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PubMed1999

A general maximum likelihood analysis of variance components in generalized linear models.

This paper describes an EM algorithm for nonparametric maximum likelihood (ML) estimation in generalized linear models with variance component structure. The algorithm provides an alternative analysis to approximate MQL and PQL analyses (McGilchrist and Aisbett, 1991, Biometrical Journal 33, 131-141; Breslow and Clayton, 1993; Journal of the American Statistical Association 88, 9-25; McGilchrist, 1994, Journal of the Royal Statistical Society, Series B 56, 61-69; Goldstein, 1995, Multilevel Statistical Models) and to GEE analyses (Liang and Zeger, 1986, Biometrika 73, 13-22). The algorithm, first given by Hinde and Wood (1987, in Longitudinal Data Analysis, 110-126), is a generalization of that for random effect models for overdispersion in generalized linear models, described in Aitkin (1996, Statistics and Computing 6, 251-262). The algorithm is initially derived as a form of Gaussian quadrature assuming a normal mixing distribution, but with only slight variation it can be used for a completely unknown mixing distribution, giving a straightforward method for the fully nonparametric ML estimation of this distribution. This is of value because the ML estimates of the GLM parameters can be sensitive to the specification of a parametric form for the mixing distribution. The nonparametric analysis can be extended straightforwardly to general random parameter models, with full NPML estimation of the joint distribution of the random parameters. This can produce substantial computational saving compared with full numerical integration over a specified parametric distribution for the random parameters. A simple method is described for obtaining correct standard errors for parameter estimates when using the EM algorithm. Several examples are discussed involving simple variance component and longitudinal models, and small-area estimation.

Adrenergic beta-Antagonists↗
PubMed2006

A Bayesian heterogeneous analysis of variance approach to inferring recent selective sweeps.

The distribution of microsatellite allele sizes in populations aids in understanding the genetic diversity of species and the evolutionary history of recent selective sweeps. We propose a heterogeneous Bayesian analysis of variance model for inferring loci involved in recent selective sweeps by analyzing the distribution of allele sizes at multiple loci in multiple populations. Our model is shown to be consistent with a multilocus test statistic, ln RV, proposed for identifying microsatellite loci involved in recent selective sweeps. Our methodology differs in that it accepts original allele size data rather than summary statistics and allows the incorporation of prior knowledge about allele frequencies using a hierarchical prior distribution consisting of log normal and gamma probability distributions. Interesting features of the model are its ability to simultaneously analyze allele size data for any number of populations and to cope with the presence of any number of selected loci. The utility of the method is illustrated by application to two sets of microsatellite allele size data for a group of West African Anopheles gambiae populations. The results are consistent with the suppressed-recombination model of speciation, and additional candidate loci on chromosomes 2 (079 and 175) and 3 (088) are discovered that escaped former analysis.

Alleles↗
PubMedDate not supplied

An analysis of variance of the pubertal and midgrowth spurts for length and width.

Using data from the first Zurich Longitudinal Growth Study characteristics of the growth of six variables--bihumeral width, biiliac width, standing height, sitting height, leg height and arm length--are studied. The main interest is in differences between boys and girls, and across variables and in particular in whether there are sex differences that are specific for some variables. For each child and variable, individual velocity and acceleration curves are estimated using a kernal smoother. From these curves, parameters characterizing the midgrowth spurt (MS) and the pubertal spurt (PS) are estimated: timings, durations and intensities. The level of childhood velocity is used for characterizing early growth. These parameters are analysed using a repeated measures analysis of variance (ANOVA) to assess the statistical significance of differences between boys and girls and across variables. This necessitates some kind of standardization and two types of standardization are used here. The MS shows negligible or small differences between boys and girls, and the same is true for velocity in childhood. Differences across variables during the MS are much more pronounced: with respect to intensity, bihumeral width has an MS about six times more intense than height. The PS is later for boys (as is well known), and there are significant differences across variables: bihumeral width and sitting height are late while legs are early. With the exception of biiliac width, the duration of the PS (which has been subdivided into three phases-early, middle and late) is slightly longer for boys for all variables: boys have a longer starting phase, the middle phase is about equal in length for both boys and girls, and girls have a slightly longer late phase. Leg height and height experience a PS of short duration while bihumeral and biiliac width experience a long one and these differences are highly statistically significant. For all variables, with the exception of biiliac width, boys have a more intense PS (in terms of maximal acceleration), even having adjusted for their larger adult size. Differences in intensity are also marked across variables, bihumeral width and sitting height having the highest intensity and legs the lowest. Differences between sexes and across variables are much smaller for the stopping intensity, characterized by maximal deceleration.

