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PubMed2003

Correcting for nonrandom ascertainment in generalized linear mixed models (GLMMs), fitted using Gibbs sampling.

Gibbs sampling-based generalized linear mixed models (GLMMs) provide a convenient and flexible way to extend variance components models for multivariate normally distributed continuous traits to other classes of phenotype. This includes binary traits and right-censored failure times such as age-at-onset data. The approach has applications in many areas of genetic epidemiology. However, the required GLMMs are sensitive to nonrandom ascertainment. In the absence of an appropriate correction for ascertainment, they can exhibit marked positive bias in the estimated grand mean and serious shrinkage in the estimated magnitude of variance components. To compound practical difficulties, it is currently difficult to implement a conventional adjustment for ascertainment because of the need to undertake repeated integration across the distribution of random effects. This is prohibitively slow when it must be repeated at every iteration of the Markov chain Monte Carlo (MCMC) procedure. This paper motivates a correction for ascertainment that is based on sampling random effects rather than integrating across them and can therefore be implemented in a general-purpose Gibbs sampling environment such as WinBUGS. The approach has the characteristic that it returns ascertainment-adjusted parameter estimates that pertain to the true distribution of determinants in the ascertained sample rather than in the general population. The implications of this characteristic are investigated and discussed. This paper extends the utility of Gibbs sampling-based GLMMs to a variety of settings in which family data are ascertained nonrandomly.

Age of Onset↗

PubMed1999

[On the problems of fitting linear regression models for hierarchically structured data in medical research].

There are a large number of the hierarchically structured data in the field of medical sciences, which have been analyzed usually by conventional linear regression models. The objective of this paper is to explore the problems and the relationship of parameter estimates of the three common linear regression models in fitting the hierarchically structured date, and the correction of the precision of parameter estimates. It is shown that the estimate of parameter and it's precision of linear regression models is related to the variation of independent variable between and within level 2 units, and the difference of residual estimates is associated with the difference of parameter estimates. The three common linear regression models are all inappropriate for the hierarchically structured data, but the standard error of the level 1 combined model can be corrected by variance inflation factor in conditions.

Analysis of Variance↗

PubMed2000

Strategies for genetic mapping of categorical traits.

The search for efficient and powerful statistical methods and optimal mapping strategies for categorical traits under various experimental designs continues to be one of the main tasks in genetic mapping studies. Methodologies for genetic mapping of categorical traits can generally be classified into two groups, linear and non-linear models. We develop a method based on a threshold model, termed mixture threshold model to handle ordinal (or binary) data from multiple families. Monte Carlo simulations are done to compare its statistical efficiencies and properties of the proposed non-linear model with a linear model for genetic mapping of categorical traits using multiple families. The mixture threshold model has notably higher statistical power than linear models. There may be an optimal sampling strategy (family size vs number of families) in which genetic mapping reaches its maximal power and minimal estimation errors. A single large-sibship family does not necessarily produce the maximal power for detection of quantitative trait loci (QTL) due to genetic sampling of QTL alleles. The QTL allelic model has a marked impact on efficiency of genetic mapping of categorical traits in terms of statistical power and QTL parameter estimation. Compared with a fixed number of QTL alleles (two or four), the model with an infinite number of QTL alleles and normally distributed allelic effects results in loss of statistical power. The results imply that inbred designs (e.g. F2 or four-way crosses) with a few QTL alleles segregating or reducing number of QTL alleles (e.g. by selection) in outbred populations are desirable in genetic mapping of categorical traits using data from multiple families.

Alleles↗

PubMed1976

A rumen linear programming model for evaluation of concepts of rumen microbial function.

A linear programming model provides for analysis of general input-output relationships in the rumen, for evaluation of competitive relationships among rumen microbes, and for computation of optimal relationships in the rumen. Eight rumen microbial groups defined on the bases of substrate specificity, nutrient requirements for growth, fermentation products, and relative metabolic activities comprise the central core of the model. Relative metabolic rates of microbial groups calculated from their cell sized were used as coefficients in the objective function. The model was used to evaluate effects of different amounts of protein from feed and various carbohydrates upon microbial population and fermentation patterns as accommodated by current concepts. During the several solutions of the model, considerable simplification of the rumen microflora occurred. This implies that current data and concepts, and the hypothesis regarding relative metabolic rate, as represented in the model, do not accommodate adequately competitions among the several rumen microbial species and, thus, that additional data and concepts regarding rumen microbial interactions are required. Also evaluated were effects of ingestion of bacteria by protozoa upon over-all rumen function, absolute microbial cell yields, cell yields per mole of adenosine triphosphate, and factors affecting these.

