Bayesian analysis of generalized odds-rate hazards models for survival data

In the analysis of censored survival data Cox proportional hazards model (1972) is extremely popular among the practitioners. However, in many real-life situations the proportionality of the hazard ratios does not seem to be an appropriate assumption. To overcome such a problem, we consider a class of nonproportional hazards models known as generalized odds-rate class of regression models. The class is general enough to include several commonly used models, such as proportional hazards model, proportional odds model, and accelerated life time model. The theoretical and computational properties of these models have been re-examined. The propriety of the posterior has been established under some mild conditions. A simulation study is conducted and a detailed analysis of the data from a prostate cancer study is presented to further illustrate the proposed methodology.     

Some recent developments for regression analysis of multivariate failure time data

Cox's seminal 1972 paper on regression methods for possibly censored failure time data popularized the use of time to an event as a primary response in prospective studies. But one key assumption of this and other regression methods is that observations are independent of one another. In many problems, failure times are clustered into small groups where outcomes within a group are correlated. Examples include failure times for two eyes from one person or for members of the same family.This paper presents a survey of models for multivariate failure time data. Two distinct classes of models are considered: frailty and marginal models. In a frailty model, the correlation is assumed to derive from latent variables (frailties) common to observations from the same cluster. Regression models are formulated for the conditional failure time distribution given the frailties. Alternatively, marginal models describe the marginal failure time distribution of each response while separately modelling the association among responses from the same cluster.We focus on recent extensions of the proportional hazards model for multivariate failure time data. Model formulation, parameter interpretation and estimation procedures are considered.     

Conjugate analysis of multivariate normal data with incomplete observations

The authors discuss prior distributions that are conjugate to the multivariate normal likelihood when some of the observations are incomplete. They present a general class of priors for incorporating information about unidentified parameters in the covariance matrix. They analyze the special case of monotone patterns of missing data, providing an explicit recursive form for the posterior distribution resulting from a conjugate prior distribution. They develop an importance sampling and a Gibbs sampling approach to sample from a general posterior distribution and compare the two methods.     

A poisson-gamma model for two-stage cluster sampling data

We propose a model for count data from two-stage cluster sampling, where observations within each cluster are subjected simultaneously to internal influences and external factors at the cluster level. This model can be seen as a two-stage hierarchical model with local and global predictors. This parameter-driven model causes the counts within a cluster to share a common latent factor and to be correlated. Maximum likelihood (ml) estimation based on an EM algorithm for the model is discussed. Simulation study is carried out to assess the benefit of using ml estimates compared to a standard Poisson regression analysis that ignores the within cluster correlation.     

A bayesian treatpent of nonresponse when sampling from a dichotomous population

In the situation where significant nonresponse is present in a sample survey, a prior distribution is developed which can reflect vague prior beliefs about the differences in the attitudes of respondents and nonrespondents. A posterior interval estimate is derived for the population proportion of interest.     

A Bayesian Analysis of Correlated Interval-Censored Data

In epidemiological studies where subjects are seen periodically on follow-up visits, interval-censored data occur naturally. The exact time the change of state (such as HIV seroconversion) occurs is not known exactly, only that it occurred within some time interval. In multi-stage sampling or partner tracing studies, individuals are grouped into smaller subgroups. Individuals within a subgroup share an unobservable specific frailty which induces correlation within the subgroup. In this paper, we consider a Bayesian model for analysing correlated interval-censored data. Parameters are estimated using the Markov chain Monte Carlo methods, specifically the Gibbs sampler.     

A Bayesian model for multinomial sampling with misclassified data

In this paper the issue of making inferences with misclassified data from a noisy multinomial process is addressed. A Bayesian model for making inferences about the proportions and the noise parameters is developed. The problem is reformulated in a more tractable form by introducing auxiliary or latent random vectors. This allows for an easy-to-implement Gibbs sampling-based algorithm to generate samples from the distributions of interest. An illustrative example related to elections is also presented.     

Bayesian analysis of multivariate mortality data with large families

This paper presents a Bayesian method for the analysis of toxicological multivariate mortality data when the discrete mortality rate for each family of subjects at a given time depends on familial random effects and the toxicity level experienced by the family. Our aim is to model and analyse one set of such multivariate mortality data with large family sizes: the potassium thiocyanate (KSCN) tainted fish tank data of O'Hara Hines. The model used is based on a discretized hazard with additional time-varying familial random effects. A similar previous study (using sodium thiocyanate (NaSCN)) is used to construct a prior for the parameters in the current study. A simulation-based approach is used to compute posterior estimates of the model parameters and mortality rates and several other quantities of interest. Recent tools in Bayesian model diagnostics and variable subset selection have been incorporated to verify important modelling assumptions regarding the effects of time and heterogeneity among the families on the mortality rate. Further, Bayesian methods using predictive distributions are used for comparing several plausible models.     

Bivariate frailty model for the analysis of multivariate survival time

Because of limitations of the univariate frailty model in analysis of multivariate survival data, a bivariate frailty model is introduced for the analysis of bivariate survival data. This provides tremendous flexibility especially in allowing negative associations between subjects within the same cluster. The approach involves incorporating into the model two possibly correlated frailties for each cluster. The bivariate lognormal distribution is used as the frailty distribution. The model is then generalized to multivariate survival data with two distinguished groups and also to alternating process data. A modified EM algorithm is developed with no requirement of specification of the baseline hazards. The estimators are generalized maximum likelihood estimators with subject-specific interpretation. The model is applied to a mental health study on evaluation of health policy effects for inpatient psychiatric care.     

