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PubMed2003

Hierarchical linear models for the development of growth curves: an example with body mass index in overweight/obese adults.

When data are available on multiple individuals measured at multiple time points that may vary in number or inter-measurement interval, hierarchical linear models (HLM) may be an ideal option. The present paper offers an applied tutorial on the use of HLM for developing growth curves depicting natural changes over time. We illustrate these methods with an example of body mass index (BMI; kg/m(2)) among overweight and obese adults. We modelled among-person variation in BMI growth curves as a function of subjects' baseline characteristics. Specifically, growth curves were modelled with two-level observations, where the first level was each time point of measurement within each individual and the second level was each individual. Four longitudinal databases with measured weight and height met the inclusion criteria and were pooled for analysis: the Framingham Heart Study (FHS); the Multiple Risk Factor Intervention Trial (MRFIT); the National Health and Nutritional Examination Survey I (NHANES-I) and its follow-up study; and the Tecumseh Mortality Follow-up Study (TMFS). Results indicated that significant quadratic patterns of the BMI growth trajectory depend primarily upon a combination of age and baseline BMI. Specifically, BMI tends to increase with time for younger people with relatively moderate obesity (25 BMI <30) but decrease for older people regardless of degree of obesity. The gradients of these changes are inversely related to baseline BMI and do not substantially depend on gender.

Adult↗

PubMed1994

Correlates of intrauterine growth rate: application of a log-linear model.

A prospective study was conducted in the North Arcot District, Tamil Nadu State, India, to determine the correlates of intrauterine growth rate (IUGR), which was assessed using Yerushalmy's classification based on birth weight and gestational age. Using a log-linear model, we studied 4220 single live births with complete information on IUGR and obstetric, paternal, maternal, and familial factors. Parental body weights, consanguinity, and area of residence were identified as important predictors of IUGR.

Adolescent↗

PubMed1991

Determination of optimal designs using linear models in crossover trials.

This study determines the optimal designs for crossover trials with fixed size of population, in order to estimate contrasts between two treatment effects, for various numbers of periods. The problem is approached in the framework of a linear model, taking into consideration the structure of a variance matrix constructed from two random sources: linked-to-subject random effect and linked-to-measurement random error. Different models, as well as different optimality criteria, are considered. For example, when two periods are planned, for the criterion of the minimization of the variance of the treatment-effect estimator, in the presence of residual effect, the optimal design corresponds to four groups of sequences, (T1, T2), (T2, T1), (T1, T1), (T2, T2); without residual effect it corresponds to two groups, (T1, T2), (T2, T1). Optimal designs are given for the comparison of two treatments when using three or four periods.

Clinical Trials as Topic↗

PubMed2000

[Two-phase linear models of leaf emergence at different tillering positions in wheat and effects of different varieties and sowing dates].

Dynamics of leaf emergence shows the development progress and its relationship with growth in wheat. It was found that two-phase linear model equations (phase I faster than phase II) divided by glum differentiation stage could describe leaf emergence progress in relation to growing degree days (GDD) after sowing in wheat. This pattern was consistent in main stems and tillers of normal development with both winter-and-spring type varieties. The beginning of phase II shifted to an earlier development stage on main stems of winter type varieties of early planting (EP, September 30) and late planting (LP, March 2), and on T3 of both varieties of EP, MP (middle planting, on October 30) and LP due to their abnormal development. The thermal rate of leaf emergence on main stem was relatively high and steady during development for winter type variety of MP, and quickened with the postponing of sowing for spring type variety. The above results illustrated the difference of leaf emergence at different tillering positions, and the biological characteristics affected by different varieties and sowing dates.

Germination↗

PubMed2003

Wavelet-based estimation of a semiparametric generalized linear model of fMRI time-series.

This paper addresses the problem of detecting significant changes in fMRI time series that are correlated to a stimulus time course. This paper provides a new approach to estimate the parameters of a semiparametric generalized linear model of fMRI time series. The fMRI signal is described as the sum of two effects: a smooth trend and the response to the stimulus. The trend belongs to a subspace spanned by large scale wavelets. The wavelet transform provides an approximation to the Karhunen-Loève transform for the long memory noise and we have developed a scale space regression that permits to carry out the regression in the wavelet domain while omitting the scales that are contaminated by the trend. In order to demonstrate that our approach outperforms the state-of-the art detrending technique, we evaluated our method against a smoothing spline approach. Experiments with simulated data and experimental fMRI data, demonstrate that our approach can infer and remove drifts that cannot be adequately represented with splines.

