The use of flat or weakly informative priors is popular due to the objective a priori belief in the absence of strong prior information. In the case of the Weibull model the improper uniform, equal parameter gamma and joint Jeffrey's priors for the shape parameter are popular choices. The effects and behaviors of these priors have yet to be established from a modeling viewpoint, especially their ability to reduce to the simpler exponential model. In this work we propose a new principled prior for the shape parameter of the Weibull model, originating from a prior on the distance function, and advocate this new prior as a principled choice in the absence of strong prior information. This new prior can then be used in models with a Weibull modeling component, like competing risks, joint and spatial models, to mention a few. This prior is available in the R-INLA for use, and is applied in a joint longitudinal-survival model framework using the INLA method.
The Weibull distribution, with shape parameter $k>0$ and scale parameter $λ>0$, is one of the most popular parametric distributions in survival analysis with complete or censored data. Although inference of the parameters of the Weibull distribution is commonly done through maximum likelihood, it is well established that the maximum likelihood estimate of the shape parameter is inadequate due to the associated large bias when the sample size is small or the proportion of censored data is large. This manuscript demonstrates how the Bayesian information-theoretic minimum message length principle…
The analysis of progressively censored data has received considerable attention in the last few years. In this paper we consider the joint progressive censoring scheme for two populations. It is assumed that the lifetime distribution of the items from the two populations follow Weibull distribution with the same shape but different scale parameters. Based on the joint progressive censoring scheme first we consider the maximum likelihood estimators of the unknown parameters whenever they exist. We provide the Bayesian inferences of the unknown parameters under a fairly general priors on the sha…
We are concerned with the flexible parametric analysis of bivariate survival data. Elsewhere, we have extolled the virtues of the "power generalized Weibull" (PGW) distribution as an attractive vehicle for univariate parametric survival analysis: it is a tractable, parsimonious, model which interpretably allows for a wide variety of hazard shapes and, when adapted (to give an adapted PGW, or APGW, distribution), covers a wide variety of important special/limiting cases. Here, we additionally observe a frailty relationship between a PGW distribution with one value of the parameter which control…
The Weibull distribution is a very applicable model for the lifetime data. For inference about two Weibull distributions using records, the shape parameters of the distributions are usually considered equal. However, there is not an appropriate method for comparing the shape parameters in the literature. Therefore, comparing the shape parameters of two Weibull distributions is very important. In this paper, we propose a method for constructing confidence interval and testing hypotheses about the ratio and difference of shape parameters using the concept of the generalized {\it p}-value and the…
A six parameter distribution so-called the McDonald modified Weibull distribution is defined and studied. The new distribution contains, as special submodels, several important distributions discussed in the literature, such as the beta modified Weibull, Kumaraswamy modified Weibull, McDonald Weibull and modified Weibull distribution,among others. The new distribution can be used effectively in the analysis of survival data since it accommodates monotone, unimodal and bathtub-shaped hazard functions. We derive the moments.We propose the method of maximum likelihood for estimating the model par…
This paper considers the three-parameter exponentiated Weibull family under type II censoring. It first graphically illustrates the shape property of the hazard function. Then, it proposes a simple algorithm for computing the maximum likelihood estimator and derives the Fisher information matrix. The latter one is represented through a single integral in terms of hazard function, hence it solves the problem of computation difficulty in constructing inference for the maximum likelihood estimator. Real data analysis is conducted to illustrate the effect of censoring rate on the maximum likelihoo…
In this paper, we introduce a new four-parameter generalization of the exponentiated Weibull (EW) distribution, called the exponentiated Weibull-logarithmic (EWL) distribution, which obtained by compounding EW and logarithmic distributions. The new distribution arises on a latent complementary risks scenario, in which the lifetime associated with a particular risk is not observable; rather, we observe only the maximum lifetime value among all risks. The distribution exhibits decreasing, increasing, unimodal and bathtub-shaped hazard rate functions, depending on its parameters and contains seve…
Applying the Weibull Shape Parameter test for signal detection in pharmacovigilance using the R package WSPsignal
Biostatistics and Medical Biometry, Medical School OWL, Bielefeld University（比勒费尔德大学OWL医学院生物统计与医学生物计量学）；School of Public Health, Bielefeld University（比勒费尔德大学公共卫生学院）；Department of Business Administration and Economics, Bielefeld University（比勒费尔德大学工商管理经济学系）
We introduce a general, flexible, parametric survival modelling framework which encompasses key shapes of hazard function (constant, increasing, decreasing, up-then-down, down-then-up), various common survival distributions (log-logistic, Burr type XII, Weibull, Gompertz), and includes defective distributions (i.e., cure models). This generality is achieved using four basic distributional parameters: two scale-type parameters and two shape parameters. Generalising to covariate dependence, the scale-type regression components correspond to accelerated failure time (AFT) and proportional hazards…
Modeling is a challenging topic and using parametric models is an important stage to reach flexible function for modeling. Weibull distribution has two parameters which are shape $α$ and scale $β$. In this study, bimodality parameter is added and so bimodal Weibull distribution is proposed by using a quadratic transformation technique used to generate bimodal functions produced due to using the quadratic expression. The analytical simplicity of Weibull and quadratic form give an advantage to derive a bimodal Weibull via constructing normalizing constant. The characteristics and properties of t…
The Cox regression, a semi-parametric method of survival analysis, is extremely popular in biomedical applications. The proportional hazards assumption is a key requirement in the Cox model. To accommodate non-proportional hazards, we propose to parameterise the shape parameter of the baseline hazard function using the additional, separate Cox-regression term which depends on the vector of the covariates. We call this model the double-Cox model. The R programs for fitting the double-Cox model are available on Github. We formally introduce the double-Cox model with shared frailty and investigat…
In this article, the analysis of left truncated and right censored competing risks data is carried out, under the assumption of the latent failure times model. It is assumed that there are two competing causes of failures, although most of the results can be extended for more than two causes of failures. The lifetimes corresponding to the competing causes of failures are assumed to follow Weibull distributions with the same shape parameter but different scale parameters. The maximum likelihood estimation procedure of the model parameters is discussed, and confidence intervals are provided usin…
This paper presents a complete methodology for Bayesian inference on a semi-Markov process, from the elicitation of the prior distribution, to the computation of posterior summaries, including a guidance for its JAGS implementation. The holding times (conditional on the transition between two given states) are assumed to be Weibull-distributed. We examine the elicitation of the joint prior density of the shape and scale parameters of the Weibull distributions, deriving a specific class of priors in a natural way, along with a method for the determination of hyperparameters based on ``learning …