Adenosine Triphosphate↗

PubMed2005

EXAMINE: a computational approach to reconstructing gene regulatory networks.

Reverse-engineering of gene networks using linear models often results in an underdetermined system because of excessive unknown parameters. In addition, the practical utility of linear models has remained unclear. We address these problems by developing an improved method, EXpression Array MINing Engine (EXAMINE), to infer gene regulatory networks from time-series gene expression data sets. EXAMINE takes advantage of sparse graph theory to overcome the excessive-parameter problem with an adaptive-connectivity model and fitting algorithm. EXAMINE also guarantees that the most parsimonious network structure will be found with its incremental adaptive fitting process. Compared to previous linear models, where a fully connected model is used, EXAMINE reduces the number of parameters by O(N), thereby increasing the chance of recovering the underlying regulatory network. The fitting algorithm increments the connectivity during the fitting process until a satisfactory fit is obtained. We performed a systematic study to explore the data mining ability of linear models. A guideline for using linear models is provided: If the system is small (3-20 elements), more than 90% of the regulation pathways can be determined correctly. For a large-scale system, either clustering is needed or it is necessary to integrate information in addition to expression profile. Coupled with the clustering method, we applied EXAMINE to rat central nervous system development (CNS) data with 112 genes. We were able to efficiently generate regulatory networks with statistically significant pathways that have been predicted previously.

Algorithms↗

PubMed1984

Parameter estimation using the quasi-linear viscoelastic model proposed by Fung.

Using the quasi-linear viscoelastic model proposed by Fung for the description of the viscoelastic properties of soft biological tissues, the parameters governing their time-dependent behavior are commonly estimated from relaxation experiments. Exact quantification is possible from the response to a step change in the strain. Since it is physically impossible to realize a true step change in the strain, in practice the response to a steplike strain change is used. In the present study the discrepancies between the exact and the estimated parameter values are investigated using a hypothetical quasi-linear viscoelastic material. The parameter tau 1, governing the fast viscous phenomena, is found to be subject to the largest errors. Methods for obtaining better estimates of tau 1 are outlined in a number of special cases.

Biomedical Engineering↗

PubMed2004

Annoyance from multiple transportation noise: statistical models and outlier detection.

OBJECTIVE: Statistical models for the annoyance from multiple transportation noise are needed to understand and predict the annoyance resulting from specific noise exposures. METHODS: Models from the class of generalized linear models are suggested and discussed. Observations which are not well explained by the considered model are regarded as outliers. Outlier detection methods are applied to the data modelled by robust estimates using different link functions. RESULTS: The discussed methods are applied to data from a laboratory experiment using generalized linear models. While considering outliers, a generalized linear model with a complementary log-log link is found to be a good choice in modelling the exposure-response relationship between noise levels and annoyance.

Humans↗

PubMed1996

Threshold for radiation-related severe mental retardation in prenatally exposed A-bomb survivors: a re-analysis.

Significant effects on the developing human brain of exposure to ionizing radiation are seen among individuals exposed in the 8th-25th week after ovulation. These effects, particularly in the highly vulnerable period of 8-15 weeks after ovulation, manifest themselves most dramatically as an increased frequency of severe mental retardation. However, the distribution of cases of severe mental retardation suggests a threshold in the low-dose region. The 95% lower bound of the threshold in those survivors exposed 8-15 weeks after ovulation was zero for the individual data based on the simple linear model, and 0.15 Gy based on the exponential linear model used in our previous report (1987), but the 95% lower bound of the threshold based on all of the data including 21 additional cases with known doses appears to be 0.05 Gy using the maximum likelihood estimates derived from an exponential-linear model. The latter model was selected because it provides the best fit from the standpoint of the stableness and reasonableness of the estimates among the five models applied to the data. When two probably non-radiation-related cases of Down's syndrome are excluded from the 19 mentally retarded cases exposed 8-15 weeks post ovulation, the 95% lower bound of the threshold is in the range of 0.15-0.25 Gy based on the exponential-linear model used in 1987, but is in the range of 0.06-0.31 Gy when the more reasonable and better model applied here is used. For exposure in the 16-25-week period based on the same model, the 95% lower bound of the threshold changed from 0.25 to 0.28 Gy, both with and without inclusion of the two probable non-radiation-related mentally retarded cases; one of these cases was probably familial in origin since there was a retarded sibling, and the other due to infection, since the individual had Japanese B encephalitis at age 4 years.

