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PubMed2006

Exploration of linear modelling techniques and their combination with multivariate adaptive regression splines to predict gastro-intestinal absorption of drugs.

In general, linear modelling techniques such as multiple linear regression (MLR), principal component regression (PCR) and partial least squares (PLS), are used to model QSAR data. This type of data can be very complex and linear modelling techniques often model only a limited part of the information captured in the data. In this study, it was tried to combine linear techniques with the flexible non-linear technique multivariate adaptive regression splines (MARS). Models were built using an MLR model, combined with either a stepwise procedure or a genetic algorithm for variable selection, a PCR model or a PLS model as starting points for the MARS algorithm. The descriptive and predictive power of the models was evaluated in a QSAR context and compared to the performances of the individual linear models and the single MARS model. In general, the combined methods resulted in significant improvements compared to the linear models and can be considered valuable techniques in modelling complex QSAR data. For the used data set the best model was obtained using a combination of PLS and MARS. This combination resulted in a model with a Pearson correlation coefficient of 0.90 and a cross-validation error, evaluated with 10-fold cross-validation of 9.9%, pointing at good descriptive and high predictive properties.

Algorithms↗
PubMedDate not supplied

Composite linear models for incomplete multinomial data.

A composite linear model (CLM) is a matrix model for incomplete multinomial data. A CLM provides a unified approach for maximum likelihood inference which is applicable to a wide variety of problems involving incomplete multinomial data. By formulating a model as a CLM, one can simplify computation of maximum likelihood estimates and asymptotic standard errors. As an example, we use CLM to test marginal homogeneity for ordered categories, subject to both ignorable and non-ignorable missing-data mechanisms.

Algorithms↗
PubMed2002

Log-linear models for gene mapping with affected sib pair data.

In genome-wide screens of genetic marker loci, non-mendelian inheritance of a marker is taken to indicate its vicinity to a disease locus. Heritable complex traits are thought to be under the influence of multiple possibly interacting susceptibility loci yet the most frequently used methods of linkage and association analysis focus on one susceptibility locus at a time. Here we introduce log-linear models for the joint analysis of multiple marker loci and interaction effects between them. Our approach focuses on affected sib pair data and identical by descent (IBD) allele sharing values observed on them. For each heterozygous parent, the IBD values at linked markers represent a sequence of dependent binary variables. We develop log-linear models for the joint distribution of these IBD values. An independence log-linear model is proposed to model the marginal means and the neighboring interaction model is advocated to account for associations between adjacent markers. Under the assumption of conditional independence, likelihood methods are applied to simulated data containing one or two susceptibility loci. It is shown that the neighboring interaction log-linear model is more efficient than the independence model, and incorporating interaction in the two-locus analysis provides increased power and accuracy for mapping of the trait loci.

Alleles↗
PubMed2003

Linear models for microarray data analysis: hidden similarities and differences.

In the past several years many linear models have been proposed for analyzing two-color microarray data. As presented in the literature, many of these models appear dramatically different. However, many of these models are reformulations of the same basic approach to analyzing microarray data. This paper demonstrates the equivalence of some of these models. Attention is directed at choices in microarray data analysis that have a larger impact on the results than the choice of linear model.

Analysis of Variance↗
PubMed1991

Linear model of accommodation and vergence can account for discrepancies between AC/A measures using the fixation disparity and phoria methods.

The AC/A ratios obtained previously by the fixation disparity method were in most cases greater than those by the phoria method. An earlier study analysed a simplified linear model of the accommodation and vergence system. It was determined that the equations corresponding to the two methods were equal, indicating that such a model could not account for the discrepancy found experimentally. However, two important components--tonic accommodation and tonic vergence--were omitted from this simplified model. In the present study, an analysis of the complete linear model showed that the equations corresponding to the two methods are different. In addition, calculation of the error between the cross-link gain and the overall accommodative input--convergence output values indicated that the AC/A should be higher using the fixation disparity than the phoria method. Therefore, the predictions of the complete linear model are consistent with the data obtained experimentally.

