scholarly journals Competing Hazards Regression Parameter Estimation Under Different Informative Priors

2021 ◽  
Author(s):  
H Rehman ◽  
Navin Chandra ◽  
Fatemeh Sadat Hosseini-Baharanchi ◽  
Ahmad Reza Baghestani
Keyword(s):  
Survival Data ◽  
Hazard Function ◽  
Failure Time ◽  
Marrow Transplant ◽  
Point Of View ◽  
Informative Priors ◽  
Baseline Model ◽  
Hazard Functions ◽  
Parametric Regression ◽  
Latent Failure

In the analysis of survival data, cause specific quantities of competing risks get considerable attention as compared to latent failure time approach. This article focuses on parametric regression analysis of survival data using cause specific hazard function with Burr type XII distribution as a baseline model. We obtained maximum likelihood and Bayes estimates of cumulative cause specific hazard functions under competing risk setup. For Bayesian point of view we proposed a class of informative priors for parameters to observe the comprehensive compatibility and their effectiveness under two different loss functions. The appropriateness of model is measured by the simulation study. Finally, we illustrate the proposed methodologies using bone marrow transplant data from the Princess Margaret Hospital Ontario, Canada.

Exploratory data analysis and the use of the hazard function for interpreting survival data: an investigator's primer.

1985 ◽  
Vol 3 (10) ◽  
pp. 1418-1431 ◽  
Author(s):  
R J Simes ◽  
M Zelen
Keyword(s):  
Survival Data ◽  
Hazard Function ◽  
Exploratory Data Analysis ◽  
Qualitative Behavior ◽  
Treatment Intervention ◽  
Patterns Of Failure ◽  
Hazard Functions ◽  
Failure Patterns ◽  
Exploratory Data ◽  
Over Time

This report discusses how one can use the hazard function to gain important insights on the patterns of failure in clinical studies when the principal endpoint is a time metric. These new insights may help gain increased understanding into the pathogenesis of a chronic disease and how it is affected by treatment intervention. The qualitative behavior of the hazard function can reveal whether mortality is increasing, decreasing, or is constant over time. Simple graphic plots are all that is necessary to show characteristic failure patterns. These informal procedures are in the spirit of carrying out exploratory analyses on the data. This report discusses the organization of clinical data using a "branch and leaf" plot, outlines the calculation of the hazard function and life table, and uses examples from lung cancer and uveal melanoma to illustrate calculations and ways of interpreting hazard functions.

scholarly journals Nonparametric Bayes estimators for hazard functions based on right censored data

2002 ◽  
Vol 33 (2) ◽  
pp. 173-190 ◽  
Author(s):  
I. W. McKeague ◽  
M. Tighiouart
Keyword(s):  
Survival Data ◽  
Hazard Rate ◽  
Markov Random Fields ◽  
Hazard Function ◽  
Right Censored Data ◽  
Hazard Functions ◽  
Censored Survival Data ◽  
Step Functions ◽  
Sample Paths ◽  
The Mean

In this article, we analyse right censored survival data by modelling their common hazard function nonparametrically. The hazard rate is assumed to be a stochastic process, with sample paths taking the form of step functions. This process jumps at times that form a time-homogeneous Poisson process, and a class of Markov random fields is used to model the values of these sample paths. Features of the posterior distribution, such as the mean hazard rate and survival probabilities, are evaluated using the Metropolis--Hastings--Green algorithm. We illustrate our methodology by simulation examples.

scholarly journals A Bayesian Approach to Competing Risks Model with Masked Causes of Failure and Incomplete Failure Times

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Yosra Yousif ◽  
Faiz A. M. Elfaki ◽  
Meftah Hrairi ◽  
Oyelola A. Adegboye
Keyword(s):  
Competing Risks ◽  
Bayesian Approach ◽  
Survival Data ◽  
Failure Time ◽  
Production Engineering ◽  
Hazard Functions ◽  
Interval Censored ◽  
Gamma Processes ◽  
The Impact ◽  
Causes Of Failure

We present a Bayesian approach for analysis of competing risks survival data with masked causes of failure. This approach is often used to assess the impact of covariates on the hazard functions when the failure time is exactly observed for some subjects but only known to lie in an interval of time for the remaining subjects. Such data, known as partly interval-censored data, usually result from periodic inspection in production engineering. In this study, Dirichlet and Gamma processes are assumed as priors for masking probabilities and baseline hazards. Markov chain Monte Carlo (MCMC) technique is employed for the implementation of the Bayesian approach. The effectiveness of the proposed approach is illustrated with simulated and production engineering applications.

