Propensity score analysis with missing data using a multi-task neural network

Propensity score analysis is increasingly used to control for confounding factors in observational studies. Unfortunately, unavoidable missing values make estimating propensity scores extremely challenging. We propose a new method for estimating propensity scores in data with missing values. Both simulated and real-world datasets are used in our experiments. The simulated datasets were constructed under 2 scenarios, the presence (T = 1) and the absence (T = 0) of the true effect. The real-world dataset comes from LaLonde's employment training program. We construct missing data with varying degrees of missing rates under three missing mechanisms: MAR, MCAR, and MNAR. Then we compare MTNN with 2 other traditional methods in different scenarios. The experiments in each scenario were repeated 20,000 times. Our code is publicly available at https://github.com/ljwa2323/MTNN . Under the three missing mechanisms of MAR, MCAR and MNAR, the RMSE between the effect and the true effect estimated by our proposed method is the smallest in simulations and in real-world data. Furthermore, the standard deviation of the effect estimated by our method is the smallest. In situations where the missing rate is low, the estimation of our method is more accurate. MTNN can perform propensity score estimation and missing value filling at the same time through shared hidden layers and joint learning, which solves the dilemma of traditional methods and is very suitable for estimating true effects in samples with missing values. The method is expected to be broadly generalized and applied to real-world observational studies.