1
|
Ding J, Li J, Han Y, McKeague IW, Wang X. Fitting additive risk models using auxiliary information. Stat Med 2023; 42:894-916. [PMID: 36599810 DOI: 10.1002/sim.9649] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2022] [Revised: 10/06/2022] [Accepted: 11/09/2022] [Indexed: 01/06/2023]
Abstract
There has been a growing interest in incorporating auxiliary summary information from external studies into the analysis of internal individual-level data. In this paper, we propose an adaptive estimation procedure for an additive risk model to integrate auxiliary subgroup survival information via a penalized method of moments technique. Our approach can accommodate information from heterogeneous data. Parameters to quantify the magnitude of potential incomparability between internal data and external auxiliary information are introduced in our framework while nonzero components of these parameters suggest a violation of the homogeneity assumption. We further develop an efficient computational algorithm to solve the numerical optimization problem by profiling out the nuisance parameters. In an asymptotic sense, our method can be as efficient as if all the incomparable auxiliary information is accurately acknowledged and has been automatically excluded from consideration. The asymptotic normality of the proposed estimator of the regression coefficients is established, with an explicit formula for the asymptotic variance-covariance matrix that can be consistently estimated from the data. Simulation studies show that the proposed method yields a substantial gain in statistical efficiency over the conventional method using the internal data only, and reduces estimation biases when the given auxiliary survival information is incomparable. We illustrate the proposed method with a lung cancer survival study.
Collapse
Affiliation(s)
- Jie Ding
- School of Mathematical Sciences, Dalian University of Technology, Liaoning, China
| | - Jialiang Li
- Department of Statistics and Data Science, National University of Singapore, Singapore, Singapore
- Duke University-NUS Graduate Medical School, National University of Singapore, Singapore, Singapore
| | - Yang Han
- Department of Mathematics, University of Manchester, Manchester, United Kingdom
| | - Ian W McKeague
- Department of Biostatistics, Mailman School of Public Health, Columbia University, New York, USA
| | - Xiaoguang Wang
- School of Mathematical Sciences, Dalian University of Technology, Liaoning, China
| |
Collapse
|
2
|
Rava D, Xu R. Doubly robust estimation of the hazard difference for competing risks data. Stat Med 2023; 42:799-814. [PMID: 36597179 DOI: 10.1002/sim.9644] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2022] [Revised: 11/09/2022] [Accepted: 12/08/2022] [Indexed: 01/05/2023]
Abstract
We consider the conditional treatment effect for competing risks data in observational studies. We derive the efficient score for the treatment effect using modern semiparametric theory, as well as two doubly robust scores with respect to (1) the assumed propensity score for treatment and the censoring model, and (2) the outcome models for the competing risks. An important property regarding the estimators is rate double robustness, in addition to the classical model double robustness. Rate double robustness enables the use of machine learning and nonparametric methods in order to estimate the nuisance parameters, while preserving the root-n $$ n $$ asymptotic normality of the estimated treatment effect for inferential purposes. We study the performance of the estimators using simulation. The estimators are applied to the data from a cohort of Japanese men in Hawaii followed since 1960s in order to study the effect of mid-life drinking behavior on late life cognitive outcomes. The approaches developed in this article are implemented in the R package "HazardDiff".
Collapse
Affiliation(s)
- Denise Rava
- Department of Mathematics, University of California, San Diego, California, USA
| | - Ronghui Xu
- Department of Mathematics, University of California, San Diego, California, USA
- Herbert Wertheim School of Public Health and Human Longevity Sciences, and Halicioglu Data Science Institute, University of California, San Diego, California, USA
| |
Collapse
|
3
|
Lee M. Semiparametric analysis of recurrent discrete time data with competing risks. J STAT COMPUT SIM 2022. [DOI: 10.1080/00949655.2022.2102171] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
Affiliation(s)
- Minjung Lee
- Department of Statistics, Kangwon National University, Chuncheon, South Korea
| |
Collapse
|
4
|
Lee M, Fine JP. Competing risks predictions with different time scales under the additive risk model. Stat Med 2022; 41:3941-3957. [PMID: 35670574 DOI: 10.1002/sim.9485] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2021] [Revised: 05/14/2022] [Accepted: 05/17/2022] [Indexed: 11/05/2022]
Abstract
In the analysis for competing risks data, regression modeling of the cause-specific hazard functions has been usually conducted using the same time scale for all event types. However, when the true time scale is different for each event type, it would be appropriate to specify regression models for the cause-specific hazards on different time scales for different event types. Often, the proportional hazards model has been used for regression modeling of the cause-specific hazard functions. However, the proportionality assumption may not be appropriate in practice. In this article, we consider the additive risk model as an alternative to the proportional hazards model. We propose predictions of the cumulative incidence functions under the cause-specific additive risk models employing different time scales for different event types. We establish the consistency and asymptotic normality of the predicted cumulative incidence functions under the cause-specific additive risk models specified on different time scales using empirical processes and derive consistent variance estimators of the predicted cumulative incidence functions. Through simulation studies, we show that the proposed prediction methods perform well. We illustrate the methods using stage III breast cancer data obtained from the Surveillance, Epidemiology, and End Results (SEER) program of the National Cancer Institute.