Brain↗

PubMed1993

Marginal modeling of binary cross-over data.

A model specified in terms of linear models for marginal logits and linear models for log-odds ratios is proposed for the analysis of two-period binary cross-over experiments. Hypothesis testing and parameter estimation are facilitated by standard likelihood methodology. Two examples are used to illustrate how the model can be used to analyze two-period binary cross-over experiments. Results from a simulation study demonstrate that this approach to the analysis of binary cross-over data compares favorably with standard procedures, such as the Mainland-Gart test for a treatment difference, Prescott's test for a treatment difference, and the Hills-Armitage test for treatment-by-period interaction.

Biometry↗

PubMed2004

Genetics of length of productive life and lifetime prolificacy in the Finnish Landrace and Large White pig populations.

The objective of this study was to estimate direct and indirect selection potential for length of productive life and lifetime prolificacy in Finnish Large White and Landrace swine populations. To study the direct selection potential, the heritabilities of these traits were estimated. The genetic correlations of length of productive life and lifetime prolificacy with prolificacy traits and overall leg conformation were estimated to evaluate whether selection for these traits could indirectly improve measures of sow longevity. In addition, correlations between length of productive life, lifetime prolificacy, ADG, and backfat thickness were estimated. Records were used from Finnish purebred Landrace (n = 26,744) and Large White (n = 24,007) sows born on operations that perform on-farm production tests on all females. Heritabilities were estimated using both a survival analysis procedure and a linear model. Due to computational limitations, correlations were estimated with the linear model only. Estimated length of productive life heritabilities obtained from linear model analyses were less (0.05 to 0.10) than those obtained from survival analyses (0.16 to 0.19). This may be indicative of the superiority of survival analysis compared with linear model analysis methods when evaluating longevity or similar types of data. All the prolificacy traits were genetically correlated with length of productive life and lifetime prolificacy, and the correlations were greater than 0.13. These results indicate that selection for increased number of piglets weaned in the first litter and for short first farrowing interval is beneficial for sow longevity and also for sow's lifetime prolificacy. The genetic correlations between length of productive life and leg conformation score also were favorable (0.32 in Landrace and 0.17 in Large White). The heritability estimates indicate that survival analysis is likely the most appropriate method of evaluating longevity traits in swine. Because of computational problems, simultaneous analysis of linear traits and longevity is not currently possible. More research is needed to develop methods for multiple linear and survival trait analyses.

Animals↗

PubMed2006

A robust approach to t linear mixed models applied to multiple sclerosis data.

We discuss a robust extension of linear mixed models based on the multivariate t distribution. Since longitudinal data are successively collected over time and typically tend to be auto-correlated, we employ a parsimonious first-order autoregressive dependence structure for the within-subject errors. A score test statistic for testing the existence of autocorrelation among the within-subject errors is derived. Moreover, we develop an explicit scoring procedure for the maximum likelihood estimation with standard errors as a by-product. The technique for predicting future responses of a subject given past measurements is also investigated. Results are illustrated with real data from a multiple sclerosis clinical trial.

Bayes Theorem↗

PubMed2005

Linear regression models for solvent accessibility prediction in proteins.