Accommodation, Ocular↗
PubMed1995

An approximate generalized linear model with random effects for informative missing data.

This paper develops a class of models to deal with missing data from longitudinal studies. We assume that separate models for the primary response and missingness (e.g., number of missed visits) are linked by a common random parameter. Such models have been developed in the econometrics (Heckman, 1979, Econometrica 47, 153-161) and biostatistics (Wu and Carroll, 1988, Biometrics 44, 175-188) literature for a Gaussian primary response. We allow the primary response, conditional on the random parameter, to follow a generalized linear model and approximate the generalized linear model by conditioning on the data that describes missingness. The resultant approximation is a mixed generalized linear model with possibly heterogeneous random effects. An example is given to illustrate the approximate approach, and simulations are performed to critique the adequacy of the approximation for repeated binary data.

Bayes Theorem↗
PubMed1992

Linear models of surface and illuminant spectra.

We describe procedures for creating efficient spectral representations for color. The representations generalize conventional tristimulus representations, which are based on the peripheral encoding by the human eye. We use low-dimensional linear models to approximate the spectral properties of surfaces and illuminants with respect to a collection of sensing devices. We choose the linear-model basis functions by minimizing the error in approximating sensor responses for collections of surfaces and illuminants. These linear models offer some conceptual simplifications for applications such as printer calibration; they also perform substantially better than principal-components approximations for computer-graphics applications.

Algorithms↗
PubMed1985

Observations on sire evaluation with categorical data using heteroscedastic mixed linear models.

The ability of three mixed linear models to rank sires correctly for dichotomous and ordered tetrachotomous traits was studied using simulated half-sib progeny data. The models differed in the assumptions made regarding homogeneity of residual variance. Ranking ability was assessed by estimating the realized response to truncation selection (20% of the candidates selected) upon sire evaluations in populations consisting of 50 such sires. Results suggested that weighting for unequal residual variances, in spite of reducing apparent prediction error variance, impairs the ability of best linear unbiased prediction to identify superior sires. This is consistent with theoretical arguments stemming from threshold models.

Animals↗
PubMed1996

Functional impairment trajectories among persons with HIV disease: a hierarchical linear models approach.

OBJECTIVE: This study investigates the level, time course, and stability of functional impairment in a population of persons with symptomatic HIV disease, and illustrates the application of hierarchical linear modeling (HLM) to trajectories of functional status in unbalanced longitudinal data. STUDY POPULATION: We utilized longitudinal interview data on a demographically diverse cohort of 246 individuals participating in New Jersey's Medicaid waiver program for persons with AIDS or symptomatic HIV disease, with a mean of nine repeated observations per individual. MEASURES AND STATISTICAL METHODS: Impairment in ability to perform 16 activities of daily living (ADL) and instrumental activities of daily living (IADL) was assessed at monthly intervals. To achieve unbiased, efficient estimation of the level and within-individual rate of change of functional status utilizing all observations for each individual, hierarchical linear models were used. Time slopes were compared to those from a single-level model estimated on the pooled observations. Stability of functional status within individuals was also evaluated. PRINCIPAL FINDINGS: A single-level pooled model showed no significant time trend in functional impairment, while the multilevel models did indicate such a trend. In the final HLM model, functional impairment was estimated to increase at a rate of .32 tasks per month. Female gender was associated with impairment in an additional 1.88 tasks and AIDS diagnosis with an additional 1.35 tasks. There was substantial variability within individuals over time, most of which was not explained by time trend. CONCLUSIONS: The multilevel models indicated a significant month-to-month worsening of functional status that was masked in the single-level model by between-person variation. Impairment was found to increase over time, but followed a variable and episodic course rather than a steady or consistent decline. Women appeared to experience special problems in performing ADL and IADL tasks. RELEVANCE/IMPACT: Results demonstrate the need for flexible and responsive systems for authorizing and managing in-home services for persons with HIV disease, systems that can respond to frequent changes in the functional status and level of care needs of these individuals. They suggest further attention to special care needs that may be experienced by women with HIV disease. They illustrate that hierarchical linear modeling can be an important tool in understanding change in functional status over time, providing a multilevel model that disaggregates within-individual and between-individual variation in functional status. This approach can be generalized to a wide variety of problems in health services research in which outcomes are observed over time with unbalanced longitudinal data.

