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PubMed1991

Evaluation of a linear model of directional selectivity in simple cells of the cat's striate cortex.

We have compared the responses of simple cells to laterally moving sinusoidal gratings and to stationary temporally-modulated gratings. From the amplitudes and temporal phases of the responses to stationary gratings of different spatial phases, it should be possible to predict the preferred direction of movement, the amplitudes of the responses to gratings moving in the preferred and nonpreferred directions and, thence, the degree of directional preference (Reid et al., 1987). The preferred direction can be predicted reliably. However, the magnitude of the directional preference cannot be predicted, since the measured amplitude of the response in the nonpreferred direction of movement is very much less than that predicted by a linear theory. Nonlinearities in the relationship between response amplitude and contrast may contribute to the failure of the predictions, but this contribution is small. We conclude that the magnitude of the directional preference seems to be determined predominantly by nonlinear suppression of the response in the nonpreferred direction of movement.

Animals↗

PubMedDate not supplied

[Cancer incidence estimates for Germany via log-linear models].

In Germany presently no nationwide cancer registration exists. To estimate national cancer incidence, Poisson regression models were fitted to incidence/mortality ratios using age and sex specific data of the cancer registry of Saarland, Germany and were then applied to national mortality. The models estimate the absolute number of incident cases at a given point in time and moreover allow the assessment of time trends. Applied to nationwide mortality the models imply a total of 347,000 new cancer cases in Germany for 1998 with 179,000 females and 168,000 males. During the nineties the age-standardised rate (European standard) has slightly decreased for males and slightly increased for females.

Cause of Death↗

PubMed1992

[Linear model of the pathogenesis of the temporomandibular pain-dysfunction syndrome].

In the research of temporomandibular pain-dysfunction syndrome the etiological model of disease was created by a statistical system not applied until now. Of this it can be concluded that for the formation of the disease psychotic factors and oral parafunctions are responsible. Of the examination it became apparent that the cross sectional examination of the casual factors of the disease should be advisably carried out together with their correlations.

Humans↗

PubMed2005

A century of GH research revisited: from linear models to network complexity.

The history of GH started with the pioneer clinical and anatomical observations of Pierre Marie, who described the symptoms of acromegaly in 1886. Progressively, histochemical and histophysiological methods made it possible to characterize most cell types responsible for normal or pathological pituitary hormone secretion. Although the methods applied were indirect, and hormonal function assigned to each cell type could only be inferred from correlations, the quality of the corresponding studies was such that most of their results proved correct. In the second half of the XXth century, biochemical methods and bioassays led, between 1943 and 1956, to the production from pituitary extracts of highly purified fractions containing somatotropin activity. The subsequent demonstration that hypothalamo-hypophyseal interactions are of a neurohumoral nature permitted isolation of neuropeptides, a new class of neurotransmitters, many of which turned into major therapeutic agents. Subsequent purification of hundreds of neuropeptides, many with hypophysiotropic activity, and mapping of neurons producing them permitted to shift from relatively simple theories, postulating that stimulatory and inhibitory peptides are sufficient to account for the physiological control of pituitary secretion to more complex models. These permitted to understand how complex neuronal networks can produce a fine tuning of multiple combinations of neuropeptides and neurotransmitters, which interact with each other to adapt hormonal secretion to discrete physiological and pathological conditions.

Animals↗

PubMed2003

General multilevel linear modeling for group analysis in FMRI.

This article discusses general modeling of multisubject and/or multisession FMRI data. In particular, we show that a two-level mixed-effects model (where parameters of interest at the group level are estimated from parameter and variance estimates from the single-session level) can be made equivalent to a single complete mixed-effects model (where parameters of interest at the group level are estimated directly from all of the original single sessions' time series data) if the (co-)variance at the second level is set equal to the sum of the (co-)variances in the single-level form, using the BLUE with known covariances. This result has significant implications for group studies in FMRI, since it shows that the group analysis requires only values of the parameter estimates and their (co-)variance from the first level, generalizing the well-established "summary statistics" approach in FMRI. The simple and generalized framework allows different prewhitening and different first-level regressors to be used for each subject. The framework incorporates multiple levels and cases such as repeated measures, paired or unpaired t tests and F tests at the group level; explicit examples of such models are given in the article. Using numerical simulations based on typical first-level covariance structures from real FMRI data we demonstrate that by taking into account lower-level covariances and heterogeneity a substantial increase in higher-level Z score is possible.

Algorithms↗

PubMed2005

Variable selection for marginal longitudinal generalized linear models.

