Estimation of predictive accuracy in survival analysis using R and S-PLUS

When the purpose of a survival regression model is to predict future outcomes, the predictive accuracy of the model needs to be evaluated before practical application. Various measures of predictive accuracy have been proposed for survival data, none of which has been adopted as a standard, and their inclusion in statistical software is disregarded. We developed the surev library for R and S-PLUS, which includes functions for evaluating the predictive accuracy measures proposed by Schemper and Henderson. The library evaluates the predictive accuracy of parametric regression models and of Cox models. The predictive accuracy of the Cox model can be obtained also when time-dependent covariates are included because of non-proportional hazards or when using Bayesian model averaging. The use of the library is illustrated with examples based on a real data set.     

RSURV: a function to perform relative survival analysis with S-PLUS or R

Relative survival is a method used to estimate net survival using the expected mortality in the general population. This method is frequently used in cancer registries, more particularly with the Esteve et al. regressive proportional hazards model. Recently, extensions of this model have been developed to account for time-dependent covariate and for time-dependent hazards using B-spline functions. We propose a function, RSurv, to take into account these extensions. Written in the R/S language this function has the same structure of the standard Cox function coxph of R and S-PLUS software with the goal to homogenise survival functions and to take advantages of the power of R and S-PLUS software. We also propose a function, plot.RSurv, for plotting relative survival curves and time-dependent hazards ratio. The usage of these functions is exemplified by a study of a breast cancer hospital-based data set.     

tdc.msm: an R library for the analysis of multi-state survival data

The aim of this paper is to present an R library, called tdc.msm, developed to analyze multi-state survival data. In this library, the time-dependent regression model and multi-state models are included as two possible approaches for such data. For the multi-state modelling five different models are considered, allowing the user to choose between Markov and semi-Markov property, as well as to use homogeneous or non-homogeneous models. Specifically, the following multi-state models in continuous time were implemented: Cox Markov model; Cox semi-Markov model; homogeneous Markov model; non-homogeneous piecewise model and non-parametric Markov model. This software can be used to fit multi-state models with one initial state (e.g., illness diagnosis), a finite number of intermediate states, representing, for example, a change of treatment, and one absorbing state corresponding to a terminal event of interest. Graphical output includes survival estimates, transition probabilities estimates and smooth log hazard for continuous covariates.     

Computer-assisted red cell survival analysis

A computer-assisted procedure for statistically analyzing red cell survival experiments is presented. The procedure utilizes a widely available statistical software (BMDP). The program allows the fitting of a wide range of parametric curves to the survival data. It calculates estimates of the parameters and their standard errors, and produces residuals plots that can be used to pick objectively the "best" fitting curve to the data. A listing of the computer statements required to produce the above analysis is given in the Appendix.     

Interactive statistical analysis of survival data

This paper describes a SAS macro which facilitates the interactive analysis of right-censored survival data. Such data commonly occur in medical studies. The program produces Kaplan-Meier survival curves on a wide variety of graphics devices. The program also performs log-rank and generalized Wilcoxon significance tests among all plotted curves and for each pairwise contrast if desired. Because the program is intelligent and does not prompt the user for information that it can independently obtain, it is quite easy to use.     

Relative efficiency of police directorates in Slovenia: A non-parametric analysis

The main purpose of the paper is to apply a non-parametric methodology for measuring public police performance in Slovenia. The paper considers how previous studies have modeled the role of policing in their specifications of inputs and output. In particular, the multiple-stage Data Envelopment Analysis (DEA) technique is presented and then applied to measure the relative efficiency of police-work-related data for eleven Police Directorates (PDs) in 2010 and also compared with the efficiency scores in 2005. The data obtained from the police databases is analyzed through the Frontier Analyst 4.0 and SPSS 19.0 statistical package software. The results show that the technical efficiency varies significantly across the police directorates and across the selected years, even when we allow for environmental factors and control for these non-discretionary inputs. Most police directorates in Slovenia could attain a higher output if they were fully efficient. Indeed, all of the inefficient police directorates can learn how to ensure a “good” performance from the efficient ones (i.e. the Maribor PD and the Novo mesto PD) by observing how they are processing their inputs and outputs. Finally, the empirical results of the paper are important indicators of the relative efficiency (or inefficiency) of police directorates that can serve as a guide to the General Police Directorate when further investigating how to enhance the performance efficiency of the various units.     

Mining for trigger events with survival analysis

This paper discusses a new application of data mining, quantifying the importance of responding to trigger events with reactive contacts. Trigger events happen during a customer’s lifecycle and indicate some change in the relationship with the company. If detected early, the company can respond to the problem and retain the customer; otherwise the customer may switch to another company. It is usually easy to identify many potential trigger events. What is needed is a way of prioritizing which events demand interventions. We conceptualize the trigger event problem and show how survival analysis can be used to quantify the importance of addressing various trigger events. The method is illustrated on four real data sets from different industries and countries.     

