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Patient-reported outcome (PRO) measures are increasingly collected as a meansof measuring healthcare quality and value. The capability to predict suchmeasures enables patient-provider shared decision making and the delivery ofpatient-centered care. However, due to their voluntary nature, PRO measuresoften suffer from a high missing rate, and the missingness may depend on manypatient factors. Under such a complex missing mechanism, statistical inferenceof the parameters in prediction models for PRO measures is challenging,especially when flexible imputation models such as machine learning ornonparametric methods are used. Specifically, the slow convergence rate of theflexible imputation model may lead to non-negligible bias, and the traditionalmissing propensity, capable of removing such a bias, is hard to estimate due tothe complex missing mechanism. To efficiently infer the parameters of interest,we propose to use an informative surrogate that can lead to a flexibleimputation model lying in a low-dimensional subspace. To remove the bias due tothe flexible imputation model, we identify a class of weighting functions asalternatives to the traditional propensity score and estimate thelow-dimensional one within the identified function class. Based on theestimated low-dimensional weighting function, we construct a one-step debiasedestimator without using any information of the true missing propensity. Weestablish the asymptotic normality of the one-step debiased estimator.Simulation and an application to real-world data demonstrate the superiority ofthe proposed method.

Efficient surrogate-assisted inference for patient-reported outcome measures with complex missing mechanism