Louisiana Chapter of the American Statistical Association Spring 2011 Meeting

Friday, 6 May 2011
9:30 am - 4:00 pm
212 Efferson Hall
LSU Agriculture Center
Louisiana State University
Baton Rouge, Louisiana

Schedule

9:30-10:00 Reception
10:00-10:30 Using Logistic Regression to Assess Survival of Honey Bees
Chelsea Deroche
Louisiana State University
10:30-11:00 Economic Design of Two-stage Control Charts
Tzong-Ru Tsai
Kansas State University
11:00-11:30 On Parameter Estimation Under a t-Model
Nabendu Pal
University of Louisiana at Lafayette
11:30-11:45 Business meeting
11:45-1:15 Lunch
1:15-1:45 Confidence Limits for Lognormal Percentiles and for Lognormal Mean based on Samples with Multiple Detection Limits
Zhao Xu
University of Louisiana at Lafayette
1:45-2:15 Analysis of Longitudinal Categorical Data with Nonignorable Dropout using Shared Random Effects Models
Myungok Lee
LSU Health Sciences Center
2:15-2:45 Analysis of Bivariate Longitudinal Quality of Life Data
Keunbaik Lee
LSU Health Sciences Center
2:45-3:00 Break
3:00-3:30 Bootstrapping Oracle Estimators in Correlation Models
Mihai C. Giurcanu
University of Louisiana at Lafayette
3:30-4:00 Use of Biplots to Identify Stable-Resistant Rice Lines
James Silva
Louisiana State University

Abstracts

Using Logistic Regression to Assess Survival of Honey Bees
Chelsea Deroche
Department of Experimental Statistics
Louisiana State University
Baton Rouge, LA

The Varroa destructor mite is a parasite of European honey bees, Apis mellifera, that weakens the population, can lead to the death of an entire honey bee colony, and is believed to be the parasite with the most economic impact on beekeeping. The purpose of this study is to estimate the odds of death given the concentration of mites found in any given colony. Also, it is of interest to assess the effect of the colony origin and the season of the year on the estimate. The data analysis is complicated by the fact that two of the genetic origins do not have failures which leads to divergence of the likelihood. To solve this issue, two data modifications are discussed. In the first approach, we omit these two origins from the analysis, and in the second, we force a failure for the largest mite concentration in the origins without failures. Also, because there are multiple observations on the same colony over a long period of time, the data are longitudinal and the observations are not independent. We compare a Generalized Estimating Equations (GEE) approach, which takes into consideration the dependency among the observations, versus the simple logistic regression that ignores the dependency. The analysis shows that the genetic origins and the season of the year are not statistically important factors in the mortality. Also, the analysis using simple logistic regression is fairly robust with respect to the more complex GEE analysis and the longitudinal observations can be treated as independent. These findings are in agreement with the understanding that the biologists have of the survival process in consideration.

Economic Design of Two-stage Control Charts
Tzong-Ru Tsai
Department of Industrial & Manufacturing System Engineering
Kansas State University
(On leave from Dept. of Statistics, Tamkang University, Tamsui, Taiwan)

Traditionally, process monitoring tool is developed based on the performance variable. However, the cost may be high to monitor the performance variable in practice but it is easier and cheaper to monitor its surrogate variable. In this talk, I will provide a novel economic design of two-stage charting procedure for dependent variables to monitor either the performance variable or its surrogate variable in an alternating fashion rather than monitoring the performance variable alone. An Illustrative example is used for demonstrating the application of the proposed method.

On Parameter Estimation Under a t-Model
Nabendu Pal
Department of Mathematics
University of Louisiana at Lafayette
Lafayette, LA

In applied problems it is very tempting to assume a normal model if the relative frequency histogram of the data looks roughly symmetric, unimodal, and/or a normality test accepts the assumption. Yet, there is always enough room for one to go wrong, especially if the data comes from a heavier tail symmetric unimodal distribution. There is a good amount of work reported in the literature on estimation of normal distribution parameters, but not so for the t distribution. In particular, most estimation methods for the t distribution assume that the degrees of freedom are known. This may be due to the complicated nature of the sampling distributions under the t-model. Also, the maximum likelihood estimators (MLEs) do not have closed expressions. In this note we propose several estimators of the parameters, including some approximations of the exact MLEs, and compare them in terms of standardized bias and mean squared error. Among other things, we have presented a simple approach to estimate the degrees of freedom efficiently, which has never been reported in the literature before. (This work is joint with Barbara Gonzalez-Arevalo)

Confidence Limits for Lognormal Percentiles and for Lognormal Mean based on Samples with Multiple Detection Limits
Zhao Xu
Department of Mathematics
University of Louisiana at Lafayette
Lafayette, LA

