ArXiv Preprint
Convolutional neural networks (CNN) have been successful in machine learning
applications. Their success relies on their ability to consider space invariant
local features. We consider the use of CNN to fit nuisance models in
semiparametric estimation of the average causal effect of a treatment. In this
setting, nuisance models are functions of pre-treatment covariates that need to
be controlled for. In an application where we want to estimate the effect of
early retirement on a health outcome, we propose to use CNN to control for
time-structured covariates. Thus, CNN is used when fitting nuisance models
explaining the treatment and the outcome. These fits are then combined into an
augmented inverse probability weighting estimator yielding efficient and
uniformly valid inference. Theoretically, we contribute by providing rates of
convergence for CNN equipped with the rectified linear unit activation function
and compare it to an existing result for feedforward neural networks. We also
show when those rates guarantee uniformly valid inference. A Monte Carlo study
is provided where the performance of the proposed estimator is evaluated and
compared with other strategies. Finally, we give results on a study of the
effect of early retirement on hospitalization using data covering the whole
Swedish population.
Mohammad Ghasempour, Niloofar Moosavi, Xavier de Luna
2023-01-27