Improved AIC selection strategy for survival analysis

In survival analysis, it is of interest to appropriately select significant predictors. In this paper, we extend the AIC_C selection procedure of Hurvich and Tsai to survival models to improve the traditional AIC for small sample sizes. A theoretical verification under a special case of the exponential distribution is provided. Simulation studies illustrate that the proposed method substantially outperforms its counterpart: AIC, in small samples, and competes it in moderate and large samples. Two real data sets are also analyzed.     

Fitting semiparametric regressions for panel count survival data with an R package spef

Observing recurrent event processes at discrete, possibly random times produces panel count data. Modeling panel count data is challenging because the event process may be associated with the observation pattern and censoring time. Various methods have been proposed to fit flexible semiparametric regression models, but no software is available to practitioners. We develop an R package spef that fits semiparametric regression models for panel count data. Existing methods in the literature are implemented as well as our recently developed estimating equations approach. Some of the implemented methods allow informative observation and censoring scheme. The package usage is illustrated with a well-known bladder tumor data set.     

SURVSOFT—Software for nonparametric survival analysis

Long-term observed and relative survival are important outcome measures of cancer patient care reported routinely by many cancer registries, but no commercial statistical software exists for estimating relative survival or performing period survival analysis. The programs publicly available focus only on certain methods, require specific input data formats and often are macros or functions which require underlying software packages. Here we introduce SURVSOFT, a comprehensive, user-friendly Windows program with graphical user interface. It can handle different input data formats and incorporates a variety of nonparametric statistical methods for survival data analysis. SURVSOFT produces high-resolution graphs, which can be printed, saved or exported to be used with standard graphics editors. The use of SURVSOFT is illustrated by the analysis of survival data from the Bavarian Cancer Registry.     

Comparison of Bayesian survival analysis and Cox regression analysis in simulated and breast cancer data sets

We aimed to compare the performance of Cox regression analysis (CRA) and Bayesian survival analysis (BSA) by using simulations and breast cancer data.Simulation study was carried out with two different algorithms that were informative and noninformative priors. Moreover, in a real data set application, breast cancer data set related to disease-free survival (DFS) that was obtained from 423 breast cancer patients diagnosed between 1998 and 2007 was used.In the simulation application, it was observed that BSA with noninformative priors and CRA methods showed similar performances in point of convergence to simulation parameter. In the informative priors’ simulation application, BSA with proper informative prior showed a good performance with too little bias. It was found out that the bias of BSA increased while priors were becoming distant from reliability in all sample sizes. In addition, BSA obtained predictions with more little bias and standard error than the CRA in both small and big samples in the light of proper priors.In the breast cancer data set, age, tumor size, hormonal therapy, and axillary nodal status were found statistically significant prognostic factors for DFS in stepwise CRA and BSA with informative and noninformative priors. Furthermore, standard errors of predictions in BSA with informative priors were observed slightly.As a result, BSA showed better performance than CRA, when subjective data analysis was performed by considering expert opinions and historical knowledge about parameters. Consequently, BSA should be preferred in existence of reliable informative priors, in the contrast cases, CRA should be preferred.     

Approximation and derivatives of probabilities of survival in structural analysis and design

Yield stresses, allowable stresses, moment capacities (plastic moments), external loadings, manufacturing errors, etc., are not fixed quantities in practice, but must be modelled as random variables with a certain joint probability distribution. In reliability-oriented structural optimization the violation of the random behavioural constraints are evaluated by means of the corresponding probabilityp _s of survival. Hence, the approximative computation ofp _s and its sensitivities is of utmost importance. After the consideration of lower bounds ofp _s based on a selection of certain redundants in the vector of internal forces/bending moments, and the consideration of upper bounds ofp _s based on an optimizational representation of the yield or safety constraints by a pair of dual linear programs, a conical representation ofp _s is introduced based on a coneY _o of admissible pairs of external loads/strength increaments. Approximations ofp _s can be constructed then by replacing the (finitely generated) coneY _o by more simple ones, e.g. spherical or ellipsoidal cones. For the direct numerical computation of sensitivities ofp _s and its bounds or approximations by using e.g. sampling methods or asymptotic expansion techniques based on Laplace integral representation of multiple integrals, exact differentiation formulae — of arbitrary order — forp _s and its bounds or approximations with respect to deterministic input or design variables are obtained by applying the transformation method/stochastic completion techniques; the derivatives ofp _s are represented again by certain expectations or multiple integrals.     