scholarly journals Generalized Topp-Leone-Weibull AFT Modelling: A Bayesian Analysis with MCMC Tools using R and Stan

2021 ◽  
Vol 50 (5) ◽  
pp. 52-76
Author(s):  
Md. Ashraf-Ul-Alam ◽  
Athar Ali Khan
Keyword(s):  
Weibull Distribution ◽  
Survival Data ◽  
Failure Time ◽  
Survival Model ◽  
Accelerated Failure Time ◽  
Baseline Model ◽  
Censored Survival Data ◽  
Aft Model ◽  
Different Types ◽  
Accelerated Failure

The generalized Topp-Leone-Weibull (GTL-W) distribution is a generalization of Weibull distribution which is obtained by using generalized Topp-Leone (GTL) distribution as a generator and considering Weibull distribution as a baseline distribution. Weibull distribution is a widely used survival model that has monotone- increasing or decreasing hazard. But it cannot accommodate bathtub shaped and unimodal shaped hazards. As a survival model, GTL-W distribution is more flexible than the Weibull distribution to accommodate different types of hazards. The present study aims at fitting GTL-W model as an accelerated failure time (AFT) model to censored survival data under Bayesian setting using R and Stan languages. The GTL-W AFT model is compared with its sub-model and the baseline model. The Bayesian model selection criteria LOOIC and WAIC are applied to select the best model.

THE SHAPE OF THE HAZARD FUNCTION IN CERVICAL CANCER SURVIVAL

2001 ◽  
Vol 09 (03) ◽  
pp. 221-233 ◽  
Author(s):  
A. V. ZORIN ◽  
A. D. TSODIKOV ◽  
G. M. ZHARINOV ◽  
A. Y. YAKOVLEV
Keyword(s):  
Cervical Cancer ◽  
Survival Data ◽  
Hazard Function ◽  
Cancer Survival ◽  
Clinical Stage ◽  
Cancer Surveillance ◽  
Cervix Uteri ◽  
Hazard Functions ◽  
Clear Cut ◽  
Data Adaptive

The shape of the hazard function is of great interest in studies of the efficacy of cancer treatment and post-treatment cancer surveillance. We present estimates of the hazard rates obtained from data on survival of patients with cervical cancer and discuss associated methodological problems. Our study was carried out on survival data for 1826 women with cancer of the cervix uteri stratified by clinical stage and tumor growth pattern. We used nonparametric and various smoothing techniques for estimating the hazard function from the data; these were a nonparametric estimator based on the Nelson-Aalen method and its kernel counterparts, the kernel local likelihood estimator with a data-adaptive bandwidth, and a parametric estimator specifically designed for two-component hazards. For all categories of patients, the estimated hazard functions pass through a clear-cut maximum, tending to zero as the follow-up time becomes sufficiently long. In one stratum of patients we observed a bimodal shape of the hazard function. There are two alternative models that provide equally plausible explanations of this observation; one of them attributes the observed pattern of the hazard function to a certain heterogeneity of tumor cell population, while the competing model refers to a heterogeneity of the subsample of patients under study. Providing the probability of cure is high, as is the case in our setting, there is no way to discriminate between the two models on the basis of survival data.

scholarly journals Competing risks joint models using R-INLA

2021 ◽  
Vol 21 (1-2) ◽  
pp. 56-71
Author(s):  
Janet van Niekerk ◽  
Haakon Bakka ◽  
Håvard Rue
Keyword(s):  
Competing Risks ◽  
Count Data ◽  
Joint Model ◽  
Point Of View ◽  
Spatial Structures ◽  
Joint Models ◽  
Hazard Functions ◽  
Longitudinal Count Data ◽  
Non Gaussian ◽  
Made In

The methodological advancements made in the field of joint models are numerous. None the less, the case of competing risks joint models has largely been neglected, especially from a practitioner's point of view. In the relevant works on competing risks joint models, the assumptions of a Gaussian linear longitudinal series and proportional cause-specific hazard functions, amongst others, have remained unchallenged. In this article, we provide a framework based on R-INLA to apply competing risks joint models in a unifying way such that non-Gaussian longitudinal data, spatial structures, times-dependent splines and various latent association structures, to mention a few, are all embraced in our approach. Our motivation stems from the SANAD trial which exhibits non-linear longitudinal trajectories and competing risks for failure of treatment. We also present a discrete competing risks joint model for longitudinal count data as well as a spatial competing risks joint model as specific examples.

