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PubMed1997

Statistical methods for estimating doubling time in in vitro cell growth.

Doubling time has been widely used to represent the growth pattern of cells. A traditional method for finding the doubling time is to apply gray-scaled cells, where the logarithmic transformed scale is used. As an alternative statistical method, the log-linear model was recently proposed, for which actual cell numbers are used instead of the transformed gray-scaled cells. In this paper, I extend the log-linear model and propose the extended log-linear model. This model is designed for extra-Poisson variation, where the log-linear model produces the less appropriate estimate of the doubling time. Moreover, I compare statistical properties of the gray-scaled method, the log-linear model, and the extended log-linear model. For this purpose, I perform a Monte Carlo simulation study with three data-generating models: the additive error model, the multiplicative error model, and the overdispersed Poisson model. From the simulation study, I found that the gray-scaled method highly depends on the normality assumption of the gray-scaled cells; hence, this method is appropriate when the error model is multiplicative with the log-normally distributed errors. However, it is less efficient for other types of error distributions, especially when the error model is additive or the errors follow the Poisson distribution. The estimated standard error for the doubling time is not accurate in this case. The log-linear model was found to be efficient when the errors follow the Poisson distribution or nearly Poisson distribution. The efficiency of the log-linear model was decreased accordingly as the overdispersion increased, compared to the extended log-linear model. When the error model is additive or multiplicative with Gamma-distributed errors, the log-linear model is more efficient than the gray-scaled method. The extended log-linear model performs well overall for all three data-generating models. The loss of efficiency of the extended log-linear model is observed only when the error model is multiplicative with log-normally distributed errors, where the gray-scaled method is appropriate. However, the extended log-linear model is more efficient than log-linear model in this case.

Cell Division↗

PubMed1997

Analysis of linear trade models and relation to scale economies.

We discuss linear Ricardo models with a range of parameters. We show that the exact boundary of the region of equilibria of these models is obtained by solving a simple integer programming problem. We show that there is also an exact correspondence between many of the equilibria resulting from families of linear models and the multiple equilibria of economies of scale models.

Journal Article↗

PubMed2002

On estimation and prediction for spatial generalized linear mixed models.

We use spatial generalized linear mixed models (GLMM) to model non-Gaussian spatial variables that are observed at sampling locations in a continuous area. In many applications, prediction of random effects in a spatial GLMM is of great practical interest. We show that the minimum mean-squared error (MMSE) prediction can be done in a linear fashion in spatial GLMMs analogous to linear kriging. We develop a Monte Carlo version of the EM gradient algorithm for maximum likelihood estimation of model parameters. A by-product of this approach is that it also produces the MMSE estimates for the realized random effects at the sampled sites. This method is illustrated through a simulation study and is also applied to a real data set on plant root diseases to obtain a map of disease severity that can facilitate the practice of precision agriculture.

Algorithms↗

PubMed1995

Model fit and measurement outcome in attachment measurements: a simulation study.

Serial attachment level measurements were simulated based on 2 hypothetical models of true change: 1) a burst model, where attachment changes rapidly over the duration of one measurement interval, but is unchanging before and after, and 2) a linear model, where attachment changes at a constant rate over time. Normally distributed measurement error was added to the modeled attachment level change to produce the series of measurement simulations. It was then determined for each series whether a burst model or a linear model best fit the simulated measurement series for a range of overall attachment level changes. For series generated by a burst model, the burst model fit better than a linear model a significant proportion of the time at all attachment level changes. However, for series generated by a linear model, the burst model provided the best fit for attachment level changes that were less than 4 times the standard deviation of the measurement error. Estimates of change based on a linear model slightly overestimated change when the true underlying model was a burst model. Estimates of change based on a burst model slightly underestimated change when the true model was a burst model, but substantially underestimated change when the underlying model was a linear model. Model fit when assessed by the least squares criterion may not be a reliable guide to model validity.

Bias↗

PubMed1993

Further results on the non-parametric linear regression model in survival analysis.

This paper gives further developments of a non-parametric linear regression model in survival analysis. Three subjects are studied. First, martingale residuals, originally developed for the Cox model, are introduced for our linear model. Their theory is developed and they are shown to be useful for judging goodness of fit. The second focus of the paper is on the use of bootstrap replications to judge which features of the cumulative regression plots are likely to reflect real phenomena and not merely random variation. In particular, this is applied to judging whether the effect of a covariate disappears over time, a problem for which no formal test exists. The third subject is density type, or kernel, estimation of the regression functions themselves. This might give more direct information than the cumulative plots. The approaches are illustrated by data from a clinical trial of carcinoma of the oropharynx, and by survival times of grafts in renal patients.

Computer Simulation↗

PubMed2006

Statistical inference in generalized linear mixed models: a review.

