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Semiparametric Estimators for the Regression Coefficients in the Linear Transformation Competing Risks Models with Missing Cause of Failure

Semiparametric Estimators for the Regression Coefficients in the Linear Transformation Competing Risks Models with Missing Cause of Failure
Author:
Publisher:
Total Pages:
Release: 2004
Genre:
ISBN:

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In many clinical studies, researchers are mainly interested in studying the effects of some prognostic factors on the hazard of failure from a specific cause while individuals may failure from multiple causes. This leads to a competing risks problem. Often, due to various reasons such as finite study duration, loss to follow-up, or withdrawal from the study, the time-to-failure is right-censored for some individuals. Although the proportional hazards model has been commonly used in analyzing survival data, there are circumstances where other models are more appropriate. Here we consider the class of linear transformation models that contains the proportional hazards model and the proportional odds model as special cases. Sometimes, patients are known to die but the cause of death is unavailable. It is well known that when cause of failure is missing, ignoring the observations with missing cause or treating them as censored may result in erroneous inferences. Under the Missing At Random assumption, we propose two methods to estimate the regression coefficients in the linear transformation models. The augmented inverse probability weighting method is highly efficient and doubly robust. In addition, it allows the possibility of using auxiliary covariates to model the missing mechanism. The multiple imputation method is very efficient, is straightforward and easy to implement and also allows for the use of auxiliary covariates. The asymptotic properties of these estimators are developed using theory of counting processes and semiparametric theory for missing data problems. Simulation studies demonstrate the relevance of the theory in finite samples. These methods are also illustrated using data from a breast cancer stage II clinical trial.


Semiparametric Estimators for the Regression Coefficients in the Linear Transformation Competing Risks Models with Missing Cause of Failure

Semiparametric Estimators for the Regression Coefficients in the Linear Transformation Competing Risks Models with Missing Cause of Failure
Author: Guozhi Gao
Publisher:
Total Pages: 71
Release: 2005
Genre:
ISBN:

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Keywords: Influence function, Multiple Imputation, Missing at random, Semiparametric estimator, Inverse probability weighted, Linear transformation model, Double Robustness, Competing risks, Cause-specific hazard.


Estimation of Regression Coefficients in the Competing Risks Model with Missing Cause of Failure

Estimation of Regression Coefficients in the Competing Risks Model with Missing Cause of Failure
Author: Kaifeng Lu
Publisher:
Total Pages: 70
Release: 2002
Genre:
ISBN:

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Keywords: cause-specific hazard, doubly robust, imputation, influence function, inverse probability weighting, locally efficient, missing at random, partial likelihood, proportional hazards model, semiparametric model.


Absolute Risk

Absolute Risk
Author: Ruth M. Pfeiffer
Publisher: CRC Press
Total Pages: 189
Release: 2017-08-10
Genre: Mathematics
ISBN: 1351643819

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Absolute Risk: Methods and Applications in Clinical Management and Public Health provides theory and examples to demonstrate the importance of absolute risk in counseling patients, devising public health strategies, and clinical management. The book provides sufficient technical detail to allow statisticians, epidemiologists, and clinicians to build, test, and apply models of absolute risk. Features: Provides theoretical basis for modeling absolute risk, including competing risks and cause-specific and cumulative incidence regression Discusses various sampling designs for estimating absolute risk and criteria to evaluate models Provides details on statistical inference for the various sampling designs Discusses criteria for evaluating risk models and comparing risk models, including both general criteria and problem-specific expected losses in well-defined clinical and public health applications Describes many applications encompassing both disease prevention and prognosis, and ranging from counseling individual patients, to clinical decision making, to assessing the impact of risk-based public health strategies Discusses model updating, family-based designs, dynamic projections, and other topics Ruth M. Pfeiffer is a mathematical statistician and Fellow of the American Statistical Association, with interests in risk modeling, dimension reduction, and applications in epidemiology. She developed absolute risk models for breast cancer, colon cancer, melanoma, and second primary thyroid cancer following a childhood cancer diagnosis. Mitchell H. Gail developed the widely used "Gail model" for projecting the absolute risk of invasive breast cancer. He is a medical statistician with interests in statistical methods and applications in epidemiology and molecular medicine. He is a member of the National Academy of Medicine and former President of the American Statistical Association. Both are Senior Investigators in the Division of Cancer Epidemiology and Genetics, National Cancer Institute, National Institutes of Health.


Statistical Modelling of Survival Data with Random Effects

Statistical Modelling of Survival Data with Random Effects
Author: Il Do Ha
Publisher: Springer
Total Pages: 288
Release: 2018-01-02
Genre: Mathematics
ISBN: 9811065578

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This book provides a groundbreaking introduction to the likelihood inference for correlated survival data via the hierarchical (or h-) likelihood in order to obtain the (marginal) likelihood and to address the computational difficulties in inferences and extensions. The approach presented in the book overcomes shortcomings in the traditional likelihood-based methods for clustered survival data such as intractable integration. The text includes technical materials such as derivations and proofs in each chapter, as well as recently developed software programs in R (“frailtyHL”), while the real-world data examples together with an R package, “frailtyHL” in CRAN, provide readers with useful hands-on tools. Reviewing new developments since the introduction of the h-likelihood to survival analysis (methods for interval estimation of the individual frailty and for variable selection of the fixed effects in the general class of frailty models) and guiding future directions, the book is of interest to researchers in medical and genetics fields, graduate students, and PhD (bio) statisticians.


Statistica Sinica

Statistica Sinica
Author:
Publisher:
Total Pages: 838
Release: 2008
Genre: Mathematical statistics
ISBN:

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Advanced Survival Models

Advanced Survival Models
Author: Catherine Legrand
Publisher: CRC Press
Total Pages: 361
Release: 2021-03-22
Genre: Mathematics
ISBN: 0429622554

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Survival data analysis is a very broad field of statistics, encompassing a large variety of methods used in a wide range of applications, and in particular in medical research. During the last twenty years, several extensions of "classical" survival models have been developed to address particular situations often encountered in practice. This book aims to gather in a single reference the most commonly used extensions, such as frailty models (in case of unobserved heterogeneity or clustered data), cure models (when a fraction of the population will not experience the event of interest), competing risk models (in case of different types of event), and joint survival models for a time-to-event endpoint and a longitudinal outcome. Features Presents state-of-the art approaches for different advanced survival models including frailty models, cure models, competing risk models and joint models for a longitudinal and a survival outcome Uses consistent notation throughout the book for the different techniques presented Explains in which situation each of these models should be used, and how they are linked to specific research questions Focuses on the understanding of the models, their implementation, and their interpretation, with an appropriate level of methodological development for masters students and applied statisticians Provides references to existing R packages and SAS procedure or macros, and illustrates the use of the main ones on real datasets This book is primarily aimed at applied statisticians and graduate students of statistics and biostatistics. It can also serve as an introductory reference for methodological researchers interested in the main extensions of classical survival analysis.