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PubMed2001

Models for combining random and systematic errors. assumptions and consequences for different models.

A series of models for handling and combining systematic and random variations/errors are investigated in order to characterize the different models according to their purpose, their application, and discuss their flaws with regard to their assumptions. The following models are considered 1. linear model, where the random and systematic elements are combined according to a linear concept (TE = absolute value(bias) + z x sigma), where TE is total error, bias is the systematic error component, sigma is the random error component (standard deviation or coefficient of variation) and z is the probability factor; 2. squared model with two sub-models of which one is the classical statistical variance model and the other is the GUM (Guide to Uncertainty in Measurements) model for estimating uncertainty of a measurement; 3. combined model developed for the estimation of analytical quality specifications according to the clinical consequences (clinical outcome) of errors. The consequences of these models are investigated by calculation of the functions of transformation of bias into imprecision according to the assumptions and model calculations. As expected, the functions turn out to be rather different with considerable consequences for these types of transformations. It is concluded that there are at least three models for combining systematic and random variation/errors, each created for its own specific purpose, with its own assumptions and resulting in considerably different results. These models should be used according to their purposes.

Algorithms↗

PubMed2006

Deconfounding microarray analysis - independent measurements of cell type proportions used in a regression model to resolve tissue heterogeneity bias.

OBJECTIVES: Microarray analysis requires standardized specimens and evaluation procedures to achieve acceptable results. A major limitation of this method is caused by heterogeneity in the cellular composition of tissue specimens, which frequently confounds data analysis. We introduce a linear model to deconfound gene expression data from tissue heterogeneity for genes exclusively expressed by a single cell type. METHODS: Gene expression data are deconfounded from tissue heterogeneity effects by analyzing them using an appropriate linear regression model. In our illustrating data set tissue heterogeneity is being measured using flow cytometry. Gene expression data are determined in parallel by real time quantitative polymerase chain reaction (qPCR) and microarray analyses. Verification of deconfounding is enabled using protein quantification for the respective marker genes. RESULTS: For our illustrating dataset, quantification of cell type proportions for peripheral blood mononuclear cells (PBMC) from tuberculosis patients and controls revealed differences in B cell and monocyte proportions between both study groups, and thus heterogeneity for the tissue under investigation. Gene expression analyses reflected these differences in celltype distribution. Fitting an appropriate linear model allowed us to deconfound measured transcriptome levels from tissue heterogeneity effects. In the case of monocytes, additional differential expression on the single cell level could be proposed. Protein quantification verified these deconfounded results. CONCLUSIONS: Deconfounding of transcriptome analyses for cellular heterogeneity greatly improves interpretability, and hence the validity of transcriptome profiling results.

Cell Physiological Phenomena↗

PubMed2002

Modelling HIV viral rebound using non-linear mixed effects models.

Individuals infected with the human immunodeficiency virus type 1 (HIV-1) who initiate antiretroviral therapy typically experience a marked decline in concentrations of HIV-1 RNA in plasma. Often, however, viral rebound occurs within the first year of treatment and this rebound may be associated with resistance to antiretroviral therapy. For this reason, it is important to study the patterns of virological response of HIV-1 RNA to treatment. In particular, there is interest in the relationship between the lowest level of plasma HIV-1 RNA attained after initiation of therapy (nadir value) and the time until rebound. To investigate this question, we implement a simple and flexible non-linear mixed effects model for the trajectory of the HIV-1 RNA until rebound. This model is also consistent with biological insights into the effects of treatment. We also show how the problem of censoring of HIV-1 RNA values at the lower limit of assay quantification can be addressed using a multiple imputation scheme. The algorithm is simple to implement and is based on accessible software. Our application makes use of data from clinical trial 315 conducted by the AIDS Clinical Trials Group (ACTG 315). We find a strong relationship between HIV-1 RNA nadir and time to rebound, with potentially important consequences for the management of HIV-infected individuals.

Adolescent↗

PubMed1987

Epidemiologic programs for computers and calculators. Inferences on odds ratios, relative risks, and risk differences based on standard regression programs.

Statistical analyses of the joint effects of several factors (covariates) on the risk of disease, death, or other dichotomous outcomes, are frequently based on a model that relates the effect of the covariates to some function of the probability of the outcome. The odds ratio, relative risk, and the difference in risks are among the simplest candidates for the outcome function. Each can be specified as a special case of the generalized linear model, but their use has been limited to researchers with access to specialized computer programs that are not yet generally available in standard computer packages. The purpose of this communication is to describe how to implement the maximum likelihood estimation procedures and hypothesis testing associated with the generalized linear model using any computer program that can perform weighted least squares analyses. The procedure is applied specifically to models for relative risks, risk differences, and odds ratios. The techniques are illustrated with SAS and SPSSx programs for data sets previously presented.

