Deep non-parametric logistic model with case-control data and external summary information

• URL: http://arxiv.org/abs/2409.01829v1
• Date: Tue, 3 Sep 2024 12:23:09 GMT
• Title: Deep non-parametric logistic model with case-control data and external summary information
• Authors: Hengchao Shi, Ming Zheng, Wen Yu,
• Abstract summary: The case-control sampling design serves as a pivotal strategy in mitigating the imbalanced structure observed in binary data. We consider the estimation of a non-parametric logistic model with the case-control data supplemented by external summary information.
• Score: 2.524439717544601
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: The case-control sampling design serves as a pivotal strategy in mitigating the imbalanced structure observed in binary data. We consider the estimation of a non-parametric logistic model with the case-control data supplemented by external summary information. The incorporation of external summary information ensures the identifiability of the model. We propose a two-step estimation procedure. In the first step, the external information is utilized to estimate the marginal case proportion. In the second step, the estimated proportion is used to construct a weighted objective function for parameter training. A deep neural network architecture is employed for functional approximation. We further derive the non-asymptotic error bound of the proposed estimator. Following this the convergence rate is obtained and is shown to reach the optimal speed of the non-parametric regression estimation. Simulation studies are conducted to evaluate the theoretical findings of the proposed method. A real data example is analyzed for illustration.

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