With explanatory covariates, the standard analysis for competing risks data involves modeling the cause-specific hazard functions via a proportional hazards assumption Unfortunately, the cause-specific hazard function does not have a direct interpretation in terms of survival probabilities for the particular failure type In recent years many clinicians have begun using the cumulative incidence function, the marginal failure probabilities for a particular cause, which is intuitively appealing and more easily explained to the nonstatistician The cumulative incidence is especially relevant in cost-effectiveness analyses in which the survival probabilities are needed to determine treatment utility Previously, authors have considered methods for combining estimates of the cause-specific hazard functions under the proportional hazards formulation However, these methods do not allow the analyst to directly assess the effect of a covariate on the marginal probability function In this article we pro

http://www.clinicalpredictionmodels.org/lib/exe/fetch.php?id=additional%3Achapter04&cache=cache&media=additional:fine_and_gray_competing_risk_1999.pdf

A Proportional Hazards Model for the Subdistribution of a Competing Risk

Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

Purpose: This paper discusses partial least squares path modeling (PLS), a powerful structural equation modeling technique for research on international marketing. While a significant body of research provides guidance for the use of covariance-based structural equation modeling (CBSEM) in international marketing, there are no subject-specific guidelines for the use of PLS so far.Methodology/approach: A literature review of the use of PLS in international marketing reveals the increasing application of this methodology.Findings: This paper reveals the strengths and weaknesses of PLS in the context of research on international marketing, and provides guidance for multi-group analysis.Originality/value of paper: The paper assists researchers in making well-grounded decisions regarding the application of PLS in certain research situations and provides specific implications for an appropriate application of the methodology.

The Use of Partial Least Squares Path Modeling in International Marketing

Statistics for Spatial Data.

/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

The Cox regression model for censored survival data specifies that covariates have a proportional effect on the hazard function of the life-time distribution of an individual. In this paper we discuss how this model can be extended to a model where covariate processes have a proportional effect on the intensity process of a multivariate counting process. This permits a statistical regression analysis of the intensity of a recurrent event allowing for complicated censoring patterns and time dependent covariates. Furthermore, this formulation gives rise to proofs with very simple structure using martingale techniques for the asymptotic properties of the estimators from such a model. Finally an example of a statistical analysis is included.

/pdf/cox-s-regression-model-for-counting-processes-a-large-sample-wj26nk7i0i.pdf

Cox's Regression Model for Counting Processes: A Large Sample Study

The first edition of this book was published in 1972. This second edition is not greatly different from the first. The two editions are divided into 5 chapters and a 50-page appendix entitled, “Review of Fundamental Concepts.” The five chapter titles are the same for the two editions and are 1. “Introduction to Data Analysis,” 2. “Elementary Statistical Inference,” 3. “Regression and Correlation Analysis,” 4. “The Analysis of Variance,” and 5. “Multivariate Statistical Methods.” The second edition is 76 pages longer than the first. This is primarily due to the addition of the following sections: in Chapter 1, “Data Screening,” in Chapter 2, “Other Measures of Association for Contingency Tables” and “Robust Estimators,” and in Chapter 5, “The Multivariate Analysis of Variance;” in Chapter 3 the subsection “Multivariate Missing Observations” is added. A number of new examples and problems have been added. All chapters have a set of problems now whereas Chapter 1 did not in the first edition. No answers are provided for the problems. Most of the examples and problems are from the fields of biology and medicine and unless one is fairly familiar with these subject areas, the examples and problems will not be very meaningful. In the preface to the first edition the authors indicate that the “book contains both elementary and advanced topics” and has “a wide range of material.” In the preface to the second edition they indicate that they have attempted “to broaden the’ scope of the book.” The breadth is perhaps best illustrated by the courses that the authors suggest might be taught from the book; namely, “Elementary Applied Statistical Analysis” (undergraduate), “Applied Statistical Analysis” (first-year graduate), “Applied Multivariate Analysis” (second-year graduate), and “Intensive Course in Data Analysis.” I feel that books aimed at a specific well-defined audience are generally more effective than those aimed at a wide general audience, and this book only confirms that opinion. I tried to put myself in the place of a person who has had only an “elementary course in the fundamentals of statistical inference” and college algebra-the minimum background that the authors feel is required to use the book. I think people with that background would find the book very difficult if they were on their own. In Chapter 1 the authors say, “. there are two main objectives of this book. The first is to present in a practical manner the fundamental techniques of classical statistical analysis-both univariate and multivariate.” They have done a good job of presenting the techniques of classical statistics. However, I do not feel that they have done a good job of interpreting their examples. Most of the interpretations of the analyses consist of little more than saying whether a statistical test is significant-with a P value--or not. In the analysis of variance (ANOVA) chapter the authors introduce a study (give a literature reference) in which, “The data consisted of measurements Y = the amount of nitrogen expired (in liters) in resting conditions under four dietary regimens.” They indicate that, “This example will be analyzed in many different ways throughout the chapter.” When they use the study to illustrate the one-way ANOVA, they present some data. This study and these data (or a subset) are then used many times as examples in the chapter. I think real experimental studies and data lose their effectiveness when used this way. One might better, I feel, generate data-and admit it-and do the generation using the model to be illustrated. When a single set of data is used to illustrate successively more complex studies and ends up illustrating the situation for the real experiment that produced the data, it is sometimes effective in that it can show why the real study was set up as it was. However, in the present case it is never indicated what the design was for the study referenced. There is a brief discussion of power in the appendix. However, I find it strange that there is nothing on power in the body of the text.

Censoring and stochastic integrals

We study counting process models for event history data where the intensities depend on unobservable quantities ("frailties"). Examples include models for dependent failure times and regression models with unobservable covariates. Estimation in both parametric and nonor semi-parametric models is performed by maximum likelihood methods using the EM algorithm. Simulations and practical examples are presented.

https://www.jstor.org/stable/info/4616223

A counting process approach to maximum likelihood estimation in frailty models

The correspondence between a survival function and its hazard or failure-rate is a central idea in survival analysis and in the theory of counting processes. This correspondence is shown to be a special case of a more general correspondence between multiplicative and additive matrix-valued measures on the real line. Additive integration of the survival function produces the hazard, while the multiplicative integral, or so-called product-integral, of the hazard yields the survival function. The easy generalization to the matrix case (noncommutative multiplication) allows an elegant and completely parallel treatment of intensity measures of Markov processes, with many possible applications in multistate survival models. However, the difficulties and multiplicity of theories of product-integration in multivariate time explain why so many different multivariate product-limit estimators exist. We give a complete and elementary treatment of the basic theory of the product-integral $\pi(1 + dX)$ together with a discussion of some of its applications. New results are given on the compact differentiability of the product-integral, to be used along with the functional $\delta$-method for getting large-sample results for product-limit estimators.

/pdf/a-survey-of-product-integration-with-a-view-toward-2hbxqkphfg.pdf

A Survey of Product-Integration with a View Toward Application in Survival Analysis

Weak convergence results are proved for the product-limit estimator on the whole line. Applications are given to confidence band construction, estimation of mean lifetime, and to the theory of $q$-functions. The results are obtained using stochastic calculus and in probability linear bounds for empirical processes.

/pdf/large-sample-behaviour-of-the-product-limit-estimator-on-the-25v6nj7lkw.pdf

Richard D. Gill

Papers

Cox's Regression Model for Counting Processes: A Large Sample Study

Censoring and stochastic integrals

A counting process approach to maximum likelihood estimation in frailty models

A Survey of Product-Integration with a View Toward Application in Survival Analysis

Large Sample Behaviour of the Product-Limit Estimator on the Whole Line