Adolescent↗
PubMed1997

Analysis of variance of microspheres blood flow measurements in rabbits.

As part of a larger study on the interpretation of angiographically derived hemodynamic parameters, blood flow in several ocular tissues was measured using the radioactively labelled microspheres technique. As an unexpected secondary results, it was found that the microspheres data gave quantitative information on hyperaemic effects in the eye. This is the subject of the present paper. The measurements were made in 13 anaesthetized pigmented rabbits. In each animal, three blood flow measurements were performed at three different ocular perfusion pressures (60-15 mmHg). The perfusion pressures of the experimental eye were varied by changing the intra-ocular pressure. The contra-lateral eye served as a control. Labelled microspheres were used as a non-recirculating blood flow indicator, enabling the estimation of regional blood flows, in this case for the iris, ciliary body, peripheral choroid and peripapillary choroid separately. Using analysis of variance with perfusion pressure as covariate and taking into account the blood flow of the control eye, hyperaemia could be quantified in the experimental eye. Apart from a difference amongst animals, hyperaemia depended on tissue type. The amount of hyperaemia proved to be more pronounced in the anterior part of the eye, iris and ciliary body, and to decrease towards the posterior pole. With regard to the causes of this hyperaemia one could speculate about the invasive handling (anterior eye needles) topical administration of tropicamide, in combination with the general anaesthesia.

Analysis of Variance↗
PubMed1989

The use of repeated measures analysis of variance for plaque and gingival indices.

Clinical trials for anti-gingivitis and anti-plaque agents commonly use the mean of Silness and Löe plaque indices and Löe and Silness gingival indices as response variables. The aim of this report is to determine if data from anti-plaque and anti-gingivitis clinical trials using Silness and Löe plaque indices and Löe and Silness gingival indices satisfy conditions necessary for the use of the univariate or multivariate approach to repeated measures. These conditions are multivariate normality, homogeneity of variance-covariance matrices, and for the univariate approach, a type-H variance-covariance matrix. Data from 5 separate clinical trials representing a wide range in sample size, pretreatment mean gingival and plaque indices and treatment effects were used to test these conditions. Either the univariate or multivariate approach to repeated measures was found to be appropriate for both responses of the 5 clinical trials. Thus, means of Silness & Löe and Löe and Silness gingival indices meet the necessary conditions for use of either the univariate and/or multivariate approach to repeated measures. However, significant time-treatment interactions are a common occurrence in these types of clinical trials and must be evaluated carefully. The analyses in this study were carried out using SAS. Other mainframe statistical software packages and many micro-computer statistical software packages have routines to analyze repeated measures experiments with analysis of variance methods. However, some of the packages may omit the multivariate approach to repeated measures or may not include interactions between within-subject and between-subject effects. These packages should be used with caution.

Alkaloids↗
PubMed1992

Analysis of variance for repeated measures. Data: a generalized estimating equations approach.

Various techniques are available for the analysis of repeated measures data, and the appropriate choice depends on distributional assumptions and study design features. A correct analysis must account for potential dependence between repeated observations on the same subject. Liang and Zeger proposed a more unified approach to the analysis of repeated measures data based on the application of generalized estimating equations. We examine the application of these methods to several types of data in which one estimates the mean response directly for each combination of discrete covariates, and uses an identity link. Computations for fitting this type of model are exceptionally simple. Numerical examples suggest that the proposed approach yields estimation and hypothesis testing results consistent with more specialized methods.

Analysis of Variance↗
PubMed1981

A statistical Wiener filter using complex analysis of variance.

The Wiener filter is a digital filter in the frequency domain which enables the detection of signals in noise on the basis of a relatively small number (N) of signals-in-noise series. However, the variance associated with the Wiener filter increases sharply with low N or low signal-to-noise ratio, sometimes resulting in large negative transfer coefficients (H(w)'s). This causes an unacceptable distortion of the extracted signal. The classical solution for this problem is rather arbitrary; clipping all H(w)'s less than zero. It can be shown that this approach has limited practical value and does not lead to optimal filtering of the signal. The solution presented in this paper is based on the fact that the large negative H(w)'s in the case of a small N are caused by using an estimate for the noise-power which deviates from the actual noise-power. This makes the use of a statistical procedure feasible. By using complex analysis of variance it is possible to test which part of the spectrum is due to the signal and which part of the spectrum is due to the noise. H(w)'s not reaching a preset significance criterion are set to zero. The statistical Wiener filter acts as an adaptive multi-band-pass filter with band-passes determined by (a posteriori) detected signal components. It is demonstrated that this procedure leads to better suppression of the noise in signal-in-noise series.

