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PubMed1989

A linear muscle model predicts the hyperbolic force-velocity relationship.

A variety of different schemes have been reported in the literature for linearizing the force-velocity relationship observed in muscle, a dominant element in the muscle. This report extends assertions that a linear muscle system has force-velocity characteristics as described by Hill's hyperbolic equation, and that no linearization whatsoever is required. The muscle is modeled as a parallel combination of passive elasticity, and series elasticity connected to the parallel combination of active state tension generator, viscosity and length tension elasticity. Each of the elements are linear. Simulation solutions of this third-order system yield a hyperbolic shaped force-velocity curve using physiologically derived estimates, based on the oculomotor system, for the parameters of the muscle model.

Elasticity↗

PubMed2006

Estimation of postmortem interval from human pericardial fluid electrolytes concentrations in Chandigarh zone of India: log transformed linear regression model.

Estimation of postmortem interval from changes in postmortem pericardial fluid electrolytes concentration is the topic of discussion in the study. Querido [Querido D. Double logarithmic, linear relationship between plasma sodium/potassium concentration ratio and postmortem interval during the 6-96h postmortem period in rats. Forensic Sci Int 1990;44:125-34; Querido D. Linearization of the relationship between postmortem plasma chloride concentration and postmortem interval in rats. Forensic Sci Int 1990;45:117-27] and Singh et al. [Singh D, Prashad R, Parkash C, Bansal YS, Sharma SK, Pandey AN. Linearization of relationship between serum sodium, potassium concentration, their ratio and time since deaths in Chandigarh zone of north west India. Forensic Sci Int 2002;130:107; Singh D, Prashad R, Parkash C, Sharma SK, Pandey AN. Double logarithmic linear relationship between plasma chloride concentration and time since death in humans in Chandigarh zone of north west India. Legal Med 2003;5:49-54] had demonstrated a highly significant double logarithmic linear relationship between the time since death and the plasma sodium/potassium ratio as well as with plasma chloride concentration in Wistar rats and human, respectively. In view of these facts, the present study was carried out to substantiate this propensity in this transcellular extension of blood plasma. Electrolytes analysis in postmortem pericardial fluid obtained from 311 subjects revealed that correlation of time since deaths with potassium, sodium/potassium ratio and phosphorus was highly significant (p<0.001) during 2.5-58h of deaths. Not withstanding, time since death although modulated by ambient temperature could be predicted by log transformed multiple regression equation derived from the combination of potassium, chloride and phosphorus electrolytes concentration with standard error (SE) of prediction (in log hours) of 0.1840h and by double logarithmic model with SE (in log hours) of 0.1959, 0.2068 and 0.2088h from potassium, sodium/potassium ratio and phosphorus electrolytes, respectively.

Electrolytes↗

PubMed1996

Plasma pharmacokinetics and urinary excretion of the polyamine analogue 1, 19-bis(ethylamino)-5, 10, 15-triazanonadecane in CD2F1 mice.

The pharmacokinetics of 1, 19-bis(ethylamino)-5, 10, 15-triazanonadecane (BE-4-4-4-4) were determined in CD2F1 female mice after administration of i.v. bolus doses of 20 mg/kg (approximately the dose lethal to 10% of the study animals, approximately LD10) as well as 15, 10, and 5 mg/kg and after s.c., i.p., or p.o. doses of 20 mg/kg. BE-4-4-4-4 in plasma and urine was derivatized with dansyl chloride and measured by gradient high-performance liquid chromatography (HPLC) with fluorescence detection. Data were modeled by noncompartmental and compartmental methods. The declines observed in plasma BE-4-4-4-4 concentrations after i.v. delivery of 20, 15, 10, and 5 mg/kg were modeled simultaneously using an interval of 2000 min between doses and were best approximated by a two-compartment, open, linear model. The time courses of plasma BE-4-4-4-4 concentrations after i.p. and s.c. delivery were fit best by a two-compartment, open, linear model with first-order absorption. Peak plasma concentrations of BE-4-4-4-4 measured following an i.v. dose of 20 mg/kg ranged between 30 and 33 microgram/ml, the terminal elimination half-life was 94 min, and the volume of distribution (Vdss) was 850 ml/kg. The plasma pharmacokinetics of BE-4-4-4-4 were linear with dose. BE-4-4-4-4 (0.5 and 2.0 microM) in mouse plasma was approximately 67% protein-bound. Bio-availabilities after i.p., s.c., and p.o. delivery were 40%, 50%, and approximately 3%, respectively. Urinary excretion of parent BE-4-4-4-4 in the first 24 h after dosing accounted for less than 30% of the delivered dose. As BE-4-4-4-4 proceeds toward and undergoes clinical evaluation, the data and analytical method presented herein should prove useful in formulating a dose-escalation strategy and, possibly, evaluating toxicities encountered.

