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The Statistical Analysis of Failure Time Data
Abstract:Preface.1. Introduction.1.1 Failure Time Data.1.2 Failure Time Distributions.1.3 Time Origins, Censoring, and Truncation.1.4 Estimation of the Survivor Function.1.5 Comparison of Survival Curves.1.6 Generalizations to Accommodate Delayed Entry.1.7 Counting Process Notation.Bibliographic Notes.Exercises and Complements.2. Failure Time Models.2.1 Introduction.2.2 Some Continuous Parametric Failure Time Models.2.3 Regression Models.2.4 Discrete Failure Time Models.Bibliographic Notes.Exercises and Complements.3. Inference in Parametric Models and Related Topics.3.1 Introduction.3.2 Censoring Mechanisms.3.3 Censored Samples from an Exponential Distribution.3.4 Large-Sample Likelihood Theory.3.5 Exponential Regression.3.6 Estimation in Log-Linear Regression Models.3.7 Illustrations in More Complex Data Sets.3.8 Discrimination Among Parametric Models.3.9 Inference with Interval Censoring.3.10 Discussion.Bibliographic Notes.Exercises and Complements.4. Relative Risk (Cox) Regression Models.4.1 Introduction.4.2 Estimation of beta.4.3 Estimation of the Baseline Hazard or Survivor Function.4.4 Inclusion of Strata.4.5 Illustrations.4.6 Counting Process Formulas. 4.7 Related Topics on the Cox Model.4.8 Sampling from Discrete Models.Bibliographic Notes.Exercises and Complements.5. Counting Processes and Asymptotic Theory.5.1 Introduction.5.2 Counting Processes and Intensity Functions.5.3 Martingales.5.4 Vector-Valued Martingales.5.5 Martingale Central Limit Theorem.5.6 Asymptotics Associated with Chapter 1.5.7 Asymptotic Results for the Cox Model.5.8 Asymptotic Results for Parametric Models.5.9 Efficiency of the Cox Model Estimator.5.10 Partial Likelihood Filtration.Bibliographic Notes.Exercises and Complements.6. Likelihood Construction and Further Results.6.1 Introduction.6.2 Likelihood Construction in Parametric Models.6.3 Time-Dependent Covariates and Further Remarks on Likelihood Construction.6.4 Time Dependence in the Relative Risk Model.6.5 Nonnested Conditioning Events.6.6 Residuals and Model Checking for the Cox Model.Bibliographic Notes.Exercises and Complements.7. Rank Regression and the Accelerated Failure Time Model.7.1 Introduction.7.2 Linear Rank Tests.7.3 Development and Properties of Linear Rank Tests.7.4 Estimation in the Accelerated Failure Time Model.7.5 Some Related Regression Models.Bibliographic Notes.Exercises and Complements.8. Competing Risks and Multistate Models.8.1 Introduction.8.2 Competing Risks.8.3 Life-History Processes.Bibliographic Notes.Exercises and Complements.9. Modeling and Analysis of Recurrent Event Data.9.1 Introduction.9.2 Intensity Processes for Recurrent Events.9.3 Overall Intensity Process Modeling and Estimation.9.4 Mean Process Modeling and Estimation.9.5 Conditioning on Aspects of the Counting Process History.Bibliographic Notes.Exercises and Complements.10. Analysis of Correlated Failure Time Data.10.1 Introduction.10.2 Regression Models for Correlated Failure Time Data.10.3 Representation and Estimation of the Bivariate Survivor Function.10.4 Pairwise Dependency Estimation.10.5 Illustration: Australian Twin Data.10.6 Approaches to Nonparametric Estimation of the Bivariate Survivor Function.10.7 Survivor Function Estimation in Higher Dimensions.Bibliographic Notes.Exercises and Complements.11. Additional Failure Time Data Topics.11.1 Introduction.11.2 Stratified Bivariate Failure Time Analysis.11.3 Fixed Study Period Survival Studies.11.4 Cohort Sampling and Case-Control Studies.11.5 Missing Covariate Data.11.6 Mismeasured Covariate Data.11.7 Sequential Testing with Failure Time Endpoints.11.8 Bayesian Analysis of the Proportional Hazards Model.11.9 Some Analyses of a Particular Data Set.Bibliographic Notes.Exercises and Complements.Glossary of Notation.Appendix A: Some Sets of Data.Appendix B: Supporting Technical Material.Bibliography.Author Index.Subject Index.
