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Keywords: cause-specific hazard, doubly robust, imputation, influence function, inverse probability weighting, locally efficient, missing at random, partial likelihood, proportional hazards model, semiparametric model.
If something can fail, it can often fail in one of several ways and sometimes in more than one way at a time. There is always some cause of failure, and almost always, more than one possible cause. In one sense, then, survival analysis is a lost cause. The methods of Competing Risks have often been neglected in the survival analysis literature.
Survival analysis is a commonly used tool in many fields but has seen little use in education research despite a common number of research questions for which it is well suited. Researchers often use logistic regression instead; however, this omits useful information. In research on retention and graduation for example, the timing of the event is an important piece of information omitted when using logistic regression. A simulation study was conducted to evaluate four methods of analyzing competing risks survival data, Cox proportional hazards regression, Weibull regression, Fine and Gray's Method, and Cox proportional hazards regression with frailty. College student retention and graduation is presented as an example. The results indicate that there is no one best model for all simulated scenarios. Instead, it appears the selection of the method of analysis should be based on the characteristics of the data. Both Cox proportional hazards and the Weibull regression are accurate with the base combination (sample size of 500 per group, continuous event time format, no correlation between event times, homogeneous shape parameter for both events for both groups, homogeneous failure rates for both events for both groups, and no frailty) as well as when one parameter is changed from the base combination. In addition, for data where the event time distribution shape does not differ by event, the accuracy of the models is quite similar. However, differences begin to emerge with some combinations of conditions. Cox performs especially poorly with data sets containing both differing event time distribution shapes by event and differing failure rates by group or event while Weibull is least accurate with the combination of homogeneous event time distribution shape, heterogeneous failure rate by group and/or event, and discrete format time. Fine and Gray's method was often ranked last by accuracy, but there are some situations where its accuracy is quite good including retention and graduation data. Cox proportional hazards regression with frailty performed very similarly to the Cox regression without frailty with no clear benefits.
Readers will find in the pages of this book a treatment of the statistical analysis of clustered survival data. Such data are encountered in many scientific disciplines including human and veterinary medicine, biology, epidemiology, public health and demography. A typical example is the time to death in cancer patients, with patients clustered in hospitals. Frailty models provide a powerful tool to analyze clustered survival data. In this book different methods based on the frailty model are described and it is demonstrated how they can be used to analyze clustered survival data. All programs used for these examples are available on the Springer website.
This book covers competing risks and multistate models, sometimes summarized as event history analysis. These models generalize the analysis of time to a single event (survival analysis) to analysing the timing of distinct terminal events (competing risks) and possible intermediate events (multistate models). Both R and multistate methods are promoted with a focus on nonparametric methods.
Handbook of Survival Analysis presents modern techniques and research problems in lifetime data analysis. This area of statistics deals with time-to-event data that is complicated by censoring and the dynamic nature of events occurring in time. With chapters written by leading researchers in the field, the handbook focuses on advances in survival analysis techniques, covering classical and Bayesian approaches. It gives a complete overview of the current status of survival analysis and should inspire further research in the field. Accessible to a wide range of readers, the book provides: An introduction to various areas in survival analysis for graduate students and novices A reference to modern investigations into survival analysis for more established researchers A text or supplement for a second or advanced course in survival analysis A useful guide to statistical methods for analyzing survival data experiments for practicing statisticians
In many clinical studies, researchers are interested in theeffects of a set of prognostic factors on the hazard of death from a specific disease even though patients may die from other competing causes. Often the time to relapse is right-censored for some individuals due to incomplete follow-up. In some circumstances, it may also be the case that patients are known to die but the cause of death is unavailable. When cause of failure is missing, excluding the missing observations from the analysis or treating them as censored may yield biased estimates and erroneous inferences. Under the assumption that cause of failure is missing at random, we propose three approaches to estimate the regression coefficients. The imputation approach isstraightforward to implement and allows for the inclusion ofauxiliary covariates, which are not of inherent interest formodeling the cause-specific hazard of interest but may be related to the missing data mechanism. The partial likelihood approach we propose is semiparametric efficient and allows for more general relationships between the two cause-specific hazards and more general missingness mechanism than the partial likelihood approach used by others. The inverse probability weighting approach isdoubly robust and highly efficient and also allows for theincorporation of auxiliary covariates. Using martingale theory and semiparametric theory for missing data problems, the asymptotic properties of these estimators are developed and the semiparametric efficiency of relevant estimators is proved. Simulation studies are carried out to assess the performance of these estimators in finite samples. The approaches are also illustrated using the data from a clinical trial in elderly women with stage II breast cancer. The inverse probability weighted doubly robust semiparametric estimator is recommended for itssimplicity, flexibility, robustness and high efficiency.
Survival Analysis Using S: Analysis of Time-to-Event Data is designed as a text for a one-semester or one-quarter course in survival analysis for upper-level or graduate students in statistics, biostatistics, and epidemiology. Prerequisites are a standard pre-calculus first course in probability and statistics, and a course in applied linear regression models. No prior knowledge of S or R is assumed. A wide choice of exercises is included, some intended for more advanced students with a first course in mathematical statistics. The authors emphasize parametric log-linear models, while also detailing nonparametric procedures along with model building and data diagnostics. Medical and public health researchers will find the discussion of cut point analysis with bootstrap validation, competing risks and the cumulative incidence estimator, and the analysis of left-truncated and right-censored data invaluable. The bootstrap procedure checks robustness of cut point analysis and determines cut point(s). In a chapter written by Stephen Portnoy, censored regression quantiles - a new nonparametric regression methodology (2003) - is developed to identify important forms of population heterogeneity and to detect departures from traditional Cox models. By generalizing the Kaplan-Meier estimator to regression models for conditional quantiles, this methods provides a valuable complement to traditional Cox proportional hazards approaches.
Observational studies and clinical trials with time-to-event data frequently involve multiple event types, known as competing risks. The cumulative incidence function (CIF) is a particularly useful parameter as it explicitly quantifies clinical prognosis. Common issues in competing risks data analysis on the CIF include interval censoring, missing event types, and left truncation. Interval censoring occurs when the event time is not observed but is only known to lie between two observation times, such as clinic visits. Left truncation, also known as delayed entry, is the phenomenon where certain participants enter the study after the onset of disease under study. These individuals with an event prior to their potential study entry time are not included in the analysis and this can induce selection bias. In order to address unmet needs in appropriate methods and software for competing risks data analysis, this thesis focuses the following development of application and methods. First, we develop a convenient and exible tool, the R package intccr, that performs semiparametric regression analysis on the CIF for interval-censored competing risks data. Second, we adopt the augmented inverse probability weighting method to deal with both interval censoring and missing event types. We show that the resulting estimates are consistent and double robust. We illustrate this method using data from the East-African International Epidemiology Databases to Evaluate AIDS (IeDEA EA) where a significant portion of the event types is missing. Last, we develop an estimation method for semiparametric analysis on the CIF for competing risks data subject to both interval censoring and left truncation. This method is applied to the Indianapolis-Ibadan Dementia Project to identify prognostic factors of dementia in elder adults. Overall, the methods developed here are incorporated in the R package intccr.