Acoustic Stimulation↗

PubMed1998

An assessment of the effect of driver age on traffic accident involvement using log-linear models.

Statistical models were developed to help understand the relationship between the driver age and several important accident-related factors and circumstances such as injury severity, collision types, average daily traffic (ADT), roadway character, speed ratio, alcohol involvement, and accident location. By using techniques of categorical analysis on the 1994 and 1995 Florida accident database, four long-linear models with three variables in each model with all possible two-way interactions were developed. In order to compare the differences in response between the age groups and a particular accident-related variable, odds multipliers were computed. The effects of age and accident-related factors were examined, and interactions among them were considered. The results indicated significant relationships between the driver age and ADT, injury severity, manner of collision, speed, alcohol involvement, and roadway character. The findings' contribution to the understanding of the effect of age on accident involvement is addressed. A discussion of how log-linear and logit modeling with estimation of 'odds multipliers' may contribute to traffic safety studies is also provided.

Accidents, Traffic↗

PubMed1991

Backcalculation of flexible linear models of the human immunodeficiency virus infection curve.

The authors present a regression approach to the backcalculation of flexible linear models of the HIV infection curve. They note that "because expected AIDS incidence can be expressed as a linear function of unknown parameters, regression methods may be used to obtain parameter and covariance estimates for a variety of interesting quantities, such as the expected number of people infected in previous time intervals and the projected AIDS incidence in future time intervals. We exploit these ideas to show that estimates based on maximum likelihood are, for practical purposes, equivalent to approximate estimates based on quasi-likelihood and on Poisson regression. These algorithms are readily implemented on a personal computer." These concepts are illustrated by projecting AIDS incidence in the United States up to 1993.

Acquired Immunodeficiency Syndrome↗

PubMed2006

affylmGUI: a graphical user interface for linear modeling of single channel microarray data.

SUMMARY: affylmGUI is a graphical user interface (GUI) to an integrated workflow for Affymetrix microarray data. The user is able to proceed from raw data (CEL files) to QC and pre-processing, and eventually to analysis of differential expression using linear models with empirical Bayes smoothing. Output of the analysis (tables and figures) can be exported to an HTML report. The GUI provides user-friendly access to state-of-the-art methods embodied in the Bioconductor software repository. AVAILABILITY: affylmGUI is an R package freely available from http://www.bioconductor.org. It requires R version 1.9.0 or later and tcl/tk 8.3 or later and has been successfully tested on Windows 2000, Windows XP, Linux (RedHat and Fedora distributions) and Mac OS/X with X11. Further documentation is available at http://bioinf.wehi.edu.au/affylmGUI CONTACT: keith@wehi.edu.au.

Bayes Theorem↗

PubMedDate not supplied

The relationship between impairment and disability in arthritis: an application of the theory of generalized linear models to the ICIDH.

We investigated the relationship between impairment, as represented by limitation in range of movement and pain in the knee joint, and disability as measured by a series of activities of daily living in 123 patients with either rheumatoid arthritis or osteoarthrosis. A log-linear modelling technique found there was a positive association between functional limitation, as measured by reduction in angle of flexion, and disability. However, there was only a marginal relationship between pain in the knee joint and disability, and no association between pain and range of movement, which suggests that conventional beliefs that pain is a key factor in assessing health outcomes may need to be reassessed.

Adolescent↗

PubMed2005

A robust two-way semi-linear model for normalization of cDNA microarray data.

BACKGROUND: Normalization is a basic step in microarray data analysis. A proper normalization procedure ensures that the intensity ratios provide meaningful measures of relative expression values. METHODS: We propose a robust semiparametric method in a two-way semi-linear model (TW-SLM) for normalization of cDNA microarray data. This method does not make the usual assumptions underlying some of the existing methods. For example, it does not assume that: (i) the percentage of differentially expressed genes is small; or (ii) the numbers of up- and down-regulated genes are about the same, as required in the LOWESS normalization method. We conduct simulation studies to evaluate the proposed method and use a real data set from a specially designed microarray experiment to compare the performance of the proposed method with that of the LOWESS normalization approach. RESULTS: The simulation results show that the proposed method performs better than the LOWESS normalization method in terms of mean square errors for estimated gene effects. The results of analysis of the real data set also show that the proposed method yields more consistent results between the direct and the indirect comparisons and also can detect more differentially expressed genes than the LOWESS method. CONCLUSIONS: Our simulation studies and the real data example indicate that the proposed robust TW-SLM method works at least as well as the LOWESS method and works better when the underlying assumptions for the LOWESS method are not satisfied. Therefore, it is a powerful alternative to the existing normalization methods.

