A Doubly Robust Framework for Addressing Outcome-Dependent Selection Bias in Multi-Cohort EHR Studies

TL;DR

A new Joint Augmented Inverse Probability Weighted method is introduced, which integrates individual-level data from multiple cohorts collected under potentially outcome-dependent selection mechanisms, with data from an external probability sample and offers double robustness by incorporating a flexible auxiliary score model to address potential misspecifications in the selection models.

Abstract

Selection bias can hinder accurate estimation of association parameters in binary disease risk models using non-probability samples like electronic health records (EHRs). The issue is compounded when participants are recruited from multiple clinics/centers with varying selection mechanisms that may depend on the disease/outcome of interest. Traditional inverse-probability-weighted (IPW) methods, based on constructed parametric selection models, often struggle with misspecifications when selection mechanisms vary across cohorts. This paper introduces a new Joint Augmented Inverse Probability Weighted (JAIPW) method, which integrates individual-level data from multiple cohorts collected under potentially outcome-dependent selection mechanisms, with data from an external probability sample. JAIPW offers double robustness by incorporating a flexible auxiliary score model to address potential misspecifications in the selection models. We outline the asymptotic properties of the JAIPW estimator, and our simulations reveal that JAIPW achieves up to six times lower relative bias and five times lower root mean square error (RMSE) compared to the best performing joint IPW methods under scenarios with misspecified selection models. Applying JAIPW to the Michigan Genomics Initiative (MGI), a multi-clinic EHR-linked biobank, combined with external national probability samples, resulted in cancer-sex association estimates closely aligned with national benchmark estimates. We also analyzed the association between cancer and polygenic risk scores (PRS) in MGI to illustrate a situation where the exposure variable is not measured in the external probability sample.

Figures (8)

• Figure 1: Figure depicts the relationship between the target population, three internal non-probability samples ($K=3$) and external data sources. $S_1$, $S_2$ and $S_3$ are the selection indicator variables of the three internal samples respectively. In the Sub-figure 1, $S_{\text{ext}}=1$ denote the individual-level external data which is NHANES in our work. In Sub-figure 2, external data sources include SEER, US Census and CDC. $D$ is the outcome of interest. For $k=1,2,3$, $\boldsymbol Z_{1k}\rightarrow D,\boldsymbol Z_{1k}\not \rightarrow S_k$, $\boldsymbol Z_{2k}\rightarrow D, \boldsymbol Z_{2k}\rightarrow S_k$ and $\boldsymbol W_{k}\not\rightarrow D,\boldsymbol W_{k}\rightarrow S_k$.
• Figure 2: Selection Directed Acyclic Graphs (DAGs) representing the relationships between different variables of interest in cohort $k$, where $k \in \{1,2,...,K\}$: $D$ (Disease Indicator), $S_k$ (Selection Indicator into the cohort $k$), $\boldsymbol Z_{1k}\rightarrow D,\boldsymbol Z_{1k}\not \rightarrow S_k$, $\boldsymbol Z_{2k}\rightarrow D, \boldsymbol Z_{2k}\rightarrow S_k$ and $\boldsymbol W_{k}\not\rightarrow D,\boldsymbol W_{k}\rightarrow S_k$. The dotted line between $\boldsymbol Z_{1k}$ and $\boldsymbol Z_{2k}$ denotes association between those two variables.
• Figure 3: Estimates of the marginal log (Odds Ratio) for the association between cancer and biological sex, with 95% confidence intervals, across Anesthesiology, MIPACT, MEND and the combined cohort. Comparisons are shown for the unweighted logistic regression (NAIVE, gray) and methods adjusting for selection bias (JPL, JPS, JAIPW-C, JAIPW-NC). For the IPW and JAIPW methods, estimates are shown either in red or blue depending on the selection model including cancer status (red, Cancer) or not (blue, No Cancer). JAIPW-C includes cancer in the auxiliary score model, while JAIPW-NC do not. The gray horizontal band represents the estimates of the log (Odds Ratio) from the SEER 2008-2016 registry.
• Figure S1: Directed Acyclic Graph Relationships between the disease and selection model variables in analysis of age-adjusted ($Z_2$) association between cancer ($D$) and biological sex ($Z_1$) in the four different cohorts of interest in the Michigan Genomics Initiative, namely MGI Anesthesiology (BB), MIPACT (Michigan Predictive Activity and Clinical Trajectories), MEND (Metabolism, Endocrinology, and Diabetes) and MHB (Mental Health BioBank). CAD, BMI, TriGly and Dep stand for Coronary Artery Disease, Body Mass Index, Triglycerides, and Depression, respectively.
• Figure S2: Directed Acyclic Graph Relationships between the disease and selection model variables in analysis of age-adjusted ($Z_2$) association between cancer ($D$) and Polygenic Risk Score (PRS)($Z_1$) for overall cancer. in the Michigan Genomics Initiative. CAD and BMI stand for Coronary Artery Disease and Body Mass Index respectively.

Theorems & Definitions (27)

• Theorem 3.1
• Theorem 3.2
• Theorem 3.3
• Theorem 3.4
• Theorem S1
• proof
• Theorem S2
• proof
• Theorem S3
• proof