# Sensitivity analysis for time-to-event data accounting for intra-individual variability in time-varying covariates with missing data

## TL;DR

This paper introduces a new method for handling missing data in time-dependent covariates in survival analysis, using delta adjustments to model non-random missingness.

## Contribution

The novel contribution is the Delta-Adjusted approach within multiple imputation for sensitivity analysis under non-random missingness assumptions.

## Key findings

- The DA approach adjusts imputed values using delta shifts to model deviations from MAR assumptions.
- DA provides interpretable sensitivity bounds for treatment effects under various missing data scenarios.
- Compared to traditional methods, DA offers more flexible and structured handling of NMAR data in survival analysis.

## Abstract

The Delta-Adjusted (DA) approach in multiple imputation (MI) is applied under several key assumptions in the Cox hazard model, where two time-dependent covariates have missing observations. Missingness in these covariates is assumed to be not missing at random (NMAR) and is modeled through delta adjustments, with different delta values specified to capture deviations from the missing at random (MAR) assumption. Within the MI framework, missing values are imputed under various plausible missingness scenarios while preserving the relationship between time-dependent covariates and the event-time outcome. Event-time dependence is accounted for by assuming that missingness in covariates is influenced by an individual’s treatment response or disease progression, thereby capturing intra-individual variability. Compared to other sensitivity analysis techniques, DA under MI explicitly adjusts imputed values using delta shifts, providing a structured approach to handling NMAR data. Unlike traditional methods that rely on pattern-mixture or selection models without direct imputation, DA generates multiple datasets with controlled sensitivity adjustments, ensuring a better variability assessment. Additionally, DA allows flexible assumptions regarding loss to follow-up (FU) and event occurrence through delta values, whereas other methods often rely on fixed assumptions about missingness. Its results are more interpretable, providing sensitivity bounds for treatment effects under different missing data scenarios.

The online version contains supplementary material available at 10.1038/s41598-025-09599-3.