A semiparametric recurrent events model with time-varying coefficients

We consider a recurrent events model with time-varying coefficients motivated by two clinical applications. We use a random effects (Gaussian frailty) model to describe the intensity of recurrent events. The model can accommodate both time-varying and time-constant coefficients. We use the penalized spline method to estimate the time-varying coefficients. We use Laplace approximation to evaluate the penalized likelihood without a closed form. We estimate the smoothing parameters in a similar way to variance components. We conduct simulations to evaluate the performance of the estimates for both time-varying and time-independent coefficients. We apply this method to analyze two data sets: a stroke study and a child wheeze study

Regression analysis of multivariate recurrent event data with time-varying covariate effects

Recurrent event data occur in many fields and many approaches have been proposed for their analyses (Andersen et al. (1993) [1]; Cook and Lawless (2007) [3]). However, most of the available methods allow only time-independent covariate effects, and sometimes this may not be true. In this paper, we consider regression analysis of multivariate recurrent event data in which some covariate effects may be time-dependent. For the problem, we employ the marginal modeling approach and, especially, estimating equation-based inference procedures are developed. Both asymptotic and finite-sample properties of the proposed estimates are established and an illustrative example is provided.Event history study Marginal models Recurrent event data Time-varying coefficients

Optimal Decision Rule for Combining Multiple Biomarkers into Tree-based Classifier and its Evaluation

In biomedical practices, multiple biomarkers are often combined using a classification rule of the form of some tree structure to make diagnostic decisions. The classification structure and cutoff point at each node of a tree are commonly chosen ad-hoc based on experience of decision makers. There is a lack of analytical approaches that lead to optimal prediction performance, and that guide the choice of optimal cutoff points of a pre-specified classification tree. In this dissertation, we propose to search for and estimate the optimal decision rule through an approach of rank correlation maximization. The proposed method is flexible and computationally feasible using data with reasonably large sample sizes when there are many biomarkers available for classification or prediction. Using this method, for a pre-specified tree-structured classification rule, we are able to guide the choice of optimal cutoff at tree nodes, as well as to estimate optimal prediction performance of multiple biomarkers combined. In this dissertation, we also propose a semi-marginal and semi-parametric regression model for gap times between successive recurrent events in the presence of time-dependent covariates. Recurrent event data is commonly encountered in longitudinal follow-up studies, when each subject experiences multiple events under observation until loss to follow-up, dropout or end of study occurs. There exists a rich literature of models and methods that focus on time-to-event data in a recurrent event setting, but for applications where time- between-events (also referred to as gap times) is of scientific interest or where there is a strong cyclical pattern, limited techniques were developed, especially for regression with time-dependent covariates. We propose a semi-marginal regression model of a proportional hazard form on gap times such that no event history is included in the conditional statistics of regression except for the time relapse from baseline to last event occurrence. The proposed method is flexible in being semi-parametric, robust to various correlation structures of gap times within subject, and also allows time-dependent covariates to be included in the conditional statistics of regression

Semiparametric analysis of multivariate longitudinal 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 August 3, 2009)Vita.Thesis (Ph. D.) University of Missouri-Columbia 2008.[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] Longitudinal studies are conducted widely in fields such as agriculture and life sciences, business and industry, demography and other social sciences, medicine and public health. In longitudinal studies, individuals are measured repeatedly over time and multivariate longitudinal data occur when subjects are measured repeatedly with regard to multiple response variables. Analysis of multivariate longitudinal data can be challenging since it requires accounting for not only correlations between repeated measures of the same subject but also correlations among different response variables. One special type of longitudinal study involves monitoring subjects continuously to record occurrences of events and thus generates so-called recurrent event data. In the first part of this dissertation, we will discuss analysis of a set of multivariate longitudinal data arising from a prospective study of alcohol and drug use in college freshmen. Several statistical models and estimation approaches are presented for joint analysis of conducting alcohol and drug use. In particular, a marginal means model is proposed that leaves the correlation between response outcomes arbitrary. In the second part, regression analysis of multivariate recurrent event data with time-varying covariate effects will be considered. For the problem, we present some marginal models for the underlying counting processes and develop estimating equation based inference approaches. The asymptotic properties of the proposed estimates are established and their finite sample properties are evaluated through simulation studies. Additionally, some procedures are presented for testing the time-dependence of covariate effects and the proposed methodology is applied to sets of univariate recurrent event data and bivariate recurrent event data. The third part of this dissertation will consider variable selection for univariate and multivariate recurrent event data in the context of regression analysis. For the problem, we adopt the idea behind the nonconcave penalized likelihood approach proposed in Fan and Li (2001) and develop a nonconcave penalized estimating function approach. The proposed approach selects variables and estimates regression coefficients simultaneously and an algorithm is presented for this process. We show that the proposed approach performs as well as the oracle procedure, yielding estimates as if the correct submodel were known. Simulation studies conducted for assessing the performance of the proposed approach suggest that it works well for practical situations. The methodology is illustrated using a set of bivariate recurrent event data.Includes bibliographical reference