Method for estimating causal effect of continuous treatment on binary outcome

[zhenyu-bolt]

Hi there,
I came across this book online. It suggests against using double machine learning or instrumental variable to estimate causal effect when treatment or outcome is binary.
Therefore, I wonder if any of the method provided in dowhy package is suitable at estimating the causal effect of continuous treatment variable on binary outcome.

[amit-sharma]

Yeah, discrete outcomes are typically difficult for causal inference because you need some kind of transformation to interpret the results (e.g., log-odds).
If you have a binary outcome, I would suggest considering it as a continuous variable between 0 and 1. That usually leads to good results and interpreting the result is also easy. If your causal effect is c, then it means that increasing the treatment by one unit increases the probability of outcome=1 by c (of course, you can fit your estimator in a way such that it does not output negative or >1 values).

If you really want to go with binary outcome, then (logistic) regression in dowhy (See GLM) or metalearners may be a good bet.

[GladysKao]

Hello, I am learning causal machine, and I have the same problem. In my dataset, treatment is continuous and outcome is binary. I see your comment, can I directly use the model in dowhy to estimate the causal effect? Then interpret the results as increasing the probability of making ouecome=1 and avoiding the use of more complex GLM models? I try this in my dataset, if I directly use the "backdoor.linear_regression method", the results seem normal, and no strange result.

[GladysKao]

Hi I tried to use LR and GLM in my dataset, then get the very similar estimate (LR is 0.037289, GLM is 0.037245)but very different P-Value(one is 0.165 and other one is 0.075) .besides, GLM takes much more time than LR. So I think LR is also suitable at estimating the causal effect of continuous treatment variable on binary outcome. To get similar estimates in less time.