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AI for Medicine
Intermediate
Topics
Computer Vision
Deep Learning
Evaluation and Monitoring
Generative Models
NLP
These functions will be learned by models called base learners, and we can choose what we want them to be. You've learned about decision trees before, and how they can capture non-linear relationships in data. The base learner can also be a linear model, or we can have two different models for the two different learners. Each of these models can learn using different parts of the randomized control trial data. mu 1 is learned from patients, who are assigned to the treatment arm, that's Wi of 1, using age and blood pressure as the inputs, and Y as the desired output. Similarly, mu 0 is learned from patients, who are assigned to the control arm, use age and BP as the inputs once again, and Y is the output. To train one of these models, we can divide up the data set into a training set and a validation set. Notice that these mu hat models are actually prognostic models, like you learned about in course 2, where mu 1 is a prognostic model giving us the risk of an adverse event for when treatment equals 1, while mu hat of 0 would be the prognostic model giving us the risk of the adverse event for when treatment equals 0. If you picked a decision tree for the base learners, then you might learn models that look like the following. Notice that both models are using blood pressure and age to output a risk score. We can see how we can use these models to now estimate the treatment effect for a new patient. For a patient who is 56 years of age and has a blood pressure of 130, we can get their expected risk using MU hat 1 under treatment. So, we see that the blood pressure is smaller than 140, and we see that the age is smaller than 60, so we have a risk score of 0.21. On the right side, we see for this patient, age is smaller than 60 and blood pressure is smaller than 160, so we output a risk score of 0.45. Now, we can subtract the two to give us the conditional average treatment effect for this patient, given their features. This is going to be 0.21 minus 0.45, which is negative 0.24. The method of using these two models, MU hat 1 and MU hat 0, and taking the difference between these two estimates to estimate the conditional average treatment effect, is called the two-tree method, or the T-Learner.