Parametrization and penalties in spline models with an application to survival analysis

A simple parametrization, built from the definition of cubic splines, is shown to facilitate the implementation and interpretation of penalized spline models, whatever configuration of knots is used. The parametrization is termed value-first derivative parametrization. Inference is Bayesian and explores the natural link between quadratic penalties and Gaussian priors. However, a full Bayesian analysis seems feasible only for some penalty functionals. Alternatives include empirical Bayes inference methods involving model selection type criteria. The proposed methodology is illustrated by an application to survival analysis where the usual Cox model is extended to allow for time-varying regression coefficients.     

Relative orientation

Before corresponding points in images taken with two cameras can be used to recover distances to objects in a scene, one has to determine the position and orientation of one camera relative to the other. This is the classic photogrammetric problem of relative orientation, central to the interpretation of binocular stereo information. Iterative methods for determining relative orientation were developed long ago; without them we would not have most of the topographic maps we do today. Relative orientation is also of importance in the recovery of motion and shape from an image sequence when successive frames are widely separated in time. Workers in motion vision are rediscovering some of the methods of photogrammetry.Described here is a simple iterative scheme for recovering relative orientation that, unlike existing methods, does not require a good initial guess for the baseline and the rotation. The data required is a pair of bundles of corresponding rays from the two projection centers to points in the scene. It is well known that at least five pairs of rays are needed. Less appears to be known about the existence of multiple solutions and their interpretation. These issues are discussed here. The unambiguous determination of all of the parameters of relative orientation is not possible when the observed points lie on a critical surface. These surfaces and their degenerate forms are analyzed as well.     

Relative blending

Solid models may be blended through filleting or rounding operations that typically replace the vicinity of concave or convex edges by blends that smoothly connect to the rest of the solid’s boundary. Circular blends, which are popular in manufacturing, are each the subset of a canal surface that bounds the region swept by a ball of constant or varying radius as it rolls on the solid while maintaining two tangential contacts. We propose to use a second solid to control the radius variation. This new formulation supports global blending (simultaneous rounding and filleting) operations and yields a simple set-theoretic formulation of the relative blending R_B(A) of a solid A given a control solid B. We propose user-interface options, describe practical implementations, and show results in 2 and 3 dimensions.     

Fiber soliton-form 3R regenerator and its performance analysis

A novel fiber optical 3R regenerator based on optical soliton-effect using highly nonlinear fiber is constructed and investigated for the needs of the high rate and long-haul optical communications. The propagation equation of the pulses in the proposed optical 3R regenerator with the control of optical modulator and filter is established. By the use of the variational approach, the evolution of the distorted optical pulses in the regenerator and the functions of reamplification, reshaping, and retiming are investigated. The relation between the construction parameters and the output performance of the regenerator is discussed. The stable operation condition of the regenerator is revealed.     

An ExPosition of multivariate analysis with the singular value decomposition in R

ExPosition is a new comprehensive R package providing crisp graphics and implementing multivariate analysis methods based on the singular value decomposition (svd). The core techniques implemented in ExPosition are: principal components analysis, (metric) multidimensional scaling, correspondence analysis, and several of their recent extensions such as barycentric discriminant analyses (e.g., discriminant correspondence analysis), multi-table analyses (e.g.,multiple factor analysis, Statis, and distatis), and non-parametric resampling techniques (e.g., permutation and bootstrap). Several examples highlight the major differences between ExPosition and similar packages. Finally, the future directions of ExPosition are discussed.     

非线性动力系统R/S法的改进及小波预测

针对固定电话和移动电话用户人数的时间序列,将小波变换与R/S分析法,多重分形相结合,探讨了系统的动力学特性和演化规律,并从分形维数、非周期循环长度、奇异性指数等方面指出电话用户人数增长趋势存在强持续性和长期记忆性以及具有多重分形特征,随着配分阶数的增大,多重分形随之增强,并得出移动电话人数的多重分形特性更强。接着对原始数据和小波重构后的数据进行了回归拟合比较,结果证明小波重构后的数据拟合程度更高,并利用重构的数据预测了未来三个月的电话用户人数。     

煤矿井下掘进巷道瓦斯涌出R/S分析

为了掌握煤与瓦斯突出危险性变化情况,分析了煤层瓦斯涌出量影响因素,采用R/S分析方法对煤矿掘进巷道瓦斯涌出情况进行研究,得出结论:掘进巷道瓦斯涌出时间序列具有分形特性,当检测到瓦斯涌出时间序列的Hurst指数出现降低趋势并有较大波动时,说明将会出现瓦斯涌出异常,需要提前采取一定的安全防范措施。