Goodness-of-fit two-phase sampling designs for time-to-event outcomes: a simulation study based on New York University Women's Health Study for breast cancer

Abstract

Background: Sub-cohort sampling designs such as a case-cohort study play a key role in studying biomarker-disease associations due to their cost effectiveness. Time-to-event outcome is often the focus in cohort studies, and the research goal is to assess the association between the event risk and risk factors. In this paper, we propose a novel goodness-of-fit two-phase sampling design for time-to-event outcomes when some covariates (e.g., biomarkers) can only be measured on a subgroup of study subjects.

Methods: Assuming that an external model, which can be the well-established risk models such as the Gail model for breast cancer, Gleason score for prostate cancer, and Framingham risk models for heart diseases, or built from preliminary data, is available to relate the outcome and complete covariates, we propose to oversample subjects with worse goodness-of-fit (GOF) based on an external survival model and time-to-event. With the cases and controls sampled using the GOF two-phase design, the inverse sampling probability weighting method is used to estimate the log hazard ratio of both incomplete and complete covariates. We conducted extensive simulations to evaluate the efficiency gain of our proposed GOF two-phase sampling designs over case-cohort study designs.

Results: Through extensive simulations based on a dataset from the New York University Women's Health Study, we showed that the proposed GOF two-phase sampling designs were unbiased and generally had higher efficiency compared to the standard case-cohort study designs.

Conclusion: In cohort studies with rare outcomes, an important design question is how to select informative subjects to reduce sampling costs while maintaining statistical efficiency. Our proposed goodness-of-fit two-phase design provides efficient alternatives to standard case-cohort designs for assessing the association between time-to-event outcome and risk factors. This method is conveniently implemented in standard software.

Keywords: Case-cohort; Cox proportional hazards model; Hazard ratio estimation; Inverse probability weighting; Relative efficiency.