- Read the references given in the Theory and Notation section below
- Fire up the Jupyter Notebook judeas-rx.ipynb
The notebook draws the GUI (graphical user interface) shown in the above jpg. By playing with this GUI, you should be able to easily figure out how to use it. If something isn't clear, read the FAQ file.
The above jpg shows the entire GUI. There aren’t any other windows to the app. It’s a single window app. The app is written in Python and runs inside a Jupyter notebook. The controls that you see are coded using ipywidgets. The bar graphs change as the sliders move.
The app considers the simple yet illustrative case of trying to prescribe a medicine differently for male versus female patients. The Rx is based on probabilities called PNS, PN and PS and an expected utility function called EU that were invented by Pearl and coworkers.
To do a Rx, one first allows the patients to take or not take the drug, according to their own discretion. Then one conducts a survey in which one collects info about who did or did not take the drug and whether they lived or died. This is called Observational Data (OD). Even though OD can be confounded, it serves to impose bounds on PNS, PN, PS and EU. After the OD stage is completed, one can follow it up with a RCT (Randomized Control Experiment). In a RCT, patients must take or not take the drug as ordered by the doctor; no insubordination is tolerated. From the RCT, one collects Experimental Data (ED). The ED imposes tighter bounds on PNS, PN, PS and EU than the bounds imposed by the OD alone.
The above GUI handles just two strata, male and female, but JudeasRx can handle any number n >= 2 of strata (strata=Z values, where Z is a confounder.) JudeasRx doesn't have a GUI for more than two strata. Instead of using sliders for input, it uses either Python dictionaries or csv files as input. You can read the doc strings attached to the Python code to learn how to use that part of JudeasRx. A Jupyter notebook with an example with 3 strata is provided.
So far, we have described only how JudeasRx can calculate analytically bounds for PNS, PN and PS, for very broad classes of DAGs (directed acyclic graphs), for an arbitrary number of strata. If one assumes a specific DAG, those bounds can be made tighter. JudeasRx can also calculate stochastically bounds for PNS, PN and PS, for a specific DAG, for an arbitrary number of strata. It does this using the very mature Python library for doing MCMC (Markov Chain Monte Carlo), PyMC3. A Jupyter notebook with an example of this is provided.
As an added bonus, JudeasRx contains software that allows you to check whether a query Q = P(y|do(X)=x, c) is Pearl-identifiable for a specific DAG. Jupyter notebooks verifying Pearl's backdoor and frontdoor adjustment formulae using our "Identifiability Checker" are provided.
The mathematical theory and notation are described in gory but entertaining detail in the chapters entitled “Personalized Treatment Effects” and "Personalized Expected Utility" of my book Bayesuvius. Those chapters are totally based on a paper by Tian and Pearl and later work by Pearl, Li and Mueller. My only contribution (?) was to change the notation to a more “personalized” notation. Bayesuvius is my free, open source book (about 570 pages so far) on Bayesian Networks and Causal Inference.