Individual Data Protected Integrative Regression Analysis of High-Dimensional Heterogeneous Data

Abstract

Evidence-based decision making often relies on meta-analyzing multiple studies, which enables more precise estimation and investigation of generalizability. Integrative analysis of multiple heterogeneous studies is, however, highly challenging in the ultra high-dimensional setting. The challenge is even more pronounced when the individual-level data cannot be shared across studies, known as DataSHIELD contraint. Under sparse regression models that are assumed to be similar yet not identical across studies, we propose in this paper a novel integrative estimation procedure for data-Shielding High-dimensional Integrative Regression (SHIR). SHIR protects individual data through summary-statistics-based integrating procedure, accommodates between-study heterogeneity in both the covariate distribution and model parameters, and attains consistent variable selection. Theoretically, SHIR is statistically more efficient than the existing distributed approaches that integrate debiased LASSO estimators from the local sites. Furthermore, the estimation error incurred by aggregating derived data is negligible compared to the statistical minimax rate and SHIR is shown to be asymptotically equivalent in estimation to the ideal estimator obtained by sharing all data. The finite-sample performance of our method is studied and compared with existing approaches via extensive simulation settings. We further illustrate the utility of SHIR to derive phenotyping algorithms for coronary artery disease using electronic health records data from multiple chronic disease cohorts.

Keywords: DataSHIELD; Distributed learning; High dimensionality; Model heterogeneity; Rate optimality; Sparsistency.

Figure 1.

The relative average absolute estimation error (AEE) of IPDpool (IPD), SHIR, ${\text{Debias}}_{\text{L\&B}}$ (Debias) and SMA compared to those of IPDpool underdifferent $M\in \{4,8\}$, $p\in \{100,800,1500\}$ and data-generation mechanisms (i)–(v) introduced in Section 5.

Figure 2.

The relative prediction error (PE) of IPDpool (IPD), SHIR, ${\text{Debias}}_{\text{L\&B}}$ (Debias), and SMA compared to those of IPDpool under different $M\in \{4,8\}$, $p\in \{100,800,1500\}$ and data-generation mechanisms (i)–(v) introduced in Section 5.

Figure 3.

The average number of misclassifications on $\left\{l\left({\beta }_j\ne 0\right),j=1,\dots ,p\right\}$ based on IPDpool (IPD), SHIR, ${\text{Debias}}_{\text{L\&B}}$ (Debias), and SMA under different $M\in \{4,8\}$, $p\in \{100,800,1500\}$ and data-generation mechanisms (i)–(iv) introduced in Section 5.

Figure 4.

The mean and 95% bootstrap confidence interval of AUC, Brier Score, $F_{5\%}$ and $F_{10\%}$ of ${\text{Debias}}_{\text{L\&B}}$, Local, SHIR and SMA on the validation data from the four studies.