Composite likelihood estimation in multivariate data analysis

The authors propose two composite likelihood estimation procedures for multivariate models with regression/univariate and dependence parameters. One is a two‐stage method based on both univariate and bivariate margins. The other estimates all the parameters simultaneously based on bivariate margins. For some special cases, the authors compare their asymptotic efficiencies with the maximum likelihood method. The performance of the two methods is reasonable, except that the first procedure is inefficient for the regression parameters under strong dependence. The second approach is generally better for the regression parameters, but less efficient for the dependence parameters under weak dependence.     

Residual-based specification of the random-effects distribution for cluster data

We propose a method for specifying the distribution of random effects included in a model for cluster data. The class of models we consider includes mixed models and frailty models whose random effects and explanatory variables are constant within clusters. The method is based on cluster residuals obtained by assuming that the random effects are equal between clusters. We exhibit an asymptotic relationship between the cluster residuals and variations of the random effects as the number of observations increases and the variance of the random effects decreases. The asymptotic relationship is used to specify the random-effects distribution. The method is applied to a frailty model and a model used to describe the spread of plant diseases.     

A bayesian analysis of autoregressive models with random normal coefficients

In this paper we consider a Bayesian analysis for an autoregressive model with random normal coefficients (RCA). For the proposed procedure we use conjugate priors for some parameters and improper vague priors for others. The inference for the parameters is made via Gibbs sampler and the convergence is assessed with multiple chains and Gelman and Rubin criterium. Forecasts are based on the predictive density of future observations. Some remarks are also made regarding order determination and stationarity. Applications to simulated and real series are given.     

A bayesian analysis of imperfect inspection models

An examination of sampling inspection models is provided for the case where inspection is not perfect and classification errors can be made. The conjugate family of distributions is obtained under t h e assumption that defective items are generated according to a Bernoulli process. To simplify analysis, the use of a single beta prior distribution is considered. Relevant predictive distributions are obtained.     

A New lifetime model for multivariate survival data with a surviving fraction

In this paper we propose a new lifetime model for multivariate survival data with a surviving fraction. We develop this model assuming that there are m types of unobservable competing risks, where each risk is related to a time of the occurrence of an event of interest. We explore the use of Markov chain Monte Carlo methods to develop a Bayesian analysis for the proposed model. We also perform a simulation study in order to analyse the frequentist coverage probabilities of credible interval derived from posteriors. Our modelling is illustrated through a real data set.     

A survey of permutation tests for censored survival data

The present paper surveys tests with censored sur-vival data for 2-and k-samples and for association by a framework which classifies them into complete or restric-ted permutation tests and into tests based on U-or Savage-scores. The formulae of the resulting twelve tests are briefly described for quick reference. Some of the tests have been applied frequently in the past as the tests by Mantel, Breslow or Gehan; others have been developed rather recently, partly by the author. The concluding discussion presents the results of a simulation study, clarifying similarities and differences of the restricted and complete permutation approach, and deals with rela-tive efficiencies of the two scoring systems.     

A new class of multivariate skew distributions with applications to bayesian regression models

Abstract: The authors develop a new class of distributions by introducing skewness in multivariate elliptically symmetric distributions. The class, which is obtained by using transformation and conditioning, contains many standard families including the multivariate skew‐normal and t distributions. The authors obtain analytical forms of the densities and study distributional properties. They give practical applications in Bayesian regression models and results on the existence of the posterior distributions and moments under improper priors for the regression coefficients. They illustrate their methods using practical examples.     

The effect of classification errors in survival data analysis

Survival data analysis aims at collecting data on durations spent in a state by a sample of units, in order to analyse the process of transition to a different state. Survival analysis applied to social and economic phenomena typically relies upon data on transitions collected, for a sample of units, in one or more follow-up surveys. We explore the effect of misclassification of the transition indicator on parameter estimates in an appropriate statistical model for the duration spent in an origin state. Some empirical investigations about the bias induced when ignoring misclassification are reported, extending the model to include the possibility that the rate of misclassification can vary across units according to the value of some covariates. Finally it is shown how a Bayesian approach can lead to parameter estimates.     

Discrete-time survival analysis under ranked set sampling: an application to Turkish motor insurance data

Survival models with continuous-time data are still superior methods of survival analysis. However when the survival data is discrete, taking it as continuous leads the researchers to incorrect results and interpretations. The discrete-time survival model has some advantages in applications such as it can be used for non-proportional hazards, time-varying covariates and tied observations. However, it has a disadvantage about the reconstruction of the survival data and working with big data sets. Actuaries are often rely on complex and big data whereas they have to be quick and efficient for short period analysis. Using the mass always creates inefficient processes and consumes time. Therefore sampling design becomes more and more important in order to get reliable results. In this study, we take into account sampling methods in discrete-time survival model using a real data set on motor insurance. To see the efficiency of the proposed methodology we conducted a simulation study.     

Effect of frailty on marginal regression estimates in survival analysis

Unexplained heterogeneity in univariate survival data and association in multivariate survival can both be modelled by the inclusion of frailty effects. This paper investigates the consequences of ignoring frailty in analysis, fitting misspecified Cox proportional hazards models to the marginal distributions. Regression coefficients are biased towards 0 by an amount which depends in magnitude on the variability of the frailty terms and the form of frailty distribution. The bias is reduced when censoring is present. Fitted marginal survival curves can also differ substantially from the true marginals.