2,717 research outputs found

    A maximum-mean-discrepancy goodness-of-fit test for censored data

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    We introduce a kernel-based goodness-of-fit test for censored data, where observations may be missing in random time intervals: a common occurrence in clinical trials and industrial life-testing. The test statistic is straightforward to compute, as is the test threshold, and we establish consistency under the null. Unlike earlier approaches such as the Log-rank test, we make no assumptions as to how the data distribution might differ from the null, and our test has power against a very rich class of alternatives. In experiments, our test outperforms competing approaches for periodic and Weibull hazard functions (where risks are time dependent), and does not show the failure modes of tests that rely on user-defined features. Moreover, in cases where classical tests are provably most powerful, our test performs almost as well, while being more general

    Comparison Of Cox Regression And Discrete Time Survival Models

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    A standard analysis of prostate cancer biochemical failure data is done by conducting two approaches in which risk factors or covariates are measured. Cox regression and discrete-time survival models were compared under different attributes: sample size, time periods, and parameters in the model. The person-period data was reconstructed when examining the same data in discrete-time survival model. Twenty-four numerical examples covering a variety of sample sizes, time periods, and number of parameters displayed the closeness of Cox regression and discrete-time survival methods in situations typical of the cancer study

    Statistical analysis of samples from the generalized exponential distribution

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    Diplomová práce se zabývá zobecněným exponenciálním rozdělením jako alternativou k Weibullovu a log-normálnímu rozdělení. Jsou popsány základní charakteristiky tohoto rozdělení a metody odhadu parametrů. Samostatná kapitola je věnována testům dobré shody. Druhá část práce se zabývá cenzorovanými výběry. Jsou uvedeny ukázkové příklady pro exponenciální rozdělení. Dále je studován případ cenzorování typu I zleva, který dosud nebyl publikován. Pro tento speciální případ jsou provedeny simulace s podrobným popisem vlastností a chování. Dále je pro toto rozdělení odvozen EM algoritmus a jeho efektivita je porovnána s metodou maximální věrohodnosti. Vypracovaná teorie je aplikována pro analýzu environmentálních dat.Thesis deals with generalized exponential distribution as an alternative distribution to Weibull and log-normal distributions. At first, properties of the generalized exponential distribution are presented, followed by the methods of parameter estimation. Separate chapter describes goodness of fit tests. Second part of the thesis deals with censored samples. Demonstrative examples of censoring on exponential distribution are presented. Moreover the type I left censored case on generalized exponential distribution, which has not been studied before, is elaborated at the end of the chapter. Simulations for this particular case of censoring are presented and studied in detail. EM algorithm is developed and its efficiency is compared to the maximum likelihood method. The derived theory is then applied on set of environmental data.

    Modelling graft survival after kidney transplantation using semi-parametric and parametric survival models

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    A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, South Africa, in ful lment of the requirements for the degree of Master of Science in Statistics November, 2017This study presents survival modelling and evaluation of risk factors of graft survival in the context of kidney transplant data generated in South Africa. Beyond the Kaplan-Meier estimator, the Cox proportional hazard (PH) model is the standard method used in identifying risk factors of graft survival after kidney transplant. The Cox PH model depends on the proportional hazard assumption, which is rarely met. Assessing and accounting for this assumption is necessary before using this model. When the PH assumption is not valid, modi cation of the Cox PH model could o er more insight into parameter estimates and the e ect of time-varying predictors at di erent time points. This study aims to identify the survival model that will e ectively describe the study data by employing the Cox PH and parametric accelerated failure time (AFT) models. To identify the risk factors that mediate graft survival after kidney transplant, secondary data involving 751 adults that received a single kidney transplant in Charlotte Maxeke Johannesburg Academic Hospital between 1984 and 2004 was analysed. The graft survival of these patients was analysed in three phases (overall, short-term and long-term) based on the follow-up times. The Cox PH and AFT models were employed to determine the signi cant risk factors. The purposeful method of variable selection based on the Cox PH model was used for model building. The performance of each model was assessed using the Cox-Snell residuals and the Akaike Information Criterion. The t of the appropriate model was evaluated using deviance residuals and the delta-beta statistics. In order to further assess how appropriately the best model t the study data for each time period, we simulated a right-censored survival data based on the model parameter-estimates. Overall, the PH assumption was violated in this study. By extending the standard Cox PH model, the resulting models out-performed the standard Cox PH model. The evaluation methods suggest that the Weibull model is the most appropriate in describing the overall graft survival, while the log-normal model is more reasonable in describing short-and long-term graft survival. Generally, the AFT models out-performed the standard Cox regression model in all the analyses. The simulation study resulted in parameter estimates comparable with the estimates from the real data. Factors that signi cantly in uenced graft survival are recipient age, donor type, diabetes, delayed graft function, ethnicity, no surgical complications, and interaction between recipient age and diabetes. Statistical inferences made from the appropriate survival model could impact on clinical practices with regards to kidney transplant in South Africa. Finally, limitations of the study are discussed in the context of further studies.MT 201

    Goodness-of-fit tests for the frailty distribution in proportional hazards models with shared frailty.

