Can the exposure-response relationship estimated within each subgroup, generated by using "partykit", have causal interpretation?
Yes, but it may need additional work.
If the data come from a randomized controlled trial, then fitting a treatment-response model in every subgroup has the same type of causal interpretation it has in the full sample.
However, in observational data, it is necessary to first estimate the propensity of treatment (i.e., the probability of treatment given the regressors) and use that in the treatment-response model in every subset. This is also known as "local centering" of the treatment indicator. Additionally, local centering of the dependent response variable may improve the performance of the model further.
See Dandl et al. (2022) for more details and comparisons. For the setup in randomized controlled trials, there is also a dedicated interface package model4you that facilitates fitting "personalized" treatment-response models using trees and random forests. See the Seibold et al. publications for details on the software and underlying methods.
Susanne Dandl, Torsten Hothorn, Heidi Seibold, Erik Sverdrup, Stefan Wager, Achim Zeileis (2022). “What Makes Forest-Based Heterogeneous Treatment Effect Estimators Work?.” arXiv:2206.10323, arXiv.org E-Print Archive. doi:10.48550/arXiv.2206.10323
Heidi Seibold, Achim Zeileis, Torsten Hothorn (2019). “model4you: An R Package for Personalised Treatment Effect Estimation.” Journal of Open Research Software, 7(17), 1-6. doi:10.5334/jors.219
Heidi Seibold, Achim Zeileis, Torsten Hothorn (2018). “Individual Treatment Effect Prediction for Amyotrophic Lateral Sclerosis Patients.” Statistical Methods in Medical Research, 27(10), 3104-3125. doi:10.1177/0962280217693034
Heidi Seibold, Achim Zeileis, Torsten Hothorn (2016). “Model-Based Recursive Partitioning for Subgroup Analyses.” The International Journal of Biostatistics, 12(1), 45-63. doi:10.1515/ijb-2015-0032