Absorption↗

PubMed1993

How do nurses assess the information received by breast cancer patients?

The aim of the study was to clarify how nurses assess the information targeted at breast cancer patients before, during and after hospitalization. The sample group consisted of 176 nurses from surgical and radiological wards and clinics in southwest Finland. The study used responses to a questionnaire investigating breast cancer patients' recovery. Of the sample, 71% responded to the questionnaire. Log-linear modelling was used for the final statistical analysis of the results. The findings obtained by log-linear modelling showed a cumulative effect. Various associations were seen in the responses of the nurses on how they assessed the information received by patients. Patients who were considered well-informed before hospitalization were similarly considered during their hospital stay. Nurses consider that they give their patients insufficient information. Further, nurses are not clear about their own role in the distribution of information.

Attitude of Health Personnel↗

PubMed2004

An improved non-linear thermodynamic model of voltage-dependent ionic currents.

Thermodynamic models of ionic currents are used to deduce exact functional form of rate constant. It is first assumed that free energy depends linearly on voltage. A major criticism of this approach is that time constant can reach arbitrarily small values resulting in an aberrant behavior. Recently, non-linear effects of electric field on the free energy were considered to solve this problem based on T-type calcium channel. In this study, we show that the current model approximately captures the voltage-dependence of the time constant only in a specific range of voltage and does not provide saturation of the time constant outside this range. Then, we propose an improved non-linear thermodynamic model and illustrate its applicability based on T-type calcium channel.

Animals↗

PubMed2005

[Statistical analysis of community-based studies -- presentation and comparison of possible solutions with reference to statistical meta-analytic methods].

PURPOSE: The statistical analysis of community-based trials and of other cluster-randomised trials, requires specific statistical methods. We show the consequences of the application of these models for study results, using data of the German Cardiovascular Prevention Study (GCP) as an example. METHODS: Data of 30,285 subjects were analysed, which were collected at the beginning and at the end of the study period. These data had been collected in 7 intervention regions and by national surveys. We grouped data of the national surveys in 7 control clusters to mimick a design typical for cluster-randomised trials. We applied the following statistical models to estimate the effect of the intervention on total cholesterol as well as on systolic blood pressure and the respective confidence intervals: a linear model, a mixed model, and fixed and random effects meta-analyses. RESULTS: While the estimates and confidence intervals for the intervention effect were similar in mixed model analysis and random effects meta-analysis, results from models incorporating fixed effects only were anti-conservative. The underestimation of variance in models incorporating fixed effects only was especially large in the analysis of systolic blood pressure data, where great heterogeneity between intervention communities was observed. Despite seemingly low intraclass correlation coefficients of 0.0019 for total cholesterol and 0.0166 for systolic blood pressure, respectively, the variance of the intervention effect was increased in the mixed model 2.8fold or 17.1fold, respectively, in comparison to the variance estimated in the linear model. Due to this variance inflation the intervention effect on systolic blood pressure lost statistical significance. CONCLUSION: Our results emphasise the importance to account for correlations in community-based trials. Besides the mixed model random effects meta-analysis can be applied as an alternative method.

Adult↗

PubMed2005

Quasi-likelihood estimation for relative risk regression models.

For a prospective randomized clinical trial with two groups, the relative risk can be used as a measure of treatment effect and is directly interpretable as the ratio of success probabilities in the new treatment group versus the placebo group. For a prospective study with many covariates and a binary outcome (success or failure), relative risk regression may be of interest. If we model the log of the success probability as a linear function of covariates, the regression coefficients are log-relative risks. However, using such a log-linear model with a Bernoulli likelihood can lead to convergence problems in the Newton-Raphson algorithm. This is likely to occur when the success probabilities are close to one. A constrained likelihood method proposed by Wacholder (1986, American Journal of Epidemiology 123, 174-184), also has convergence problems. We propose a quasi-likelihood method of moments technique in which we naively assume the Bernoulli outcome is Poisson, with the mean (success probability) following a log-linear model. We use the Poisson maximum likelihood equations to estimate the regression coefficients without constraints. Using method of moment ideas, one can show that the estimates using the Poisson likelihood will be consistent and asymptotically normal. We apply these methods to a double-blinded randomized trial in primary biliary cirrhosis of the liver (Markus et al., 1989, New England Journal of Medicine 320, 1709-1713).

