Semi-competing risks data frequently arise in clinical and observational studies. In these cases, the subject can experience both non-terminal and terminal events where the terminal event (e.g., death) censors the non-terminal event (e.g., relapse) but not vice-versa. Typically, the two events are correlated. An approach based on latent failure times has been advocated for the analysis of such data, where the joint survival function of two event times is assumed to follow a copula function over the positive quadrant with observation restricted to the upper wedge. We argue, that similar to models for competing risks, latent failure times should generally be avoided in modeling such data.  We consider an illness-death process which circumvents any need for latent times and provides for easy incorporation of covariates. Nonparametric maximum likelihood estimation is used for inference, a simple iterative procedure is developed and needed asymptotic results are obtained. Simulation studies are conducted to assess the finite sample performance of the proposed estimators and the methods are illustrated in an analysis of data on nasopharyngeal cancer from a randomized clinical trial in Singapore.

This is joint work with Jinfeng Xu, and Beechoo Tai, National University of Singapore

Empirical likelihood is a popular nonparametric or semi-parametric statistical method with many nice statistical properties. Yet when the sample size is small, or the dimension of the accompanying estimating function is high, the application of the empirical likelihood method can be hindered by low precision of the chisquare approximation or if the estimating equations have no solutions. In this paper, the adjusted empirical likelihood is found to be effective at addressing both problems. If we choose a precise level of adjustment, the adjusted empirical likelihood achieves the high-order precision of the Bartlett correction, in addition to the advantage of a guaranteed solution to the estimating equations. Simulation results indicate that the confidence regions constructed by the adjusted empirical likelihood have coverage probabilities comparable to or substantially more accurate than the original empirical likelihood enhanced by the Bartlett correction.

This non technical talk describes an innovative and successful use of technology, through a virtual process, to aid in the teaching of statistical concepts and methodology. The virtual process simulates a manufacturing process for automobile camshafts that has a number of processing steps and many inputs.
 
At the start of an upper year undergraduate course Stat 435/835: Statistical Methods for Process Improvement, each team of students is given a budget and assigned the task of reducing variation in a critical output characteristic of a different version of the virtual process. Throughout the term, the teams plan and analyze a series of process investigations (~1/week) to first learn about how their process works and, by the end of term, how to improve it. The teams interact with the virtual process through a web interface. Each team submits a weekly written report describing their recent progress and twice per term presents to the class at a “management review meeting.” The virtual process is also used as the context for all midterms and exams. Based on anecdotal evidence and survey results, students find interacting with the virtual process fun, stimulating and challenging.
 
The goals of this talk are to show how the virtual process aids in the teaching of material and concepts in Stat 435/835 and to describe its main pedagogical benefits. With thought and some adaptation something similar should be possible for other applied statistics courses.
 

 

Many financial time series have been found to be heteroscedastic with autocorrelated volatility.  The traditional and widely used approaches for modeling volatility are the autoregressive conditional heteroscedastic (ARCH) or generalized autoregressive conditional heteroscedastic (GARCH) models. The stochastic volatility (SV) model enters as an alternative to the above models.  Compared with ARCH and GARCH models, the main difficulty for SV model is the evaluation of likelihood function, which evolves calculating a multi-dimensional integral. The Composite Likelihood method presented here is an alternative approach for estimating the SV model. The idea of Composite Likelihood is to reduce the dimension of integrals for the likelihood being calculated. For the bivariate case, the composite log-likelihood is the sum of log-likelihood of consecutive pairs. The performance of composite likelihood method will be compared with quasi-maximum likelihood (QML) and Monte Carlo Likelihood (MCL). Some interesting findings will also be discussed.

Linear mixed models have been frequently used to provide estimates in small areas. However, when aggregating small areas within the same region, the sum of these small area estimates does not generally match up with the estimate obtained using an appropriate estimator for the larger region.

Then, benchmarking the model-dependent estimates to the ones obtained at certain level of aggregation is needed.

In this paper, we propose a small area estimator based on a linear mixed effects model with restrictions to guarantee the concordance between the aggregations of small area estimates and those reported by statistical agencies for larger domains using a synthetic estimator. The mean squared prediction error of the restricted estimator is also derived and its performance is evaluated through a simulation study.

The procedure is applied to the 2002 Business Survey of the Basque Country, Spain. This is joint work with Ana F. Militino and T. Goicoa

This talk includes a review of the importance of reliability research on life distributions in various areas.