Variable selection is an essential part of any statistical analysis and yet has been somewhat neglected in the context of longitudinal data analysis. In this article, we propose a generalized version of Mallows's C(p) (GC(p)) suitable for use with both parametric and nonparametric models. GC(p) provides an estimate of a measure of model's adequacy for prediction. We examine its performance with popular marginal longitudinal models (fitted using GEE) and contrast results with what is typically done in practice: variable selection based on Wald-type or score-type tests. An application to real data further demonstrates the merits of our approach while at the same time emphasizing some important robust features inherent to GC(p).

Bias↗

PubMed2002

Multivariate multiple regression analyses: a permutation method for linear models.

A multivariate extension of a univariate procedure for the analysis of experimental designs is presented. A Euclidean-distance permutation procedure is used to evaluate multivariate residuals obtained from a regression algorithm, also based on Euclidean distances. Applications include various completely randomized and randomized block experimental designs such as one-way, Latin square, factorial, nested, and split-plot designs, with and without covariates. Unlike parametric procedures, the only required assumption is the randomization of subjects to treatments.

Child↗

PubMed2006

Robust estimation in mixed linear models with non-monotone missingness.

We introduce a model to account for abrupt changes among repeated measures with non-monotone missingness. Development of likelihood inferences for such models is hard because it involves intractable integration to obtain the marginal likelihood. We use hierarchical likelihood to overcome such difficulty. Abrupt changes among repeated measures can be well described by introducing random effects in the dispersion. A simulation study shows that the resulting estimator is efficient, robust against misspecification of fatness of tails. For illustration we use a schizophrenic behaviour data presented by Rubin and Wu.

Computer Simulation↗

PubMed2000

The micromechanical environment of intervertebral disc cells: effect of matrix anisotropy and cell geometry predicted by a linear model.

Cells of the intervertebral disc exhibit spatial variations in phenotype and morphology that may be related to differences in their local mechanical environments. In this study, the stresses, strains, and dilatations in and around cells of the intervertebral disc were studied with an analytical model of the cell as a mechanical inclusion embedded in a transversely isotropic matrix. In response to tensile loading of the matrix, the local mechanical environment of the cell differed among the anatomic regions of the disc and was strongly influenced by changes in both matrix anisotropy and parameters of cell geometry. The results of this study suggest that the local cellular mechanical environment may play a role in determining both cell morphology in situ and the inhomogeneous response to mechanical loading observed in cells of the disc.

Animals↗

PubMedDate not supplied

A linear model for the pharmacokinetics of azithromycin in healthy volunteers.

The pharmacokinetic profile of azithromycin, after oral ingestion of 500 mg, was determined in 10 healthy volunteers. Statistical and biochemical reason seemed to indicate a zero-order absorption of the drug. The disposition of azithromycin was described by a two-compartment model (plasma compartment and extravascular compartment) with elimination from the plasma compartment. The absorption process ends abruptly after a time T = 2.3 +/- 0.49 h, from the administration. The transfer rate constant from the plasma compartment to the extravascular compartment (k12 = 0.12 +/- 0.04 h-1) and the mean residence time of the drug in the extravascular compartment (MRT2 = 43.53 +/- 13.80 h) indicate a rapid and extensive distribution of azithromycin from the serum into the extravascular fluids. The results confirmed the efficacy of a single daily dose of 500 mg per os for clinical use.

Administration, Oral↗

PubMed2006

A hybrid Newton-type method for censored survival data using double weights in linear models.

As an alternative to the Cox model, the rank-based estimating method for censored survival data has been studied extensively since it was proposed by Tsiatis [Tsiatis AA (1990) Ann Stat 18:354-372] among others. Due to the discontinuity feature of the estimating function, a significant amount of work in the literature has been focused on numerical issues. In this article, we consider the computational aspects of a family of doubly weighted rank-based estimating functions. This family is rich enough to include both estimating functions of Tsiatis (1990) for the randomly observed data and of Nan et al. [Nan B, Yu M, Kalbfleisch JD (2006) Biometrika (to appear)] for the case-cohort data as special examples. The latter belongs to the biased sampling problems. We show that the doubly weighted rank-based discontinuous estimating functions are monotone, a property established for the randomly observed data in the literature, when the generalized Gehan-type weights are used. Though the estimating problem can be formulated to a linear programming problem as that for the randomly observed data, due to its easily uncontrollable large scale even for a moderate sample size, we instead propose a Newton-type iterated method to search for an approximate solution of the (system of) discontinuous monotone estimating equation(s). Simulation results provide a good demonstration of the proposed method. We also apply our method to a real data example.

