Data integration with high dimensionality

Abstract

SummaryWe consider situations where the data consist of a number of responses for each individual, which may include a mix of discrete and continuous variables. The data also include a class of predictors, where the same predictor may have different physical measurements across different experiments depending on how the predictor is measured. The goal is to select which predictors affect any of the responses, where the number of such informative predictors tends to infinity as the sample size increases. There are marginal likelihoods for each experiment; we specify a pseudolikelihood combining the marginal likelihoods, and propose a pseudolikelihood information criterion. Under regularity conditions, we establish selection consistency for this criterion with unbounded true model size. The proposed method includes a Bayesian information criterion with appropriate penalty term as a special case. Simulations indicate that data integration can dramatically improve upon using only one data source.

Doubly Robust Inference when Combining Probability and Non-Probability Samples with High Dimensional Data

“…There is a large literature on variable-selection methods for prediction, but little work on variable selection for data integration that can successfully recognize the strengths and the limitations of each source of data and utilize all information captured for finite population inference. Gao and Carroll (2017) proposed a pseudolikelihood approach to combining multiple non-survey data with high dimensionality; this approach requires that all likelihoods are correctly specified and therefore is sensitive to model misspecification. Chen, Valliant and Elliott (2018) proposed a model-based calibration approach using lasso regression; this approach relies on a correctly specified outcome model.…”

A surrogateℓ0sparse Cox's regression with applications to sparse high‐dimensional massive sample size time‐to‐event data

“…Since BAR aims to approximate ℓ 0 ‐penalized regression, it directly provides a surrogate optima to some popular information criteria with some prefixed λ n . For example, performing BAR with for some c >0 leads to a surrogate optima for the directly optimizing the extended BIC . For thoroughness, in addition to using a 25‐value grid for c , we also include simulation results in Table for BAR with some prefixed values and .…”

“…For example, performing BAR with n = c log(p n ) for some c > 0 leads to a surrogate optima for the directly optimizing the extended BIC. [44][45][46] For thoroughness, in addition to using a 25-value grid for c, we also include simulation results in Table 1 for BAR with some prefixed values n = 0.5 log(p n ) and n = log(p n ). Not surprisingly, BAR with these prefixed values produced sometimes slightly suboptimal, but generally comparable estimation and selection performance.…”

Integration of Survival and Binary Data for Variable Selection and Prediction: A Bayesian Approach

“…For the tumour samples in the CGA there are two experiments with survival outcome and disease status as the responses whereas the predictors are the same. In this situation, because of the reasons that were indicated in Gao and Carroll (), some kind of data integration is necessary to achieve better survival prediction by integrating both of the measurements. Towards this objective, we develop a joint survival and binary model using the latent variables.…”

“…On the basis of the idea of group variable regularization, Gao and Carroll () proposed a data integration method in high dimensional settings, which accommodates multiple responses from the same set of covariates. Parameter estimation is achieved via maximizing a pseudolikelihood.…”