Collapse
Affiliation(s)
- Minjung Lee
- Department of Statistics, Kangwon National University, Chuncheon, Gangwon, Korea
| | - Jason P Fine
- Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, USA
| |
Collapse
|
5
|
Wang X, Wang Z. EM algorithm for the additive risk mixture cure model with interval-censored data. LIFETIME DATA ANALYSIS 2021; 27:91-130. [PMID: 33001344 DOI: 10.1007/s10985-020-09507-z] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/06/2018] [Accepted: 09/19/2020] [Indexed: 06/11/2023]
Abstract
Interval-censored failure time data arise in a number of fields and many authors have recently paid more attention to their analysis. However, regression analysis of interval-censored data under the additive risk model can be challenging in maximizing the complex likelihood, especially when there exists a non-ignorable cure fraction in the population. For the problem, we develop a sieve maximum likelihood estimation approach based on Bernstein polynomials. To relieve the computational burden, an expectation-maximization algorithm by exploiting a Poisson data augmentation is proposed. Under some mild conditions, the asymptotic properties of the proposed estimator are established. The finite sample performance of the proposed method is evaluated by extensive simulations, and is further illustrated through a real data set from the smoking cessation study.
Collapse
Affiliation(s)
- Xiaoguang Wang
- School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, Liaoning, China.
| | - Ziwen Wang
- School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, Liaoning, China
| |
Collapse
|
6
|
Zheng C, Chen YQ. On a Shape-Invariant Hazard Regression Model with application to an HIV Prevention Study of Mother-to-Child Transmission. STATISTICS IN BIOSCIENCES 2020; 12:340-352. [PMID: 33312265 DOI: 10.1007/s12561-019-09260-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Abstract
In survival analysis, Cox model is widely used for most clinical trial data. Alternatives include the additive hazard model, the accelerated failure time (AFT) model and a more general transformation model. All these models assume that the effects for all covariates are on the same scale. However, it is possible that for different covariates, the effects are on different scales. In this paper, we propose a shape-invariant hazard regression model that allows us to estimate the multiplicative treatment effect with adjustment of covariates that have non-multiplicative effects. We propose moment-based inference procedures for the regression parameters. We also discuss the risk prediction and the goodness of fit test for our proposed model. Numerical studies show good finite sample performance of our proposed estimator. We applied our method to the HIVNET 012 study, a milestone trial of single-dose nevirapine in prevention of mother-to-child transmission of HIV. From the HIVNET 012 data analysis, single-dose nevirapine treatment is shown to improve 18-month infant survival significantly with appropriate adjustment of the maternal CD4 counts and the virus load.
Collapse
Affiliation(s)
- Cheng Zheng
- Zilber School of Public Health, University of Wisconsin-Milwaukee, 1240 N. 10th St, Room 378, Milwaukee, USA
| | - Ying Qing Chen
- Program in Biostatistics and Biomathematics, Fred Hutchinson Cancer Research Center, 1100 Fairview Ave N. Arnorld Building M2-C200, Seattle, USA
| |
Collapse
|
7
|
Hao M, Zhao X, Xu W. Competing risk modeling and testing for X-chromosome genetic association. Comput Stat Data Anal 2020. [DOI: 10.1016/j.csda.2020.107007] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
|
8
|
Lee U, Sun Y, Scheike TH, Gilbert PB. Analysis of Generalized Semiparametric Regression Models for Cumulative Incidence Functions with Missing Covariates. Comput Stat Data Anal 2018; 122:59-79. [PMID: 29892140 DOI: 10.1016/j.csda.2018.01.003] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Abstract
The cumulative incidence function quantifies the probability of failure over time due to a specific cause for competing risks data. The generalized semiparametric regression models for the cumulative incidence functions with missing covariates are investigated. The effects of some covariates are modeled as non-parametric functions of time while others are modeled as parametric functions of time. Different link functions can be selected to add flexibility in modeling the cumulative incidence functions. The estimation procedures based on the direct binomial regression and the inverse probability weighting of complete cases are developed. This approach modifies the full data weighted least squares equations by weighting the contributions of observed members through the inverses of estimated sampling probabilities which depend on the censoring status and the event types among other subject characteristics. The asymptotic properties of the proposed estimators are established. The finite-sample performances of the proposed estimators and their relative efficiencies under different two-phase sampling designs are examined in simulations. The methods are applied to analyze data from the RV144 vaccine efficacy trial to investigate the associations of immune response biomarkers with the cumulative incidence of HIV-1 infection.
Collapse
Affiliation(s)
- Unkyung Lee
- Department of Statistics, Texas A&M University, College Station, TX 77843, U.S.A
| | - Yanqing Sun
- Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223, USA
| | - Thomas H Scheike
- Department of Biostatistics, University of Copenhagen, Øster Farimagsgade 5, DK-1014, Denmark
| | - Peter B Gilbert
- Department of Biostatistics, University of Washington, Seattle, WA 98195, U.S.A.,Vaccine and Infectious Disease and Public Health Sciences Divisions, Fred Hutchinson Cancer Research Center, Seattle, WA 98109, U.S.A
| |
Collapse
|
9
|
Qiu Z, Wan ATK, Zhou Y, Gilbert PB. Smoothed Rank Regression for the Accelerated Failure Time Competing Risks Model with Missing Cause of Failure. Stat Sin 2018; 29:23-46. [PMID: 30740005 DOI: 10.5705/ss.202016.0231] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
This paper examines the accelerated failure time competing risks model with missing cause of failure using the monotone class rank-based estimating equations approach. We handle the non-smoothness of the rank-based estimating equations using a kernel smoothed estimation method, and estimate the unknown selection probability and the conditional expectation by non-parametric techniques. Under this setup, we propose three methods for estimating the unknown regression parameters based on 1) inverse probability weighting, 2) estimating equations imputation and 3) augmented inverse probability weighting. We also obtain the associated asymptotic theories of the proposed estimators and investigate the estimators' small sample behaviour in a simulation study. A direct plug-in method is suggested for estimating the asymptotic variances of the proposed estimators. A real data application based on a HIV vaccine efficacy trial study is considered.