Antibiotics, Antineoplastic↗

PubMed2003

[Test-retest reliability of measures of social network in the "Pró -Saúde" Study].

OBJECTIVE: To evaluate test-retest reliability of social network-related information of the" Pr -Sa de" study. METHODS: A test-retest reliability study was conducted using a multidimensional questionnaire applied to a cohort of university employees. The same questionnaire was filled out twice by 192 non-permanent employees with two weeks apart. Agreement was estimated using kappa statistics (categorical variables), weighted kappa statistics, log-linear models (ordinal variables), and intraclass correlation coefficient (discrete variables). RESULTS: Estimates of reliability were higher than 0.70 for most variables. Stratified analyses revealed no consistently varying patterns of reliability according to gender, age or schooling strata. Log-linear modelling showed that, for the study ordinal variables, the model of best fit was "diagonal agreement plus linear by linear association". CONCLUSIONS: The high level of reliability estimated in this study suggests that the process of measurement of social network-related aspects was adequate. Validation studies, which are currently being conducted, will complete the quality assessment of this information.

Adult↗

PubMed2001

Biological and statistical approaches to predicting human lung cancer risk from silica.

Chronic inflammation is a key step in the pathogenesis of particle-elicited fibrosis and lung cancer in rats, and possibly in humans. In this study, we compute the excess risk estimates for lung cancer in humans with occupational exposure to crystalline silica, using both rat and human data, and using both a threshold approach and linear models. From a toxicokinetic/dynamic model fit to lung burden and pulmonary response data from a subchronic inhalation study in rats, we estimated the minimum critical quartz lung burden (Mcrit) associated with reduced pulmonary clearance and increased neutrophilic inflammation. A chronic study in rats was also used to predict the human excess risk of lung cancer at various quartz burdens, including mean Mcrit (0.39 mg/g lung). We used a human kinetic lung model to link the equivalent lung burdens to external exposures in humans. We then computed the excess risk of lung cancer at these external exposures, using data of workers exposed to respirable crystalline silica and using Poisson regression and lifetable analyses. Finally, we compared the lung cancer excess risks estimated from male rat and human data. We found that the rat-based linear model estimates were approximately three times higher than those based on human data (e.g., 2.8% in rats vs. 0.9-1% in humans, at mean Mcrit lung burden or associated mean working lifetime exposure of 0.036 mg/m3). Accounting for variability and uncertainty resulted in 100-1000 times lower estimates of human critical lung burden and airborne exposure. This study illustrates that assumptions about the relevant biological mechanism, animal model, and statistical approach can all influence the magnitude of lung cancer risk estimates in humans exposed to crystalline silica.

Air Pollutants, Occupational↗

PubMed1995

Defining the relationship of oxygen delivery and consumption: use of biologic system models.

To determine the most appropriate mathematical description of the relationship between oxygen consumption and oxygen delivery, we compared the statistical validity of a piecewise linear model to two different biologic system models--Michaelis-Menten (MM) kinetics (used for enzyme systems) and the exponential dose-response relationship (used to describe drug administration and induced response). Nine rabbits underwent five incremental steps of normovolemic hemodilution to progressively decrease DO2. VO2 was measured concurrently by a metabolic gas monitor. All three models (piecewise linear, Michaelis-Menten, and exponential) provided a very close population curve fit to the data points (r2 = 0.88, 0.91, and 0.92). However, there were significant differences in maximum predicted VO2 (VO2max)--6.8, 9.9, 7.2 ml O2.kg-1.min-1 (P < 0.0002)--and a wide range in the model-specific parameters for individual rabbits (critical DO2 6.5-11.8 ml O2.kg-1.min-1, Km 4.2-11.4 ml O2.kg-1.min-1, and kappa 0.12-0.23 ml O2-1.kg.min). In the curvilinear models, average and population parameters were not significantly different. However, in the piecewise linear model, population critical DO2 (10.9 ml O2.kg-1.min-1) was 30% more than the average critical DO2 (8.4 ml O2.kg-1.min-1) for the nine rabbits (P < 0.005). VO2max values predicted by the piecewise linear and exponential dose-response model were more consistent with those in previous publications than was the higher VO2max predicted by the MM model. The difference in the average versus population critical DO2 in the piecewise linear model meant that population modeling was inaccurate because it yielded a critical DO2 higher than that demonstrated by eight of nine individual rabbits.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals↗

PubMed1993

Modelling overdispersion in toxicological mortality data grouped over time.

