Xiaogang Su

Linear Regression Analysis: Theory and Computing

This volume presents in detail the fundamental theories of linear regression analysis and diagnosis, as well as the relevant statistical computing techniques so that readers are able to actually model the data using the methods and techniques described in the book. It covers the fundamental theories in linear regression analysis and is extremely useful for future research in this area. The examples of regression analysis using the Statistical Application System (SAS) are also included. This book is suitable for graduate students who are either majoring in statistics/biostatistics or using linear regression analysis substantially in their subject fields. Introduction Simple Linear Regression Multiple Linear Regression Detection of Outliers and Influential Observations in Multiple Linear Regression Model Selection Model Diagnostics Extensions of Least Squares Generalized Linear Models Bayesian Linear Regression

Subgroup Analysis via Recursive Partitioning

Subgroup analysis is an integral part of comparative analysis where assessing the treatment effect on a response is of central interest. Its goal is to determine the heterogeneity of the treatment effect across subpopulations. In this paper, we adapt the idea of recursive partitioning and introduce an interaction tree (IT) procedure to conduct subgroup analysis. The IT procedure automatically facilitates a number of objectively defined subgroups, in some of which the treatment effect is found prominent while in others the treatment has a negligible or even negative effect. The standard CART (Breiman et al., 1984) methodology is inherited to construct the tree structure. Also, in order to extract factors that contribute to the heterogeneity of the treatment effect, variable importance measure is made available via random forests of the interaction trees. Both simulated experiments and analysis of census wage data are presented for illustration.

Transition From Treatment to Survivorship: Effects of a Psychoeducational Intervention on Quality of Life in Breast Cancer Survivors

PURPOSE/OBJECTIVES To examine the effectiveness of a psychoeducational intervention on quality of life (QOL) in breast cancer survivors in post-treatment survivorship. DESIGN A randomized controlled trial. SETTING An academic center collaborating with a regional cancer center in the southeastern United States. SAMPLE 256 breast cancer survivors. METHODS Women were randomly assigned to the experimental or wait control group. The Breast Cancer Education Intervention (BCEI) study was delivered in three face-to-face sessions and five monthly follow-up sessions (three by telephone and two in person). The control group received four monthly attention control telephone calls and the BCEI at month 6. Data were collected at baseline, three and six months after the BCEI for the experimental group, and one month after the BCEI (at month 7) for the wait control group. MAIN RESEARCH VARIABLES Primary endpoints were overall QOL and physical, psychological, social, and spiritual well-being. FINDINGS No differences in QOL were reported at baseline between groups. The experimental group reported improved QOL at three months, whereas the wait control group reported a significant decline in QOL. The experimental group reported continued maintenance of QOL at six months. Although the wait control group reported improved QOL at six months, significant differences continued to exist between the groups. CONCLUSIONS The BCEI was an effective intervention in improving QOL during the first year of breast cancer survivorship. Treatment effects were durable over time. IMPLICATIONS FOR NURSING Post-treatment survivorship has not been empirically studied to a large degree. The BCEI is one of the few interventions demonstrating effectiveness among survivors after primary treatment, suggesting that oncology nurses may be uniquely positioned to provide safe passage using education and support.

Using hierarchical tree-based regression model to predict train-vehicle crashes at passive highway-rail grade crossings.

This paper applies a nonparametric statistical method, hierarchical tree-based regression (HTBR), to explore train-vehicle crash prediction and analysis at passive highway-rail grade crossings. Using the Federal Railroad Administration (FRA) database, the research focuses on 27 years of train-vehicle accident history in the United States from 1980 through 2006. A cross-sectional statistical analysis based on HTBR is conducted for public highway-rail grade crossings that were upgraded from crossbuck-only to stop signs without involvement of other traffic-control devices or automatic countermeasures. In this study, HTBR models are developed to predict train-vehicle crash frequencies for passive grade crossings controlled by crossbucks only and crossbucks combined with stop signs respectively, and assess how the crash frequencies change after the stop-sign treatment is applied at the crossbuck-only-controlled crossings. The study results indicate that stop-sign treatment is an effective engineering countermeasure to improve safety at the passive grade crossings. Decision makers and traffic engineers can use the HTBR models to examine train-vehicle crash frequency at passive crossings and assess the potential effectiveness of stop-sign treatment based on specific attributes of the given crossings.

Interaction Trees with Censored Survival Data

We propose an interaction tree (IT) procedure to optimize the subgroup analysis in comparative studies that involve censored survival times. The proposed method recursively partitions the data into two subsets that show the greatest interaction with the treatment, which results in a number of objectively defined subgroups: in some of them the treatment effect is prominent while in others the treatment may have a negligible or even negative effect. The resultant tree structure can be used to explore the overall interaction between treatment and other covariates and help identify and describe possible target populations on which an experimental treatment demonstrates desired efficacy. We follow the standard CART (Breiman, et al., 1984) methodology to develop the interaction tree structure. Variable importance information is extracted via random forests of interaction trees. Both simulated experiments and an analysis of the primary billiary cirrhosis (PBC) data are provided for evaluation and illustration of the proposed procedure.

