Bootstrapping a change-point Cox model for survival data

Xu, Gongjun; Sen, Bodhisattva; Ying, Zhiliang

doi:10.1214/14-ejs927

Cited by 13 publications

(16 citation statements)

References 38 publications

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“…An alternative to confidence intervals based on the asymptotic distribution relies on the bootstrap. Studies on bootstrap confidence intervals in the Cox model are investigated in Burr (1994) and Xu et al (2014). We follow one of their proposals for a smooth bootstrap.…”

Section: Numerical Results For Pointwise Confidence Intervalsmentioning

confidence: 99%

Isotonized smooth estimators of a monotone baseline hazard in the Cox model

Lopuhaä

Musta

2017

Journal of Statistical Planning and Inference

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We consider two isotonic smooth estimators for a monotone baseline hazard in the Cox model, a maximum smooth likelihood estimator and a Grenander-type estimator based on the smoothed Breslow estimator for the cumulative baseline hazard. We show that they are both asymptotically normal at rate n m/(2m+1) , where m ≥ 2 denotes the level of smoothness considered, and we relate their limit behavior to kernel smoothed isotonic estimators studied in Lopuhaä and Musta (2016). It turns out that the Grenander-type estimator is asymptotically equivalent to the kernel smoothed isotonic estimators, while the maximum smoothed likelihood estimator exhibits the same asymptotic variance but a different bias. Finally, we present numerical results on pointwise confidence intervals that illustrate the comparable behavior of the two methods.

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Section: Numerical Results For Pointwise Confidence Intervalsmentioning

confidence: 99%

Isotonized smooth estimators of a monotone baseline hazard in the Cox model

Lopuhaä

Musta

2017

Journal of Statistical Planning and Inference

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“…Such method is widely used in non‐standard problems, such as non‐differentiable objective functions (Huang et al, ; Chakraborty et al, ) and non’

n^{- 1 / 2}

asymptotics (Abrevaya and Huang, ; Sen et al, ). In addition, Xu et al () proved the consistency of the m out of n bootstrap in the case of the Cox proportional hazards model with a change point. Xu et al () applied m out of n bootstrap based on some fixed values of m , which are

n^{4 / 5}

n^{9 / 10}

, and

n^{14 / 15}

.…”

Section: Methodsmentioning

confidence: 99%

“…In addition, Xu et al () proved the consistency of the m out of n bootstrap in the case of the Cox proportional hazards model with a change point. Xu et al () applied m out of n bootstrap based on some fixed values of m , which are

n^{4 / 5}

n^{9 / 10}

, and

n^{14 / 15}

. Based on this group of pre‐specified m , the poor coverage rates have been reported in their simulations.…”

Section: Methodsmentioning

confidence: 99%

Proportional Hazards Model with a Change Point for Clustered Event Data

et al. 2017

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Summary In many epidemiology studies, family data with survival endpoints are collected to investigate the association between risk factors and disease incidence. Sometimes the risk of the disease may change when a certain risk factor exceeds a certain threshold. Finding this threshold value could be important for disease risk prediction and diseases prevention. In this work, we propose a change-point proportional hazards model for clustered event data. The model incorporates the unknown threshold of a continuous variable as a change point in the regression. The marginal pseudo-partial likelihood functions are maximized for estimating the regression coefficients and the unknown change point. We develop a supremum test based on robust score statistics to test the existence of the change point. The inference for the change point is based on the m out of n bootstrap. We establish the consistency and asymptotic distributions of the proposed estimators. The finite-sample performance of the proposed method is demonstrated via extensive simulation studies. Finally, the Strong Heart Family Study dataset is analyzed to illustrate the methods.

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“…The long-term results could be assumed according to the stability potentially observed after re-sampling. Several manuscripts on re-sampling in survival analysis are limited on the re-sampled Cox proportional hazards model and on estimating standard errors of the survival and hazard functions such as in [6,[10][11][12][13] where bootstrap is involved [13][14][15][16]; in which the jackknife is implicated or [17][18][19][20][21][22] where hazard and survival functions with their respective standard errors are of interest. The present study analyses the bootstrap-based MRSM with 1000 replicates and the jackknife-based MRSM.…”

Section: Introductionmentioning

confidence: 99%

Comparison of three classes of Marginal Risk Set Model in predicting infant mortality among newborn babies at Kigali University Teaching Hospital, Rwanda, 2016

Gatabazi¹,

Melesse²,

Ramroop³

2020

BMC Pediatr

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Background: The Infant Mortality Rate (IMR) in Sub-Saharan Africa (SSA) remains the highest relatively to the rest of the world. In the past decade, the policy on reducing infant mortality in SSA was reinforced and both infant mortality and parental death decreased critically for some countries of SSA. The analysis of risk to death or attracting chronic disease may be done for helping medical practitioners and decision makers and for better preventing the infant mortality. Methods: This study uses popular statistical methods of re-sampling and one selected model of multiple events analysis for measuring the survival outcomes for the infants born in 2016 at Kigali University Teaching Hospital (KUTH) in Rwanda, a country of SSA, amidst maternal and child's socio-economic and clinical covariates. Dataset comprises the newborns with correct information on the covariates of interest. The Bootstrap Marginal Risk Set Model (BMRSM) and Jackknife Marginal Risk Set Model (JMRSM) for the available maternal and child's socioeconomic and clinical covariates were conducted and then compared to the outcome with Marginal Risk Set Model (MRSM). That was for measuring stability of the MRSM. Results: The 2117 newborns had the correct information on all the covariates, 82 babies died along the study time, 69 stillborn babies were observed while 1966 were censored. Both BMRSM JMRSM and MRSM displayed the close results for significant covariates. The BMRSM displayed in some instance, relatively higher standard errors for nonsignificant covariates and this emphasized their insignificance in MRSM. The models revealed that female babies survive better than male babies. The risk is higher for babies whose parents are under 20 years old parents as compared to other parents' age groups, the risk decreases as the APGAR increases, is lower for underweight babies than babies with normal weight and overweight and is lower for babies with normal circumference of head as compared to those with relatively small head. Conclusion: The results of JMRSM were closer to MRSM than that of BMRSM. Newborns of mothers aged less than 20 years were at relatively higher risk of dying than those who their mothers were aged 20 years and above. Being abnormal in weight and head increased the risk of infant mortality. Avoidance of teenage pregnancy and provision of clinical care including an adequate dietary intake during pregnancy would reduce the IMR in Kigali.

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Bootstrapping a change-point Cox model for survival data

Cited by 13 publications

References 38 publications

Isotonized smooth estimators of a monotone baseline hazard in the Cox model

Isotonized smooth estimators of a monotone baseline hazard in the Cox model

Proportional Hazards Model with a Change Point for Clustered Event Data

Comparison of three classes of Marginal Risk Set Model in predicting infant mortality among newborn babies at Kigali University Teaching Hospital, Rwanda, 2016

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