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    Frailty models account for the clustering present in grouped event time data. A proportional hazards model with shared frailties expresses the hazard for each subject. Often a one-parameter gamma distribution is assumed for the frailties. The choice of a particular frailty distribution is, most of the time, based on the availability of software, rather than on the way it fits the data. In this paper we construct formal goodness-of-fit tests to test for gamma frailties. We construct a new class of frailty models that extend the gamma frailty model by using certain polynomial expansions that are orthogonal with respect to the gamma density. For this extended family we obtain an explicit expression for the marginal likelihood of the data. The order selection test is based on finding the best fitting model in such a series of expanded models. A bootstrap is used to obtain p-values for the tests. Simulations and data examples illustrate the test's performance.Gamma distribution; Goodness-of-fit test; Frailty model; Order selection test; Orthogonal polynomial;

    Applicability of multiplicative and additive hazards regression models in survival analysis

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    Background: Survival analysis is sometimes called “time-to-event analysis”. The Cox model is used widely in survival analysis, where the covariates act multiplicatively on unknown baseline hazards. However, the Cox model requires the proportionality assumption, which limits its applications. The additive hazards model has been used as an alternative to the Cox model, where the covariates act additively on unknown baseline hazards. Objectives and methods: In this thesis, performance of the Cox multiplicative hazards model and the additive hazards model have been demonstrated and applied to the transfer, lifting and repositioning (TLR) injury prevention study. The TLR injury prevention study was a retrospective, pre-post intervention study that utilized a non-randomized control group. There were 1,467 healthcare workers from six hospitals in Saskatchewan, Canada who were injured from January 1, 1999 to December 1, 2006. De-identified data sets were received from the Saskatoon Health Region and Regina Qu’appelle Health Region. Time to repeated TLR injury was considered as the outcome variable. The models’ goodness of fit was also assessed. Results: Of a total of 1,467 individuals, 149 (56.7%) in the control group and 114 (43.3%) in the intervention group had repeated injuries during the study period. Nurses and nursing aides had the highest repeated TLR injuries (84.8%) among occupations. Back, neck and shoulders were the most common body parts injured (74.9%). These covariates were significant in both Cox multiplicative and additive hazards models. The intervention group had 27% fewer repeated injuries than the control group in the multiplicative hazards model (HR= 0.63; 95% CI=0.48-0.82; p-value=0.0002). In the additive model, the hazard difference between the intervention and the control groups was 0.002. Conclusion: Both multiplicative and additive hazards models showed similar results, indicating that the TLR injury prevention intervention was effective in reducing repeated injuries. The additive hazards model is not widely used, but the coefficient of the covariates is easy to interpret in an additive manner. The additive hazards model should be considered when the proportionality assumption of the Cox model is doubtful

    Bootstrap distribution for testing a change in the cox proportional hazard model.

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    Lam Yuk Fai.Thesis (M.Phil.)--Chinese University of Hong Kong, 2000.Includes bibliographical references (leaves 41-43).Abstracts in English and Chinese.Chapter 1 --- Basic Concepts --- p.9Chapter 1.1 --- Survival data --- p.9Chapter 1.1.1 --- An example --- p.9Chapter 1.2 --- Some important functions --- p.11Chapter 1.2.1 --- Survival function --- p.12Chapter 1.2.2 --- Hazard function --- p.12Chapter 1.3 --- Cox Proportional Hazards Model --- p.13Chapter 1.3.1 --- A special case --- p.14Chapter 1.3.2 --- An example (continued) --- p.15Chapter 1.4 --- Extension of the Cox Proportional Hazards Model --- p.16Chapter 1.5 --- Bootstrap --- p.17Chapter 2 --- A New Method --- p.19Chapter 2.1 --- Introduction --- p.19Chapter 2.2 --- Definition of the test --- p.20Chapter 2.2.1 --- Our test statistic --- p.20Chapter 2.2.2 --- The alternative test statistic I --- p.22Chapter 2.2.3 --- The alternative test statistic II --- p.23Chapter 2.3 --- Variations of the test --- p.24Chapter 2.3.1 --- Restricted test --- p.24Chapter 2.3.2 --- Adjusting for other covariates --- p.26Chapter 2.4 --- Apply with bootstrap --- p.28Chapter 2.5 --- Examples --- p.29Chapter 2.5.1 --- Male mice data --- p.34Chapter 2.5.2 --- Stanford heart transplant data --- p.34Chapter 2.5.3 --- CGD data --- p.34Chapter 3 --- Large Sample Properties and Discussions --- p.35Chapter 3.1 --- Large sample properties and relationship to goodness of fit test --- p.35Chapter 3.1.1 --- Large sample properties of A and Ap --- p.35Chapter 3.1.2 --- Large sample properties of Ac and A --- p.36Chapter 3.2 --- Discussions --- p.3
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