Acquired Immunodeficiency Syndrome↗
PubMed2001

Use of repeated measure linear modeling to analyze longitudinal data from experimental parasite infections.

Here the use of repeated measure linear modeling to analyze experimental infections is demonstrated. This method of analysis makes full use of serial measurements on the same host throughout the course of an infection while taking into account correlations between measures within the same host. As an example, repeated measure linear modeling is used to analyze worm output from an experimental infection of Strongyloides ratti, a nematode parasite of rats. This analysis allows differences in the temporal dynamics of infection of two lines of S. ratti to be dissected.

Animals↗
PubMed1975

Simultaneous estimation of parameters in different linear models and applications to biometric problems.

Empirical Bayes procedure is employed in simultaneous estimation of vector parameters from a number of Gauss-Markoff linear models. It is shown that with respect to quadratic loss function, empirical Bayes estimators are better than least squares estimators. While estimating the parameter for a particular linear model, a suggestion has been made for distinguishing between the loss due to decision maker and the loss due to individual. A method has been proposed but not fully studied to achieve balance between the two losses. Finally the problem of predicting future observations in a linear model has been considered.

Bayes Theorem↗
PubMedDate not supplied

Dose-response relationship between total cadmium intake and prevalence of renal dysfunction using general linear models.

To determine the maximum allowable intake limits for chronic dietary exposure to cadmium (Cd), the dose-response relationship between total Cd intake and prevalence of renal dysfunction was examined using general linear models considering the effect of age as a confounder. The target population comprised 1850 Cd-exposed and 294 non-exposed inhabitants of Ishikawa, Japan. They were divided into 96 subgroups by sex, age (four categories) cadmium concentrations in rice (three categories) and length of residence (four categories). As indicators of the cadmium-induced renal dysfunction, glucose, total protein, amino nitrogen, beta 2-microglobulin and metallothionein in urine were employed. General linear models were fitted statistically to the relationship among prevalence of renal dysfunction, sex, age and total Cd intake. Prevalence of abnormal urinary findings other than glucosuria had significant associations with total Cd intake. When total Cd intake corresponding to the mean prevalence of each abnormal urinary finding in the non-exposed subjects was calculated using general linear models, total Cd intakes corresponding to glucosuria, proteinuria, aminoaciduria (men only) and proteinuria with glucosuria were determined to be ca. 2.2-3.8 g and those corresponding to prevalence of metallothioneinuria were calculated as ca. 1.5-2.6 g. The low-molecular-weight protein in urine was confirmed to be a more sensitive indicator of renal dysfunction, and these total Cd intake values were close to those calculated previously by simple regression analysis, suggesting them to be reasonable values as the maximum allowable intake of Cd.

Age Distribution↗
PubMed2002

A non-linear model for a sexually transmitted disease with contact tracing.

A non-linear model is developed for an epidemic with contact tracing, and its dynamic is studied. We present the data for the Cuban HIV/AIDS epidemic and fit the non-linear model, we obtain estimates for the size of the Cuban HIV epidemic, and for the mean time for detecting a person that is infected with HIV.

Acquired Immunodeficiency Syndrome↗
PubMed2000

On the possibility of linear modelling the human arm neuromuscular apparatus.

