In many longitudinal studies one is concerned with analyzing the causal effects of dynamic treatment regimes on an outcome of interest. A dynamic treatment regime is a rule which at each point in time determines the assigned treatment by evaluating a particular function of scores extracted from the observed history of the subject. Robins introduces and analyzes structural nested failure time models which model a so called counterfactual blip function which represents the causal effect of a final treatment action at time $t$, adjusted for the whole past of the subject, which is assumed to include all confounders of treatment. If the dynamic treatment regimes of interest and to be compared are only functions of some scores included in the observed past, then the blip function only adjusting for these scores is the parameter of interest. Therefore we introduce marginal structural nested models. In particular, we use the generalized blip function as a building block for modelling the causal effect of a dynamic treatment regime on the response distribution. We discuss estimators of this blip function and the distribution of response to a dynamic treatment regime in experimental and observational studies.

Many ecological studies suffer because of insufficient data on the phenomenon under study. Limited data usually lead to flat likelihood and uncertain inferences. Although hard data or actual observations may be difficult to obtain, there is usually wealth of information in terms of expert opinions. A common approach to incorporating expert opinion in statistical analysis is via the Bayesian paradigm. Bayesian approach, however, faces several problems: 1) Opinions of unreliable experts adversely affect conclusions, 2) Eliciting prior beliefs in terms of probability distributions is unnatural because field experts, generally, are unfamiliar with the statistical models. Statistical models are constructs of the statisticians and experts do not necessarily think in terms of statistical models, and, 3) Eliciting priors for many parameters simultaneously and consistently is nearly impossible. In this paper, I propose an alternative approach to eliciting expert opinion in terms of data or guess values. Such expert guess values are easier to obtain than eliciting prior distributions on the parameters of a statistical model. These expert guesses or elicited data are then combined with the observed data using a hierarchical model. An important feature of this approach is that, unlike the Bayesian approach, even an expert opinion that is negatively associated with the truth, in other words, even an intentionally misleading expert opinion, improves the statistical analysis. I will illustrate an application of this methodology for the prediction of presence of certain shrew species in western Montana.

Researchers at SFU, UBC and UVic now have greater access to Statistics Canada's household survey data for conducting academic and policy research. Lee Grenon from Statistics Canada will introduce the newly opened British Columbia Interuniversity Research Data Centre (BCIRDC). This new centre is part of a national network of nine research data centres opening at universities across Canada. The new BCIRDC provides faculty and graduate students with access to Statistics Canada's master data files that offer much more in depth information than do the public-use datasets. Most importantly, the centre provides access to data from Statistics Canada's longitudinal surveys which are a very powerful resource for quantitative analyses of child development, economic, educational, family, health, income, labour and social issues.

The presentation will explain: What is the Research Data Centres Program? What data will be available to researchers What type of research is being conducted at the RDCs? Who is eligible to apply for access to the RDC Program How to apply for access to a Research Data Centre

The opening of the BCIRDC and other Research Data Centres across Canada is an unique opportunity for faculty and graduate students to collaborate on a wide range of multi disciplinary research projects. To find out more please join us on
Tuesday, October 9th at 4:00pm
Room 301 Leonard Klinck Building

Also for further information on the BC Interuniversity Research Data Centre please visit our website at: http://data.library.ubc.ca/rdc/

You are invited to an academic buffet (lots of brain food provided) where various items on the menu of psychometricians will be presented. This talk will allow you to sample tasty items such as classical test theory, modern item-response theory, differential item functioning, dimensionality of tests, and cognitive models. To make these items digestible, basic vocabulary in the field will be discussed and graphs and some formulas will be presented for your pleasure. The talk is designed for people new to the field who would like to have a solid overview of the field and a basic idea of what applied and theoretical psychometricians actually do. The presentation should leave you mentally saturated without any negative side effects - and you won't even have to stand in line.

It is the speaker's experience that statisticians can have influential roles in decision making for the resolution of international trade disputes and the formulation of policies and regulations governing global trade. However, there are very few occasions when the use of statistically sound arguments alone can influence decision makers in business or government.

In this talk the speaker's thoughts on possible careers and the role and influence of statisticians in businesses and governments engaged in global trade are presented and illustrated with real examples from Canada's wood building products sector.

