Heterogeneity in survival analysis

Epidemiological models generally assume that the number of susceptible individuals that become infected within a unit of time depends on the density of the hosts and the concentration of parasites (i.e. mass-action principle). However, empirical studies have found significant deviations from this assumption due to biotic and abiotic factors, such as seasonality, the spatial structure of the host population and host heterogeneity with respect to immunity and susceptibility. In this paper, we examine the effect of the dose level of the bacterial endoparasite Pasteuria ramosa on the infection rate of its host, the water flea Daphnia magna. Using seven host clones and two parasite isolates, we measure the fraction of infected hosts after exposure to eight different parasite doses to determine whether there is variation in the infection process across different host clone-parasite isolate combinations. In five combinations, a pronounced dose-dependent infection pattern was found. Using a likelihood approach, we compare the infection data of these five combinations to the fit of three mathematical models: a mass-action model, a parasite antagonism model (i.e. an increase in the parasite dose leads to an under-proportionate increase in the infection rate per host) and a heterogeneous host model. We found that the host heterogeneity model, in which we assumed the existence of non-inherited phenotypic differences in host susceptibilities to the parasite, provides the best fit. Our analysis suggests that among 5 out of the 14 host clone-parasite isolate combinations that resulted in appreciable infections, non-genetic host heterogeneity plays an important role.

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“…This is a standard extension of simple survival models referred to as frailty models (Hougaard 1986;Aalen 1988).…”

Section: (B) Experimental Setupmentioning

confidence: 99%

A quantitative test of the relationship between parasite dose and infection probability across different host–parasite combinations

2008

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“…. , s, given the history before (k − 1)h, is roughly γ j (kh)h, while the conditional probability of no event in this interval is roughly 1 − γ(kh)h. The probability of a realization of the process from 0 to τ will therefore include a product of N (τ ) terms of the type γ j (kh)h, corresponding to the observed events, and which in the limit as h → 0 (after dividing by the normalization h N (τ ) ) gives the product term on the right-hand side of (2). The exponential part of (2) comes from taking the limit of the product of the terms 1 − γ(kh)h ≈ exp{− kh (k−1)h γ(t) dt} for the intervals that contain no event, assuming continuity of γ(·).…”

Section: Notation and Basic Definitionsmentioning

confidence: 99%

“…This in turn leads to a decreasing population hazard, which has often been misinterpreted. Important references on heterogeneity in the biostatistics literature are [62], [32] and [2]. It should be noted that heterogeneity is, in general, unidentifiable if it is considered as an individual quantity.…”

Section: Unobserved Heterogeneity In Repairable Systemsmentioning

confidence: 99%

Statistical Modeling and Analysis of Repairable Systems

Lindqvist

1999

Statistical and Probabilistic Models in Reliability

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Abstract. We review basic modeling approaches for failure and maintenance data from repairable systems. In particular we consider imperfect repair models, defined in terms of virtual age processes, and the trend-renewal process which extends the nonhomogeneous Poisson process and the renewal process. In the case where several systems of the same kind are observed, we show how observed covariates and unobserved heterogeneity can be included in the models. We also consider various approaches to trend testing. Modern reliability data bases usually contain information on the type of failure, the type of maintenance and so forth in addition to the failure times themselves. Basing our work on recent literature we present a framework where the observed events are modeled as marked point processes, with marks labeling the types of events. Throughout the paper the emphasis is more on modeling than on statistical inference.

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“…This in turn leads to a decreasing population hazard, which has often been misinterpreted in the same manner as mentioned for the reliability applications. Important references on heterogeneity in the biostatistics literature are Vaupel et al [33], Hougaard [16] and Aalen [1]. It should be noted that heterogeneity is in general unidentifiable if being considered an individual quantity.…”

Section: Discussionmentioning

confidence: 99%

“…Figure 2 illustrates the definition. For the cited property of the NHPP, the lower axis would be an HPP with unit intensity, HPP (1). For the TRP, this process is instead taken to be any renewal process, RP(F), where F has expectation 1.…”

Section: The Trend-renewal Processmentioning

confidence: 99%

Maintenance of Repairable Systems

Lindqvist

Springer Series in Reliability Engineering

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A commonly used definition of a repairable system (Ascher and Feingold [3]) states that this is a system which, after failing to perform one or more of its functions satisfactorily, can be restored to fully satisfactory performance by any method other than replacement of the entire system. In order to cover more realistic applications, and to cover much recent literature on the subject, we need to extend this definition to include the possibility of additional maintenance actions which aim at servicing the system for better performance. This is referred to as preventive maintenance (PM), where one may further distinguish between condition based PM and planned PM. The former type of maintenance is due when the system exhibits inferior performance while the latter is performed at predetermined points in time.Traditionally, the literature on repairable systems is concerned with modelling of the failure times only, using point process theory. A classical reference here is Ascher and Feingold [3]. The most commonly used models for the failure process of a repairable system are renewal processes (RP), including the homogeneous Poisson processes (HPP), and nonhomogeneous Poisson processes (NHPP). While such models often are sufficient for simple reliability studies, the need for more complex models is clear. In this chapter we consider some generalizations and extensions of the basic models, with the aim to arrive at more realistic models which give better fit to data. First we consider the Trend Renewal Process (TRP) introduced and studied in Lindqvist, Elvebakk and Heggland [22]. The TRP includes NHPP and RP as special cases, and the main new feature is to allow a trend in processes of non-Poisson (renewal) type.As exemplified by some real data, in the case where several systems of the same kind are considered, there may be unobserved heterogeneity between the systems which, if overlooked, may lead to non-optimal or possibly completely wrong decisions. We will consider this in the framework of the TRP process, which in Lindqvist et al. [22] is extended to the so called HTRP model which includes the possibility of heterogeneity. Heterogeneity can be thought of as an effect of an unobserved covariate.Another extension of the basic models is to allow the systems to be preventively maintained. We review some recent research in this direction, where this 1

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Heterogeneity in survival analysis

Cited by 330 publications

References 24 publications

A quantitative test of the relationship between parasite dose and infection probability across different host–parasite combinations

A quantitative test of the relationship between parasite dose and infection probability across different host–parasite combinations

Statistical Modeling and Analysis of Repairable Systems

Maintenance of Repairable Systems

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