Collapse
Affiliation(s)
- Zhiping Qiu
- School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China.,Research Center for Applied Statistics and Big Data, Huaqiao University, Xiamen 361021, China
| | - Alan T K Wan
- City University of Hong Kong, Kowloon, Hong Kong
| | - Yong Zhou
- School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433, China.,Institute of Applied Mathematics, Chinese Academy of Science, Beijing 100190, China
| | - Peter B Gilbert
- Department of Biostatistics, University of Washington and Fred Hutchinson Cancer Research Center, Seattle, Washington 98109, USA
| |
Collapse
|
10
|
Affiliation(s)
- Wanxing Li
- Department of Mathematics, School of Information, Renmin University of China, Beijing, P.R. China
| | - Xiaoming Xue
- Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, P.R. China
| | - Yonghong Long
- Department of Mathematics, School of Information, Renmin University of China, Beijing, P.R. China
| |
Collapse
|
11
|
Zheng C, Dai R, Hari PN, Zhang MJ. Instrumental variable with competing risk model. Stat Med 2017; 36:1240-1255. [PMID: 28064466 DOI: 10.1002/sim.7205] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2016] [Revised: 11/28/2016] [Accepted: 12/01/2016] [Indexed: 11/10/2022]
Abstract
In this paper, we discuss causal inference on the efficacy of a treatment or medication on a time-to-event outcome with competing risks. Although the treatment group can be randomized, there can be confoundings between the compliance and the outcome. Unmeasured confoundings may exist even after adjustment for measured covariates. Instrumental variable methods are commonly used to yield consistent estimations of causal parameters in the presence of unmeasured confoundings. On the basis of a semiparametric additive hazard model for the subdistribution hazard, we propose an instrumental variable estimator to yield consistent estimation of efficacy in the presence of unmeasured confoundings for competing risk settings. We derived the asymptotic properties for the proposed estimator. The estimator is shown to be well performed under finite sample size according to simulation results. We applied our method to a real transplant data example and showed that the unmeasured confoundings lead to significant bias in the estimation of the effect (about 50% attenuated). Copyright © 2017 John Wiley & Sons, Ltd.
Collapse
Affiliation(s)
- Cheng Zheng
- Joseph. J. Zilber School of Public Health, University of Wisconsin-Milwaukee, Milwaukee, WI, U.S.A
| | - Ran Dai
- Department of Statistics, University of Chicago, Chicago, IL, U.S.A
| | - Parameswaran N Hari
- Division of Hematology and Oncology, Medical College of Wisconsin, Milwaukee, WI, U.S.A
| | - Mei-Jie Zhang
- Division of Biostatistics, Medical College of Wisconsin, Milwaukee, WI, U.S.A
| |
Collapse
|
12
|
Lee M, Gouskova NA, Feuer EJ, Fine JP. On the choice of time scales in competing risks predictions. Biostatistics 2016; 18:15-31. [PMID: 27335117 DOI: 10.1093/biostatistics/kxw024] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2015] [Revised: 04/13/2016] [Accepted: 04/18/2016] [Indexed: 12/23/2022] Open
Abstract
In the standard analysis of competing risks data, proportional hazards models are fit to the cause-specific hazard functions for all causes on the same time scale. These regression analyses are the foundation for predictions of cause-specific cumulative incidence functions based on combining the estimated cause-specific hazard functions. However, in predictions arising from disease registries, where only subjects with disease enter the database, disease-related mortality may be more naturally modeled on the time since diagnosis time scale while death from other causes may be more naturally modeled on the age time scale. The single time scale methodology may be biased if an incorrect time scale is employed for one of the causes and an alternative methodology is not available. We propose inferences for the cumulative incidence function in which regression models for the cause-specific hazard functions may be specified on different time scales. Using the disease registry data, the analysis of other cause mortality on the age scale requires left truncating the event time at the age of disease diagnosis, complicating the analysis. In addition, standard Martingale theory is not applicable when combining regression models on different time scales. We establish that the covariate conditional predictions are consistent and asymptotically normal using empirical process techniques and propose consistent variance estimators for constructing confidence intervals. Simulation studies show that the proposed two time scales method performs well, outperforming the single time-scale predictions when the time scale is misspecified. The methods are illustrated with stage III colon cancer data obtained from the Surveillance, Epidemiology, and End Results program of National Cancer Institute.
