scholarly journals Flexible parametric model for survival data subject to dependent censoring

2019 ◽  
Vol 62 (1) ◽  
pp. 136-156 ◽  
Author(s):  
Negera Wakgari Deresa ◽  
Ingrid Van Keilegom
Keyword(s):  
Survival Data ◽  
Parametric Model ◽  
Dependent Censoring ◽  
Flexible Parametric Model ◽  
Data Subject

scholarly journals Targeted Minimum Loss-Based Estimation of Causal Effects in Right-Censored Survival Data with Time-Dependent Covariates: Warfarin, Stroke, and Death in Atrial Fibrillation

2013 ◽  
Vol 1 (2) ◽  
pp. 235-254 ◽  
Author(s):  
Jordan C. Brooks ◽  
Mark J. van der Laan ◽  
Daniel E. Singer ◽  
Alan S. Go
Keyword(s):  
Survival Data ◽  
Causal Effect ◽  
Estimating Equation ◽  
Dependent Censoring ◽  
Time Dependent ◽  
Causal Effects ◽  
Consistent Estimation ◽  
Censored Survival Data ◽  
Inverse Probability ◽  
Time Dependent Covariates

AbstractCausal effects in right-censored survival data can be formally defined as the difference in the marginal cumulative event probabilities under particular interventions. Conventional estimators, such as the Kaplan-Meier (KM), fail to consistently estimate these marginal parameters under dependent treatment assignment or dependent censoring. Several modern estimators have been developed that reduce bias under both dependent treatment assignment and dependent censoring by incorporating information from baseline and time-dependent covariates. In the present article we describe a recently developed targeted minimum loss-based estimation (TMLE) algorithm for general longitudinal data structures and present in detail its application in right-censored survival data with time-dependent covariates. The treatment-specific marginal cumulative event probability is defined via a series of iterated conditional expectations in a time-dependent counting process framework. The TMLE involves an initial estimator of each conditional expectation and sequentially updates these such that the resulting estimator solves the efficient influence curve estimating equation in the nonparametric statistical model. We describe the assumptions required for consistent estimation of statistical parameters and additional assumptions required for consistent estimation of the causal effect parameter. Using simulated right-censored survival data, the mean squared error, bias, and 95% confidence interval coverage probability of the TMLE is compared with those of the conventional KM and the inverse probability of censoring weight estimating equation, conventional maximum likelihood substitution estimator, and the double robustaugmented inverse probability of censoring weighted estimating equation. We conclude the article with estimation of the causal effect of warfarin medical therapy on the probability of “stroke or death” within a 1-year time frame using data from the ATRIA-1 observational cohort of persons with atrial fibrillation. Our results suggest that a fixed policy of warfarin treatment for all patients would result in 2% fewer deaths or strokes within 1-year as compared with a policy of withholding warfarin from all patients.

scholarly journals A parametric model for estimating nuptiality patterns in modern populations

2015 ◽  
Vol 42 (1-2) ◽  
pp. 130 ◽  
Author(s):  
Anastasia Kostaki ◽  
Paraskevi Peristera
Keyword(s):  
Mixture Models ◽  
Parametric Model ◽  
Parametric Models ◽  
Human Populations ◽  
Marriage Rates ◽  
First Marriage ◽  
Flexible Parametric Model ◽  
Typical Shape

Nuptiality is a phenomenon closely related to fertility. The age-specific marriage distribution has a typical shape common in all human populations. In order to estimate this pattern, alternative parametric models have been proposed. However recent evidence suggests that mixture models are required to estimate nuptiality patterns. In this paper, a flexible parametric model is proposed in three versions, appropriate to describe the age pattern of first marriage rates. For evaluation purposes the models as well as the alternative existing models are fitted to a variety of empirical datasets.

scholarly journals A bivariate power generalized Weibull distribution: A flexible parametric model for survival analysis

2019 ◽  
Vol 29 (8) ◽  
pp. 2295-2306 ◽  
Author(s):  
MC Jones ◽  
Angela Noufaily ◽  
Kevin Burke
Keyword(s):  
Survival Analysis ◽  
Weibull Distribution ◽  
Survival Data ◽  
Frailty Model ◽  
Weibull Model ◽  
Flexible Parametric Model ◽  
Shared Frailty Model ◽  
Shared Frailty ◽  
Power Variance ◽  
Parametric Survival

We are concerned with the flexible parametric analysis of bivariate survival data. Elsewhere, we argued in favour of an adapted form of the ‘power generalized Weibull’ distribution as an attractive vehicle for univariate parametric survival analysis. Here, we additionally observe a frailty relationship between a power generalized Weibull distribution with one value of the parameter which controls distributional choice within the family and a power generalized Weibull distribution with a smaller value of that parameter. We exploit this relationship to propose a bivariate shared frailty model with power generalized Weibull marginal distributions linked by the BB9 or ‘power variance function’ copula, then change it to have adapted power generalized Weibull marginals in the obvious way. The particular choice of copula is, therefore, natural in the current context, and the corresponding bivariate adapted power generalized Weibull model a novel combination of pre-existing components. We provide a number of theoretical properties of the models. We also show the potential of the bivariate adapted power generalized Weibull model for practical work via an illustrative example involving a well-known retinopathy dataset, for which the analysis proves to be straightforward to implement and informative in its outcomes.

scholarly journals STEREOLOGICAL ANALYSIS OF SHAPE

2011 ◽  
Vol 21 (4) ◽  
pp. 23 ◽  
Author(s):  
Asger Hobolth ◽  
Eva B Vedel Jensen
Keyword(s):  
Parametric Model ◽  
Rotational Invariance ◽  
Rotation Invariant ◽  
Stereological Analysis ◽  
Flexible Parametric Model

This paper concerns the problem of making stereological inference about the shape variability in a population of spatial particles. Under rotational invariance the shape variability can be estimated from central planar sections through the particles. A simple, but flexible, parametric model for rotation invariant spatial particles is suggested. It is shown how the parameters of the model can be estimated from observations on central sections. The corresponding model for planar particles is also discussed in some detail.

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