Cox regression is robust to inaccurate EHR-extracted event time: an application to EHR-based GWAS

Abstract

Motivation: Logistic regression models are used in genomic studies to analyze the genetic data linked to electronic health records (EHRs), and do not take full usage of the time-to-event information available in EHRs. Previous work has shown that Cox regression, which can account for left truncation and right censoring in EHRs, increased the power to detect genotype-phenotype associations compared to logistic regression. We extend this to evaluate the relative performance of Cox regression and various logistic regression models in the presence of positive errors in event time (delayed event time), relating to recorded event time accuracy.

Results: One Cox model and three logistic regression models were considered under different scenarios of delayed event time. Extensive simulations and a genomic study application were used to evaluate the impact of delayed event time. While logistic regression does not model the time-to-event directly, various logistic regression models used in the literature were more sensitive to delayed event time than Cox regression. Results highlighted the importance to identify and exclude the patients diagnosed before entry time. Cox regression had similar or modest improvement in statistical power over various logistic regression models at controlled type I error. This was supported by the empirical data, where the Cox models steadily had the highest sensitivity to detect known genotype-phenotype associations under all scenarios of delayed event time.

Availability and implementation: Access to individual-level EHR and genotype data is restricted by the IRB. Simulation code and R script for data process are at: https://github.com/QingxiaCindyChen/CoxRobustEHR.git.

Supplementary information: Supplementary data are available at Bioinformatics online.

Fig. 1.

Results from Simulation 1 when the event time was generated from a Cox model with baseline hazard from an exponential distribution, the censoring time was generated from a uniform distribution with left truncation, and the observations with simulated event times before truncation were removed from the analysis (removal-practice). The parameters led to a small number of observations with a misclassified event status (detailed in Supplementary Appendix SA). *Type I error evaluated at log(1). Power evaluated at log(1.1), log(1.15), log(1.25), log(1.5), log(2)

Fig. 2.

Results from Simulation 1 when the event time was generated from a Cox model with baseline hazard from an exponential distribution, the censoring time was generated from a uniform distribution with left truncation, and the observations with simulated event times before truncation were removed from the analysis (removal-practice). The parameters led to a large number of observations with a misclassified event status (detailed in Supplementary Appendix SA). *Type I error evaluated at log(1). Power evaluated at log(1.1), log(1.15), log(1.25), log(1.5), log(2)

Fig. 3.

Results from Simulation 1 when the event time was generated from a Cox model with baseline hazard from an exponential distribution, the censoring time was generated from a uniform distribution with left truncation, and the observations with simulated event times before truncation were considered censored (censor-practice). The parameters led to a large number of observations with a misclassified event status (detailed in Supplementary Appendix SA). *Type I error evaluated at log(1). Power evaluated at log(1.1), log(1.15), log(1.25), log(1.5), log(2)

Fig. 4.

Average true positive rates for detecting significant SNPs from all ten phecodes for each model and delayed event time combination, using Model 1 (Cox) with no delayed event time as the gold standard. This application corresponds to the delayed diagnosis set-up. *Based on Model 1 (Cox)—no delayed event time

Fig. 5.

False positive and false negative SNPs for each model and delayed event time combination, using Model 1 (Cox) with no delayed event time as the gold standard, for all ten phecodes. Dark green lines correspond to $P\le 5\times {10}^{-8}$ and light green lines correspond to $P\le 1\times {10}^{-5}$

Fig. 6.

Sensitivity of each model and delayed event time combination for detecting known genotype–phenotype associations