Collapse
Affiliation(s)
- Minjung Lee
- Department of Statistics, Kangwon National University, Chuncheon, Gangwon 24341, South Korea
| | - Natalia A Gouskova
- Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA
| | - Eric J Feuer
- Statistical Research and Applications Branch, Division of Cancer Control and Population Studies, National Cancer Institute, Bethesda, MD 20892, USA
| | - Jason P Fine
- Department of Biostatistics and Department of Statistics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA
| |
Collapse
|
13
|
Mondal S, Subramanian S. Simultaneous confidence bands for Cox regression from semiparametric random censorship. LIFETIME DATA ANALYSIS 2016; 22:122-144. [PMID: 25691289 DOI: 10.1007/s10985-015-9323-2] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2014] [Accepted: 02/09/2015] [Indexed: 06/04/2023]
Abstract
Cox regression is combined with semiparametric random censorship models to construct simultaneous confidence bands (SCBs) for subject-specific survival curves. Simulation results are presented to compare the performance of the proposed SCBs with the SCBs that are based only on standard Cox. The new SCBs provide correct empirical coverage and are more informative. The proposed SCBs are illustrated with two real examples. An extension to handle missing censoring indicators is also outlined.
Collapse
Affiliation(s)
- Shoubhik Mondal
- Center for Applied Mathematics and Statistics, Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ, USA
| | - Sundarraman Subramanian
- Center for Applied Mathematics and Statistics, Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ, USA.
| |
Collapse
|
14
|
Shen PS. Additive Transformation Models for Clustered Doubly Censored Data. COMMUN STAT-SIMUL C 2015. [DOI: 10.1080/03610918.2013.835405] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
|
15
|
He P, Eriksson F, Scheike TH, Zhang MJ. A Proportional Hazards Regression Model for the Sub-distribution with Covariates Adjusted Censoring Weight for Competing Risks Data. Scand Stat Theory Appl 2015; 43:103-122. [PMID: 27034534 DOI: 10.1111/sjos.12167] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
With competing risks data, one often needs to assess the treatment and covariate effects on the cumulative incidence function. Fine and Gray proposed a proportional hazards regression model for the subdistribution of a competing risk with the assumption that the censoring distribution and the covariates are independent. Covariate-dependent censoring sometimes occurs in medical studies. In this paper, we study the proportional hazards regression model for the subdistribution of a competing risk with proper adjustments for covariate-dependent censoring. We consider a covariate-adjusted weight function by fitting the Cox model for the censoring distribution and using the predictive probability for each individual. Our simulation study shows that the covariate-adjusted weight estimator is basically unbiased when the censoring time depends on the covariates, and the covariate-adjusted weight approach works well for the variance estimator as well. We illustrate our methods with bone marrow transplant data from the Center for International Blood and Marrow Transplant Research (CIBMTR). Here cancer relapse and death in complete remission are two competing risks.
Collapse
Affiliation(s)
- Peng He
- Division of Biostatistics, Medical College of Wisconsin, U.S.A
| | - Frank Eriksson
- Department of Biostatistics, University of Copenhagen, Denmark
| | | | - Mei-Jie Zhang
- Division of Biostatistics, Medical College of Wisconsin, U.S.A
| |
Collapse
|
16
|
Shen PS. Additive Transformation Models for Multivariate Interval-Censored Data. COMMUN STAT-THEOR M 2015. [DOI: 10.1080/03610926.2012.762398] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
|
17
|
He K, Schaubel DE. Semiparametric methods for center effect measures based on the ratio of survival functions. LIFETIME DATA ANALYSIS 2014; 20:619-644. [PMID: 24577567 PMCID: PMC4190619 DOI: 10.1007/s10985-014-9293-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/24/2012] [Accepted: 02/10/2014] [Indexed: 06/03/2023]
Abstract
The survival function is often of chief interest in epidemiologic studies of time to an event. We develop methods for evaluating center-specific survival outcomes through a ratio of survival functions. The proposed method assumes a center-stratified additive hazards model, which provides a convenient framework for our purposes. Under the proposed methods, the center effects measure is cast as the ratio of subject-specific survival functions under two scenarios: the scenario in which the subject is treated at center [Formula: see text]; and that wherein the subject is treated at a hypothetical center with survival function equal to the population average. The proposed measure reduces to the ratio of baseline survival functions, but is invariant to the choice of baseline covariate level. We derive the asymptotic properties of the proposed estimators, and assess finite-sample characteristics through simulation. The proposed methods are applied to national kidney transplant data.
Collapse
Affiliation(s)
- Kevin He
- Department of Biostatistics, University of Michigan, 1420 Washington Hts., Ann Arbor, MI, 48109-2029, phone: (734)709-6355
| | - Douglas E. Schaubel
- Department of Biostatistics, University of Michigan, 1420 Washington Hts., Ann Arbor, MI, 48109-2029, phone: (734)395-5992
| |
Collapse
|
18
|
Kovalchik SA, Pfeiffer RM. Population-based absolute risk estimation with survey data. LIFETIME DATA ANALYSIS 2014; 20:252-275. [PMID: 23686614 PMCID: PMC3883938 DOI: 10.1007/s10985-013-9258-4] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2012] [Accepted: 04/24/2013] [Indexed: 06/02/2023]
Abstract
Absolute risk is the probability that a cause-specific event occurs in a given time interval in the presence of competing events. We present methods to estimate population-based absolute risk from a complex survey cohort that can accommodate multiple exposure-specific competing risks. The hazard function for each event type consists of an individualized relative risk multiplied by a baseline hazard function, which is modeled nonparametrically or parametrically with a piecewise exponential model. An influence method is used to derive a Taylor-linearized variance estimate for the absolute risk estimates. We introduce novel measures of the cause-specific influences that can guide modeling choices for the competing event components of the model. To illustrate our methodology, we build and validate cause-specific absolute risk models for cardiovascular and cancer deaths using data from the National Health and Nutrition Examination Survey. Our applications demonstrate the usefulness of survey-based risk prediction models for predicting health outcomes and quantifying the potential impact of disease prevention programs at the population level.
