Data Integration through outcome adaptive LASSO and a collaborative propensity score approach

Administrative data, or non-probability sample data, are increasingly being used to obtain official statistics due to their many benefits over survey methods. In particular, they are less costly, provide a larger sample size, and are not reliant on the response rate. However, it is difficult to obtain an unbiased estimate of the population mean from such data due to the absence of design weights. Several estimation approaches have been proposed recently using an auxiliary probability sample which provides representative covariate information of the target population. However, when this covariate information is high-dimensional, variable selection is not a straight-forward task even for a subject matter expert. In the context of efficient and doubly robust estimation approaches for estimating a population mean, we develop two data adaptive methods for variable selection using the outcome adaptive LASSO and a collaborative propensity score, respectively. Simulation studies are performed in order to verify the performance of the proposed methods versus competing methods. Finally, we presented an anayisis of the impact of Covid-19 on Canadians.