Fertility progression in Germany: An analysis using flexible nonparametric cure survival models

Bremhorst, Vincent; Kreyenfeld, Michaela; Lambert, Philippe

doi:10.4054/demres.2016.35.18

Cited by 20 publications

(25 citation statements)

References 50 publications

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“…Using version v31.0, Bremhorst et al . () studied the transition to the second and third birth. Only one‐child and two‐child German women living in West Germany who were still of childbearing age (17–49 years) between 1984 and 2013 were considered in the sample.…”

Section: Application To Fertility Studiesmentioning

confidence: 99%

“…The main interest of Bremhorst et al . () was to study the effect of the educational attainments of the women and of their partners on the probability and on the timing of an additional child. In their analyses, the educational levels were frozen at the onset of the process (i.e.…”

Section: Application To Fertility Studiesmentioning

confidence: 99%

“…These latent factors ( Y 1 ,…, Y N ) are assumed to be directly active at the beginning of the follow‐up, independent and identically distributed (with a proper cumulative distribution function F ( t ) independent of N ). In the realm of fertility studies a latent factor might be interpreted as a potential decisive argument to decide to have an additional child and the ‘time for its detection’ as the time that is required for it to be convincing (Bremhorst et al ., ).…”

Section: Introductionmentioning

confidence: 97%

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Inclusion of Time-Varying Covariates in Cure Survival Models with an Application in Fertility Studies

Lambert

Bremhorst

2019

Journal of the Royal Statistical Society Series A: Statistics in Society

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Summary Cure survival models are used when we desire to acknowledge explicitly that an unknown proportion of the population studied will never experience the event of interest. An extension of the promotion time cure model enabling the inclusion of time‐varying covariates as regressors when modelling (simultaneously) the probability and the timing of the monitored event is presented. Our proposal enables us to handle non‐monotone population hazard functions without a specific parametric assumption on the baseline hazard. This extension is motivated by and illustrated on data from the German Socio‐Economic Panel by studying the transition to second and third births in West Germany.

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Section: Application To Fertility Studiesmentioning

confidence: 99%

Section: Application To Fertility Studiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

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Inclusion of Time-Varying Covariates in Cure Survival Models with an Application in Fertility Studies

Lambert

Bremhorst

2019

Journal of the Royal Statistical Society Series A: Statistics in Society

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“…For the inclusion of baseline covariates, we follow Bremhorst and Lambert () and Bremhorst et al. () with the log‐linear model for the cure probability and a (flexible) proportional hazards (PH) model to complete the specification of the event time distribution. The baseline survival function,

S_{0} false(y_{i} false) = exp (0true - \int_{0}^{y_{i}} h_{0} false(t false) d t) = exp \{0true - \int_{0}^{y_{i}} exp (0true \sum_{k = 1}^{K} b_{k} false(t false) ϕ_{k}) d t\},

is specified through the log of the baseline hazard

h_{0} false(t false)

(Rosenberg, ) using a cubic B‐spline basis

{b_{k} false(\cdot false) : k = 1, \dots, K}

(0, t_{trueprefixmax})

where

t_{max}

denotes the considered minimum follow‐up duration required to ensure that an event‐free subject by that time will not experience the event of interest.…”

Section: The Conditional Promotion Time Cure Modelmentioning

confidence: 99%

“…Then,

Y = min {W_{i} : i = 1, \dots, N}

is the time required to diagnose a relapse and it has an improper survival distribution

\begin{matrix} true \\ right S_{p} (y) & = & left prefixPr (Y > y) = prefixPr (N = 0) + prefixPr (W_{1} > y, \dots, W_{N} > y, N \geq 1) = \\ = & left {normale}^{- θ} + \sum_{N = 1}^{+ \infty} {(1 - F (y))}^{N} {normale}^{- θ} \frac{θ^{N}}{N!} = exp false{- θ F (y) false} . \end{matrix}

The proportion of ‘cured’ subjects is given by

Pr false(N = 0 false) = S_{p} false(+ \infty false) = exp false(- θ false)

. But the preceding biological motivation is not essential to come up with the proposed expression for the population survival function

S_{p} false(t false)

, opening its use in non‐medical areas such as demography (Bremhorst, Kreyenfeld, & Lambert, , ). Indeed, if a fraction of the population is really “cured” or “nonsusceptible” (to experience the event of interest), then the underlying cumulative hazard

Λ (t)

has a finite positive limiting value (say θ), yielding the former expression for

S_{p} false(t false)

with the normalized cumulative hazard

F (t) = Λ (t) / θ

.…”

Section: Introductionmentioning

confidence: 99%

Estimation and identification issues in the promotion time cure model when the same covariates influence long‐ and short‐term survival

Lambert

Bremhorst

2018

Biometrical J

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The promotion time cure model is a survival model acknowledging that an unidentified proportion of subjects will never experience the event of interest whatever the duration of the follow‐up. We focus our interest on the challenges raised by the strong posterior correlation between some of the regression parameters when the same covariates influence long‐ and short‐term survival. Then, the regression parameters of shared covariates are strongly correlated with, in addition, identification issues when the maximum follow‐up duration is insufficiently long to identify the cured fraction. We investigate how, despite this, plausible values for these parameters can be obtained in a computationally efficient way. The theoretical properties of our strategy will be investigated by simulation and illustrated on clinical data. Practical recommendations will also be made for the analysis of survival data known to include an unidentified cured fraction.

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Generalized parametric cure models for relative survival

2020

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Cure models are used in time‐to‐event analysis when not all individuals are expected to experience the event of interest, or when the survival of the considered individuals reaches the same level as the general population. These scenarios correspond to a plateau in the survival and relative survival function, respectively. The main parameters of interest in cure models are the proportion of individuals who are cured, termed the cure proportion, and the survival function of the uncured individuals. Although numerous cure models have been proposed in the statistical literature, there is no consensus on how to formulate these. We introduce a general parametric formulation of mixture cure models and a new class of cure models, termed latent cure models, together with a general estimation framework and software, which enable fitting of a wide range of different models. Through simulations, we assess the statistical properties of the models with respect to the cure proportion and the survival of the uncured individuals. Finally, we illustrate the models using survival data on colon cancer, which typically display a plateau in the relative survival. As demonstrated in the simulations, mixture cure models which are not guaranteed to be constant after a finite time point, tend to produce accurate estimates of the cure proportion and the survival of the uncured. However, these models are very unstable in certain cases due to identifiability issues, whereas LC models generally provide stable results at the price of more biased estimates.

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Fertility progression in Germany: An analysis using flexible nonparametric cure survival models

Cited by 20 publications

References 50 publications

Inclusion of Time-Varying Covariates in Cure Survival Models with an Application in Fertility Studies

Inclusion of Time-Varying Covariates in Cure Survival Models with an Application in Fertility Studies

Estimation and identification issues in the promotion time cure model when the same covariates influence long‐ and short‐term survival

Generalized parametric cure models for relative survival

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