scholarly journals Weibull-like Model of Cancer Development in Aging

2010 ◽  
Vol 9 ◽  
pp. CIN.S5460 ◽  
Author(s):  
Tengiz Mdzinarishvili ◽  
Simon Sherman
Keyword(s):  
Mathematical Modeling ◽  
Hazard Function ◽  
White Men ◽  
Cancer Registries ◽  
Incidence Rates ◽  
Linear Functions ◽  
Cancer Development ◽  
Additional Parameter ◽  
Men And Women ◽  
Hazard Functions

Mathematical modeling of cancer development is aimed at assessing the risk factors leading to cancer. Aging is a common risk factor for all adult cancers. The risk of getting cancer in aging is presented by a hazard function that can be estimated from the observed incidence rates collected in cancer registries. Recent analyses of the SEER database show that the cancer hazard function initially increases with the age, and then it turns over and falls at the end of the lifetime. Such behavior of the hazard function is poorly modeled by the exponential or compound exponential-linear functions mainly utilized for the modeling. In this work, for mathematical modeling of cancer hazards, we proposed to use the Weibull-like function, derived from the Armitage-Doll multistage concept of carcinogenesis and an assumption that number of clones at age t developed from mutated cells follows the Poisson distribution. This function is characterized by three parameters, two of which ( r and λ) are the conventional parameters of the Weibull probability distribution function, and an additional parameter ( C0) that adjusts the model to the observational data. Biological meanings of these parameters are: r—the number of stages in carcinogenesis, λ—an average number of clones developed from the mutated cells during the first year of carcinogenesis, and C0—a data adjustment parameter that characterizes a fraction of the age-specific population that will get this cancer in their lifetime. To test the validity of the proposed model, the nonlinear regression analysis was performed for the lung cancer (LC) data, collected in the SEER 9 database for white men and women during 1975–2004. Obtained results suggest that: (i) modeling can be improved by the use of another parameter A- the age at the beginning of carcinogenesis; and (ii) in white men and women, the processes of LC carcinogenesis vary by A and C0, while the corresponding values of r and λ are nearly the same. Overall, the proposed Weibull-like model provides an excellent fit of the estimates of the LC hazard function in aging. It is expected that the Weibull-like model can be applicable to fit estimates of hazard functions of other adult cancers as well.

scholarly journals Comparison of the marginal hazard model and the sub-distribution hazard model for competing risks under an assumed copula

2019 ◽  
Vol 29 (8) ◽  
pp. 2307-2327 ◽  
Author(s):  
Takeshi Emura ◽  
Jia-Han Shih ◽  
Il Do Ha ◽  
Ralf A Wilke
Keyword(s):  
Competing Risks ◽  
Hazard Function ◽  
Cox Regression ◽  
Cox Model ◽  
Hazard Model ◽  
Numerical Comparison ◽  
Hazard Functions ◽  
Different Types ◽  
Competing Risks Data ◽  
The Relationship

For the analysis of competing risks data, three different types of hazard functions have been considered in the literature, namely the cause-specific hazard, the sub-distribution hazard, and the marginal hazard function. Accordingly, medical researchers can fit three different types of the Cox model to estimate the effect of covariates on each of the hazard function. While the relationship between the cause-specific hazard and the sub-distribution hazard has been extensively studied, the relationship to the marginal hazard function has not yet been analyzed due to the difficulties related to non-identifiability. In this paper, we adopt an assumed copula model to deal with the model identifiability issue, making it possible to establish a relationship between the sub-distribution hazard and the marginal hazard function. We then compare the two methods of fitting the Cox model to competing risks data. We also extend our comparative analysis to clustered competing risks data that are frequently used in medical studies. To facilitate the numerical comparison, we implement the computing algorithm for marginal Cox regression with clustered competing risks data in the R joint.Cox package and check its performance via simulations. For illustration, we analyze two survival datasets from lung cancer and bladder cancer patients.

Sign in / Sign up

Export Citation Format

Share Document