Algorithms↗

PubMed2000

Linear modeling of genetic networks from experimental data.

In this paper, the regulatory interactions between genes are modeled by a linear genetic network that is estimated from gene expression data. The inference of such a genetic network is hampered by the dimensionality problem. This problem is inherent in all gene expression data since the number of genes by far exceeds the number of measured time points. Consequently, there are infinitely many solutions that fit the data set perfectly. In this paper, this problem is tackled by combining genes with similar expression profiles in a single prototypical 'gene'. Instead of modeling the genes individually, the relations between prototypical genes are modeled. In this way, genes that cannot be distinguished based on their expression profiles are grouped together and their common control action is modeled instead. This process reduces the number of signals and imposes a structure on the model that is supported by the fact that biological genetic networks are thought to be redundant and sparsely connected. In essence, the ambiguity in model solutions is represented explicitly by providing a generalized model that expresses the basic regulatory interactions between groups of similarly expressed genes. The modeling approach is illustrated on artificial as well as real data.

Animals↗

PubMed2000

Quantitative analysis of the neuroendocrine-immune axis: linear modeling of the effects of exogenous corticosterone and restraint stress on lymphocyte subpopulations in the spleen and thymus in female B6C3F1 mice.

The effects of exogenous corticosterone and restraint stress on the number and percentage of lymphocyte subpopulations in the spleen and thymus were evaluated. The data were used to generate linear models that describe the relationship between these parameters and the area under the corticosterone concentration vs time curve (AUC). Comparison of the models revealed that the number of nucleated cells in the spleen was decreased similarly by exogenous corticosterone and restraint (at equivalent corticosterone AUC values). However, exogenous corticosterone caused a greater decrease in cell number in the thymus than it did in the spleen. Corticosterone preferentially depleted CD4+CD8+ cells in the thymus, whereas the same corticosterone exposure produced by restraint stress did not. In the spleen, cell number for all major cell types was decreased by both treatments, but there were minor differences in the change in percentage of some subpopulations induced by exogenous corticosterone as compared to restraint. The models derived here provide quantitative data that indicate the magnitude of corticosterone and stress-induced effects on lymphocyte populations in the spleen and thymus. These results have mechanistic implications, and they may be useful in future efforts to extrapolate from mouse to human by completing a risk assessment parallelogram.

Animals↗

PubMed1992

Linear models for the prediction of stature from foot and boot dimensions.

Estimation of stature from the dimensions of foot or shoeprints has considerable forensic value in developing descriptions of suspects from evidence at the crime scene and in corroborating height estimates from witnesses. This study extends the findings of previous researchers by exploring linear models with and without gender and race indicators, and by validating the most promising models on a large, recently collected military database. Boot size and outsole dimensions are also examined as predictors of stature. The results of this study indicate that models containing both foot length and foot breadth are significantly better than those containing only foot length. Models with race/gender indicators also perform significantly better than do models without race/gender indicators. However, the difference in performance is slight, and the availability of reliable gender and race information in most forensic situations is uncertain. Analogous results were obtained for models utilizing boot size/width and outsole length/width, and in this study these variables performed nearly as well as the foot dimensions themselves. Although the adjusted R2 values for these models clearly reflect a strong relationship between foot/boot length and stature, individual 95% prediction limits for even the best models are +/- 86 mm (3.4 in.). This suggests that models estimating stature from foot/shoe-prints may be useful in the development of subject descriptions early in a case but, because of their imprecision, may not always be helpful in excluding individual suspects from consideration.

Anthropometry↗

PubMedDate not supplied

Ethnic differences in the effect of parenting on gang involvement and gang delinquency: a longitudinal, hierarchical linear modeling perspective.