Receiver operating characteristic (ROC) curves are popular method for characterizing the accuracy of diagnostic tests when the test result is not binary. Various methodologies for estimating and comparing ROC curves have been developed. One approach, due to Pepe (1997, 2000a), uses a parametric regression model $ROC_x(t) = g(h_0(t) + ~ x)$ with the baseline function $h_0(t)$ specified up to finite dimensional parameters. In this paper, we extend the regression models by allowing arbitrary non-parametric baseline functions. We also provide asymptotic distribution theory and procedures for making statistical inference. We illustrate our approach with datasets from two studies of cancer biomarkers. Simulation studies suggested that the extra flexibility inherent in the semi-parametric method is gained with little loss in statistical efficiency.

This is the technical part of an earlier talk given at the Peter Wall Institute at UBC.

Click here for more information.

When dealing with the case-control data, it is often the case that the exposure to a risk factor of interest is subject to misclassification. Methods for correcting the odds ratios are available when the misclassification probabilities are known. In practice, however, good guesses rather than the exact values are available for these probabilities. We show that when these guesses are treated as exact even the smallest differencies between the true and guessed values can lead to very erroneous odds-ratio estimates. This problem is alleviated by a Bayesian analysis which incorporates the uncertainty about the misclassification probabilities as prior information.

In practice, data on the exposure variable are quite often available from more than one source. We review three methods for improving the odds-ratio estimates that combine information from two sources. We then develop a Bayesian approach which is based on latent class analysis, and apply it to the sudden infant death syndrome data.

The inference required the use of the Metropolis-Hastings algorithm and/or the Gibbs sampler.

Drop-outs are a common problem in longitudinal studies. In terms of statistical models for the data, there are three types of drop-out mechanisms: drop-out occurring completely at random (CRD), drop-out occurring at random (RD) and informative drop-out (ID). The drop-out mechanism is classified as CRD if the drop-out mechanism is independent of the measurements; as RD if the drop-out mechanism depends only on the observed but not the unobserved measurements, and as ID if the drop-out mechanism depends on both the observed and unobserved measurements. CRD and RD are referred to as ignorable because the drop-out mechanism can be ignored for the purpose of making inferences about the observed measurements, while ID is non-ignorable. Analyses based on an assumption of ignorable drop-out, when in reality the drop-out mechanism is non-ignorable, can lead to misleading or biased results. Likelihood-based models for continuous and categorical longitudinal data subject to non-ignorable drop-out have been developed. In this talk, we focus on exploring likelihood-based models for binary longitudinal data subject to informative drop-out.

The two modelling approaches considered are a selection model proposed by Baker (1995) and a transition model proposed by Liu et al. (1999). We apply these models to a data set from a multiple sclerosis (MS) clinical trial. The aims of the analyses are to investigate whether there is an indication of informative drop-out in this data, and to assess the sentivity of inferences concerning the treatment effects to the underlying drop-out mechanisms. We do not attempt to provide a definitive analyses of the data set, but rather to explore a variety of models which incorporate informative drop-out.

* This work in progress is joint with Peter Gilbert

Error of measurement is pervasive in data arising from social and behavioral research (including research in education and the health sciences). Methods for quantifying and studying this error of measurement have evolved over the last nearly 100 years into a coherent statistical approach. However, there has been some confusion as to the role of apparent "assumptions" such as correlated errors in the models. I will present an approach to conceptualizing psychometric models that brings to light relations among concepts in probability, statistics, and measurement. Furthermore this approach clarifies some of the confusion that is creeping into research methodology in the social and behavioral sciences about the various assumptions in the models. Where appropriate I will also present some examples with real data from the social and health sciences.

There are several well-known tests of the null hypothesis that the hazard function is non-increasing. However, these tests were designed to have power against the alternative that the hazard function is always increasing. They do not have much power when, say, the hazard is increasing on only a small interval. Fortunately we can modify these tests so that they can detect an increase on a small interval. Specifically, the test of Proschan and Pyke (1967), based on normalized spacings, is modified to a more local test. The significance level of the local test is attained when the data are exponentially distributed, and thus we can easily calculate p-values via simulation. The idea of localizing the Proschan and Pyke test is inspired by recent developments in nonparametric inference in bump-hunting in regression analysis

*This is joint work with
Irene Gijbels
Institute of Statistics
Catholic University of Louvain

*Directions (thanks to Anona Thorne -- and for organizing this session!)

