria, which are beyond the scope of this blog post (the interested reader can jump to the pointers section below), but luckily for us, the do-calculus has been implemented in libraries such as DoWhy<\/a> or DAGitty<\/a>, and identification can be easily automated.<\/p>\n

\"A
In this graph, in order to measure the causal effect of the treatment on the outcome, it is necessary to „adjust for“ gender, i.e., to analyze the data separately for each gender. The DAGitty<\/a> library directly provides a list of variables that need to be „adjusted for“ and colors the spurious correlation paths in red.<\/figcaption><\/figure>\n

Estimating causal effects from data<\/h2>\n

Once a causal effect has been identified, the next step is to estimate that effect using the available data. This is where Machine Learning comes into play. Note that we are not talking about classical Machine Learning algorithms, but about algorithms dedicated to the estimation of causal effects, such as TARNet, T-learner, or X-learner (the adventurous reader can refer to chapter 7 of Brady Neal’s lecture Introduction to Causal Inference <\/span>from a Machine Learning Perspective<\/span><\/a>). Again, several implementations are available: Besides DoWhy, which was already mentioned above, CausalML<\/a> is also worth a look.<\/p>\n

Refutation: challenging the effect found<\/h2>\n

Now that a causal effect has been both identified and estimated, how can we trust our results? In science, ultimately, we can never prove that a causal effect is true. We can only try to falsify it. Here, it is interesting to take a look at the DoWhy<\/a> library and the proposed refutation methods<\/a>. Here are some methods for illustration:<\/p>\n