We present a review of statistical inference in generalized linear mixed models (GLMMs). GLMMs are an extension of generalized linear models and are suitable for the analysis of non-normal data with a clustered structure. A GLMM contains parameters common to all clusters (fixed regression effects and variance components) and cluster-specific parameters. The latter parameters are assumed to be randomly drawn from a population distribution. The parameters of this population distribution (the variance components) have to be estimated together with the fixed effects. We focus on the case in which the cluster-specific parameters are normally distributed. The cluster-specific effects are integrated out of the likelihood so that the fixed effects and variance components can be estimated. Unfortunately, the integral over the cluster-specific effects is intractable for most GLMMs with a normal mixing distribution. Within a classical statistical framework, we distinguish between two broad classes of methods to handle this intractable integral: methods that rely on a numerical approximation to the integral and methods that use an analytical approximation to the integrand. Finally, we present an overview of available methods for testing hypotheses about the parameters of GLMMs.

Analysis of Variance↗

PubMed1997

Body measurements and body weights of special-fed Holstein veal calves.

Changes in various body dimensions of special fed veal calves were measured and correlated with body weight (BW) at three specific times during the growth period as contemporaries and over the entire feeding period as noncontemporaries. The calves (n = 826) were weighed and measured for body length, heart girth, wither height, and hip width at 2, 8, and 16 wk after arrival at the veal farms. Each of the four measurements, expressed as ratios to BW, decreased over the feeding period; decline in the ratio of hip width to BW was less than the decreases in the other ratios. Linear models to predict contemporary BW within each age group based on all body measurements were developed; R2 values for models for 2, 8, and 16 wk were 0.72, 0.77, and 0.76, respectively. Within each of the three age classes, a model including linear, quadratic, and cubic terms of heart girth yielded the highest R2 values of any single measurement (0.46, 0.63, and 0.67 for data for 2, 8, and 16 wk, respectively). The addition of heart girth as a second linear measurement to three-term models containing only one other measurement increased the R2 more than did the addition of any other single linear expression, except for the equation based on body length. When all records on all calves were combined and the observations were treated as noncontemporaries, the R2 was 0.97 for a linear model that included all four measurements. However, this R2 was essentially the same as the R2 from a three-term model using only heart girth. The cubic models in descending order of R2 values were heart girth, body length, hip width, and wither height. These results suggest that BW can be predicted accurately in a group of noncontemporary male veal calves ranging from 2 to 16 wk after the start of the feeding period. However, the BW of calves within contemporary groups (2, 8, and 16 wk) cannot be predicted accurately according to R2 values.

Aging↗

PubMed1996

Normalization of temporal-distance parameters in pediatric gait.

Several techniques for the normalization of temporal-distance parameters in pediatric gait are given. The resulting normalized data can be used to compare (or discriminate) individuals or groups of individuals without the effect of variables such as age and height. The normalization with respect to a reference data set or with respect to the data set itself can be accommodated. Three novel techniques for normalization of gait data have been given: offset, decorrelation and detrending. For normalization of stride length with respect to height, all three are superior to the commonly accepted technique of dividing by the height. The offset technique has obscure units and will have a residual correlation. The decorrelation technique also has obscure units but will have zero correlation provided it is being normalized using a linear model (or piecewise linear model) fitted to the data in a least-squares sense. The detrending technique will also result in a zero correlation if piecewise linear or polynomial models, fitted to the data in a least-squares sense, are used. The detrending technique is the most useful of the three techniques proposed as it will also generate the same units as the original data set and can be easily scaled so that its magnitude is also comparable with the original data. Both the decorrelation and detrending techniques can be used simultaneously to normalize data with respect to two or more variables.

Age Factors↗

PubMed1992

Permanent implants using Au-198, Pd-103 and I-125: radiobiological considerations based on the linear quadratic model.

Based on the linear-quadratic model, we perform calculations to compare the possible radiobiologic results achieved with permanent implants using Au-198, Pd-103, and I-125. We examine the influence of the radiobiophysical parameters (i.e. alpha, beta, SLD repair kinetics, tumor doubling time (Tp), tumor growth delay, and prescribed dose) on the calculated radiobiologic indices or endpoints. The radiobiologic indices or endpoints include the effective treatment time (Teff) (beyond which the additional dose delivered is wasted), the biologically effective dose (BED), and cell surviving fractions. Within the range of reported values of the various parameters, Tp is the most significant in affecting Teff, BED, and the degree of cell inactivation. The effect of Tp and Teff and BED is larger for isotopes with longer half-lives, for which the rate of tumor regrowth is more important. For Tp of 5 to 30 days, the Teff are 14 to 21 days for Au-198, 58 to 102 days for Pd-103, and 120 to 275 days for I-125. For this range of Tp, the wasted doses are less than 5% for Au-198, 15 to 3% for Pd-103, and 30 to 5% for I-125. For reference prescription doses of 60, 120, and 160 Gy for implants using Au-198, Pd-103, and I-125, respectively, the BED and the associated cell-kill is the lowest for Au-198, whereas Pd-103 and I-125 implants are more effective for fast-growth (Tp less than 10 days) and slow-growth (Tp greater than 10 days) tumors, respectively.