Maximum Likelihood Regression Trees

We propose a method of constructing regression trees within the framework of maximum likelihood. It inherits the backward fitting idea of classification and regression trees (CART) but has more rigorous justification. Simulation studies show that it provides more accurate tree model selection compared to CART. The analysis of a baseball dataset is given as an illustration.

Preliminary evaluation of psychoeducational support interventions on quality of life in rural breast cancer survivors after primary treatment.

Although most cancer survivors are at risk for being lost in the transition from treatment to survivorship, rural breast cancer survivors face special challenges that might place them at particular risk. This small-scale preliminary study had 2 specific aims: (aim 1) establish the feasibility of rural breast cancer survivors participation in a longitudinal quality of life (QOL) intervention trial and (aim 2) determine the effects of the Breast Cancer Education Intervention (BCEI) on overall QOL. Fifty-three rural breast cancer survivors were randomized to either an experimental (n = 27) or a wait-control arm (n = 26). Participants in the experimental arm received the BCEI consisting of 3 face-to-face education and support sessions and 2 face-to-face and 3 telephone follow-up sessions, along with supplemental written and audiotape materials over a 6-month period. Breast Cancer Education Intervention modules and interventions are organized within a QOL framework. To address the possible effects of attention, wait-control participants received 3 face-to-face sessions and 3 telephone sessions during the first 6 months of participation in the study, but not the BCEI intervention. Research questions addressing aim 1 were as follows: (a) can rural breast cancer survivors be recruited into a longitudinal intervention trial, and (b) can their participation be retained. Research questions for aim 2 were as follows: (a) do participants who received the BCEI show improvement in overall QOL, and (b) is the QOL improvement sustained over time. Data were analyzed using repeated-measures general linear mixed models. Results demonstrated the ability to recruit and retain 53 rural breast cancer survivors, that the experimental arm showed improvement in overall QOL (P = .013), and that there were significant differences in overall QOL between the experimental and wait-control groups at both months 3 and 6. Thus, it appears that at least some rural breast cancer survivors can and will participate in a larger trial and will maintain their participation and that those that do participate experience significant QOL benefit.

Exploring factors associated with pressure ulcers: A data mining approach

BACKGROUND Pressure ulcers are associated with a nearly three-fold increase in in-hospital mortality. It is essential to investigate how other factors besides the Braden scale could enhance the prediction of pressure ulcers. Data mining modeling techniques can be beneficial to conduct this type of analysis. Data mining techniques have been applied extensively in health care, but are not widely used in nursing research. PURPOSE To remedy this methodological gap, this paper will review, explain, and compare several data mining models to examine patient level factors associated with pressure ulcers based on a four year study from military hospitals in the United States. METHODS The variables included in the analysis are easily accessible demographic information and medical measurements. Logistic regression, decision trees, random forests, and multivariate adaptive regression splines were compared based on their performance and interpretability. RESULTS The random forests model had the highest accuracy (C-statistic) with the following variables, in order of importance, ranked highest in predicting pressure ulcers: days in the hospital, serum albumin, age, blood urea nitrogen, and total Braden score. CONCLUSION Data mining, particularly, random forests are useful in predictive modeling. It is important for hospitals and health care systems to use their own data over time for pressure ulcer risk prediction, to develop risk models based upon more than the total Braden score, and specific to their patient population.

Trees for Correlated Survival Data by Goodness of Split, With Applications to Tooth Prognosis

In this article the regression tree method is extended to correlated survival data and applied to the problem of developing objective prognostic classification rules in periodontal research. The robust logrank statistic is used as the splitting statistic to measure the between-node difference in survival, while adjusting for correlation among failure times from the same patient. The partition-based survival function estimator is shown to converge to the true conditional survival function. Tooth loss data from 100 periodontal patients (2,509 teeth) was analyzed using the proposed method. The goal is to assign each tooth to one of the five prognosis categories (good, fair, poor, questionable, or hopeless). After the best-sized tree was identified, an amalgamation procedure was used to form five prognostic groups. The prognostic rules established here may be used by periodontists, general dentists, and insurance companies in devising appropriate treatment plans for periodontal patients.

Development of prognostic indicators using classification and regression trees for survival

The development of an accurate prognosis is an integral component of treatment planning in the practice of periodontics. Prior work has evaluated the validity of using various clinical measured parameters for assigning periodontal prognosis as well as for predicting tooth survival and change in clinical conditions over time. We critically review the application of multivariate Classification And Regression Trees (CART) for survival in developing evidence-based periodontal prognostic indicators. We focus attention on two distinct methods of multivariate CART for survival: the marginal goodness-of-fit approach, and the multivariate exponential approach. A number of common clinical measures have been found to be significantly associated with tooth loss from periodontal disease, including furcation involvement, probing depth, mobility, crown-to-root ratio, and oral hygiene. However, the inter-relationships among these measures, as well as the relevance of other clinical measures to tooth loss from periodontal disease (such as bruxism, family history of periodontal disease, and overall bone loss), remain less clear. While inferences drawn from any single current study are necessarily limited, the application of new approaches in epidemiologic analyses to periodontal prognosis, such as CART for survival, should yield important insights into our understanding, and treatment, of periodontal diseases.