LAUSR

Logistic regression is a popular method that is used for estimating causal effects in observational studies using propensity scores.We examine the use of deep learning models such as the deep neural network (DNN), PropensityNet (PN), convolutional neural network (CNN), and convolutional neural network-long short-term memory network (CNN-LSTM)) to estimate propensity scores and evaluate causal inference. Deep learning models, unlike logistic regression, do not depend on assumptions regarding (i) how variables are selected, (ii) specification of the correct functional form, (iii) statistical distributions of the variables, and (iv) interactions are specified. If these assumptions are not met when using logistic regression, one may obtain biased estimates of treatment effects due to not achieving covariate balance. We conducted studies using simulated data with different sample sizes (N = 500, N = 1000, N = 2000), 15 covariates, a continuous outcome and a binary exposure. These data were used in seven scenarios that were different in the degree of nonlinearity and non-additivity associations between the exposure and covariates. The estimation of propensity scores was considered as a classification task, and performance metrics that included the classification accuracy, the receiver operating characteristic curve area under the curve (AUCROC), the covariate balance, the standard error, the absolute bias, and the 95% confidence interval coverage were evaluated for each model. Overall, CNN and CNN-LSTM achieved good results for covariate balance, classification accuracy, AUCROC, and Cohen’s Kappa. Logistic regression provided substantially better bias reduction, but it had subpar performance based on classification accuracy, AUCROC, Cohen’s Kappa, and 95% confidence interval coverage. The results suggest that deep learning methods, especially CNN, may be useful for estimating propensity scores that are used to estimate causal effects.