Collapse
Affiliation(s)
- Stephanie A. Kovalchik
- Division of Cancer Epidemiology and Genetics, National Cancer Institute, 6120 Executive Blvd., EPS 8047, Rockville, MD 20852, Tele: 626-319-9890, Fax: 301-402-0081
| | - Ruth M. Pfeiffer
- Division of Cancer Epidemiology and Genetics, National Cancer Institute, 6120 Executive Blvd., EPS 8030, Rockville, MD 20852, Tel: 301 5947832, Fax: 301-402-0081
| |
Collapse
|
19
|
Zhang MJ, Zhang X, Scheike TH. Modeling cumulative incidence function for competing risks data. Expert Rev Clin Pharmacol 2014; 1:391-400. [PMID: 19829754 DOI: 10.1586/17512433.1.3.391] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
A frequent occurrence in medical research is that a patient is subject to different causes of failure, where each cause is known as a competing risk. The cumulative incidence curve is a proper summary curve, showing the cumulative failure rates over time due to a particular cause. A common question in medical research is to assess the covariate effects on a cumulative incidence function. The standard approach is to construct regression models for all cause-specific hazard rate functions and then model a covariate-adjusted cumulative incidence curve as a function of all cause-specific hazards for a given set of covariates. New methods have been proposed in recent years, emphasizing direct assessment of covariate effects on cumulative incidence function. Fine and Gray proposed modeling the effects of covariates on a subdistribution hazard function. A different approach is to directly model a covariate-adjusted cumulative incidence function, including a pseudovalue approach by Andersen and Klein and a direct binomial regression by Scheike, Zhang and Gerds. In this paper, we review the standard and new regression methods for modeling a cumulative incidence function, and give the sources of computer packages/programs that implement these regression models. A real bone marrow transplant data set is analyzed to illustrate various regression methods.
Collapse
Affiliation(s)
- Mei-Jie Zhang
- Division of Biostatistics, Medical College of Wisconsin, 8701 Watertown Plank Road, Milwaukee, WI 53226, U.S.A. Tel: +1 414-456-8375
| | | | | |
Collapse
|
20
|
Shen PS. Additive Mixed Effect Model for Clustered Doubly Censored Data. COMMUN STAT-SIMUL C 2013. [DOI: 10.1080/03610918.2012.697241] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
|
21
|
Zhao Y, Nguyen D. Tests for comparison of competing risks under the additive risk model. J Stat Plan Inference 2013. [DOI: 10.1016/j.jspi.2012.10.011] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
|
22
|
Proportional hazards model for competing risks data with missing cause of failure. J Stat Plan Inference 2012; 142:1767-1779. [PMID: 22468017 DOI: 10.1016/j.jspi.2012.02.037] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We consider the semiparametric proportional hazards model for the cause-specific hazard function in analysis of competing risks data with missing cause of failure. The inverse probability weighted equation and augmented inverse probability weighted equation are proposed for estimating the regression parameters in the model, and their theoretical properties are established for inference. Simulation studies demonstrate that the augmented inverse probability weighted estimator is doubly robust and the proposed method is appropriate for practical use. The simulations also compare the proposed estimators with the multiple imputation estimator of Lu and Tsiatis (2001). The application of the proposed method is illustrated using data from a bone marrow transplant study.
Collapse
|
23
|
Uhm D, Huffer FW, Park C. Additive Risk Model Using Piecewise Constant Hazard Function. COMMUN STAT-SIMUL C 2011. [DOI: 10.1080/03610918.2011.575508] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
|
24
|
Zhang X, Akcin H, Lim HJ. Regression analysis of competing risks data via semi-parametric additive hazard model. STAT METHOD APPL-GER 2011. [DOI: 10.1007/s10260-011-0161-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
|
25
|
Zhang X, Zhang MJ, Fine J. A proportional hazards regression model for the subdistribution with right-censored and left-truncated competing risks data. Stat Med 2011; 30:1933-51. [PMID: 21557288 DOI: 10.1002/sim.4264] [Citation(s) in RCA: 66] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2009] [Accepted: 03/21/2011] [Indexed: 11/07/2022]
Abstract
With competing risks failure time data, one often needs to assess the covariate effects on the cumulative incidence probabilities. Fine and Gray proposed a proportional hazards regression model to directly model the subdistribution of a competing risk. They developed the estimating procedure for right-censored competing risks data, based on the inverse probability of censoring weighting. Right-censored and left-truncated competing risks data sometimes occur in biomedical researches. In this paper, we study the proportional hazards regression model for the subdistribution of a competing risk with right-censored and left-truncated data. We adopt a new weighting technique to estimate the parameters in this model. We have derived the large sample properties of the proposed estimators. To illustrate the application of the new method, we analyze the failure time data for children with acute leukemia. In this example, the failure times for children who had bone marrow transplants were left truncated.