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A influência da manutenção industrial no índice global de eficiência (OEE)
2012
摘要
xi ABSTRACT Maintenance plays a fundamental key in any organization, revealing itself as a determinant factor for any organization success. Regarding high competitiveness between organizations, they are looking to maximize availability and reliability resources and equipments, to produce the desired amount of products with quality specifications required, in the estimated deadline. In maintenance, more particularly in the area of reliability, the study’s practical development consisted of applying statistical models to reparable systems and the main goal is to identify equipments that contribute negatively to the reliability of the production line. This study could be sectioned into three phases. Initially, in a global way, it was evaluated the production downtime of the production line equipments. The second phase analyses the importance of failures into production downtime. Based on Laplace Test is possible to develop statistical analysis, in order to understand the tendency of failures. Finally, was used Weibull distribution in order to model times between interventions. It was developed a preventive maintenance plan to the critical equipment, which comprehend the intervention period and the tasks to be performed. It is expected a significant improvement from OEE (Overall Equipment Effectiveness) allowing to increase reliability and availability from those systems and, consequently, performance and quality. The developed methodology can be applied to all repairable equipments of the line in study, as well as other production line.
Statistical inference for uniform stochastic ordering in several populations
1991
摘要
tion for k-population problems under uniform stochastic ordering restrictions. We derive closed-form estimates even with right-censored data by a reparameterization which reduces the problem to a well-known isotonic regression problem. We also derive the asymptotic distribution of the likelihood ratio statistic for testing equality of the k populations against the uniform stochastic ordering restriction. This asymptotic distribution is of the chi-bar-square type as discussed by Robertson, Wright and Dykstra. These distributional results are obtained by appealing to elegant results from empirical process theory and showing that the proposed test is asymptotically distribution free. Recurrence formulas are derived for the weights of the chi-bar-square distribution for particular cases. The theory developed in this paper is illustrated by an example involving data for survival times for carcinoma of the oropharynx.
The Career Paths of Teachers: Implications for Teacher Supply and Methodological Lessons for Research.
1988
摘要
these questions matter to various actors in the educational system, including school board members and superintendents evaluating the adequacy of teacher salaries and teacher recruitment budgets and college students assessing the potential attractiveness of careers in teaching. The primary sources of quantitative information for addressing these questions are teacher supply and demand models. In fact, numerical projections of the size of the impending teacher shortage or surplus, based on the National Center for Education Statistics'
Advanced Econometric Marketing Models
2003
摘要
textabstractDe recente toename in de beschikbaarheid van grote marketingdatabases heeft geleid tot een groei in de vraag naar geschikte econometrische modellen. Over het algemeen bevatten deze databases gegevens over de voorkeuren van consumenten. Deze voorkeuren kunnen worden weergegeven door marktaandelen, totale verkopen of merkkeuzebeslissingen. Econometrische modellen vormen handige hulpmiddelen om nuttige informatie over consumentengedrag uit deze databases te halen. In dit proefschrift bespreken wij econometrische modellen voor marktaandelen, tussenaankooptijden en merkkeuzebeslissingen. Deze modellen kunnen bijvoorbeeld worden gebruikt om inzicht te verkrijgen in het effect van marketinginstrumenten op het gedrag van consumenten. Voorbeelden van de onderwerpen die worden besproken zijn heterogeniteit in beslissingsprocessen en de ontwikkeling van eenvoudig te interpreteren modellen voor dynamische eigenschappen van marktaandelen en tussenaankooptijden. Daarnaast leveren wij een bijdrage aan de econometrische literatuur door de uitbreiding en ontwikkeling van modellen en schattingstechnieken.
Duration models and proportional hazards in political science
2001
摘要
period. In recent years political scientists have increasingly adopted a wide range of techniques for modeling duration data. But while the use of duration models by political scientists has increased dramatically, a concomitant examination of the modeling assumptions underlying these methods has not accompanied this growth. An important characteristic of most of these models is the assumption that the relative hazards over different covariate values are proportional. This consideration is important because, as has been widely shown in the statistics literature, estimation of proportional hazards models when hazards are, in fact, nonproportional can result in biased estimates, incorrect standard errors, and faulty inferences about the substantive impact of independent variables (e.g., Kalbfleisch and Prentice 1980; Schemper 1992; Collett 1994; Klein and Moeschberger 1997). But while the proportional hazards assumption is central to the proper estimation and interpretation of these models, it has received little attention by political scientists modeling duration data. This is unfortunate because, absent explicit examinations of the validity of these assumptions, the reader is often unable to infer whether or not the assumption holds for any particular analysis. This difficulty is exacerbated by the fact that, in many circumstances, both substantive theories and empirical data suggest that the assumption itself is of dubious accuracy. In fact, it is often the case that many substantively interesting hypotheses imply time-dependence or other forms of nonproportionality in the conditional probability of failure. Thus, it is important that, as political scientists begin to use these models more often in applied research, they take care to examine the extent to which this assumption is consistent with their data and to be aware of methods for analyzing duration data in which hazards are not proportional.