Conference Rooom 6 is in the conference centre on the "basement" level of the Providence Building. The easiest way to get to it is to go there from the information wicket, which is at the South end of the Burrard building (the old building that fronts on Burrard): - follow the blue line on the floor from there through the Providence wing to the elevators at the end of that wing (you'll see various signs on the way that indicate you're on the way to the conference centre, among other places) - take the elevator down to level 1 - when you get out of the elevator, you'll see a sign directing you to the conference centre - Conference Room 6 is near the end of the hallway on the left. The St. Paul's Hospital parking lot is often full at that time of day, but there are many other parking lots in the neighbourhood.

In this talk, I describe the use of a deterministic rule, applied to the parameters of the gene expression distribution, to select a target subset of genes. The target subset is the parameter of interest, which can be estimated by applying the subset rule to observed sample statistics. I will discuss the conditions necessary for consistency of the subset estimator and will provide a sample size formula. Important features of the sampling distribution are estimated with the parametric bootstrap. The practical performance of the method is illustrated with a data analysis in breast cancer.

Tuesday, January 30, 2001, 16:00
Leonard S. Klinck 301
6356 Agricultural Road

The microarray image technology makes it possible to measure the simultaneous expressions of thousands of genes. It has become the standard tool to investigate fundamental biological functions. It is widely used in laboratories of academia and industry, producing vast quantities of image data. Experiments are expensive and future re-processing of the data may be necessary due to the still evolving statistical modeling. For these reasons, the full image data are always kept, resulting in immense storage requirements. This calls for compression schemes which take into account the statistical inference that is to follow, or a new definition of "irrelevance" of image features based on the loss of statistical information rather than visual distortion.

In this talk I present a microarray image compression scheme with a multi-level (lossless or lossy) coded data structure which facilitates statistical analysis and data transmission. As components, it uses adaptive segmentation, predictive coding, and wavelet transforms.

The high noise levels of microarray image data suggests the use of lossy compression. However, lossy compression necessarily leads to the loss of statistical information, which may affect future statistical modeling and inference. I address the question of optimal statistical estimation based on lossily compressed data and present a new upper bound on the minimum achievable loss of estimation efficiency due to compression. This is an interesting information-theoretic result in the field of multiterminal data compression, and can be used to evaluate the performance of practical compression schemes applied to microarray images.

Time permitting, I will briefly discuss the use of a statistical modeling principle based on data compression or coding: Rissanen's minimum description length (MDL) principle, for gene subset selection based on microarray data for classification of types of Leukemia.

The Internet has spawned a renewed interest in the analysis of co-occurrence data. Correspondence analysis can be applied to such data to yield useful information. A less well-known technique called canonical correspondence analysis (CCA) is suitable when such data come with covariates. We show that CCA is equivalent to a classification technique known as linear discriminant analysis (LDA). Both CCA and LDA are examples of a general feature extraction problem.

LDA as a feature extraction technique, however, is restrictive: it can not pick up high-order features in the data. We propose a much more general method, of which LDA is a special case. Our method does not assume the density functions of each class to belong to any parametric family. We then compare our method in the QDA (quadratic discriminant analysis) setting with a competitor, known as the sliced average variance estimator (SAVE). Our study shows that SAVE over-emphasizes second-order differences among classes.

Our approach to feature extraction is exploratory and has applications in dimension reduction, automatic exploratory data analysis, and data visualization. We also investigate strategies to incorporate the exploratory feature extraction component into formal probabilistic models. In particular, we study the problem of reduced-rank non-parametric discriminant analysis by combining our work in feature extraction with projection pursuit density estimation.

Cox proportional hazards regression model usually assumes that covariates have log-linear effects on the hazard function. Now we consider a more general proportional hazards regression model with a nonparametric link function. We mainly focus on the situation when the baseline hazard function is also unspecified. A two-step iterative algorithm is proposed to estimate the link function and the covariate effects. We make inference based on a local version of the partial likelihood.