Collapse
Affiliation(s)
- Xu Zhang
- Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, USA.
| | | | | |
Collapse
|
26
|
Lee J, Hyun S. Confidence bands for the difference of two survival functions under the additive risk model. J Appl Stat 2011. [DOI: 10.1080/02664761003692308] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
|
27
|
Abstract
We propose an additive mixed effect model to analyze clustered failure time data. The proposed model assumes an additive structure and includes a random effect as an additional component. Our model imitates the commonly used mixed effect models in repeated measurement analysis but under the context of hazards regression; our model can also be considered as a parallel development of the gamma-frailty model in additive model structures. We develop estimating equations for parameter estimation and propose a way of assessing the distribution of the latent random effect in the presence of large clusters. We establish the asymptotic properties of the proposed estimator. The small sample performance of our method is demonstrated via a large number of simulation studies. Finally, we apply the proposed model to analyze data from a diabetic study and a treatment trial for congestive heart failure.
Collapse
Affiliation(s)
- Jianwen Cai
- Department of Biostatistics, University of North Carolina at Chapel Hill, North Carolina 27599-7420, USA.
| | | |
Collapse
|
28
|
Schoop R, Beyersmann J, Schumacher M, Binder H. Quantifying the predictive accuracy of time-to-event models in the presence of competing risks. Biom J 2011; 53:88-112. [DOI: 10.1002/bimj.201000073] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2010] [Revised: 11/05/2010] [Accepted: 11/08/2010] [Indexed: 11/12/2022]
|
29
|
Zhang X, Zhang MJ. SAS macros for estimation of direct adjusted cumulative incidence curves under proportional subdistribution hazards models. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2011; 101:87-93. [PMID: 20724020 PMCID: PMC3377442 DOI: 10.1016/j.cmpb.2010.07.005] [Citation(s) in RCA: 97] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/05/2010] [Revised: 06/29/2010] [Accepted: 07/13/2010] [Indexed: 05/15/2023]
Abstract
The cumulative incidence function is commonly reported in studies with competing risks. The aim of this paper is to compute the treatment-specific cumulative incidence functions, adjusting for potentially imbalanced prognostic factors among treatment groups. The underlying regression model considered in this study is the proportional hazards model for a subdistribution function [1]. We propose estimating the direct adjusted cumulative incidences for each treatment using the pooled samples as the reference population. We develop two SAS macros for estimating the direct adjusted cumulative incidence function for each treatment based on two regression models. One model assumes the constant subdistribution hazard ratios between the treatments and the alternative model allows each treatment to have its own baseline subdistribution hazard function. The macros compute the standard errors for the direct adjusted cumulative incidence estimates, as well as the standard errors for the differences of adjusted cumulative incidence functions between any two treatments. Based on the macros' output, one can assess treatment effects at predetermined time points. A real bone marrow transplant data example illustrates the practical utility of the SAS macros.
Collapse
Affiliation(s)
- Xu Zhang
- Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, USA.
| | | |
Collapse
|
30
|
Zeng D, Cai J. Additive transformation models for clustered failure time data. LIFETIME DATA ANALYSIS 2010; 16:333-52. [PMID: 20012358 PMCID: PMC2919578 DOI: 10.1007/s10985-009-9145-1] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2008] [Accepted: 11/27/2009] [Indexed: 05/28/2023]
Abstract
We propose a class of additive transformation risk models for clustered failure time data. Our models are motivated by the usual additive risk model for independent failure times incorporating a frailty with mean one and constant variability which is a natural generalization of the additive risk model from univariate failure time to multivariate failure time. An estimating equation approach based on the marginal hazards function is proposed. Under the assumption that cluster sizes are completely random, we show the resulting estimators of the regression coefficients are consistent and asymptotically normal. We also provide goodness-of-fit test statistics for choosing the transformation. Simulation studies and real data analysis are conducted to examine the finite-sample performance of our estimators.
Collapse
Affiliation(s)
- Donglin Zeng
- Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA,
| | - Jianwen Cai
- Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA,
| |
Collapse
|
31
|
Hyun S, Sun Y, Sundaram R. Assessing cumulative incidence functions under the semiparametric additive risk model. Stat Med 2010; 28:2748-68. [PMID: 19585462 DOI: 10.1002/sim.3640] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
In analyzing competing risks data, a quantity of considerable interest is the cumulative incidence function. Often, the effect of covariates on the cumulative incidence function is modeled via the proportional hazards model for the cause-specific hazard function. As the proportionality assumption may be too restrictive in practice, we consider an alternative more flexible semiparametric additive hazards model of (Biometrika 1994; 81:501-514) for the cause-specific hazard. This model specifies the effect of covariates on the cause-specific hazard to be additive as well as allows the effect of some covariates to be fixed and that of others to be time varying. We present an approach for constructing confidence intervals as well as confidence bands for the cause-specific cumulative incidence function of subjects with given values of the covariates. Furthermore, we also present an approach for constructing confidence intervals and confidence bands for comparing two cumulative incidence functions given values of the covariates. The finite sample property of the proposed estimators is investigated through simulations. We conclude our paper with an analysis of the well-known malignant melanoma data using our method.
