Generating Survival Times Using Cox Proportional Hazards Models with Cyclic and Piecewise Time-Varying Covariates

Huang, Yunda; Zhang, Yuanyuan; Zong, Zhi‐Min; Gilbert, Peter B.

doi:10.1007/s12561-020-09266-3

Cited by 4 publications

(3 citation statements)

References 31 publications

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“…The following is the function of the Cox proportional hazards model.

where z ( t ) denotes the time-varying covariate that is invariant for the outcome risk and is represented by the regression coefficient β ; x denotes the time-invariant covariates; η is the vector of regression coefficients associated with the vector of fixed covariates x ; and h 0 ( t ) is the baseline hazard function, i.e., the hazard function of the outcome for those participants, with x = 0 and z ( t ) = 0 [ 34 ]. The data analysis was performed using SAS 9.4 software and SPSS 26 software (IBM Corp., Armonk, NY, USA).…”

Section: Methodsmentioning

confidence: 99%

Association between the Systolic Blood Pressure Trajectory and Risk of Stroke in a Health-Management Population in Jiaozuo, China

Zhang

Xiang-dong

et al. 2022

Journal of Healthcare Engineering

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The trajectories of systolic blood pressure (SBP) in a screening population in Jiaozuo were examined, and the association between the different types of SBP trajectories and the risk of stroke was evaluated. Data of a fixed cohort population from the Jiaozuo Stroke Prevention and Control Project Management Special Database System that underwent community screening in 2015, 2017, 2019, and 2021 were collected. Ultimately, a total of 1,451 participants who met the inclusion criteria for this study were included in the analysis, which was performed using group trajectory modeling. The baseline SBP for each trajectory subgroup was characterized at follow-up. Kaplan–Meier analysis for each trajectory group was also performed, and the relationship between the SBP trajectory and risk of stroke onset during follow-up was validated using a Cox proportional hazards model. Based on the SBP from 2015 to 2021, this cohort population was divided into three groups based on the trajectory development patterns: the low-stable group (37.6%), the moderate-increasing group (53.4%), and the high-acutely increasing group (9%). Gender, age, body mass index, diastolic blood pressure, and fasting blood glucose level were predictive factors for the SBP trajectory group. The cumulative survival risk in the high-acutely increasing group was higher than that of the other two groups. After adjusting for potential confounding factors and using the low-stable group as a reference, the hazard ratios (95% confidence interval) for the risk of stroke onset in the moderate-increasing and high-acutely increasing groups were 1.38 (0.91–2.07) and 1.51 (0.82–2.76), respectively. The results of the analysis demonstrate that higher blood pressure trajectories are associated with a higher risk of stroke and that the risk of stroke can be reduced by better control and management of the SBP.

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“…The following is the function of the Cox proportional hazards model.

Section: Methodsmentioning

confidence: 99%

Association between the Systolic Blood Pressure Trajectory and Risk of Stroke in a Health-Management Population in Jiaozuo, China

Zhang

Xiang-dong

et al. 2022

Journal of Healthcare Engineering

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“…Huang et al [7] proposed two novel simulation approaches to generating event times following the Cox proportional hazards models with both time-independent covariates and continuous cyclic and piecewise time-dependent covariates. One was based on simulating survival data under a single-dose regimen first before data are aggregated over multiple dosing cycles, and the other was based on simulating survival data directly under a multiple-dose regimen.…”

Section: © International Chinese Statistical Association 2020mentioning

confidence: 99%

Introduction to Special Issue on ‘Statistical Methods for HIV/AIDS Research’

Chen

2020

Stat Biosci

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“…This includes the survsim package and flexsurv, the latter of which is capable of fitting even more flexible parametric distributions [10,11]. The use of these distributions has been extended to include methods for generating survival times with time-invariant covariates as well as cyclic and piecewise time-varying covariate [12]. Current research is being conducted for the generation of right-censored survival times as a function of time-varying covariates [13][14][15].…”

mentioning

confidence: 99%

Simulating time-to-event data under the Cox proportional hazards model: assessing the performance of the non-parametric Flexible Hazards Method

Delzeit,

Koestler

2023

Front. Appl. Math. Stat.

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Numerous methods and approaches have been developed for generating time-to-event data from the Cox Proportional Hazards (CPH) model; however, they often require specification of a parametric distribution for the baseline hazard even though the CPH model itself makes no assumptions on the distribution of the baseline hazards. In line with the semi-parametric nature of the CPH model, a recently proposed method called the Flexible Hazards Method generates time-to-event data from a CPH model using a non-parametric baseline hazard function. While the initial results of this method are promising, it has not yet been comprehensively assessed with increasing covariates or against data generated under parametric baseline hazards. To fill this gap, we conducted a comprehensive study to benchmark the performance of the Flexible Hazards Method for generating data from a CPH model against parametric methods. Our results showed that with a single covariate and large enough assumed maximum time, the bias in the Flexible Hazards Method is 0.02 (with respect to the log hazard ratio) with a 95% confidence interval having coverage of 84.4%. This bias increases to 0.054 when there are 10 covariates under the same settings and the coverage of the 95% confidence interval decreases to 46.7%. In this paper, we explain the plausible reasons for this observed increase in bias and decrease in coverage as the number of covariates are increased, both empirically and theoretically, and provide readers and potential users of this method with some suggestions on how to best address these issues. In summary, the Flexible Hazards Method performs well when there are few covariates and the user wishes to simulate data from a non-parametric baseline hazard.

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Generating Survival Times Using Cox Proportional Hazards Models with Cyclic and Piecewise Time-Varying Covariates

Cited by 4 publications

References 31 publications

Association between the Systolic Blood Pressure Trajectory and Risk of Stroke in a Health-Management Population in Jiaozuo, China

Association between the Systolic Blood Pressure Trajectory and Risk of Stroke in a Health-Management Population in Jiaozuo, China

Introduction to Special Issue on ‘Statistical Methods for HIV/AIDS Research’

Simulating time-to-event data under the Cox proportional hazards model: assessing the performance of the non-parametric Flexible Hazards Method

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