The reliability of a system can be interpreted as the "probability that, when operating under stated environmental conditions, the system will perform its intended functions adequately for a specified interval of time". The life distribution describes the behavior of a subject (such as human life, life length of a system, etc.) as a function of its age.

A brief introduction to the literature on life distributions will be presented and several criteria of classifying life distributions will be discussed. Some properties of nonparametric classes of life distributions and their applications in system maintenance, software reliability and network reliability will be presented.

Abstract:
Circular data arise in scientific disciplines as diverse as meteorology,
the earth sciences, biology, medicine and the political
sciences. For instance, they might represent the directions
of prevailing winds in the vicinity of a wind farm, the
orientations of fault lines in geological bedrock, the directions
of migrating birds, the degree of flexibility of the legs of injured
cyclists, or the times of violent attacks in occupied Iraq.

In my talk I will provide an introduction to the world
of circular statistics; starting with some illustrative data
sets and moving on to a consideration of the standard
descriptive measures used in the analysis of circular data, their
population counterparts and results for large sample inference.
As a spinoff, the latter provide a simple means of testing
for circular reflective symmetry. The major part of the talk will be
devoted to a consideration of models for circular data with emphasis
on the limitations of classical models and the flexibility
of alternatives proposed recently in the literature. The
application of some of the models, and the inference
associated with them, will be illustrated using real data.
 

Graph-structured networks are often used to represent relationships between persons in organizations or communities and the need of classifying such data is growing. We consider two scenarios in which graph-structured data can arise: a directly observed social network, and a social network implied by email transactions. 

In both cases, the data are in an unusual format (a graph with edges, or a long list of transactions). In order to apply "off the shelf" supervised learning methods, we first map the unusual data into a more familiar format, converting the raw data into a matrix of predictors (or features).  Complimentary information arises from these two scenarios, with one yielding features that capture "who talks to whom" and the other, "how one interacts with others".  Some examples will be given to demonstrate these techniques.

For the normal linear model regression setup, we extend Zellner's g-prior for the case where the number of predictors p exceeds the number of observations n. From exact analytical calculation of the marginal density under this prior, we give a new closed form Bayesian variable selection criterion.We also give some numerical results.

This is a joint work with Professor E. George at the University of Pennsylvania.

Correlated data, including longitudinal and clustered data, arise frequently in health and medical studies. These data may occur when subsampling the primary sampling units or repeatedly collecting measurements over time for subjects in the study. As is well-known, standard univariate analysis methods may not be suitable to handle correlated data. There has been extensive research interest in analysis methods for such data. However, a number of challenges, such as how to accommodate complex mean and association structures of data and how to facilitate different missing data mechanisms, still remain. In this talk, I will discuss some marginal and conditional methods for analysis of correlated data.

1. What are the boundaries for signal strength and sparsity for true discovery?
2. How to improve power by utilizing prior information in a stratified fashion (Sun et al., 2006; Celia et al., 2007)?
3. What is the comparative performance between the stratified method and the weighted p-value approach (Roeder et al., 2006)? Can we unify the two?
4. Does it make a difference in an application to an on-going GWA study of data from the Illumina 1M chip in DCCT/EDIC for association with diabetic retinopathy using previous genome-wide linkage results as prior information?
   

Nearly all statistical theory and methods begin with the assumption that the parameter of interest is identified by the data-generating process. Indeed, this identification assumption functions as a fundamental axiom of frequentism, and is in turn adopted uncritically in “objective” Bayesian theory and methods. But the assumption is justified only to the extent it is enforced by a perfectly randomized study design (purely random in allocation, sampling, and measurement error).

The identification assumption has no justification at all for observational studies in the health and social sciences. Tragically, indiscriminate use of methods that rely on the assumption has contributed to costly medical mistakes. An appropriate if unlikely response by the statistics community would be to cease reliance on the identification assumption, and adopt instead theory and methods that allow the target parameters to remain nonidentified by the data generating process alone.

The present talk will describe some theories and methods for inference on nonidentified parameters as they have developed in the health sciences over the past decade or so. Once one sees that identification does not follow from the study design and execution, only informative prior distributions remain to narrow the possibilities. Thus, to the extent these theories provide identification, they have a large informative-Bayesian component.