Collapse
Affiliation(s)
- Seunggeun Hyun
- Division of Mathematics and Computer Science, University of South Carolina Upstate, Spartanburg, SC 29303, USA
| | | | | |
Collapse
|
32
|
Sun J, Shen J. Efficient estimation for the proportional hazards model with competing risks and current status data. CAN J STAT 2009. [DOI: 10.1002/cjs.10033] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
|
33
|
Estimating crude cumulative incidences through multinomial logit regression on discrete cause-specific hazards. Comput Stat Data Anal 2009. [DOI: 10.1016/j.csda.2009.01.001] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
34
|
Scheike TH, Zhang MJ. Flexible competing risks regression modeling and goodness-of-fit. LIFETIME DATA ANALYSIS 2008; 14:464-83. [PMID: 18752067 PMCID: PMC2715961 DOI: 10.1007/s10985-008-9094-0] [Citation(s) in RCA: 48] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/29/2008] [Accepted: 07/24/2008] [Indexed: 05/04/2023]
Abstract
In this paper we consider different approaches for estimation and assessment of covariate effects for the cumulative incidence curve in the competing risks model. The classic approach is to model all cause-specific hazards and then estimate the cumulative incidence curve based on these cause-specific hazards. Another recent approach is to directly model the cumulative incidence by a proportional model (Fine and Gray, J Am Stat Assoc 94:496-509, 1999), and then obtain direct estimates of how covariates influences the cumulative incidence curve. We consider a simple and flexible class of regression models that is easy to fit and contains the Fine-Gray model as a special case. One advantage of this approach is that our regression modeling allows for non-proportional hazards. This leads to a new simple goodness-of-fit procedure for the proportional subdistribution hazards assumption that is very easy to use. The test is constructive in the sense that it shows exactly where non-proportionality is present. We illustrate our methods to a bone marrow transplant data from the Center for International Blood and Marrow Transplant Research (CIBMTR). Through this data example we demonstrate the use of the flexible regression models to analyze competing risks data when non-proportionality is present in the data.
Collapse
Affiliation(s)
- Thomas H. Scheike
- Department of Biostatistics, University of Copenhagen, Copenhagen, Denmark
| | - Mei-Jie Zhang
- Division of Biostatistics, Medical College of Wisconsin, Milwaukee, WS, USA e-mail:
| |
Collapse
|
35
|
Andersen PK, Pohar Perme M. Inference for outcome probabilities in multi-state models. LIFETIME DATA ANALYSIS 2008; 14:405-31. [PMID: 18791824 PMCID: PMC2735091 DOI: 10.1007/s10985-008-9097-x] [Citation(s) in RCA: 59] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/05/2008] [Accepted: 08/12/2008] [Indexed: 05/26/2023]
Abstract
In bone marrow transplantation studies, patients are followed over time and a number of events may be observed. These include both ultimate events like death and relapse and transient events like graft versus host disease and graft recovery. Such studies, therefore, lend themselves for using an analytic approach based on multi-state models. We will give a review of such methods with emphasis on regression models for both transition intensities and transition- and state occupation probabilities. Both semi-parametric models, like the Cox regression model, and parametric models based on piecewise constant intensities will be discussed.
Collapse
Affiliation(s)
- Per Kragh Andersen
- Department of Biostatistics, University of Copenhagen, O. Farimagsgade 5, PB 2099, 1014, Copenhagen K, Denmark.
| | | |
Collapse
|
36
|
|
37
|
SCHEIKE THOMASH, ZHANG MEIJIE. Direct Modelling of Regression Effects for Transition Probabilities in Multistate Models. Scand Stat Theory Appl 2007. [DOI: 10.1111/j.1467-9469.2006.00544.x] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
|
38
|
Al-Awadhi F, Aly EEAA. Confidence regions for the quantile function in the Cox proportional hazards model. J Nonparametr Stat 2007. [DOI: 10.1080/10485250600759413] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Fahimah Al-Awadhi
- a Department of Statistics and Operations Research, Faculty of Science , Kuwait University , P.O. Box 5969, Safat, 13060, Kuwait
| | - Emad-Eldin A. A. Aly
- a Department of Statistics and Operations Research, Faculty of Science , Kuwait University , P.O. Box 5969, Safat, 13060, Kuwait
| |
Collapse
|
39
|
Dixon BS, Beck GJ, Dember LM, Depner TA, Gassman JJ, Greene T, Himmelfarb J, Hunsicker LG, Kaufman JS, Lawson JH, Meyers CM, Middleton JP, Radeva M, Schwab SJ, Whiting JF, Feldman HI. Design of the Dialysis Access Consortium (DAC) Aggrenox Prevention Of Access Stenosis Trial. Clin Trials 2006; 2:400-12. [PMID: 16317809 DOI: 10.1191/1740774505cn110oa] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
Abstract
BACKGROUND Surgically created arteriovenous (AV) grafts are the most common type of hemodialysis vascular access in the United States, but fail frequently due to the development of venous stenosis. The Dialysis Access Consortium (DAC) Aggrenox Prevention of Access Stenosis Trial tests the hypothesis that Aggrenox (containing dipyridamole and aspirin) can prevent stenosis and prolong survival of arteriovenous grafts. METHODS This is a multicenter, randomized, double-blind, placebo-controlled trial that will enroll 1056 subjects over four years with one-half year follow-up. Subjects undergoing placement of a new AV graft for hemodialysis are randomized to treatment with Aggrenox or placebo immediately following access surgery. The primary outcome is primary unassisted patency defined as the time from access placement until thrombosis or an access procedure carried out to maintain or restore patency. The major secondary outcome is cumulative access patency. Monthly access flow monitoring is incorporated in the study design to enhance detection of a hemodynamically significant access stenosis before it leads to thrombosis. RESULTS This paper describes the key issues in trial design, broadly including: 1) ethical issues surrounding the study of a clinical procedure that, although common, is no longer the clinical intervention of choice; 2) acceptable risk (bleeding) from the primary intervention; 3) inclusion of subjects already receiving a portion of the study intervention; 4) inclusion of subjects with incident rather than prevalent qualifying clinical conditions; 5) timing of the study intervention to balance safety and efficacy concerns; and 6) the selection of primary and secondary study endpoints. CONCLUSIONS This is the first, large, multicenter trial evaluating a pharmacologic approach to prevent AV graft stenosis and failure, an important and costly problem in this patient population. Numerous design issues were addressed in implementing the trial and these will form a roadmap for future trials in this area.