Maximum likelihood estimation of measurement error models based on the Monte Carlo EM algorithm
2007
摘要
of Dissertation Submitted to the Faculty of the Graduate School of the State University of New York at Buffalo in partial fulfillment of the requirements for the Degree of Doctor of Philosophy MAXIMUM LIKELIHOOD ESTIMATION OF MEASUREMENT ERROR MODELS BASED ON THE MONTE CARLO EM ALGORITHM By Antara Majumdar June 1, 2007 Chair: Randy L. Carter Major Department: Department of Biostatistics Likelihood based estimation of stochastic models when one of the explanatory variables is masked by measurement error, is presented. Special methods are required to estimate the parameters of a model with one or more explanatory variables that are measured with error. In such models, the variable measured with error is unobservable. Only an unbiased manifestation is observable. The method proposed, provides an adjustment to obtain unbiased estimates of model parameters. The correction of bias, however, is not possible without additional identifying information. An instrumental variable is a practical form of additional information that can be used for this purpose. By treating the unobservable explanatory variable as ‘missing’ data the Markov Chain Monte Carlo Expectation Maximization (MCEM) algorithm is applied for maximum likelihood estimation of the parameters of a measurement error model with identifying information in the form of an instrumental variable. Implementation strategies, computational aspects, behavior of the estimators and inference resulting from application of the MCEM algorithm to the instrumental variable measurement error model
Modeling conversions in online advertising
2010
摘要
ii Acknowledgements iii
Hospital results of Total Therapy Study XIIIB at St Jude Children's Research Improved outcome for children with acute lymphoblastic leukemia:
2013
摘要
doi:10.1182/blood-2004-04-1616Prepublished online July 13, 2004;2004 104: 2690-2696€€€€EvansKun, Susana C. Raimondi, Frederick G. Behm, James R. Downing, Mary V. Relling and William E. Jeffrey E. Rubnitz, Bassem I. Razzouk, Scott C. Howard, Melissa M. Hudson, Cheng Cheng, Larry E.Ching-Hon Pui, John T. Sandlund, Deqing Pei, Dario Campana, Gaston K. Rivera, Raul C. Ribeiro,€
Outcomes in Hypertensive Black and Nonblack Patients Treated With Chlorthalidone, Amlodipine, and Lisinopril
2005
摘要
and nonblacks, respectively, the RRs for stroke were 1.40 (95% CI, 1.17-1.68) and 1.00 (95%CI,0.85-1.17)andforcombinedCVDwere1.19(95%CI,1.09-1.30)and1.06(95% CI, 1.00-1.13). For HF, the RRs were 1.30 (95% CI, 1.10-1.54) and 1.13 (95% CI, 1.001.28),withnosignificantinteractionbyrace.Time-dependentBPadjustmentdidnotsignificantly alter differences in outcome for lisinopril vs chlorthalidone in blacks. Conclusions In blacks and nonblack subgroups, rates were not lower in the amlodipine or lisinopril groups than in the chlorthalidone group for either the primary CHD or any other prespecified clinical outcome, and diuretic-based treatment resulted in the lowest risk of heart failure. While the improved outcomes with chlorthalidone were more pronounced for some outcomes in blacks than in nonblacks, thiazide-type diuretics remain the drugs of choice for initial therapy of hypertension in both black and nonblack hypertensive patients.
