Functional linear models are useful in analyzing data from designed experiments and observational studies with functional responses, as well as longitudinal data with a large number of repeated measures on each subject. We propose a quasi F-test for functional linear models with functional covariates and outcomes. We develop a numerical procedure and an efficient approximation for computing p-values, and present a simple way to test individual predictors. For illustration, we apply the proposed procedure to a longitudinal depression data set with repeatedly measured methamphetamine use as a predictor. We conduct a simulation study to assess the size and the power of the test.
[Show abstract][Hide abstract] ABSTRACT: To evaluate relapse prevention (relapse prevention) and contingency management (contingency management) for optimizing smoking cessation outcomes using nicotine replacement therapy for methadone-maintained tobacco smokers.
Experimental, 2 (relapse prevention)x2 (contingency management) repeated measures design using a platform of nicotine replacement therapy featuring a 2-week baseline period, followed by randomization to 12 weeks of treatment, and 6- and 12-month follow-up visits.
Three narcotic treatment centers in Los Angeles.
One hundred and seventy-five participants who met all inclusion and no exclusion criteria.
Participants received 12 weeks of nicotine replacement therapy and assignment to one of four conditions: patch-only, relapse prevention + patch, contingency management + patch and relapse prevention + contingency management + patch.
Thrice weekly samples of breath (analyzed for carbon monoxide) and urine (analyzed for metabolites of opiates and cocaine) and weekly self-reported numbers of cigarettes smoked.
Participants (73.1%) completed 12 weeks of treatment. During treatment, those assigned to receive contingency management showed statistically higher rates of smoking abstinence than those not assigned to receive contingencies (F3,4680=6.3, P=0.0003), with no similar effect observed for relapse prevention. At follow-up evaluations, there were no significant differences between conditions. Participants provided more opiate and cocaine-free urines during weeks when they met criteria for smoking abstinence than during weeks when they did not meet these criteria (F1,2054=14.38, P=0.0002; F1,2419=16.52, P<0.0001).
Contingency management optimized outcomes using nicotine replacement therapy for reducing cigarette smoking during treatment for opiate dependence, although long-term effects are not generally maintained. Findings document strong associations between reductions in cigarette smoking and reductions in illicit substance use during treatment.
[Show abstract][Hide abstract] ABSTRACT: Longitudinal data sets in biomedical research often consist of large numbers of repeated measures. In many cases, the trajectories do not look globally linear or polynomial, making it difficult to summarize the data or test hypotheses using standard longitudinal data analysis based on various linear models. An alternative approach is to apply the approaches of functional data analysis, which directly target the continuous nonlinear curves underlying discretely sampled repeated measures. For the purposes of data exploration, many functional data analysis strategies have been developed based on various schemes of smoothing, but fewer options are available for making causal inferences regarding predictor-outcome relationships, a common task seen in hypothesis-driven medical studies. To compare groups of curves, two testing strategies with good power have been proposed for high-dimensional analysis of variance: the Fourier-based adaptive Neyman test and the wavelet-based thresholding test. Using a smoking cessation clinical trial data set, this paper demonstrates how to extend the strategies for hypothesis testing into the framework of functional linear regression models (FLRMs) with continuous functional responses and categorical or continuous scalar predictors. The analysis procedure consists of three steps: first, apply the Fourier or wavelet transform to the original repeated measures; then fit a multivariate linear model in the transformed domain; and finally, test the regression coefficients using either adaptive Neyman or thresholding statistics. Since a FLRM can be viewed as a natural extension of the traditional multiple linear regression model, the development of this model and computational tools should enhance the capacity of medical statistics for longitudinal data.
Statistics in Medicine 03/2008; 27(6):845-63. DOI:10.1002/sim.2952 · 1.83 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The varying coefficient models are very important tool to explore the dynamic pattern in many scientific areas, such as economics, finance, politics, epidemiology, medical science, ecology and so on. They are natural extensions of classical parametric models with good interpretability and are becoming more and more popular in data analysis. Thanks to their flexibility and interpretability, in the past ten years, the varying coefficient models have experienced deep and exciting developments on methodological, theoretical and applied sides. This paper gives a selective overview on the major methodological and theoretical developments on the varying coefficient models.
Statistics and its interface 02/2008; 1(1):179-195. DOI:10.4310/SII.2008.v1.n1.a15 · 2.93 Impact Factor
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