Target Aggregate Data Adjustment Method for Transportability Analysis Utilizing Summary-Level Data From the Target Population

Abstract

Transportability analysis is a causal inference framework used to evaluate the external validity of studies by transporting treatment effects from a study sample to an external target population by adjusting for differences in the distributions of their effect modifiers. Most existing methods require individual patient-level data (IPD) for both the source and the target population, narrowing its applicability when only target aggregate-level data (AgD) are available. For survival analysis, accounting for censoring may be needed to reduce bias, yet AgD-based transportability methods in the presence of informative-censoring remain underexplored. Here, we propose a two-stage weighting framework named "Target Aggregate Data Adjustment" (TADA) that can simultaneously adjust for both censoring bias and distributional imbalances of effect modifiers. In our framework, the final weights are the product of the time-varying inverse probability of censoring weights and participation weights derived using the method of moments. We have conducted an extensive simulation study to evaluate TADA's performance. We have applied our methods to a real case study on the squamous non-small-cell lung cancer trial (NCT00981058). Our results indicate that TADA can effectively control the bias resulting from moderate censoring representative of most practical scenarios, and enhance the application and clinical interpretability of transportability analyses in settings with limited data availability.

Keywords: aggregate‐level data; causal inference; inverse probability of censoring weights; method of moments; survival analysis; transportability analysis.

FIGURE 1

The boxplots of overall censoring proportion for scenarios 1 to 10 when the average overall censoring proportion among all scenarios is around (A) 20% and (B) 30%. The numbers aligned with each boxplot from left to right represent the minimum, mean and maximum of the overall censoring proportion among 500 simulation replicates.

FIGURE 2

The boxplots of treatment (bright orange) and control (light blue) group censoring proportion for scenarios 1 to 10 when the average overall censoring proportion among all scenarios is around (A) 20% and (B) 30%. The numbers aligned with each boxplot from bottom to top represent the minimum (blue), mean (black) and maximum (red) of corresponding censoring proportion among 500 simulation replicates.

FIGURE 3

An illustration of the final weights truncation threshold decision. The horizontal axis represents the value of raw final weights. The vertical axis indicates the percentage of observations in each weight bin, relative to the total sample. Blue bars depict the distribution of raw final weights. Red vertical dashed lines from left to right indicate the candidate thresholds at the 90th, 95th, and 99th percentiles, respectively.

FIGURE 4

Original Kaplan–Meier curve and Transported Kaplan–Meier curves under various adjustments. Top panel: Original naive K–M curve versus Transported K–M curve that adjusted for covariate imbalance and without censoring adjustment. Bottom panel: Original naive K–M curve versus Transported K–M curve fully adjusted by TADA, incorporating both censoring and covariate imbalance adjustments. Dashed vertical lines in grey indicate the estimated median OS for the naive curve. Dashed vertical lines in red indicate the estimated median OS for the transported curves.

FIGURE 5

Distribution of overall survival times by event status when only conduct censoring adjustment for the source SQUIRE population. The grey bars represent the status of event. The navy blue bars represent the status of censor. The red dashed line indicates the value of median OS.