Carcinoma↗

PubMed1988

A linear model for symmetric receptive fields: implications for classification tests with flashed and moving images.

The purpose of this study was to explore the effects of spatial and temporal properties on the expected responses of visual neurons that have linear receptive fields (RFs), particularly those having a mirror symmetric distribution of spatial subregions. Receptive fields that are symmetric in at least one spatial dimension occur in neurons of the retina, the lateral geniculate nucleus (LGN), and the visual cortex of mammals. Responses to flashing bars, moving bars, and moving edges were studied for different configurations of an analog RF model in which spatial and temporal aspects were varied independently. Responses of the model at intermediate stimulus speeds were found to agree with responses in the literature for X and Y units of the LGN and often for simple units of the visual cortex. In particular, having separated regions of response to light and dark edges, an identifying property of simple cells, was found to be a linear consequence of RF regions responding inversely to stimuli of opposite polarity. Model differences from responses of cortical complex units show that a linear model cannot mimic their responses, and imply that complex units employ major nonlinearities in coding image polarity (light vs dark), which signifies a nonlinearity in coding intensity. Because sudden flux changes inherent in flashing bars test mainly temporal RF properties, and slowly moving edges test mainly spatial properties, these two tests form a useful minimal set with which to describe and classify RFs. The usefulness of this set derives both from its sensitivity to spatial and temporal variables, and from the correlation between the linearity of a cell's processing of stimulus intensity and its RF classification.

Mathematics↗

PubMed1998

Tests of a linear model of visual-vestibular interaction using the technique of parameter estimation.

The goal of this study was to test whether a superposition model of smooth-pursuit and vestibuloocular reflex (VOR) eye movements could account for the stability of gaze that subjects show as they view a stationary target, during head rotations at frequencies that correspond to natural movements. Horizontal smooth-pursuit and the VOR were tested using sinusoidal stimuli with frequencies in the range 1.0-3.5 Hz. During head rotation, subjects viewed a stationary target either directly or through an optical device that required eye movements to be approximately twice the amplitude of head movements in order to maintain foveal vision of the target. The gain of compensatory eye movements during viewing through the optical device was generally greater than during direct viewing or during attempted fixation of the remembered target location in darkness. This suggests that visual factors influence the response, even at high frequencies of head rotation. During viewing through the optical device, the gain of compensatory eye movements declined as a function of the frequency of head rotation (P < 0.001) but, at any particular frequency, there was no correlation with peak head velocity 9P > 0.23), peak head acceleration (P > 0.22) or retinal slip speed (P > 0.22). The optimal values of parameters of smooth-pursuit and VOR components of a simple superposition model were estimated in the frequency domain, using the measured responses during head rotation, as each subject viewed the stationary target through the optical device. We then compared the model's prediction of smooth-pursuit gain and phase, at each frequency, with values obtained experimentally. Each subject's pursuit showed lower gain and greater phase lag than the model predicted. Smooth-pursuit performance did not improve significantly if the moving target was a 10 deg x 10 deg Amsler grid, or if sinusoidal oscillation of the target was superimposed on ramp motion. Further, subjects were still able to modulate the gain of compensatory eye movements during pseudo-random head perturbations, making improved predictor performance during visual-vestibular interactions unlikely. We conclude that the increase in gain of eye movements that compensate for head rotations when subjects view, rather than imagine, a stationary target cannot be adequately explained by superposition of VOR and smooth-pursuit signals. Instead, vision may affect VOR performance by determining the context of the behavior.

Adult↗

PubMed2003

Examination of a linear model in an informational masking study.

When multitone maskers are used in a two-interval, forced choice experiment, the amount of masking is larger when the masker is randomly chosen on each presentation interval compared to on each trial (the same masker in the two listening intervals). These conditions are referred to as having within- versus between-trial randomization. If it is assumed that an observer's ultimate detection decision depends on a single decision variable (DV), it is probable that the DV's variance will be substantially larger in the within-trial randomization condition compared to the between-trial randomization condition. The goal of the current experiment is to evaluate the degree to which this stimulus-based change in DV variance can account for the difference in thresholds in the within-versus between-trial randomization conditions. Thresholds are measured for the detection of a tone added to a six-component masker in between- and within-trial randomization conditions. The slopes of the psychometric functions provide an estimate of the variance in the DV for the between- and within-trial randomization conditions. Additionally, a channel model is fitted to the psychophysical results in the within-trial randomization condition. The resulting model is then used to predict the value of the DV for each trial, and ultimately to estimate the proportion of the total variance in the within-trial randomization condition that is attributable to changes in maskers across intervals. The variance of the DV in the between-trial randomization condition accounted for approximately 65% of the total variance in the DV in the within-trial randomization condition. Stimulus-based interval-by-interval masker randomization accounted for approximately 20% of the total variance of the within-trial randomization DV. The remaining 15% of the DV variance in the within-trial randomization condition remained unaccounted for. This result is fairly stable whether the maskers are drawn from a small versus large pool of potential maskers.