Toxicologists frequently conduct toxicity experiments in which different treatment conditions are applied to groups of animals and the resulting mortality in each group is measured at a number of discrete time points over the course of the experiment. Both survival analysis and generalized linear models have been proposed for analyzing this type of data. Whatever the approach taken, the model should allow for the presence of extra-multinomial variation arising from the use of groups of animals rather than individuals as the experimental units. We consider a number of models for overdispersion that can be incorporated into the generalized linear model framework for multinomial data. These models are extensions of ones proposed for binomial data by Williams (1982, Applied Statistics 31, 144-148) and Moore (1986, Biometrika 73, 583-588; 1987, Applied Statistics 36, 8-14). In addition, we examine robust asymptotic covariance matrix estimators for regression parameters, similar to those given in Liang and Zeger (1986, Biometrika 73, 13-22) and Zeger and Liang (1986, Biometrics 42, 121-130), and compare them to the model-based asymptotic estimators. Recommendations for analysis are given.

Analysis of Variance↗

PubMed1985

On the problem of time, dose and fractionation (TDF) in the linear-quadratic model.

In many problems of modern radiotherapy such as multifractionation, interstitial and intracavitary therapy with implanats the NSD-formula is hardly applicable. Serious difficulties arise, when this formula is used for an estimation of late responses of tissues, because it mainly appreciates acute effects. On the basis of the linear-quadratic survival model S = exp (-alpha D - beta D2) the TDF-problem is investigated with the help of kinetic principles.

Cell Survival↗

PubMed2005

The prediction of human oral absorption for diffusion rate-limited drugs based on heuristic method and support vector machine.

Support vector machine (SVM), as a novel machine learning technique, was used for the prediction of the human oral absorption for a large and diverse data set using the five descriptors calculated from the molecular structure alone. The molecular descriptors were selected by heuristic method (HM) implemented in CODESSA. At the same time, in order to show the influence of different molecular descriptors on absorption and to well understand the absorption mechanism, HM was used to build several multivariable linear models using different numbers of molecular descriptors. Both the linear and non-linear model can give satisfactory prediction results: the square of correlation coefficient R(2) was 0.78 and 0.86 for the training set, and 0.70 and 0.73 for the test set respectively. In addition, this paper provides a new and effective method for predicting the absorption of the drugs from their structures and gives some insight into structural features related to the absorption of the drugs.

Administration, Oral↗

PubMed2004

Differences in characteristics of heroin inhalers and heroin injectors at admission to treatment: a preliminary study using a large database of client records.

AIMS: To compare the characteristics of heroin injectors vs. inhalers at their first admission to publicly funded treatment in Texas. METHODS: The sample consisted of 9732 unique clients who entered publicly funded treatment programs in Texas between 1997 and 2001 and who had a primary problem with either injected or inhaled heroin, which they had used in the past 30 days. The records were analyzed using a generalized linear model of logistic regression with the outcomes modeled as binomial and multinomial distribution and a hierarchical linear model for continuous outcomes to compare heroin inhalers and injectors. FINDINGS: There were large statistically significant differences between injectors and inhalers. Inhalers were more likely to be older at first use of heroin, to have entered treatment sooner, to have minor children at home, to have higher annual incomes, to be first admissions to treatment, and to have a secondary drug problem with crack cocaine. They were also more likely to be Hispanic [odds ratio (OR) = 1.74] or African-American (OR = 12.32). CONCLUSIONS: Even though the race/ethnic differences in the Texas population and the type of heroin available for use in Texas differs from that studied elsewhere, many of the characteristics of heroin users are similar. Inhalers have more strengths in many areas, and these findings raise the possibility that there are factors, particularly among African-American participants in Texas, that lessen the risk of injecting heroin. Efforts should be directed to providing therapeutic interventions to discourage the transition to injecting and to encourage inhalers to enter treatment earlier rather than progressing on to injecting. This analysis is the first part of a larger study of heroin users in public and private treatment.

