Inference for Shared-Frailty Survival Models with Left-Truncated Data

Berg, Gérard J. van den; Drepper, Bettina

doi:10.1080/07474938.2014.975640

Cited by 35 publications

(28 citation statements)

References 20 publications

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“…The frailty distribution for analysing left-truncated failure time data has been previously studied in the literature. 9,10,1,11,12 For treating left truncation we must write a likelihood conditional on T ij 4 L ij (see details in Appendix) and the marginal log-likelihood becomes…”

Section: Inference In the Standard Frailty Modelsmentioning

confidence: 99%

Dynamic prediction models for clustered and interval-censored outcomes: Investigating the intra-couple correlation in the risk of dementia

Rondeau

Mauguen

Laurent

et al. 2015

Stat Methods Med Res

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The use of settings such as cohorts or clinical trials with interval-censored data and clustered event times are increasingly popular designs. First, the observed outcomes cannot be considered as independent and random effects survival models were introduced. Second, the failure time is not known exactly but it is only known to have occurred within a certain interval. We propose here an extension of shared frailty models to handle simultaneously the interval censoring, the clustering and also left truncation due to delayed entry in the cohort. A simulation study to evaluate the proposed method was conducted. The estimated results are used to obtain dynamic predictions for clustered patients, with interval-censored failure times and with a given history. We apply our method to the Three-City study, a prospective cohort with periodic follow-up in order to study prognostic factors of dementia. In this application scheme, couples are natural clusters and an intra-couple correlation might be present with a possible increased risk for dementia for subjects whose partner already developed incident dementia. No significant intra-couple correlation for the risk of dementia was observed before and after adjustments for covariates. We also present individual predictions of dementia underlining the usefulness of dynamic prognostic tools that can take into account the clustering. The consideration of frailty models for interval-censoring data and left-truncated data permits useful analysis of very complex clustered data. It could help to improve estimation of the impact of proposed prognostic features in a study with clustering. We proposed here a tractable model and a dynamic prediction tool that can easily be implemented using the R package Frailtypack.

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Section: Inference In the Standard Frailty Modelsmentioning

confidence: 99%

Dynamic prediction models for clustered and interval-censored outcomes: Investigating the intra-couple correlation in the risk of dementia

Rondeau

Mauguen

Laurent

et al. 2015

Stat Methods Med Res

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“…Within a survival analysis setting, this occurs, for example, when using age as the timescale, which can be an improved way of controlling for the effect of age [10]. Here, we can draw parallels with the challenges that arise when incorporating random effects into a delayed entry survival model [11,12]. Not only do we have the 'weeding out' process induced by the frailties, where patients with smaller frailties are more likely to have longer survival times, but the delayed entry causes a second selection issue, where patients with smaller frailties are more likely to reach the threshold set by an entry time.…”

Section: Introductionmentioning

confidence: 99%

Joint modelling of longitudinal and survival data: incorporating delayed entry and an assessment of model misspecification

Crowther

Andersson

Lambert

et al. 2015

Statistics in Medicine

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A now common goal in medical research is to investigate the inter‐relationships between a repeatedly measured biomarker, measured with error, and the time to an event of interest. This form of question can be tackled with a joint longitudinal‐survival model, with the most common approach combining a longitudinal mixed effects model with a proportional hazards survival model, where the models are linked through shared random effects. In this article, we look at incorporating delayed entry (left truncation), which has received relatively little attention. The extension to delayed entry requires a second set of numerical integration, beyond that required in a standard joint model. We therefore implement two sets of fully adaptive Gauss–Hermite quadrature with nested Gauss–Kronrod quadrature (to allow time‐dependent association structures), conducted simultaneously, to evaluate the likelihood. We evaluate fully adaptive quadrature compared with previously proposed non‐adaptive quadrature through a simulation study, showing substantial improvements, both in terms of minimising bias and reducing computation time. We further investigate, through simulation, the consequences of misspecifying the longitudinal trajectory and its impact on estimates of association. Our scenarios showed the current value association structure to be very robust, compared with the rate of change that we found to be highly sensitive showing that assuming a simpler trend when the truth is more complex can lead to substantial bias. With emphasis on flexible parametric approaches, we generalise previous models by proposing the use of polynomials or splines to capture the longitudinal trend and restricted cubic splines to model the baseline log hazard function. The methods are illustrated on a dataset of breast cancer patients, modelling mammographic density jointly with survival, where we show how to incorporate density measurements prior to the at‐risk period, to make use of all the available information. User‐friendly Stata software is provided. © 2015 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

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“…Their analysis is based on specific parametric frailty models accounting for the truncation. Wienke (2011) and van der Berg & Drepper (2011) also consider clustered left-truncated data, with a focus on parametric frailty models. The parametric assumptions may seem appealing as the analysis becomes simple, but a drawback is that the dependence parameters are rather sensitive to the specific parametric assumptions on the baseline hazard function.…”

Section: Introductionmentioning

confidence: 99%

Clustered Survival Data with Left‐truncation

Eriksson

Martinussen

Scheike

2015

Scandinavian J Statistics

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Left-truncation occurs frequently in survival studies, and it is well known how to deal with this for univariate survival times. However, there are few results on how to estimate dependence parameters and regression effects in semiparametric models for clustered survival data with delayed entry. Surprisingly, existing methods only deal with special cases. In this paper, we clarify different kinds of left-truncation and suggest estimators for semiparametric survival models under specific truncation schemes. The large-sample properties of the estimators are established. Small-sample properties are investigated via simulation studies, and the suggested estimators are used in a study of prostate cancer based on the Finnish twin cohort where a twin pair is included only if both twins were alive in 1974.

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Inference for Shared-Frailty Survival Models with Left-Truncated Data

Cited by 35 publications

References 20 publications

Dynamic prediction models for clustered and interval-censored outcomes: Investigating the intra-couple correlation in the risk of dementia

Dynamic prediction models for clustered and interval-censored outcomes: Investigating the intra-couple correlation in the risk of dementia

Joint modelling of longitudinal and survival data: incorporating delayed entry and an assessment of model misspecification

Clustered Survival Data with Left‐truncation

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