The relative solvent accessibility (RSA) of an amino acid residue in a protein structure is a real number that represents the solvent exposed surface area of this residue in relative terms. The problem of predicting the RSA from the primary amino acid sequence can therefore be cast as a regression problem. Nevertheless, RSA prediction has so far typically been cast as a classification problem. Consequently, various machine learning techniques have been used within the classification framework to predict whether a given amino acid exceeds some (arbitrary) RSA threshold and would thus be predicted to be "exposed," as opposed to "buried." We have recently developed novel methods for RSA prediction using nonlinear regression techniques which provide accurate estimates of the real-valued RSA and outperform classification-based approaches with respect to commonly used two-class projections. However, while their performance seems to provide a significant improvement over previously published approaches, these Neural Network (NN) based methods are computationally expensive to train and involve several thousand parameters. In this work, we develop alternative regression models for RSA prediction which are computationally much less expensive, involve orders-of-magnitude fewer parameters, and are still competitive in terms of prediction quality. In particular, we investigate several regression models for RSA prediction using linear L1-support vector regression (SVR) approaches as well as standard linear least squares (LS) regression. Using rigorously derived validation sets of protein structures and extensive cross-validation analysis, we compare the performance of the SVR with that of LS regression and NN-based methods. In particular, we show that the flexibility of the SVR (as encoded by metaparameters such as the error insensitivity and the error penalization terms) can be very beneficial to optimize the prediction accuracy for buried residues. We conclude that the simple and computationally much more efficient linear SVR performs comparably to nonlinear models and thus can be used in order to facilitate further attempts to design more accurate RSA prediction methods, with applications to fold recognition and de novo protein structure prediction methods.

Amino Acids↗

PubMed2002

Informational masking with small set sizes.

Informational masking refers to interference in the detectability of a sound, or discrimination of some property of a sound, beyond that which can be attributed to interactions at the auditory periphery. In the current experiments the signal to be detected was a tone added to a 6-tone masker, and informational masking was introduced by randomly choosing the frequencies of the tones that comprise the masker. The primary question was whether small numbers of maskers could replace randomly drawn maskers without sacrificing the underlying detection schemes adopted by observers. Similar to the method used by Wright and Saberi [J. Acoust. Soc. Am. 105, 1765-1775 (1999)], detection thresholds were measured for different masker set sizes, where set size refers to the number of 6-tone maskers from which any one masker was drawn. Set sizes of 3, 6, 12, and 24 were tested as well as conditions in which the maskers were chosen at random. In addition, observers' memory for maskers was coarsely evaluated. Large differences in thresholds were found across observers and across different masker sets. Even for set sizes of 24, the memory test suggests some recognition of maskers for some observers. Post hoc analysis of the data included an evaluation of the relative contribution of different frequencies using a single linear model. As a base for comparison, a linear model fitted to each condition was also evaluated. Although the data were fitted better using many rather than one linear model, the reduction in quality of fit was modest. This result suggests substantial consistency in decision strategies regardless of masker set size.

Adult↗

PubMed1997

Estimation of excess risk from case-control data using Aalen's linear regression model.

We introduce methods for statistical inference in Aalen's non-parametric linear regression model of disease incidence (Aalen, 1989, Statistics in Medicine 8, 907-925) from nested case-control data. These methods provide the basis for estimation of excess risk as a linear function of dose and absolute risk for a given exposure history. The methods are illustrated by estimating excess and absolute risks associated with radon exposure and smoking from nested case-control samples from the Colorado Plateau uranium miners cohort.

Adult↗

PubMedDate not supplied

[Characteristics of the hydrodynamic situation in the urinary tract in vesico-ureteral reflux based on an analysis of a general type of equation of the linear transport model].

Upper urinary tract urodynamics are described through a linear deterministic chamber model. An analysis of possible urodynamic variants in vesico-ureteral reflux (VUR), using a mathematical model, has suggested that hydrodynamic situation in the refluxing ureter will be dependent on vesical and ureteral activity where ureterovesical incompetence and VUR are of similar grades. Where ureteral anatomy and function remain fairly intact, urinary regurgitation under high pressure shall be accompanied by the development of a considerable intraureteral hypertension. Besides, VUR-associated urodynamic disorder must have an obstructive component whose markedness will depend on the extent of arterial motor impairment, intravesical hypertension or a combination of the two. Urodynamic and radioisotopic studies have completely confirmed the theoretical postulations. In second- or third-degree VUR, for example, the highest intraureteral pressure developed in children with uninhibited bladder, while in fourth-degree VUR the bladder showed no response to gradual intravesical pressure rise. Urodynamic disturbance was already shown to have a functional/obstructive component in those cases of second-degree VUR where the bladder was uninhibited and be free of it in cases of normal bladder reflex and third-degree VUR.