Brachytherapy↗

PubMed1998

Doses and models in risk assessment analysis for bronchial hyperresponsiveness.

The aims of this study are: (1) to evaluate whether the estimates of the association of risk factors with bronchial hyperresponsiveness (BHR) depends on the accumulated dose administered in challenge tests; and (2) to verify whether a model developed for survival studies (Weibull regression) is suited to analyze methacholine dose-response curves. For these purposes, 863 challenge tests, from EC Respiratory Health Survey in Italy, up to a cumulative dose of 6 mg methacholine, were analyzed by Weibull regression and by traditional methods (logistic model and linear model), both before and after truncation of the curves at 2 mg. With all methods the main risk factors for BHR were respiratory symptoms and atopy while age and airway caliber exerted a protective action. Our results confirmed that in epidemiological surveys 2 mg methacholine is enough to fully appreciate the effect of risk factors on BHR and showed that the Weibull model explains the observed variability better than linear and logistic regressions.

Adult↗

PubMed2003

A Bayesian hierarchical model for categorical data with nonignorable nonresponse.

Log-linear models have been shown to be useful for smoothing contingency tables when categorical outcomes are subject to nonignorable nonresponse. A log-linear model can be fit to an augmented data table that includes an indicator variable designating whether subjects are respondents or nonrespondents. Maximum likelihood estimates calculated from the augmented data table are known to suffer from instability due to boundary solutions. Park and Brown (1994, Journal of the American Statistical Association 89, 44-52) and Park (1998, Biometrics 54, 1579-1590) developed empirical Bayes models that tend to smooth estimates away from the boundary. In those approaches, estimates for nonrespondents were calculated using an EM algorithm by maximizing a posterior distribution. As an extension of their earlier work, we develop a Bayesian hierarchical model that incorporates a log-linear model in the prior specification. In addition, due to uncertainty in the variable selection process associated with just one log-linear model, we simultaneously consider a finite number of models using a stochastic search variable selection (SSVS) procedure due to George and McCulloch (1997, Statistica Sinica 7, 339-373). The integration of the SSVS procedure into a Markov chain Monte Carlo (MCMC) sampler is straightforward, and leads to estimates of cell frequencies for the nonrespondents that are averages resulting from several log-linear models. The methods are demonstrated with a data example involving serum creatinine levels of patients who survived renal transplants. A simulation study is conducted to investigate properties of the model.

Algorithms↗

PubMed2006

Fluctuation-dissipation theorem and the linear Glauber model.

We obtain exact expressions for the two-time autocorrelation and response functions of the -dimensional linear Glauber model. Although this linear model does not obey detailed balance in dimensions d > or = 2, we show that the usual form of the fluctuation-dissipation ratio still holds in the stationary regime. In the transient regime, we show the occurrence of aging, with a special limit of the fluctuation-dissipation ratio, x(infinity) = 1/2, for a quench at the critical point.

Journal Article↗

PubMed1997

Neural network and linear regression models in residency selection.

For many years, multiple linear regression models have been used at a residency program to generate preliminary rank lists of residency applicants. These lists are then used by the admissions committee as an aid in developing a final ranking to submit to the National Residency Match Program (NRMP). A study was undertaken to compare predictions made using linear regression with those generated by a newer technique, an artificial neural network. A prospective cohort design was used. Seventy-four applicants to an emergency medicine program were evaluated by faculty and resident interviewers with regard to medical school grades, autobiography, interviews, letters of recommendation, and National Board scores. Normalization of these scores (by linear transformation of interviewer means) was used to correct for differences among interviewers. Multivariate linear regression and neural network models were developed using data from the previous 5 years' applicants. These models were used to forecast provisional rank orderings of the candidates. These rankings were combined into a single hybrid list that was used by the admissions committee as the starting point for development of the final rank list by consensus. Each model's predictions were tested for goodness of fit against the final NRMP rank using Wilks' test. Using the final submitted NRMP rank order as the dependent variable, the neural network yielded a correlation coefficient of 0.77 and an R2 of 59.4%. The linear regression model exhibited a correlation coefficient of 0.74 and an R2 of 54.0%. No significant difference was found (chi 2 = 1.08, P = .7). A neural network performs as well as a linear regression model when used for forecasting the rank order of residency applicants.