Analysis of Variance↗
PubMed2002

Analysis of variance study of the rat cortical layer 4 barrel and layer 5b neurones.

Unique formation of rodent cortical barrels by layer 4 neurones attracts study of the sensory function of cortical input stage neurones (layer 4) compared with that of output stage neurones (layer 5). We have recorded extracellular responses from rat somatosensory cortical neurones to deflections of contralateral vibrissae. Thirty-two layer 4 barrel neurones and 29 layer 5b neurones were studied. Whisker stimulations were ramp-and-hold deflections with one of six different ramp velocities (100-2.5 mm s(-1)) and one of four different plateau amplitudes (2000-200 microm). Twenty-four (6 x 4) different stimulus forms were applied to the tip of a whisker trimmed to 10 mm in a predetermined order in stimulus cycles of 20-50 repetitions. Spike counts for a period of 2560 ms in 10 ms bins were summed to construct a matrix of 24 peristimulus histograms for each neurone. Twenty-four amplitude and 24 velocity values were computed from counts during the plateau and ramp phases, respectively. To determine the amplitude- and velocity dependence of a neurone, an amplitude F value (the ratio of variations among-/within-amplitude of the amplitude value) and a velocity F value (ratio of variations among-/within-velocity of the velocity value) were derived by analysis of variance. The amplitude F value of the layer 4 barrel neurones was greater than that of the layer 5b neurones (P < 0.0001). The velocity F value of the barrel neurones was smaller than that of the layer 5b neurones (P = 0.0226). The results suggests that barrel neurones and layer 5b neurones tend to detect amplitude and velocity components of whisker deflection, respectively.

Analysis of Variance↗
PubMed1993

Left ventricular measurements with cine and spin-echo MR imaging: a study of reproducibility with variance component analysis.

The authors studied the reproducibility of repeated measurements of left ventricular volumes, weight, and wall stress as determined with cine and spin-echo magnetic resonance (MR) imaging. Two observers analyzed 40 serial MR imaging examinations twice, yielding a total of 160 repeated measurements. Estimates of 95% ranges for change were ejection fraction, 10% and 12%; wall mass, 16% and 21%; and wall stress, 22% and 20%, for measurements derived from cine MR imaging and spin-echo MR imaging, respectively. Reproducibility was not significantly different between cine and spin-echo MR imaging. Intraobserver, interobserver, and interexamination errors were quantitated with variance component analysis. Interexamination variability was the single most important contributor to total variance. Reproducibility of left ventricular chamber volume measurements with MR imaging is superior to that of other imaging modalities. In addition, MR imaging can provide reliable estimates of wall mass and wall stress. Efforts to improve reproducibility should be aimed at lowering interexamination variability.

Adult↗
PubMed2000

The three point vernier alignment or acuity test (3Pt VA test): an analysis of variance.

A very useful clinical vernier acuity or vernier alignment test has been developed in this and associated laboratories over a span of two decades. We seek to refine further this test, to seek internal inconsistencies and to optimize parameters used in a variety of devices and environments. Vernier testing, and many aspects of this work have been considered by numerous able scientists over a long time period (not reviewed here), but none have encountered conditions faced by this group, particularly in the developing world. The three point vernier alignment (acuity) threshold test (3Pt VeA test) employed here has broad applications; it can be used as a clinical test of vision status, for triage, and as a reference standard for vision testing (in general). As one example, if sufficient luminance is employed, the test is applicable in the presence of truly dense media disorders, even advanced leucomas, mature cataracts, intraocular bleeds, as well as combinations of these disorders, with or without a window to the retina. Only retinal and centrally-based neural disorders, eccentricity from fixation, and about 50% of hypermature cataracts affect outcomes. With minor alterations, this test can be employed to assess the visual field. An analysis of variance (ANOVA) was performed on a defined set of parameters, to enable us to understand better the special properties and requirements associated with this test. Results are not significantly altered between ages 10-94 years (not assessed here). Employing settings well above threshold for test spot detection and well separated individual test spots, changes in test spot luminance, or background luminance (or adaptation level), contrast, veiling glare, test spot size, clear and variously degraded images, seem not to affect meaningfully measured outcomes. If an observer can define well a center of gravity for each test spot viewed, he can align the three points with remarkable precision.

Adult↗