The Cox model: introduction and history
2013
摘要
a celebration of an incredibly influential paper:
the most cited paper in the whole history of JRSS
the third most cited paper in medical journals
it has a total of nearly 30,000 citations (according to Web of
Science)
and this is still increasing
Correlations between earthquakes and large mud volcano eruptions
2007
摘要
[1] We examine the potential triggering relationship between large earthquakes and methane mud volcano eruptions. Our data set consists of a 191-year catalog (1810–2001) of eruptions from 77 volcanoes in Azerbaijan, central Asia, supplemented with reports from mud volcano eruptions in Japan, Romania, Pakistan, and the Andaman Islands. We compare the occurrence of historical regional earthquakes (M > 5) with the occurrence of Azerbaijan mud volcano eruptions and find that the number of same-day earthquake/eruption pairs is significantly higher than expected if the eruptions and earthquakes are independent Poisson processes. The temporal correlation between earthquakes and eruptions is most pronounced for nearby earthquakes (within ∼100 km) that produce seismic intensities of Mercalli 6 or greater at the location of the mud volcano. This assumed magnitude/distance relationship for triggering observed in the Azerbaijan data is consistent with documented earthquake-induced mud volcano eruptions elsewhere. We also find a weak correlation that heightened numbers of mud volcano eruptions occur within 1 year after large earthquakes. The distribution of yearly eruptions roughly approximates a Poisson process, although the repose times somewhat favor a nonhomogenous failure rate, which implies that the volcanoes require some time after eruption to recharge. The volcanic triggering likely results from some aspect of the seismic wave's passage, but the precise mechanism remains unclear.
Regressionsmodelle für gruppierte Verweildauern und Lebenszeiten
Z. Oper. Research
1985
摘要
ZusammenfassungEs werden allgemeine Regressionsmodelle für den Fall entwickelt, daß lediglich Zeitintervalle angegeben werden können, in denen Zustandswechsel aufgetreten oder bestimmte Ereignisse stattgefunden haben. Es werden sowohl „Competing-Risks“-Ansätze als auch Modelle für mehrere aufeinanderfolgende Episoden dargestellt. Ferner werden Möglichkeiten zur Einbeziehung von zeitabhängigen Kovariablen erörtert. Zur Schätzung der unbekannten Modellparameter wird die Maximum-Likelihood-Methode unter Berücksichtigung eventueller Zensierungen der letzten Episode herangezogen. Schließlich werden mit den vorgestellten Ansätzen zwei empirische Datensätze zur Analyse der Dauer der Arbeitslosigkeit und zur Untersuchung der Überlebenszeit nach einer Mannakarzinom-Operation ausgewertet.
Standing on the Shoulders of Others: Career Interdependence in Job Mobility
1992
摘要
William P. Barnett Stanford University Anne S. Miner University of Wisconsin-Madison Organizations often hire workers whom they will not promote, a practice we believe triggers career interdependence, where hiring nonpromotable workers sometimes harms but in some cases helps the mobility chances of other employees. We identify conditions that should shape such interdependence and test our ideas by analyzing how the hiring of temporary workers affected the mobility of permanent workers in a large organization. We expected that hiring temporary workers (1) would slow mobility among permanent workers at lower ranks and (2) speed mobility among advanced workers and that these effects (3) would hold for vacancy promotions but not for upgrade promotions. These hypotheses were largely supported by rate-dependent accelerated duration models estimated using event-history data on 6,850 workers over a 14-year period. The results indicate that the hiring of nonpromotable workers can create a "hidden escalator" favoring core workers and suggest the value of more research into the institutional sources of career interdependence.'
Imputation for semiparametric transformation models with biased-sampling data
Lifetime Data Analysis
2012
摘要
Widely recognized in many fields including economics, engineering, epidemiology, health sciences, technology and wildlife management, length-biased sampling generates biased and right-censored data but often provide the best information available for statistical inference. Different from traditional right-censored data, length-biased data have unique aspects resulting from their sampling procedures. We exploit these unique aspects and propose a general imputation-based estimation method for analyzing length-biased data under a class of flexible semiparametric transformation models. We present new computational algorithms that can jointly estimate the regression coefficients and the baseline function semiparametrically. The imputation-based method under the transformation model provides an unbiased estimator regardless whether the censoring is independent or not on the covariates. We establish large-sample properties using the empirical processes method. Simulation studies show that under small to moderate sample sizes, the proposed procedure has smaller mean square errors than two existing estimation procedures. Finally, we demonstrate the estimation procedure by a real data example.
