Ascertainment correction in frailty models for recurrent events data

Balan, Theodor A.; Jonker, Marianne A.; Johannesma, Paul C; Putter, Hein

doi:10.1002/sim.6968

Cited by 6 publications

(3 citation statements)

References 20 publications

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“… 69 In the case of recurrent events, such selection schemes may arise when individuals are included into the study only if they experience a certain number of events. 70 Such scenarios usually require ad-hoc estimation procedures and are not generally supported by the main software packages.…”

Section: Frailty Models In Practicementioning

confidence: 99%

A tutorial on frailty models

Balan

Putter

2020

Stat Methods Med Res

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171

126

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The hazard function plays a central role in survival analysis. In a homogeneous population, the distribution of the time to event, described by the hazard, is the same for each individual. Heterogeneity in the distributions can be accounted for by including covariates in a model for the hazard, for instance a proportional hazards model. In this model, individuals with the same value of the covariates will have the same distribution. It is natural to think that not all covariates that are thought to influence the distribution of the survival outcome are included in the model. This implies that there is unobserved heterogeneity; individuals with the same value of the covariates may have different distributions. One way of accounting for this unobserved heterogeneity is to include random effects in the model. In the context of hazard models for time to event outcomes, such random effects are called frailties, and the resulting models are called frailty models. In this tutorial, we study frailty models for survival outcomes. We illustrate how frailties induce selection of healthier individuals among survivors, and show how shared frailties can be used to model positively dependent survival outcomes in clustered data. The Laplace transform of the frailty distribution plays a central role in relating the hazards, conditional on the frailty, to hazards and survival functions observed in a population. Available software, mainly in R, will be discussed, and the use of frailty models is illustrated in two different applications, one on center effects and the other on recurrent events.

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Section: Frailty Models In Practicementioning

confidence: 99%

A tutorial on frailty models

Balan

Putter

2020

Stat Methods Med Res

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171

126

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show abstract

“…The first are derived from symmetric confidence intervals on the log-scale. The resulting asymmetric confidence interval has been shown to provide good coverage (Balan et al 2016b). The second, more computationally intensive, are referred to as "likelihood-based confidence intervals".…”

Section: Standard Errors and Confidence Intervalsmentioning

confidence: 99%

frailtyEM: An R Package for Estimating Semiparametric Shared Frailty Models

Balan¹,

Putter²

2019

J. Stat. Soft.

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When analyzing correlated time to event data, shared frailty (random effect) models are particularly attractive. However, the estimation of such models has proved challenging. In semiparametric models, this is further complicated by the presence of the nonparametric baseline hazard. Although recent years have seen an increased availability of software for fitting frailty models, most software packages focus either on a small number of distributions of the random effect, or support only on a few data scenarios. frailtyEM is an R package that provides maximum likelihood estimation of semiparametric shared frailty models using the expectation-maximization algorithm. The implementation is consistent across several scenarios, including possibly left truncated clustered failures and recurrent events in both calendar time and gap time formulation. A large number of frailty distributions belonging to the power variance function family are supported. Several methods facilitate access to predicted survival and cumulative hazard curves, both for an individual and on a population level. An extensive number of summary measures and statistical tests are also provided.

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“…Several studies have discussed handling left truncation in shared frailty models for clustered survival data (e.g., Jensen et al, 2004;van den Berg and Drepper, 2016). In a recurrent event setting, Balan et al (2016) considered event dependent selection; i.e., individuals were included in the study only if they had experienced at least one recurrent event in a given time period. Recurrent event studies with selection dependent on survival were briefly discussed in Cook and Lawless (2007), but not specifically in the context of frailty models.…”

Section: Introductionmentioning

confidence: 99%

Incorporating delayed entry into the joint frailty model for recurrent events and a terminal event

Böhnstedt¹,

Gampe²,

Caljouw³

et al. 2021

Preprint

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In studies of recurrent events, joint modeling approaches are often needed to allow for potential dependent censoring by a terminal event such as death. Joint frailty models for recurrent events and death with an additional dependence parameter have been studied for cases in which individuals are observed from the start of the event processes. However, the samples are often selected at a later time, which results in delayed entry. Thus, only individuals who have not yet experienced the terminal event will be included in the study. We propose a method for estimating the joint frailty model from such left-truncated data. The frailty distribution among the selected survivors differs from the frailty distribution in the underlying population if the recurrence process and the terminal event are associated. The correctly adjusted marginal likelihood can be expressed as a ratio of two integrals over the frailty distribution, which may be approximated using Gaussian quadrature. The baseline rates are specified as piecewise constant functions, and the covariates are assumed to have multiplicative effects on the event rates. We assess the performance of the estimation procedure in a simulation study, and apply the method to estimate age-specific rates of recurrent urinary tract infections and mortality in an older population.

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Ascertainment correction in frailty models for recurrent events data

Cited by 6 publications

References 20 publications

A tutorial on frailty models

A tutorial on frailty models

frailtyEM: An R Package for Estimating Semiparametric Shared Frailty Models

Incorporating delayed entry into the joint frailty model for recurrent events and a terminal event

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