Attention↗

PubMed2003

Identifying epidemiological factors affecting sea lice Lepeophtheirus salmonis abundance on Scottish salmon farms using general linear models.

The variation in Lepeophtheirus salmonis sea lice numbers across 40 Scottish salmon farm sites during 1996 to 2000 was analysed using mean mobile abundance for 3 important 6 mo periods within the production cycle. Using statistical regression techniques, over 20 management and environmental variables suspected to have an effect on controlling lice populations were investigated as potential risk factors. The findings and models developed provide a picture of mobile L. salmonis infestation patterns on Scottish farm sites collectively. The results identified level of treatment, type of treatment, cage volume, current speed, loch flushing time and sea lice levels in the preceding 6 mo period to be key explanatory factors. Factors such as stocking density, site biomass, water temperature and the presence of neighbours, previously cited to be important correlates of sea lice risk from analysis of individual sites over time, were not found to be important. Variation in mobile abundance in the first half of the second year of production could be adequately explained (adjusted R2 between 55 and 72%) by the recorded data, suggesting that there is scope for management to control L. salmonis abundance, though much of the variation remains unexplained.

Animals↗

PubMed1998

A randomized biomechanical study of zone II human flexor tendon repairs analyzed in a linear model.

Komanduri et al showed that dorsal tendon repairs using Kessler and Bunnell techniques were stronger than the standard volar repair (J Hand Surg 1996;21 A:605-611). They concluded that when testing in the anatomic curvilinear mode, the differences in strength were due to tension banding. Soejima et al challenged that concept by stating that the difference in strength was in the biomechanics of the dorsal tendon itself (J Hand Surg 1995;20A:801-807). We set out to confirm Soejima et al's theory by using more core suture techniques. We compared the tensile strength at 2-mm gap and the ultimate tensile strength of Kessler, Strickland, Robertson, and modified Becker sutures. Ten repairs of each suture type were placed either dorsally or volarly in matched human cadaver flexor tendons. There was no statistical difference between volar and dorsal placement for either maximum tensile force or force at 2-mm gap. Our study does not confirm Soejima et al's in any of the four suturing techniques.

Biomechanical Phenomena↗

PubMed1996

Analysis of multivariate reliability structures and the induced bias in linear model estimation.

Least squares provides consistent estimates of the regression coefficients beta in the model E[Y [symbol: see text] x] = beta x when fully accurate measurements of x are available. However, in biomedical studies one must frequently substitute unreliable measurements X in place of x. This induces bias in the least squares coefficient estimates. In the univariate case, the bias manifests itself as a shrinkage toward zero, but this result does not generalize. When x is multivariate, then there are no predictable relationships between the signs or magnitudes of actual and estimated regression coefficients. In this article, we characterize the estimation bias, and review a relatively simple adjustment procedure to correct it. We also show that several natural conjectures about the bias are false. We present three definitions of reliability coefficient matrices that generalize the univariate case, and we illustrate their application to dietary intake data from a cancer prevention study.

Bias↗

PubMed2006

Factorial coding of natural images: how effective are linear models in removing higher-order dependencies?

The performance of unsupervised learning models for natural images is evaluated quantitatively by means of information theory. We estimate the gain in statistical independence (the multi-information reduction) achieved with independent component analysis (ICA), principal component analysis (PCA), zero-phase whitening, and predictive coding. Predictive coding is translated into the transform coding framework, where it can be characterized by the constraint of a triangular filter matrix. A randomly sampled whitening basis and the Haar wavelet are included in the comparison as well. The comparison of all these methods is carried out for different patch sizes, ranging from 2x2 to 16x16 pixels. In spite of large differences in the shape of the basis functions, we find only small differences in the multi-information between all decorrelation transforms (5% or less) for all patch sizes. Among the second-order methods, PCA is optimal for small patch sizes and predictive coding performs best for large patch sizes. The extra gain achieved with ICA is always less than 2%. In conclusion, the edge filters found with ICA lead to only a surprisingly small improvement in terms of its actual objective.

Algorithms↗