It has been widely claimed that linear models of the neuromuscular apparatus give very inaccurate approximations of human arm reaching movements. The present paper examines this claim by quantifying the contributions of the various non-linear effects of muscle force generation on the accuracy of linear approximation. We performed computer simulations of a model of a two-joint arm with six monarticular and biarticular muscles. The global actions of individual muscles resulted in a linear dependence of the joint torques on the joint angles and angular velocities, despite the great nonlinearity of the muscle properties. The effect of time delay in force generation is much more important for model accuracy than all the non-linear effects, while ignoring this time delay in linear approximation results in large errors. Thus, the viscosity coefficients are rather underestimated and some of them can even be paradoxically estimated to be negative. Similarly, our computation showed that ignoring the time delay resulted in large errors in the estimation of the hand equilibrium trajectory. This could explain why experimentally estimated hand equilibrium trajectories may be complex, even during a simple reaching movement. The hand equilibrium trajectory estimated by a linear model becomes simple when the time delay is taken into account, and it is close to that actually used in the non-linear model. The results therefore provide a theoretical basis for estimating the hand equilibrium trajectory during arm reaching movements and hence for estimating the time course of the motor control signals associated with this trajectory, as set out in the equilibrium point hypothesis.

Arm↗
PubMed1999

What Can Studies of Problem-Based Learning Tell Us? Synthesizing and Modeling PBL Effects on National Board of Medical Examination Performance: Hierarchical Linear Modeling Meta-Analytic Approach.

This meta-analytic study 1) examines outcomes from primary research comparing the impact of problem-based learning (PBL) and traditional curricula on medical students' National Board of Medical Examiners (NBME) I and II performance and 2) explores the use of Hierarchical Linear Modeling (HLM) in identifying study and PBL implementation characteristics that predict these outcomes. NBME I and II overall scores were used as dependent variables, with study design (randomized/non-randomized), publication year, and PBL experience (number of years since the adoption of PBL as an instructional method at the time of the reported NBME results) as explanatory variables. Initial unconditional HLM (i.e., without inclusion of potential explanatory variables) results indicated PBL curricula had: 1) a positive, albeit not statistically significant, effect on NBME II, with an average effect size of 0.16; and 2) a negative effect on NBME I, with an average effect size of -0.15. Including explanatory variables in HLM analyses explained additional variability in NBME I effect sizes, and identified study design (gamma^1 = 0.82, p = 0.01) and PBL experience (gamma^3 = 0.07, p = 0.02) as significant predictors of positive PBL effects. Publication year, in contrast, had significant negative effects (gamma^2 = -0.06, p = 0.02). This study explained variability in NBME I effect sizes and clarified the impact of PBL discerned in previous reviews. Implications for future research include the need to examine curriculum features that operationally define PBL, as well as extend the consideration of outcomes on which PBL's impact can be examined.

Journal Article↗
PubMed1991

Testing for association between disease and linked marker loci: a log-linear-model analysis.

One approach frequently used for identifying genetic factors involved in the process of a complex disease is the comparison of patients and controls for a number of genetic markers near a candidate gene. The analysis of such association studies raises some specific problems because of the fact that genotypic and not gametic data are generally available. We present a log-linear-model analysis providing a valid method for analyzing such studies. When studying the association of disease with one marker locus, the log-linear model allows one to test for the difference between allelic frequencies among affected and unaffected individuals, Hardy-Weinberg (H-W) equilibrium in both groups, and interaction between the association of alleles at the marker locus and disease. This interaction provides information about the dominance of the disease susceptibility locus, with dominance defined using the epidemiological notion of odds ratio. The degree of dominance measured at the marker locus depends on the strength of linkage disequilibrium between the marker locus and the disease locus. When studying the association of disease with several linked markers, the model becomes rapidly complex and uninterpretable unless it is assumed that affected and unaffected populations are in H-W equilibrium at each locus. This hypothesis must be tested before going ahead in the analysis. If it is not rejected, the log-linear model offers a stepwise method of identification of the parameters causing the difference between populations. This model can be extended to any number of loci, alleles, or populations.

Alleles↗
PubMed2005

On the slow convergence of EM and VBEM in low-noise linear models.

We analyze convergence of the expectation maximization (EM) and variational Bayes EM (VBEM) schemes for parameter estimation in noisy linear models. The analysis shows that both schemes are inefficient in the low-noise limit. The linear model with additive noise includes as special cases independent component analysis, probabilistic principal component analysis, factor analysis, and Kalman filtering. Hence, the results are relevant for many practical applications.

Algorithms↗