Child↗

PubMed1996

Application of the linear-quadratic model to myelotoxicity associated with radioimmunotherapy.

The purposes of this study were: (1) to use the linear-quadratic model to determine time-dependent biologically effective doses (BEDs) that were delivered to the bone marrow by multiple infusions of radiolabeled antibodies, and (2) to determine whether granulocyte and platelet counts correlate better with BED than administered radioactivity, which does not take stem cell repopulation, i.e., time, into consideration. Twenty patients with B-cell malignancies that had progressed despite intensive chemotherapy and who had a significant number of malignant cells in their bone marrow were treated with multiple 0.7-3.7 GBq/m2 (18-100 mCi/m2) intravenous infusions of Lym-1, a murine monoclonal antibody that binds to a tumour-associated antigen, labeled with iodine-131. Granulocyte and platelet counts were measured in order to assess bone marrow toxicity. BEDs were calculated according to the formula: BED=D(1+gD/(alpha/beta))-0.693(Tn-Tk)/alphaTp, where D represents the absorbed dose of radiation delivered to the red marrow by penetrating emissions of 131I throughout the whole body and nonpenetrating emissions of 131I in the blood and bone marrow, g is a factor that depends on the duration of irradiation relative to the repair half-life of human bone marrow, alpha is the coefficient of nonrepairable damage per Gy, beta is the coefficient of repairable damage per Gy2, Tn is the time required to reach the granulocyte or platelet count nadir after an 131I-Lym-1 infusion, Tk is the time at which bone marrow proliferation begins after the start of treatment and Tp is the doubling time of the bone marrow after the granulocyte or platelet count nadir has been reached. The cumulative 131I-Lym-1 radioactivity administered to each patient was calculated. Biologically effective doses from multiple 131I-Lym-1 infusions were summated in order to arrive at a total BED for each patient. There was a weak association between granulocyte and platelet counts and radioactivity (the correlation coefficients were -0.23 and -0.60, respectively). Likewise, there was a weak association between granulocyte and platelet counts and BED (the correlation coefficients were -0.27 and -0.40, respectively). The attempt to take bone marrow absorbed doses and overall treatment time into consideration with the linear-quadratic model did not produce a stronger association than was observed between peripheral blood counts and administered radioactivity. The association between granulocyte and platelet counts and BED may have been weakened by several factors, including variable bone marrow reserve at the start of 131I-Lym-1 therapy and the delivery of heterogeneous absorbed doses of radiation to the bone marrow.

Agranulocytosis↗

PubMed2005

Goodness-of-fit methods for generalized linear mixed models.

We develop graphical and numerical methods for checking the adequacy of generalized linear mixed models (GLMMs). These methods are based on the cumulative sums of residuals over covariates or predicted values of the response variable. Under the assumed model, the asymptotic distributions of these stochastic processes can be approximated by certain zero-mean Gaussian processes, whose realizations can be generated through Monte Carlo simulation. Each observed process can then be compared, both visually and analytically, to a number of realizations simulated from the null distribution. These comparisons enable one to assess objectively whether the observed residual patterns reflect model misspecification or random variation. The proposed methods are particularly useful for checking the functional form of a covariate or the link function. Extensive simulation studies show that the proposed goodness-of-fit tests have proper sizes and are sensitive to model misspecification. Applications to two medical studies lead to improved models.

Anti-HIV Agents↗

PubMed1998

Generalized linear mixed models in dairy cattle breeding.

Fitness and fertility traits of dairy cattle are of increasing importance and are often measured on a discrete scale. The development and application of generalized linear mixed models to the genetic analysis of these traits are reviewed. Because current genetic evaluation systems are predominantly based on animal models, the inferential challenges of highly parameterized generalized linear mixed models are discussed. Development and adoption of new methods for drawing appropriate inferences on dispersion parameters are essential. Recent hierarchical extensions have been proposed for generalized linear mixed models, allowing for complex dispersion patterns that accommodate heteroscedasticity and outlier robustness. Steady advances in available computing power have facilitated multiple-trait analyses involving continuous and discrete measures. Full Bayesian inference via the development of Markov Chain Monte Carlo methods will continue to allow even greater generality and dimensions in the genetic model.

Animals↗