The Fitting of Exponential, Weibull and Extreme Value Distributions to Complex Censored Survival Data Using GLIM

Aitkin, Murray; Clayton, David

doi:10.2307/2986301

Cited by 277 publications

(148 citation statements)

References 8 publications

(14 reference statements)

Supporting

Mentioning

145

Contrasting

Order By: Relevance

“…when yjh > 1 for some j), ML estimates under the Poisson assumption yield estimates of 8 that maximize the generalized partial likelihood function based on Peto's approximation (Peto, 1972). This leads one to conclude that algorithms for fitting generalized linear models can be used to analyze censored survival data (see Holford, 1980;Whitehead, 1980;Aitkin and Clayton, 1980). In this note, we show that this type of analysis can be viewed as a weighted least squares regression and that the results can be extended to apply to any reasonable regression function-i.e.…”

Section: Introductionmentioning

confidence: 84%

The Analysis of Rates Using Poisson Regression Models

Frome¹

1983

Biometrics

394

209

View full text Add to dashboard Cite

Models are considered in which the underlying rate at which events occur can be represented by a regression function that describes the relation between the predictor variables and the unknown parameters. Estimates of the parameters can be obtained by means of iteratively reweighted least squares (IRLS). When the events of interest follow the Poisson distribution, the IRLS algorithm is equivalent to using the method of scoring to obtain maximum likelihood (ML) estimates. The general Poisson regression models include log-linear, quasilinear and intrinsically nonlinear models. The approach considered enables one to concentrate on describing the relation between the dependent variable and the predictor variables through the regression model. Standard statistical packages that support IRLS can then be used to obtain ML estimates, their asymptotic covariance matrix, and diagnostic measures that can be used to aid the analyst in detecting outlying responses and extreme points in the model space. Applications of these methods to epidemiologic follow-up studies with the data organized into a life-table type of format are discussed. The method is illustrated by using a nonlinear model, derived from the multistage theory of carcinogenesis, to analyze lung cancer death rates among British physicians who were regular cigarette smokers.

show abstract

Section: Introductionmentioning

confidence: 84%

The Analysis of Rates Using Poisson Regression Models

Frome¹

1983

Biometrics

394

209

View full text Add to dashboard Cite

show abstract

“…One dimensional versions of the calculations we describe below were given previously in [2] for models without random components and in [15] for mixed models for continuous time models (piece-wise constant baselines). For one-dimensional discrete times models without random components see [19].…”

Section: The Basic Set-up and Genetic Scenariomentioning

confidence: 99%

“…Additionally, a discrete explanatory variable counting the order of the time period for each individual should be included in the model in order to represent the baseline function. The model should also specify the covariance structure of the random components given in equation (2). Furthermore, each marginal model includes a dispersion parameter φ j (known in the literature of generalized linear mod-els as an over-dispersion parameter for binomial and Poisson models), which allowed us to better characterizing the genetic scenario.…”

Section: The Basic Set-up and Genetic Scenariomentioning

confidence: 99%

“…The continuous time models (CTM) will be suitable approximations of the semi-parametric Cox proportional model in which the hazard function will be assumed to be piece-wise constant. These models allow for regular parametric likelihood-based inference by exploring a coincidence of their likelihood functions and the likelihood function of a Poisson model applied to a specially constructed data [2]. When including gaussian random components (log gaussian frailties) the inference can be based on a Laplace approximation to a high dimensional integral [4,24,28].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Multivariate survival mixed models for genetic analysis of longevity traits

Maia

Madsen

Labouriau

2013

Journal of Applied Statistics

View full text Add to dashboard Cite

A class of multivariate mixed survival models for continuous and discrete time with a complex covariance structure is introduced in a context of quantitative genetic applications. The methods introduced can be used in many applications in quantitative genetics although the discussion presented concentrates on longevity studies. The framework presented allows to combine models based on continuous time with models based on discrete time in a joint analysis. The continuous time models are approximations of the frailty model in which the hazard function will be assumed to be piece-wise constant. The discrete time models used are multivariate variants of the discrete relative risk models. These models allow for regular parametric likelihood-based inference by exploring a coincidence of their likelihood functions and the likelihood functions of suitably defined multivariate generalized linear mixed models. The models include a dispersion parameter, which is essential for obtaining a decomposition of the variance of the trait of interest as a sum of parcels representing the additive genetic effects, environmental effects and unspecified sources of variability; as required in quantitative genetic applications. The methods presented are implemented in such a way that large and complex quantitative genetic data can be analyzed.

show abstract

“…The proposed model is more general than other frailty models, having as special members regular frailty models, such as shared frailty and bivariate frailty models if we ignore the time-modulated component in the model. Using the well-known connection to Poisson regression (Aitkin and Clayton, 1980), the derived model is a generalized linear mixed model (glmm). We adopt a robust approach for estimating some parameters using the generalized estimating equations (GEE) in this Poisson regression setting.…”

Section: Introductionmentioning

confidence: 99%

Vol. 1, No. 2 (Full Issue)

2002

J. Mod. App. Stat. Meth.

View full text Add to dashboard Cite

The Fitting of Exponential, Weibull and Extreme Value Distributions to Complex Censored Survival Data Using GLIM

Cited by 277 publications

References 8 publications

The Analysis of Rates Using Poisson Regression Models

The Analysis of Rates Using Poisson Regression Models

Multivariate survival mixed models for genetic analysis of longevity traits

Vol. 1, No. 2 (Full Issue)

Contact Info

Product

Resources

About