The problem of assessing occupational exposure using the mean or an upper percentile of a lognormal distribution is addressed. Inferential methods for constructing an upper confidence limit for an upper percentile of a lognormal distribution and for finding confidence intervals for a lognormal mean based on samples with multiple detection limits are proposed. The proposed methods are based on the maximum likelihood estimates. They perform well with respect to coverage probabilities as well as power, and are applicable to small sample sizes. The proposed approaches are applicable for finding confidence limits for the percentiles of a gamma distribution. Computational details and a source for the computer programs are given.An advantage of the proposed approach is the ease of computation and implementation. Illustrative examples with real data sets and a simulated data set are given.

Analysis of Longitudinal Categorical Data with Nonignorable Dropout using Shared Random Effects Models
Myungok Lee
Biostatistics Program
LSU Health Sciences Center
New Orleans, LA

In longitudinal studies investigators frequently have to assess and address potential biases introduced by missing data. This paper proposes new methods for modeling longitudinal categorical data with nonignorable dropout using marginalized transition models and shared parameter models. Random effects are introduced for both serial dependence of outcomes and nonignorable missingness. Fisher-scoring and Quasi-Newton algorithms are developed for parameter estimation. We use the Korean Genomic Epidemiology Study data to illustrate the models. (This work is joint with Keunbaik Lee.)

Analysis of Bivariate Longitudinal Quality of Life Data
Keunbaik Lee
Biostatistics Program
LSU Health Sciences Center
New Orleans, LA

Random effects models are commonly used to analyze longitudinal categorical data. Marginalized random effects models (MREMs) are a class of models that permit direct estimation of marginal mean parameters and characterize serial dependence for longitudinal categorical data via random effects (Heagerty, 1999; Lee and Daniels, 2008). In this paper, to capture serial dependence we consider more general models than first-order autoregressive correlation structure (AR(1)), by re-parameterizing the correlation matrix using partial autocorrelations (Daniels and Pourahmadi, 2009). We use these in a model that extends previous models to multivariate longitudinal ordinal data using the partial autocorrelation. A maximum marginal likelihood estimation method is proposed utilizing a Quasi-Newton algorithm with Quasi-Monte Carlo integration of the random effects. We analyze quality of life data from a colorectal cancer clinical trial using our methods. Dropout occurs at a high rate and is often due to tumor progression or death. To deal with progression/death, we will show how principal stratification can be used to draw causal inferences about the joint distribution of two ordinal quality of life measures using our multivariate longitudinal model to deal with missingness unrelated to death. (This work is joint with Michael J. Daniels, Department of Statistics, University of Florida.)

Bootstrapping Oracle Estimators in Correlation Models
Mihai C. Giurcanu
Department of Mathematics
University of Louisiana at Lafayette
Lafayette, LA

In this talk, I describe the large sample local behavior of some oracle estimators which are often used in the estimation of sparse correlation models. I then present the large sample properties of the standard bootstrap, the m-out-of-n bootstrap, and the oracle bootstrap (Giurcanu and Presnell, 2009) estimators of their distributions. These results show that, although some bootstrap estimators are consistent if the model is sparse, they are inconsistent if some of the regression parameters are "small". In an empirical study, I compare the finite sample properties of the bootstrap estimators of the regularization parameter and of the bias and the standard error of the adaptive LASSO estimator in a correlation model. (This work is joint with Brett Presnell from the University of Florida.)

Use of Biplots to Identify Stable-Resistant Rice Lines
James Silva
Department of Experimental Statistics
Louisiana State University
Baton Rouge, LA

Development of cultivars resistant to sheath blight disease caused by the fungal pathogen Rhizoctonia solani is an important breeding objective for the southern U.S. rice (Oryza sativa L.) industry. The aim of this research was to assess performance and stability of sheath blight resistance in the SB2 doubled-haploid (DH) mapping population using biplot. Genetic material was evaluated in replicated plots for two years (2006 and 2007) in Louisiana and Arkansas. GGE biplots methods were used to analyze genotype by environment interaction, stability and overall level of resistance. A "mega-environment" was identified consisting of three of the four year-location combinations. The Heritability-adjusted GGE biplot analyses of the 2006 and 2007 data identified 12 lines, including the resistant parent used to develop SB2, with high, stable levels of resistance at both locations. Five susceptible lines with greater stability than the susceptible parent of SB2 were also identified. The material identified in this study represents a potential source of good mean performance stable sheath blight resistance for cultivar development that warrants additional field-plot evaluation across different years and locations. (This is joint work with Dr. D. E. Groth, J.H. Oard, and K. Moldenhauer.)