Cohort Studies↗

PubMed1982

A linear stochastic model of the single motor unit.

The production of force and of the electrical signal by an active motor unit is theoretically described. Neural spikes are modelled using the Dirac delta function. Mechanisms for the generation of random impulse trains and the properties of the corresponding stochastic processes are discussed; the "renewal" model is proposed as the most appropriate. The possibility of using a linear model for the systems that produce force and electrical signal in the unit is examined. It is concluded that the linear assumption is justifiable during steady, constant-strength contractions of muscle. This linear stochastic model of the motor unit is used in two subsequent papers to study the muscle force and the electromyogram.

Animals↗

PubMed2000

[Quantitative evaluation for risk assessment of neoplasms caused by exposure to chemical substances].

This work is based on the assumption that work safety and hygiene inspectors or a work hygiene inspectors in sanitary and epidemiological station will not develop their own dose-response models on the basis of background data. They should be equipment with a tool allowing them to assess a given risk in the most simple way. Dose-response models for assessing cancer risk induced by carcinogenic chemicals are presented in the "Guidelines on health risk assessment of carcinogenic agents" published since 1995 by The Nofer Institute of Occupational Medicine in Łódź. Nevertheless, it seemed advisable to gather in one publication all models published thus far, and by adding relevant comments and necessary formulas for calculations, produce a simple set of practical rules of risk assessment. All models already published in Guidelines may be divided into two groups: linear and non-linear models. In addition, among linear models one may differentiate those for asbestos dust exposure because of different nature of the relationship between the extent of exposure and likelihood of cancer occurrence. The models are given in three tables under the following headings: linear models for 21 chemicals, non-linear models for 12 chemicals and linear models for asbestos. There are also included formulas that allow to convert dose into concentration and concentration into dose, and occupational exposure into equivalent exposure over the course of a lifetime, as well as conversion coefficients enabling the use of animal experiment results in the assessment of human risk.

Asbestos↗

PubMed2004

A generalized additive model for microarray gene expression data analysis.

Microarray technology allows the measurement of expression levels of a large number of genes simultaneously. There are inherent biases in microarray data generated from an experiment. Various statistical methods have been proposed for data normalization and data analysis. This paper proposes a generalized additive model for the analysis of gene expression data. This model consists of two sub-models: a non-linear model and a linear model. We propose a two-step normalization algorithm to fit the two sub-models sequentially. The first step involves a non-parametric regression using lowess fits to adjust for non-linear systematic biases. The second step uses a linear ANOVA model to estimate the remaining effects including the interaction effect of genes and treatments, the effect of interest in a study. The proposed model is a generalization of the ANOVA model for microarray data analysis. We show correspondences between the lowess fit and the ANOVA model methods. The normalization procedure does not assume the majority of genes do not change their expression levels, and neither does it assume two channel intensities from the same spot are independent. The procedure can be applied to either one channel or two channel data from the experiments with multiple treatments or multiple nuisance factors. Two toxicogenomic experiment data sets and a simulated data set are used to contrast the proposed method with the commonly known lowess fit and ANOVA methods.

Algorithms↗

PubMed1998

Application of artificial neural networks as a non-linear modular modeling technique to describe bacterial growth in chilled food products.

In many chilled, prepared food products, the effects of temperature, pH and %NaCl on microbial activity interact and this should be taken into account. A grey box model for prediction of microbial growth is developed. The time dependence is modeled by a Gompertz model-based, non-linear differential equation. The influence of temperature, pH and %NaCl reflected in the model parameters is described by using low-complexity, black box artificial neural networks (ANN's). The use of this non-linear modeling technique makes it possible to describe more accurately interacting effects of environmental factors when compared with classical predictive microbiology models. When experimental results on the influence of other environmental factors become available, the ANN models can be extended simply by adding more neurons and/or layers.

Bacteria↗

PubMed1999

Linear viscoelastic model of a maturing gelatin solution.

The linear viscoelastic model proposed in this work considers the viscoelastic nature of maturing gelatin solutions through a relaxation modulus that depends on temperature and maturation. This modulus is defined in the conceptual contexts of the classical rubber elasticity theory and the rheometric gel theory. An analysis of the relationship between the equilibrium elastic modulus and the percolation variable around the gel point is also included yielding a percolation exponent close to 1.7 as expected from previous theoretical predictions. Additionally, a simple kinetic model is proposed to follow the microstructural changes obtained as a consequence of the generation of junction zones, the number of which vary with time during the dynamic rheometric tests used in this work. Thus, the storage and loss moduli are measured at different temperatures and frequencies, during the period of gelatin maturation. The theoretical aspects of the rheological model are presented emphasizing the quantitative changes of rheological parameters with the maturation.

Animals↗