Survival Model and Estimation for Lung Cancer Patients.

Lung cancer is the most frequent fatal cancer in the United States. Following the notion in actuarial math analysis, we assume an exponential form for the baseline hazard function and combine Cox proportional hazard regression for the survival study of a group of lung cancer patients. The covariates in the hazard function are estimated by maximum likelihood estimation following the proportional hazards regression analysis. Although the proportional hazards model does not give an explicit baseline hazard function, the baseline hazard function can be estimated by fitting the data with a non-linear least square technique. The survival model is then examined by a neural network simulation. The neural network learns the survival pattern from available hospital data and gives survival prediction for random covariate combinations. The simulation results support the covariate estimation in the survival model

Flexible Models for Competing Risks and Weighted Analyses of Composite Endpoints

In many clinical studies the occurrence of different types of disease events over time is of interest. For example, in cardiovascular studies, disease events such as death, stroke or myocardial infarction are of interest. As another example, in central nervous system infections such as cryptococcal meningitis, unfavourable events such as death or neurological events and favourable events such as coma or fungal clearance are relevant. In statistical terminology, competing risks refer to data where the time and type of the first disease event are analysed. Such data arise naturally if a nonfatal disease event is of interest but is precluded by death in a substantial proportion of subjects. Competing risks are the topic of the first four chapters of this thesis. An alternative approach used in many randomized controlled clinical trials is to combine different harmful events to a single composite endpoint. The analysis of trials with a composite endpoints is the topic of the fifth chapter. This thesis is organised as follows: Chapters 1 and 2 are introductory chapters and provide an overview of statistical approaches to competing risks and semi-nonparametric (SNP) density estimation. Two concepts that form the basis for the work in Chapters 3 and 4 are introduced here: the cumulative incidence function (CIF) and SNP densities. For competing risks data, the CIF describes the absolute risk of different event types depending on time and is the most important quantity for data description, prognostic modelling, and medical decision making. SNP densities are densities that can be expressed as the product of a squared polynomial (of variable degree) and a base density which is chosen as the standard normal or the exponential density in this work. Chapter 3 presents a novel approach to CIF-estimation. The underlying statistical model is specified via a mixture factorization of the joint distribution of the event type and time and the time to event distributions conditional on the event type are modelled using SNP densities. One key strength of the approach is that it can handle arbitrary censoring and truncation. A stepwise forward algorithm for model estimation and adaptive selection of SNP polynomial degrees is presented, implemented in the statistical software R, evaluated in a sequence of simulation studies, and applied to data sets from clinical trials in central nervous system infections. The simulations demonstrate that the SNP approach frequently outperforms both parametric and nonparametric alternatives. They also support the use of “ad hoc” asymptotic inference to derive confidence intervals despite a lack of a formal mathematical verification for the relevant asymptotic properties. Chapter 4 extends the work of Chapter 3 to regression modelling, i.e. the quantification of cov-ariate effects on the CIF. A careful discussion of interpretational and identifiability issues which are intrinsic to models based on the mixture factorization is provided and the usage of the model is only recommended in settings with sufficient follow-up relative to the timing of the events. A simulation study demonstrates that the proposed approach is competitive compared to common statistical models for competing risks in terms of accuracy of parameter estimates and predictions. However, it also shows that “ad hoc” asymptotic inference is only valid if sample size is large. The chapter also provides a suggestion for model diagnostics of the proposed model, an area that has been somewhat neglected for competing risks data. Chapter 5 discusses the analysis of composite endpoints. A common critique of traditional analyses of composite endpoints is that all disease events are equally weighted whereas their clinical relevance may differ substantially. This chapter addresses this by introducing a framework for the weighted analysis of composite endpoints that handles both binary and time-to-event data. To address the difficulty in selecting an exact set of weights, it proposes a method for constructing simultaneous confidence intervals and tests that protect the familywise type I error in the strong sense across families of weights which satisfy flexible inequality and order constraints based on the theory of χ-2-distributions. It is then demonstrated in several simulation scenarios as well as applications that the proposed method achieves the nominal simultaneous overall coverage rate with lower efficiency loss compared to the standard Scheffe’s procedure. Final remarks are given in Chapter 6 together with an outlook for potential future research directions

Accelerated failure tima models for multivariate interval-censored data with flexible distributional assumptions

Department of Probability and Mathematical StatisticsKatedra pravděpodobnosti a matematické statistikyFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult

Statistical analysis of multivariate interval-censored failure time data

The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file.Title from title screen of research.pdf file viewed on (May 2, 2007)Vita.Thesis (Ph.D.) University of Missouri-Columbia 2006.Interval-censored failure time data commonly arise in clinical trials and medical studies. In such studies, the failure time of interest is often not exactly observed, but known to fall within some interval. For multivariate interval-censored data, each subject may experience multiple events, each of which is interval-censored. This thesis studies four research problems related to regression analysis and association study of multivariate interval-censored data. In particular, in Chapter 2, we propose a goodness-of-fit test for the marginal Cox model approach, which is the most commonly, used approach in multivariate regression analysis. Chapter 3 presents a two-stage estimation procedure for the association parameter for case 2 bivariate interval-censored data. In Chapter 4 we give a simple procedure to estimate the regression parameter for case 2 interval-censored data and Chapter 5 studies the efficient estimation of regression parameters and association parameter simultaneously for bivariate current status data. All the proposed methods are assessed by simulation studies and illustrated using real-life applications.Includes bibliographical reference

Practical Methods for Optimizing Equipment Maintenance Strategies Using an Analytic Hierarchy Process and Prognostic Algorithms

Many large organizations report limited success using Condition Based Maintenance (CbM). This work explains some of the causes for limited success, and recommends practical methods that enable the benefits of CbM. The backbone of CbM is a Prognostics and Health Management (PHM) system. Use of PHM alone does not ensure success; it needs to be integrated into enterprise level processes and culture, and aligned with customer expectations. To integrate PHM, this work recommends a novel life cycle framework, expanding the concept of maintenance into several levels beginning with an overarching maintenance strategy and subordinate policies, tactics, and PHM analytical methods. During the design and in-service phases of the equipment’s life, an organization must prove that a maintenance policy satisfies specific safety and technical requirements, business practices, and is supported by the logistic and resourcing plan to satisfy end-user needs and expectations. These factors often compete with each other because they are designed and considered separately, and serve disparate customers. This work recommends using the Analytic Hierarchy Process (AHP) as a practical method for consolidating input from stakeholders and quantifying the most preferred maintenance policy. AHP forces simultaneous consideration of all factors, resolving conflicts in the trade-space of the decision process. When used within the recommended life cycle framework, it is a vehicle for justifying the decision to transition from generalized high-level concepts down to specific lower-level actions. This work demonstrates AHP using degradation data, prognostic algorithms, cost data, and stakeholder input to select the most preferred maintenance policy for a paint coating system. It concludes the following for this particular system: A proactive maintenance policy is most preferred, and a predictive (CbM) policy is more preferred than predeterminative (time-directed) and corrective policies. A General Path prognostic Model with Bayesian updating (GPM) provides the most accurate prediction of the Remaining Useful Life (RUL). Long periods between inspections and use of categorical variables in inspection reports severely limit the accuracy in predicting the RUL. In summary, this work recommends using the proposed life cycle model, AHP, PHM, a GPM model, and embedded sensors to improve the success of a CbM policy