Large sample properties are discussed and several simulation studies are conducted to evaluate the performance of this estimation procedure.

We apply this method to data with longitudinal covariates and provide a way to handle possible missing values using functional principal components analysis.

Stock market returns are often non-Gaussian by virtue of containing outliers. Modeling stock returns and calculating portfolio risk is almost invariably accomplished by fitting a linear model, called a "factor" model in the finance community, using the sanctified method of ordinary least squares (OLS). However, it is well-known that stock returns are often non-Gaussian by virtue of containing outliers, and that OLS estimates are not robust toward outliers. Modern robust regression methods are now available that are not f stock returns using firm size and book-to-market as the factors, where we show that OLS gives a misleading result. Then we show how Trellis graphics displays can be used to obtain quick, penetrating visualization of stock returns factor model data, and to obtain convenient comparisons of OLS and robust factor model fits. Last but not least, we point out that robust factor model fits and Trellis graphics displays are in effect powerful "data mining tools" for better understanding of financial data. Our examples are constructed using a new S-PLUS Robust Methods library and S-PLUS Trellis graphics displays.

Nonparametric modelling is an indispensible tool in many applications and its formulation in an hierarchical Bayesian context, using the entire posterior distribution rather than particular expectations, increases its flexibility. In this paper, focus is on nonparametric estimation through a mixture of triangular distributions. The optimality of this methodology is addressed and bounds on the accuracy of this approximation are derived. Although our approach is more widely applicable, we focus for simplicity on estimation of a monotone nondecreasing regression on [0,1] with additive error, effectively approximating the function of interest by a function having a piecewise linear derivative. Computationally accessible methods of estimation are described through an amalgamation of existing MCMC algorithms. Simulations and examples illustrate the approach.

*This work was based on a common project with K. Mengersen of Queensland University of Technology

This talk concerns inference about complex computer codes. There is growing concern amongst users of computer models about how to assess their validity and accuracy. In the environmental sciences, for example, computer codes are widely used to model atmospheric and marine dispersion, radioactive waste disposal risks, effects of ingesting toxic chemicals, wildfire events, etc. The EPA recently organised a three-day workshop to explore ways of addressing the validation of complex environmental models. Quantifying uncertainties in the use of computer codes is clearly a statistical question, but conventional statistical methods are ill-equipped to tackle some of the issues that arise. This talk will review such problems and a Bayesian methodology that is proving to be a powerful tool in addressing them.

Thursday, January 18, 2001
LSK 301 (formerly CSCI 301)
6356 Agricultural Road, UBC

A common problem in the analysis of environmental time series is how to deal with a possible trend component, which is usually thought of as large scale (or low frequency) variations or patterns in the series that might be best modelled separately from the rest of the series. Trend is often confounded with low frequency stochastic fluctuations, particularly in the case of models such as fractionally differenced (FD) processes, which can account for long memory dependence (slowly decaying auto-correlation) and can be extended to encompass non-stationary processes exhibiting quite significant low frequency components. In this talk we assume a model of polynomial trend plus FD noise and apply the discrete wavelet transform (DWT) to separate a time series into pieces that can be used to estimate both the FD process parameters and the trend. The estimation of the process parameters is based on an approximative maximum likelihood approach that is made possible by the fact that the DWT decorrelates FD process approximately. Once the parameters have been estimated, we can then test for a non-zero trend. After outlining the work that we have done to date on testing for non-zero trends, we demonstrate our methodology by applying it to a popular climate dataset.

Reference priors originally emerged from maximizing the asymptotic expression for the Shannon mutual information between a parameter and a data set. The idea was to interpret estimation information-theoretically. In the absence of nuisance parameters, Jeffreys prior achieves the maximum and later extensions cover cases involving nuisance parameters.

Here, we replace the data set with a statistic and permit more elaborate conditioning. Thus we examine conditional Shannon mutual informations between a parameter and a function of the data, given a nuisance parameter and another statistic. This leads to new reference priors, a calibration of sufficiency, and to priors that depend on the data, a case ruled out by the conventional Bayesian paradigm.