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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Lifetime data analysis 1 (1995), S. 7-18 
    ISSN: 1572-9249
    Keywords: accelerated life model ; aging ; bivariate hazard function ; equivalency ; time-dependent covariates
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In some problems in survival analysis there may be more than one plausible measure of time for each individual. For example mileage may be a better indication of the age of a car than months. This paper considers the possibility of combining two (or more) time scales measured on each individual into a single scale. A collapsibility condition is proposed for regarding the combined scale as fully informative regarding survival. The resulting model may be regarded as a generalization of the usual accelerated life model that allows time-dependent covariates. Parametric methods for the choice of time scale, for testing the validity of the collapsibility assumption and for parametric inference about the failure distribution along the new scale are discussed. Two examples are used to illustrate the methods, namely Hyde's (1980) Channing House data and a large cohort mortality study of asbestos workers in Quebec.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1572-9249
    Keywords: Efficient estimation ; estimating equations ; hazard models ; matched case-control ; profile likelihood ; semiparametric models
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A general approach to estimation, that can lead to efficient estimation in two stages, is presented. The method will not always be available, but sufficient conditions for efficiency are provided together with four examples of its use: (1) estimation of the odds ratio in 1:M matched case-control studies with a dichotomous exposure variable; (2) estimation of the relative hazard in a two-sample survival setting; (3) estimation of the regression parameters in the proportional excess hazards model; and (4) estimation in a partly linear parametric additive hazards model. The method depends upon finding a family of weighted estimating equations, which includes a simple initial equation yielding a consistent estimate and also an equation that yields an efficient estimate, provided the optiomal weights are used.
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Lifetime data analysis 1 (1995), S. 101-109 
    ISSN: 1572-9249
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In estimation of a survival function, current status data arises when the only information available on individuals is their survival status at a single monitoring time. Here, we briefly review extensions of this form of data structure in two directions: (i) doubly censored current status data, where there is incomplete information on the origin of the failure time random variable, and (ii) current status information on more complicated stochastic processes. Simple examples of these data forms are presented for motivation.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Lifetime data analysis 1 (1995), S. 145-156 
    ISSN: 1572-9249
    Keywords: test of homogeneity ; overdispersion ; survival data ; partial likelihood ; counting processes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract If follow-up is made for subjects which are grouped into units, such as familial or spatial units then it may be interesting to test whether the groups are homogeneous (or independent for given explanatory variables). The effect of the groups is modelled as random and we consider a frailty proportional hazards model which allows to adjust for explanatory variables. We derive the score test of homogeneity from the marginal partial likelihood and it turns out to be the sum of a pairwise correlation term of martingale residuals and an overdispersion term. In the particular case where the sizes of the groups are equal to one, this statistic can be used for testing overdispersion. The asymptotic variance of this statistic is derived using counting process arguments. An extension to the case of several strata is given. The resulting test is computationally simple; its use is illustrated using both simulated and real data. In addition a decomposition of the score statistic is proposed as a sum of a pairwise correlation term and an overdispersion term. The pairwise correlation term can be used for constructing a statistic more robust to departure from the proportional hazard model, and the overdispesion term for constructing a test of fit of the proportional hazard model.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Lifetime data analysis 1 (1995), S. 157-158 
    ISSN: 1572-9249
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Lifetime data analysis 1 (1995), S. 159-159 
    ISSN: 1572-9249
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
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  • 7
    ISSN: 1572-9249
    Keywords: Orthogonal arrays ; orthogonal contrasts ; censoring ; half-normal plots ; Taguchi ; proportional hazards ; Weibull regression
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Smith (1991) presents a paper proposing the use of Weibull regression models to establish dependence of failure data (usually times) on covariates related to the design of the test specimens and test procedures. In his article Smith made the point that good experimental design was as important in reliability applications as elsewhere, and in view of the current interest in design inspired by Taguchi and others, we pay some attention in this article to that topic. A real case study from the Ford Motor Company is presented. Our main approach is to utilize suggestions in the literature for applying standard least squares techniques of experimental analysis even when there is likely to be nonnormal error, and censoring. This approach lacks theoretical justification, but its appeal is its simplicity and flexibility. For completeness we also include some analysis based on the proportional hazards model, and in an attempt to link back to Smith (1991), look at a Weibull regression model.
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  • 8
    ISSN: 1572-9249
    Keywords: Coherent system ; hazard functions ; load-sharing ; marked point process ; Markov chain ; parallel system ; software reliability ; structure function ; series-parallel system ; Primary: 62N05 ; Secondary: 62E15, 60G55
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A dynamic approach to the stochastic modelling of reliability systems is further explored. This modelling approach is particularly appropriate for load-sharing, software reliability, and multivariate failure-time models, where component failure characteristics are affected by their degree of use, amount of load, or extent of stresses experienced. This approach incorporates the intuitive notion that when a set of components in a coherent system fail at a certain time, there is a ‘jump’ from one structure function to another which governs the residual lifetimes of the remaining functioning components, and since the component lifetimes are intrinsically affected by the structure function which they constitute, then at such a failure time there should also be a jump in the stochastic structure of the lifetimes of the remaining components. For such dynamically-modelled systems, the stochastic characteristics of their jump times are studied. These properties of the jump times allow us to obtain the properties of the lifetime of the system. In particular, for a Markov dynamic model, specific expressions for the exact distribution functions of the jump times are obtained for a general coherent system, a parallel system, and a series-parallel system. We derive a new family of distribution functions which describes the distributions of the jump times for a dynamically-modelled system.
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Lifetime data analysis 2 (1996), S. 51-61 
    ISSN: 1572-9249
    Keywords: interval-censored data ; censored regression ; Buckley-James estimators ; product-limit estimator
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this note we provide a general framework for describing interval-censored samples including estimation of the magnitude and rank positions of data that have been interval-censored so as to counteract the effect of censoring. This process of sample adjustment, or renovation, allows samples to be compared graphically, using diagrams (such as boxplots) which are based on ranks. The renovation process is based on Buckley-James regression estimators for linear regression with censored data.
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Lifetime data analysis 2 (1996), S. 63-71 
    ISSN: 1572-9249
    Keywords: Censored data ; frailty ; lifetime data ; random effects
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The Weibull distribution is a natural starting point in the modelling of failure times in reliability, material strength data and many other applications that involve lifetime data. In recent years there has been a growing interest in modelling heterogeneity within this context. A natural approach is to consider a mixture, either discrete or continuous, of Weibull distributions. A judicious choice of mixing distribution yields a tractable and flexible generalization of the Weibull distribution. In this note a score test for detecting heterogeneity in this context is discussed and illustrated using some infant nutrition data.
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