Exploring relationships between phenological and weather data using smoothing

Stepwise regression is often used to draw associations between phenological records and weather data. For example, the dates that a species first flowers each year might be regressed on monthly mean temperatures for a period preceding flowering. The months that 'best' explain the variation in first flowering dates would be selected by stepwise regression. However, daily records of weather are usually available. Stepwise regression on daily temperatures would not be appropriate because of high correlations between neighbouring days. Smoothing methods provide a way of avoiding such difficulties. Regression coefficients can be smoothed by penalising differences in slopes between neighbouring regressors. The resultant curve of regression gradients is intuitively attractive. Various possible approaches to smoothing regression coefficients are discussed. We illustrate the use of one method, P-spline signal regression, which is particularly appropriate when there are many more regressors than observations. Smoothing can be applied to more than one set of regressors. This results in a multi-dimensional surface of regression coefficients. We use this approach to investigate how the time of year that a plant species tends to flower affects its relationship with temperature records. Using this method, we found that later species tend to be affected by later temperatures.     

Discriminant analysis of event-related potential curves using smoothed principal components

Principal component analysis enhanced by the use of smoothing is used in conjunction with discriminant analysis techniques to devise a statistical classification method for the analysis of event-related potential data. A training set of premedication potentials collected from adolescents with attention-deficit hyperactive disorder (ADHD) is used to predict whether adolescents from an independent subject group will respond to long-term medication. Comparison of outcome prediction rates demonstrates that this method, which uses information from the whole ERP curve, is superior to the classification technique currently used by clinicians, which is based on a single ERP curve feature. The need to administer an initial dose of medication to classify patients is also eliminated.     

Semiparametric modeling of labeled-cell kinetics,with application to isotope labeling of erythrocytes

We propose a stochastic model for the kinetics of cells that have been tagged with a chemical label. The proposed model consists of two components: a parametrically specified distribution for the time to incorporation of the label into the cells and a nonparametric survival function reflecting the survival time of the label-cell combination. The target quantity of this modeling approach is the fraction of labeled cells among all cells, viewed as a function of time. Longitudinal measurements of this labeled-cell fraction are available from a recent experiment with folate-labeled red blood cells. The proposed semiparametric model is fitted to these data and some of the implications are explored. The proposed method also includes bootstrap-based inference.     

Inference in spline-based models for multiple time-to-event data, with applications to a breast cancer prevention trial

As part of the National Surgical Adjuvant Breast and Bowel Project, a controlled clinical trial known as the Breast Cancer Prevention Trial (BCPT) was conducted to assess the effectiveness of tamoxifen as a preventive agent for breast cancer. In addition to the incidence of breast cancer, data were collected on several other, possibly adverse, outcomes, such as invasive endometrial cancer, ischemic heart disease, transient ischemic attack, deep vein thrombosis and/or pulmonary embolism. In this article, we present results from an illustrative analysis of the BCPT data, based on a new modeling technique, to assess the effectiveness of the drug tamoxifen as a preventive agent for breast cancer. We extended the flexible model of Gray (1994, Spline-based test in survival analysis, Biometrics 50, 640-652) to allow inference on multiple time-to-event outcomes in the style of the marginal modeling setup of Wei, Lin, and Weissfeld (1989, Regression analysis of multivariate incomplete failure time data by modeling marginal distributions, Journal of the American Statistical Association 84, 1065-1073). This proposed model makes inference possible for multiple time-to-event data while allowing for greater flexibility in modeling the effects of prognostic factors with nonlinear exposure-response relationships. Results from simulation studies on the small-sample properties of the asymptotic tests will also be presented.     

Negative binomial additive models

The generalized additive model is extended to handle negative binomial responses. The extension is complicated by the fact that the negative binomial distribution has two parameters and is not in the exponential family. The methodology is applied to data involving DNA adduct counts and smoking variables among ex-smokers with lung cancer. A more detailed investigation is made of the parametric relationship between the number of adducts and years since quitting while retaining a smooth relationship between adducts and the other covariates.     

A regression-based method for estimating mean treatment cost in the presence of right-censoring

In many clinical trials and evaluations using medical care administrative databases it is of interest to estimate not only the survival time of a given treatment modality but also the total associated cost. The most widely used estimator for data subject to censoring is the Kaplan-Meier (KM) or product-limit (PL) estimator. The optimality properties of this estimator applied to time-to-event data (consistency, etc.) under the assumptions of random censorship have been established. However, whenever the relationship between cost and survival time includes an error term to account for random differences among patients' costs, the dependency between cumulative treatment cost at the time of censoring and at the survival time results in KM giving biased estimates. A similar phenomenon has previously been noted in the context of estimating quality-adjusted survival time. We propose an estimator for mean cost which exploits the underlying relationship between total treatment cost and survival time. The proposed method utilizes either parametric or nonparametric regression to estimate this relationship and is consistent when this relationship is consistently estimated. We then present simulation results which illustrate the gain in finite-sample efficiency when compared with another recently proposed estimator. The methods are then applied to the estimation of mean cost for two studies where right-censoring was present. The first is the heart failure clinical trial Studies of Left Ventricular Dysfunction (SOLVD). The second is a Health Maintenance Organization (HMO) database study of the cost of ulcer treatment.