Statistical inference for case-control logistic regression via integrating external summary data

• URL: http://arxiv.org/abs/2405.20655v1
• Date: Fri, 31 May 2024 07:47:38 GMT
• Title: Statistical inference for case-control logistic regression via integrating external summary data
• Authors: Hengchao Shi, Xinyi Liu, Ming Zheng, Wen Yu,
• Abstract summary: Case-control sampling is a commonly used retrospective sampling design to alleviate imbalanced structure of binary data. An empirical likelihood based approach is proposed to make inference for the logistic model by incorporating the internal case-control data and external information.
• Score: 8.369377566749202
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: Case-control sampling is a commonly used retrospective sampling design to alleviate imbalanced structure of binary data. When fitting the logistic regression model with case-control data, although the slope parameter of the model can be consistently estimated, the intercept parameter is not identifiable, and the marginal case proportion is not estimatable, either. We consider the situations in which besides the case-control data from the main study, called internal study, there also exists summary-level information from related external studies. An empirical likelihood based approach is proposed to make inference for the logistic model by incorporating the internal case-control data and external information. We show that the intercept parameter is identifiable with the help of external information, and then all the regression parameters as well as the marginal case proportion can be estimated consistently. The proposed method also accounts for the possible variability in external studies. The resultant estimators are shown to be asymptotically normally distributed. The asymptotic variance-covariance matrix can be consistently estimated by the case-control data. The optimal way to utilized external information is discussed. Simulation studies are conducted to verify the theoretical findings. A real data set is analyzed for illustration.

Related papers

• Deep non-parametric logistic model with case-control data and external summary information [2.524439717544601]
  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.
  arXiv  Detail & Related papers  (2024-09-03T12:23:09Z)
• Geometry-Aware Instrumental Variable Regression [56.16884466478886]
  We propose a transport-based IV estimator that takes into account the geometry of the data manifold through data-derivative information. We provide a simple plug-and-play implementation of our method that performs on par with related estimators in standard settings.
  arXiv  Detail & Related papers  (2024-05-19T17:49:33Z)
• Efficient semi-supervised inference for logistic regression under case-control studies [3.5485531932219243]
  We consider an inference problem in semi-supervised settings where the outcome in the labeled data is binary. Case-control sampling is an effective sampling scheme for alleviating imbalance structure in binary data. We find out that with the availability of the unlabeled data, the intercept parameter can be identified in semi-supervised learning setting.
  arXiv  Detail & Related papers  (2024-02-23T14:55:58Z)
• Extrapolation-Aware Nonparametric Statistical Inference [8.090257544386482]
  Extrapolating occurs in many data analysis applications and can invalidate the resulting conclusions if not taken into account. We extend the nonparametric statistical model to explicitly allow for extrapolation and introduce a class of extrapolation assumptions.
  arXiv  Detail & Related papers  (2024-02-15T07:16:50Z)
• Bayesian Federated Inference for regression models based on non-shared multicenter data sets from heterogeneous populations [0.0]
  In a regression model, the sample size must be large enough relative to the number of possible predictors. Pooling data from different data sets collected in different (medical) centers would alleviate this problem, but is often not feasible due to privacy regulation or logistic problems. An alternative route would be to analyze the local data in the centers separately and combine the statistical inference results with the Bayesian Federated Inference (BFI) methodology. The aim of this approach is to compute from the inference results in separate centers what would have been found if the statistical analysis was performed on the combined data.
  arXiv  Detail & Related papers  (2024-02-05T11:10:27Z)
• Approximating Counterfactual Bounds while Fusing Observational, Biased and Randomised Data Sources [64.96984404868411]
  We address the problem of integrating data from multiple, possibly biased, observational and interventional studies. We show that the likelihood of the available data has no local maxima. We then show how the same approach can address the general case of multiple datasets.
  arXiv  Detail & Related papers  (2023-07-31T11:28:24Z)
• Learning to Bound Counterfactual Inference in Structural Causal Models from Observational and Randomised Data [64.96984404868411]
  We derive a likelihood characterisation for the overall data that leads us to extend a previous EM-based algorithm. The new algorithm learns to approximate the (unidentifiability) region of model parameters from such mixed data sources. It delivers interval approximations to counterfactual results, which collapse to points in the identifiable case.
  arXiv  Detail & Related papers  (2022-12-06T12:42:11Z)
• MINIMALIST: Mutual INformatIon Maximization for Amortized Likelihood Inference from Sampled Trajectories [61.3299263929289]
  Simulation-based inference enables learning the parameters of a model even when its likelihood cannot be computed in practice. One class of methods uses data simulated with different parameters to infer an amortized estimator for the likelihood-to-evidence ratio. We show that this approach can be formulated in terms of mutual information between model parameters and simulated data.
  arXiv  Detail & Related papers  (2021-06-03T12:59:16Z)
• Leveraging Global Parameters for Flow-based Neural Posterior Estimation [90.21090932619695]
  Inferring the parameters of a model based on experimental observations is central to the scientific method. A particularly challenging setting is when the model is strongly indeterminate, i.e., when distinct sets of parameters yield identical observations. We present a method for cracking such indeterminacy by exploiting additional information conveyed by an auxiliary set of observations sharing global parameters.
  arXiv  Detail & Related papers  (2021-02-12T12:23:13Z)
• On Disentangled Representations Learned From Correlated Data [59.41587388303554]
  We bridge the gap to real-world scenarios by analyzing the behavior of the most prominent disentanglement approaches on correlated data. We show that systematically induced correlations in the dataset are being learned and reflected in the latent representations. We also demonstrate how to resolve these latent correlations, either using weak supervision during training or by post-hoc correcting a pre-trained model with a small number of labels.
  arXiv  Detail & Related papers  (2020-06-14T12:47:34Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.