Proximal Survival Analysis for Dependent Left Truncation
Abstract
In prevalent cohort studies with delayed entry, time-to-event outcomes are often subject to left truncation where only subjects that have not experienced the event at study entry are included, leading to selection bias. Existing methods for handling left truncation mostly rely on the (quasi-)independence assumption or the weaker conditional (quasi-)independence assumption which assumes that conditional on observed covariates, the left truncation time and the event time are independent on the observed region. In practice, however, our analysis of the Honolulu Asia Aging Study (HAAS) suggests that the conditional quasi-independence assumption may fail because measured covariates often serve only as imperfect proxies for the underlying mechanisms, such as latent health status, that induce dependence between truncation and event times. To address this gap, we propose a proximal weighting identification framework that admits the dependence-inducing factors may not be fully observed. We then construct an estimator based on the framework and study its asymptotic properties. We examine the finite sample performance of the proposed estimator by comprehensive simulations, and apply it to analyzing the cognitive impairment-free survival probabilities using data from the Honolulu Asia Aging Study.
Summary
This paper addresses the problem of selection bias in prevalent cohort studies where time-to-event outcomes are subject to left truncation. Existing methods often assume independence or conditional independence between the left truncation time and the event time, given observed covariates. However, the authors argue that this assumption may fail in practice because measured covariates are often imperfect proxies for latent factors, such as health status, that induce dependence. To overcome this limitation, they propose a proximal weighting identification framework that allows for unmeasured dependence by leveraging proxy variables. The framework classifies covariates into three types: those directly associated with both truncation and event times, truncation proxies (associated with truncation and indirectly with the event), and event time proxies (associated with the event and indirectly with truncation). Based on this framework, the authors construct an estimator and study its asymptotic properties. They introduce the concept of a "truncation-inducing bridge process" derived from integral equations involving the identified proxy variables. The estimator's finite sample performance is evaluated through simulations, and the method is applied to analyze cognitive impairment-free survival probabilities using data from the Honolulu Asia Aging Study (HAAS). The paper highlights the importance of accounting for unmeasured dependence in left-truncated data and provides a novel approach for doing so using proxy variables, offering a potentially more accurate assessment of survival probabilities compared to methods relying on stricter independence assumptions. This work is significant as it offers a more robust way to analyze survival data in situations where the standard independence assumptions are likely to be violated.
Key Insights
- •Novel Proximal Framework: The paper introduces a novel proximal weighting identification framework for handling dependent left truncation using proxy variables, a first in this context.
- •Truncation-Inducing Bridge Process: The concept of a "truncation-inducing bridge process" is introduced, which is a solution to a set of integral equations leveraging different types of proxy variables.
- •Classification of Covariates: The paper provides a clear classification of measured covariates into three types: those directly associated with both truncation and event times (Z), truncation proxies (W1), and event time proxies (W2). This classification is crucial for applying the proposed framework.
- •Asymptotic Properties: The paper provides a theoretical analysis of the proposed estimator, establishing its consistency and asymptotic normality under generic assumptions on the bridge process estimator.
- •Simulation Results: The simulation results demonstrate that the proposed "PQB" estimator has a small bias and close to nominal coverage probability when the sample size is large, unlike the IPQW estimator which has a larger bias.
- •HAAS Application: The application to the HAAS data reveals notable differences in estimated cognitive impairment-free survival (DFS) probabilities compared to methods that ignore unmeasured dependence, suggesting that common methods may underestimate the risk of cognitive decline and mortality.
- •Computational Considerations: The authors used AI tools (ChatGPT) to convert part of the code from R to C++, significantly reducing the computation time of the proposed estimator.
Practical Implications
- •Improved Survival Analysis: The proposed method can be used to improve survival analysis in prevalent cohort studies with delayed entry where the conditional independence assumption is likely to be violated.
- •Applications in Aging Studies: The method is particularly relevant for aging studies, where latent factors like health status can induce dependence between study entry age and time-to-event outcomes such as cognitive impairment.
- •Targeted Interventions: The more accurate survival estimates provided by the proposed method can inform the timing of preventive interventions for cognitive decline and mortality risk, as well as the planning and allocation of public health resources.
- •Practitioner Guidance: Practitioners can use the proposed framework by carefully classifying measured covariates into the three types of proxies and implementing the estimation procedure described in the paper, potentially using the provided code.
- •Future Research: The paper opens up several avenues for future research, including developing sensitivity analysis for potential violations of the proximal independence assumption and exploring nonparametric estimation methods for the bridge process.