Search results for " hazards"

Sample size planning for survival prediction with focus on high-dimensional data

2011

Sample size planning should reflect the primary objective of a trial. If the primary objective is prediction, the sample size determination should focus on prediction accuracy instead of power. We present formulas for the determination of training set sample size for survival prediction. Sample size is chosen to control the difference between optimal and expected prediction error. Prediction is carried out by Cox proportional hazards models. The general approach considers censoring as well as low-dimensional and high-dimensional explanatory variables. For dimension reduction in the high-dimensional setting, a variable selection step is inserted. If not all informative variables are included…

Bayesian regularization for flexible baseline hazard functions in Cox survival models.

2019

Fully Bayesian methods for Cox models specify a model for the baseline hazard function. Parametric approaches generally provide monotone estimations. Semi-parametric choices allow for more flexible patterns but they can suffer from overfitting and instability. Regularization methods through prior distributions with correlated structures usually give reasonable answers to these types of situations. We discuss Bayesian regularization for Cox survival models defined via flexible baseline hazards specified by a mixture of piecewise constant functions and by a cubic B-spline function. For those "semi-parametric" proposals, different prior scenarios ranging from prior independence to particular c…

Generating survival times to simulate Cox proportional hazards models by Ralf Bender, Thomas Augustin and Maria Blettner,Statistics in Medicine 2005;…

2006

A weighted combined effect measure for the analysis of a composite time-to-first-event endpoint with components of different clinical relevance

2018

Composite endpoints combine several events within a single variable, which increases the number of expected events and is thereby meant to increase the power. However, the interpretation of results can be difficult as the observed effect for the composite does not necessarily reflect the effects for the components, which may be of different magnitude or even point in adverse directions. Moreover, in clinical applications, the event types are often of different clinical relevance, which also complicates the interpretation of the composite effect. The common effect measure for composite endpoints is the all-cause hazard ratio, which gives equal weight to all events irrespective of their type …

Generating survival times to simulate Cox proportional hazards models

2005

Simulation studies present an important statistical tool to investigate the performance, properties and adequacy of statistical models in pre-specified situations. One of the most important statistical models in medical research is the proportional hazards model of Cox. In this paper, techniques to generate survival times for simulation studies regarding Cox proportional hazards models are presented. A general formula describing the relation between the hazard and the corresponding survival time of the Cox model is derived, which is useful in simulation studies. It is shown how the exponential, the Weibull and the Gompertz distribution can be applied to generate appropriate survival times f…

Using Statistical and Computer Models to Quantify Volcanic Hazards

2009

Risk assessment of rare natural hazards, such as large volcanic block and ash or pyroclastic flows, is addressed. Assessment is approached through a combination of computer modeling, statistical modeling, and extreme-event probability computation. A computer model of the natural hazard is used to provide the needed extrapolation to unseen parts of the hazard space. Statistical modeling of the available data is needed to determine the initializing distribution for exercising the computer model. In dealing with rare events, direct simulations involving the computer model are prohibitively expensive. The solution instead requires a combination of adaptive design of computer model approximation…

PROBABILISTIC QUANTIFICATION OF HAZARDS: A METHODOLOGY USING SMALL ENSEMBLES OF PHYSICS-BASED SIMULATIONS AND STATISTICAL SURROGATES

2015

This paper presents a novel approach to assessing the hazard threat to a locale due to a large volcanic avalanche. The methodology combines: (i) mathematical modeling of volcanic mass flows; (ii) field data of avalanche frequency, volume, and runout; (iii) large-scale numerical simulations of flow events; (iv) use of statistical methods to minimize computational costs, and to capture unlikely events; (v) calculation of the probability of a catastrophic flow event over the next T years at a location of interest; and (vi) innovative computational methodology to implement these methods. This unified presentation collects elements that have been separately developed, and incorporates new contri…

Sparse kernel methods for high-dimensional survival data

2008

Abstract Sparse kernel methods like support vector machines (SVM) have been applied with great success to classification and (standard) regression settings. Existing support vector classification and regression techniques however are not suitable for partly censored survival data, which are typically analysed using Cox's proportional hazards model. As the partial likelihood of the proportional hazards model only depends on the covariates through inner products, it can be ‘kernelized’. The kernelized proportional hazards model however yields a solution that is dense, i.e. the solution depends on all observations. One of the key features of an SVM is that it yields a sparse solution, dependin…

Coupled variable selection for regression modeling of complex treatment patterns in a clinical cancer registry.

2013

For determining a manageable set of covariates potentially influential with respect to a time-to-event endpoint, Cox proportional hazards models can be combined with variable selection techniques, such as stepwise forward selection or backward elimination based on p-values, or regularized regression techniques such as component-wise boosting. Cox regression models have also been adapted for dealing with more complex event patterns, for example, for competing risks settings with separate, cause-specific hazard models for each event type, or for determining the prognostic effect pattern of a variable over different landmark times, with one conditional survival model for each landmark. Motivat…

On statistical inference for the random set generated Cox process with set-marking.

2007

Cox point process is a process class for hierarchical modelling of systems of non-interacting points in ℝd under environmental heterogeneity which is modelled through a random intensity function. In this work a class of Cox processes is suggested where the random intensity is generated by a random closed set. Such heterogeneity appears for example in forestry where silvicultural treatments like harvesting and site-preparation create geometrical patterns for tree density variation in two different phases. In this paper the second order property, important both in data analysis and in the context of spatial sampling, is derived. The usefulness of the random set generated Cox process is highly…