The road to professionalization: a study on the determinants of creation of a middle management level by Italian high-tech start-ups
2007
摘要
Why do founders (i.e. top managers) of some new technology-based firms (NTBFs) decide to introduce a middlemanagement level into their firms and others do not? The question is extremely relevant because firm performance may be positively and sensibly affected by an increase in enterprise’s “profesionalization”. This contribution aims at analyzing the issue through an econometric investigation. Relying on the (thin) previous empirical literature on the topic and focusing on a large sample of Italian NTBFs we analyze the determinants of introduction of a middle-management level into firm organizational design, distinguish between the fact that the new intermediate managerial position was created through an internal upgrade of in-house workers or oppositely by hiring an external individual from labor market. Results highlight that the nature and the spectrum of the competencies possessed by the founding (i.e. top management) team have a prominent role: on the one hand, mixed competencies reduce the need for fresh managerial capabilities; on the other hand, more educated and experienced owner-managers are more likely to introduce a middlemanagement level into firm’s organizational structure. As the complexity and the size of the firm increase there is the need for a more hierarchical structure. If the introduction of the first manager is found to be affected by firm-specific characteristics (e.g. academic spin-offs, reception of public subsidies), the role of firms’ business environment should not be under valuated. In particular, firms operating in uncertain, less complex and highly competitive markets are more likely to introduce a middle-management level into their organizational structure.
Two-sample location-scale estimation from semiparametric random censorship models
J. Multivar. Anal.
2014
摘要
When two survival functions belong to a location-scale family of distributions, and the available two-sample data are each right censored, the location and scale parameters can be estimated using a minimum distance criterion combined with Kaplan-Meier quantiles. In this paper, it is shown that using the estimated quantiles from a semiparametric random censorship framework produces improved parameter estimates. The semiparametric framework was originally proposed for the one-sample case (Dikta, 1998), and uses a model for the conditional probability that an observation is uncensored given the observed minimum. The extension to the two-sample setting assumes the availability of good fitting models for the group-specific conditional probabilities. When the models are correctly specified for each group, the new location and scale estimators are shown to be asymptotically as or more efficient than the estimators obtained using the Kaplan-Meier based quantiles. Individual and joint confidence intervals for the parameters are developed. Simulation studies show that the proposed method produces confidence intervals that have correct empirical coverage and that are more informative. The proposed method is illustrated using two real data sets.
Confidence intervals for the effect of a prognostic factor after selection of an ‘optimal’ cutpoint
Statistics in medicine
2004
摘要
When investigating the effects of potential prognostic or risk factors that have been measured on a quantitative scale, values of these factors are often categorized into two groups. Sometimes an ‘optimal’ cutpoint is chosen that gives the best separation in terms of a two‐sample test statistic. It is well known that this approach leads to a serious inflation of the type I error and to an overestimation of the effect of the prognostic or risk factor in absolute terms. In this paper, we illustrate that the resulting confidence intervals are similarly affected. We show that the application of a shrinkage procedure to correct for bias, together with bootstrap resampling for estimating the variance, yields confidence intervals for the effect of a potential prognostic or risk factor with the desired coverage. Copyright © 2004 John Wiley & Sons, Ltd.
Evaluation of sample size and power for analyses of survival with allowance for nonuniform patient entry, losses to follow-up, noncompliance, and stratification.
Biometrics
1986
摘要
When designing a clinical trial to test the equality of survival distributions for two treatment groups, the usual assumptions are exponential survival, uniform patient entry, full compliance, and censoring only administratively at the end of the trial. Various authors have presented methods for estimation of sample size or power under these assumptions, some of which allow for an R-year accrual period with T total years of study, T greater than R. The method of Lachin (1981, Controlled Clinical Trials 2, 93-113) is extended to allow for cases where patients enter the trial in a nonuniform manner over time, patients may exit from the trial due to loss to follow-up (other than administrative), other patients may continue follow-up although failing to comply with the treatment regimen, and a stratified analysis may be planned according to one or more prognostic covariates.
Proportional hazards model with covariates subject to measurement error.
Biometrics
1992
摘要
When covariates of a proportional hazards model are subject to measurement error, the maximum likelihood estimates of regression coefficients based on the partial likelihood are asymptotically biased. Prentice (1982, Biometrika 69, 331-342) presents an example of such bias and suggests a modified partial likelihood. This paper applies the corrected score function method (Nakamura, 1990, Biometrika 77, 127-137) to the proportional hazards model when measurement errors are additive and normally distributed. The result allows a simple correction to the ordinary partial likelihood that yields asymptotically unbiased estimates; the validity of the correction is confirmed via a limited simulation study.
Cumulative Incidence Estimation in the Presence of Competing Risks
2004
摘要
When competing risks are present, the appropriate estimate of the failure probabilities is the cumulative incidence. stcompet creates new variables containing the estimate of this function, its standard error, and ln(– ln) transformed confidence bounds. Two examples are presented to illustrate the use of the new command and some key features of the cumulative incidence.