Administration, Inhalation↗

PubMed2005

FEDMA--a simple algorithm for theoretical modeling of linear metabolic pathways: from fuzzy data sets to prediction and experiment.

A theoretical model of a chain of irreversible Michaelis-Menten reactions proceeding inside a living cell, taking cell growth, division and subcellular compartmentation into account, was proposed. It became a basis for the construction of a "fuzzy" enzymatic data-modeling algorithm (FEDMA) - a procedure allowing the estimation of missing parameter values for the modeled system, in accordance both with the derived theoretical rules and the available experimental data. The obtained tool was tested to model the heme biosynthesis pathway in Saccharomyces cerevisiae, where about 40% of parameters remain unknown. The missing parameters estimated by means of FEDMA fall in the range of expected values.

Algorithms↗

PubMed2000

Testing for concordant equilibria between population samples.

A substantial body of theory has been developed to assess the effect of evolutionary forces on the distribution of genotypes, both single and multilocus, within populations. One area where the potential for application of this theory has not been fully appreciated concerns the extent to which population samples differ. Within populations, the divergence of genotype or haplotype frequencies from that expected under Hardy-Weinberg (HW) or linkage equilibrium can be measured as disequilibria coefficients. To assess population samples for concordant equilibria, an analytical framework for comparing disequilibria coefficients between populations is necessary. Here we present log-linear models to evaluate such hypotheses. These models have broad utility ranging from conventional population genetics to genetic epidemiology. We demonstrate the use of these log-linear models (1) as a test for genetic association with disease and (2) as a test for different levels of linkage disequilibria between human populations.

Animals↗

PubMed1988

Models for the statistical analysis of infectious disease data.

The Longini-Koopman model (1982, Biometrics 38, 115-126) describes the process underlying the transmission of an infectious disease in terms of household and community level transmission probabilities. This model is generalized by allowing for different transmission probabilities that may correspond to various levels of risk factors on both the household and community levels. Two types of models are considered: (i) models for household data, where the numbers of susceptible and infected members in each household are known along with the values of household level risk factors; and (ii) models for individual data, where the infection status and risk factor level are known for each individual in the household. Although the type (i) models can be expressed as special cases of the type (ii) models, they deserve special attention as they can be represented and analyzed as log-linear models. Both types of models can be analyzed using maximum likelihood methods, while the type (i) models, when expressed as log-linear models, can also be analyzed by the weighted least squares method. Data from influenza epidemics in Tecumseh, Michigan and Seattle, Washington are used to illustrate these methods.

Adult↗

PubMed2006

Artificial neural network for the joint modelling of discrete cause-specific hazards.

OBJECTIVE: Artificial neural network (ANN) based regression methods have been introduced for modelling censored survival data to account for complex prognostic patterns. In the framework of ANN extensions of generalized linear models for survival data, PLANN is a partial logistic ANN, suitable for smoothed discrete hazard estimation as a function of time and covariates. An extension of PLANN for competing risks analysis (PLANNCR) is now proposed for discrete or grouped survival times, resorting to the multinomial likelihood. METHODS AND MATERIALS: PLANNCR is built by assigning input nodes to the explanatory variables with the time interval treated as an ordinal variable. The logistic function is used as activation for the hidden nodes of the network, whereas the softmax, which corresponds to the canonical link of generalized linear models for polytomous regression, is adopted for multiple output nodes, to provide a smoothed estimation of discrete conditional event probabilities for each event. The Kullback-Leibler distance is used as error function for the target vectors, amounting to half of the deviance of a multinomial logistic regression model. PLANNCR can jointly model non-linear, non-proportional and non-additive effects on cause-specific hazards (CSHs). The degree of smoothing is modulated by the number of hidden nodes and penalization of the error function (weight decay). Model optimisation is achieved by quasi-Newton algorithms, while non-linear cross-validation (NCV) and the Network Information Criterion (NIC) were adopted for model selection. PLANNCR was applied to data on 1793 women with primary invasive breast cancer, histologically N-, who underwent surgery at the Milan Cancer Institute between 1981 and 1986. RESULTS: Differential effects of covariates and time on the shape of the CSH for the three main failure causes, namely intra-breast tumor recurrences, distant metastases and contralateral breast cancer, have been enlightened. CONCLUSIONS: PLANNCR can be suitably adopted in an exploratory framework for a thorough evaluation of the disease dynamics in the presence of competing risks.

Adult↗