This study examined the relative influence of peer and parenting behavior on changes in adolescent gang involvement and gang-related delinquency. An ethnically diverse sample of 300 ninth-grade students was recruited and assessed on eight occasions during the school year. Analyses were conducted using hierarchical linear modeling. Results indicated that, in general, adolescents decreased their level of gang involvement over the course of the school year, whereas the average level of gang delinquency remained constant over time. As predicted, adolescent gang involvement and gang-related delinquency were most strongly predicted by peer gang involvement and peer gang delinquency, respectively. Nevertheless, parenting behavior continued to significantly predict change in both gang involvement and gang delinquency, even after controlling for peer behavior. A significant interaction between parenting and ethnic and cultural heritage found the effect of parenting to be particularly salient for Black students, for whom higher levels of behavioral control and lower levels of lax parental control were related to better behavioral outcomes over time, whereas higher levels of psychological control predicted worse behavioral outcomes.

Adolescent↗

PubMed2002

Predicting longitudinal change in language production and comprehension in individuals with Down syndrome: hierarchical linear modeling.

Longitudinal change in syntax comprehension and production skill, measured four times across a 6-year period, was modeled in 31 individuals with Down syndrome who were between the ages of 5 and 20 years at the start of the study. Hierarchical Linear Modeling was used to fit individual linear growth curves to the measures of syntax comprehension (TACL-R) and mean length of spontaneous utterances obtained in 12-min narrative tasks (MLU-S), yielding two parameters for each participant's comprehension and production: performance at study start and growth trajectory. Predictor variables were obtained by fitting linear growth curves to each individual's concurrent measures of nonverbal visual cognition (Pattern Analysis subtest of the Stanford-Binet), visual short-term memory (Bead Memory subtest), and auditory short-term memory (digit span), yielding two individual predictor parameters for each measure: performance at study start and growth trajectory. Chronological age at study start (grand-mean centered), sex, and hearing status were also taken as predictors. The best-fitting HLM model of the comprehension parameters uses age at study start, visual short-term memory, and auditory short-term memory as predictors of initial status and age at study start as a predictor of growth trajectory. The model accounted for 90% of the variance in intercept parameters, 79% of the variance in slope parameters, and 24% of the variance at level 1. The some predictors were significant predictors of initial status in the best model for production, with no measures predicting slope. The model accounted for 81% of the intercept variance and 43% of the level 1 variance. When comprehension parameters are added to the predictor set, the best model, accounting for 94% of the intercept and 22% of the slope variance, uses only comprehension at study start as a predictor of initial status and comprehension slope as a predictor of production slope. These results reflect the fact that expressive language acquisition continues in adolescence and is predicted by syntax comprehension and its growth trajectory.

Adolescent↗

PubMed1996

An application of hierarchical linear models to longitudinal studies.

Nursing researchers are increasingly interested in studying changes in patients' outcomes, such as physiologic and psychological status, across time. The most frequently used approaches, univariate repeated measures, multivariate repeated measures, and pre- and posttest differences, have restrictive assumptions and unrealistic data requirements. Therefore, a more flexible approach is needed. Hierarchical linear models (HLM) can be used to solve these problems. The advantages of HLM are (a) it describes each individual's growth trajectory and its relationship with initial status, (b) it is not restricted by unrealistic assumptions, (c) if solves the commonly observed problems of missing data, (d) it does not require fixed time intervals, and (e) it provides more precise estimation.

Analysis of Variance↗

PubMed1989

A log-linear model for ordinal data to characterize differential change among treatments.

We propose a family of log-linear models for ordinal data that contain parameters reflecting change patterns to compare treatments relative to change from baseline. Under the most general model, rates of change can depend not only upon the direction of change, but also upon the level of the baseline classification. We describe methods for selection of a parsimonious model and for tests of hypotheses concerning treatment differences. Interpretation of treatment differences in the follow-up response profiles, within baseline strata, employs the concept of stochastic ordering. Data from two clinical trials illustrate the proposed procedure.

Analysis of Variance↗

PubMed2000

Standard errors for EM estimates in generalized linear models with random effects.

A procedure is derived for computing standard errors of EM estimates in generalized linear models with random effects. Quadrature formulas are used to approximate the integrals in the EM algorithm, where two different approaches are pursued, i.e., Gauss-Hermite quadrature in the case of Gaussian random effects and nonparametric maximum likelihood estimation for an unspecified random effect distribution. An approximation of the expected Fisher information matrix is derived from an expansion of the EM estimating equations. This allows for inferential arguments based on EM estimates, as demonstrated by an example and simulations.

Algorithms↗