Collapse
Affiliation(s)
- Bradley S Dixon
- Nephrology Division, Veterans Affairs Medical Center and University of Iowa School of Medicine, Iowa City 52242-1081, USA.
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
Collapse
|
40
|
Abstract
Competing risks arise commonly in the analysis of cancer studies. Most common are the competing risks of relapse and death in remission. These two risks are the primary reason that patients fail treatment. In most medical papers the effects of covariates on the three outcomes (relapse, death in remission and treatment failure) are model by distinct proportional hazards regression models. Since the hazards of relapse and death in remission must add to that of treatment failure, we argue that this model leads to internal inconsistencies. We argue that additive models for either the hazard rates or the cumulative incidence functions are more natural and that these models properly partition the effect of a covariate on treatment failure into its component parts. We illustrate the use and interpretation of additive models for the hazard rate or for the cumulative incidence function using data from a study of the efficacy of two preparative regimes for hematopoietic stem cell transplantation.
Collapse
Affiliation(s)
- John P Klein
- Division of Biostatistics, Medical College of Wisconsin, 8701 Watertown Plank Road, Milwaukee, WI 53226, USA.
| |
Collapse
|
41
|
ZHAO YICHUAN, HSU YUSHENG. Semiparametric Analysis for Additive Risk Model via Empirical Likelihood. COMMUN STAT-SIMUL C 2005. [DOI: 10.1081/sac-200047114] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
|
42
|
Abstract
Cox's regression model is the standard regression tool for survival analysis in most applications. Often, however, the model only provides a rough summary of the effect of some covariates. Therefore, if the aim is to give a detailed description of covariate effects and to consequently calculate predicted probabilities, more flexible models are needed. In another article, Scheike and Zhang (2002, Scandinavian Journal of Statistics 29, 75-88), we suggested a flexible extension of Cox's regression model, which aimed at extending the Cox model only for those covariates where additional flexibility are needed. One important advantage of the suggested approach is that even though covariates are allowed a nonparametric effect, the hassle and difficulty of finding smoothing parameters are not needed. We show how the extended model also leads to simple formulae for predicted probabilities and their standard errors, for example, in the competing risk framework.
Collapse
Affiliation(s)
- Thomas H Scheike
- Department of Biostatistics, University of Copenhagen, Blegdamsvej 3, DK-2000, Denmark
| | | |
Collapse
|
43
|
Yin G, Hu J. Two simulation methods for constructing confidence bands under the additive risk model. J Biopharm Stat 2004; 14:389-402. [PMID: 15206535 DOI: 10.1081/bip-120037188] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Abstract
With right-censored failure time data, we propose procedures to construct simultaneous confidence bands for the survival curve of a given subject under the additive risk model. The distribution of the subject-specific cumulative hazard function can be approximated with a zero-mean Gaussian process, which can be generated through simulation methods. We propose two different simulation schemes to obtain the distribution of the supremum of the cumulative hazard process over the entire time range. The two simulation approaches are asymptotically equivalent, whereas the numerical forms are different. We construct two types of confidence bands, namely the equal precision band and the Hall-Wellner type band, through choosing suitable weight functions. Monte Carlo simulation studies show that both of the proposed confidence bands are appropriate for finite sample sizes. We illustrate the new proposal with a real example.
Collapse
Affiliation(s)
- Guosheng Yin
- Department of Biostatistics, The University of Texas, M. D. Anderson Cancer Center, Houston, Texas 77030, USA.
| | | |
Collapse
|
44
|
McKeague IW, Gilbert PB, Kanki PJ. Omnibus tests for comparison of competing risks with adjustment for covariate effects. Biometrics 2001; 57:818-28. [PMID: 11550933 DOI: 10.1111/j.0006-341x.2001.00818.x] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
Abstract
This article develops omnibus tests for comparing cause-specific hazard rates and cumulative incidence functions at specified covariate levels. Confidence bands for the difference and the ratio of two conditional cumulative incidence functions are also constructed. The omnibus test is formulated in terms of a test process given by a weighted difference of estimates of cumulative cause-specific hazard rates under Cox proportional hazards models. A simulation procedure is devised for sampling from the null distribution of the test process, leading to graphical and numerical technques for detecting significant differences in the risks. The approach is applied to a cohort study of type-specific HIV infection rates.
Collapse
Affiliation(s)
- I W McKeague
- Department of Statistics, Florida State University, Tallahassee 32306, USA.
| | | | | |
Collapse
|
45
|
Chi GY, Liu Q. The attractiveness of the concept of a prospectively designed two-stage clinical trial. J Biopharm Stat 1999; 9:537-47. [PMID: 10576402 DOI: 10.1081/bip-100101194] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Affiliation(s)
- G Y Chi
- Division of Biometrics I, Center for Drug Evaluation and Research, United States Food and Drug Administration, Rockville, Maryland, USA
| | | |
Collapse
|