[Paper Review] Two-phase analysis and study design for survival models with error-prone exposures

Kyunghee Han, Thomas Lumley+2 more|arXiv (Cornell University)|May 12, 2020

Statistical Methods and Inference22 references4 citations

TL;DR

This paper extends the mean score method to two-phase survival analysis with error-prone exposures, using auxiliary data from unvalidated covariates to correct for measurement error. It proposes an adaptive sampling design that improves estimation efficiency by minimizing variance under cost constraints, achieving near-oracle performance in simulations and real data, especially with optimal pilot sampling and stratum-specific allocation.

ABSTRACT

Increasingly, medical research is dependent on data collected for non-research purposes, such as electronic health records data (EHR). EHR data and other large databases can be prone to measurement error in key exposures, and unadjusted analyses of error-prone data can bias study results. Validating a subset of records is a cost-effective way of gaining information on the error structure, which in turn can be used to adjust analyses for this error and improve inference. We extend the mean score method for the two-phase analysis of discrete-time survival models, which uses the unvalidated covariates as auxiliary variables that act as surrogates for the unobserved true exposures. This method relies on a two-phase sampling design and an estimation approach that preserves the consistency of complete case regression parameter estimates in the validated subset, with increased precision leveraged from the auxiliary data. Furthermore, we develop optimal sampling strategies which minimize the variance of the mean score estimator for a target exposure under a fixed cost constraint. We consider the setting where an internal pilot is necessary for the optimal design so that the phase two sample is split into a pilot and an adaptive optimal sample. Through simulations and data example, we evaluate efficiency gains of the mean score estimator using the derived optimal validation design compared to balanced and simple random sampling for the phase two sample. We also empirically explore efficiency gains that the proposed discrete optimal design can provide for the Cox proportional hazards model in the setting of a continuous-time survival outcome.

Motivation & Objective

• To address measurement error in survival outcomes when gold-standard exposure data are unavailable for all subjects.
• To extend the mean score method—previously used for discrete-time survival and binary outcomes—to continuous-time survival models with error-prone exposures.
• To develop an optimal two-phase sampling design that minimizes variance of the target regression parameter under fixed cost constraints.
• To propose an adaptive design using a pilot phase to estimate nuisance parameters needed for optimal stratum allocation.
• To evaluate efficiency gains of the proposed design compared to simple random and balanced sampling in both simulated and real-world data.

Proposed method

• Uses a two-phase sampling design: phase one collects readily available error-prone exposure data on all subjects; phase two validates a subset to estimate error structure.
• Applies the mean score method to correct regression parameter estimates in discrete-time proportional hazards models using the error-prone exposure as an auxiliary variable.
• Derives optimal sampling proportions via Neyman allocation, minimizing variance of the target parameter under a fixed validation sample size.
• Introduces a multi-wave sampling strategy: a pilot phase estimates nuisance parameters (e.g., stratum-specific means and variances), enabling adaptive allocation in the main phase.
• Employs a modified adaptive design that adjusts sampling based on pilot data, improving performance over balanced or simple random sampling.
• Extends findings to continuous-time survival analysis using the Cox proportional hazards model, demonstrating efficiency gains with the same design framework.

Experimental results

Research questions

• RQ1 Can the mean score method be effectively extended to two-phase analysis of discrete-time survival models with error-prone exposures?
• RQ2 How can optimal sampling proportions be derived to minimize variance of the target regression parameter under a fixed cost constraint?
• RQ3 What is the impact of using a pilot phase to estimate nuisance parameters on the efficiency of the adaptive sampling design?
• RQ4 How does the proposed adaptive design compare to simple random and balanced sampling in terms of variance reduction and estimation efficiency?
• RQ5 To what extent can the derived optimal design improve efficiency in continuous-time survival analysis using the Cox model?

Key findings

• The proposed mean score estimator with adaptive sampling design achieved significant variance reduction—up to 14%—compared to balanced and simple random sampling in the National Wilms Tumor Study data.
• The adaptive design with a pilot phase closely approximated the performance of the oracle design (which uses true population parameters), especially when the pilot sample was strategically selected to avoid oversampling uninformative strata.
• Including intermittently censored individuals (n = 158) excluded in earlier analyses further improved precision, particularly for the MS-BAL and MS-A estimators.
• The method demonstrated consistent efficiency gains over complete case analysis and other sampling strategies as the phase two sample size increased.
• The adaptive design outperformed both simple random and balanced sampling across all simulation settings and data examples, showing robustness and practical utility.
• The approach was successfully extended to continuous-time survival outcomes using the Cox model, with efficiency gains observed under both type I and random right censoring.