Computers↗

PubMed2003

Prospective evaluation of a D-optimal designed population pharmacokinetic study.

Recently, methods for computing D-optimal designs for population pharmacokinetic studies have become available. However there are few publications that have prospectively evaluated the benefits of D-optimality in population or single-subject settings. This study compared a population optimal design with an empirical design for estimating the base pharmacokinetic model for enoxaparin in a stratified randomized setting. The population pharmacokinetic D-optimal design for enoxaparin was estimated using the PFIM function (MATLAB version 6.0.0.88). The optimal design was based on a one-compartment model with lognormal between subject variability and proportional residual variability and consisted of a single design with three sampling windows (0-30 min, 1.5-5 hr and 11-12 hr post-dose) for all patients. The empirical design consisted of three sample time windows per patient from a total of nine windows that collectively represented the entire dose interval. Each patient was assigned to have one blood sample taken from three different windows. Windows for blood sampling times were also provided for the optimal design. Ninety six patients were recruited into the study who were currently receiving enoxaparin therapy. Patients were randomly assigned to either the optimal or empirical sampling design, stratified for body mass index. The exact times of blood samples and doses were recorded. Analysis was undertaken using NONMEM (version 5). The empirical design supported a one compartment linear model with additive residual error, while the optimal design supported a two compartment linear model with additive residual error as did the model derived from the full data set. A posterior predictive check was performed where the models arising from the empirical and optimal designs were used to predict into the full data set. This revealed the "optimal" design derived model was superior to the empirical design model in terms of precision and was similar to the model developed from the full dataset. This study suggests optimal design techniques may be useful, even when the optimized design was based on a model that was misspecified in terms of the structural and statistical models and when the implementation of the optimal designed study deviated from the nominal design.

Adult↗

PubMed2000

Evaluation of the cobalt requirement of beef cattle based on vitamin B12, folate, homocysteine and methylmalonic acid.

This investigation was designed to estimate the Co requirement of growing cattle on the basis of plasma and liver levels of vitamin B(12) and folate, plasma levels of homocysteine and methylmalonic acid (MMA) and haematological variables. For this purpose thirty-four male intact cattle of the German Simmental breed (236 kg) were assigned randomly to ten groups and were fed corn silage-based diets which contained 70, 90, 109, 147, 184, 257, 327, 421, 589 or 689 microg Co/kg DM for 40 weeks. One-slope broken-line model analysis and a quadratic model with plateau were used to estimate the Co requirement. The broken-line model estimated the dietary Co requirement of growing cattle to be 257 (se 29) microg/kg dietary DM based on plasma vitamin B(12) as response criterion. The dietary Co levels needed to maximise the liver vitamin B(12) and liver folate were 236 (se 8) and 190 (se 8) microg/kg dietary DM respectively. Plasma folate did not show any response to the different Co levels. The dietary Co was inversely correlated with the plasma concentrations of homocysteine and MMA. Estimates of the dietary Co concentration required to minimise homocysteine were 161 (se 10) microg/kg DM. When MMA was used as response criterion, the linear model yielded a Co requirement of 124 (se 3) microg/kg dietary DM. The quadratic model did not provide a better closeness of regression fit and yielded similar requirements to the linear model. Haemoglobin concentration and haematocrit tended to have a slight response to increasing dietary Co and were only decreased in cattle on diets containing less than 100 microg Co/kg DM. On the basis of the present data, recommended levels of dietary Co for normal folate metabolism and minimum homocysteine and MMA levels can be set to be 150-200 microg/kg DM; for maximum vitamin B12 levels, the desired Co content in the diet seems to be 250 microg/kg DM.

Animals↗

PubMed1987

The morbidity and mortality of vermiculite miners and millers exposed to tremolite-actinolite: Part II. Mortality.

The vermiculite ore and concentrate of a mine and mill located near Libby, Montana was found to be contaminated with a fiber of the tremolite/acetinolite series. A study was conducted to estimate the exposure-response relationship for mortality for 575 men who had been hired prior to 1970 and employed at least 1 year at the Montana site. Individual cumulative fiber exposure (fiber-years) was calculated. Results indicated that mortality from nonmalignant respiratory disease (NMRD) and lung cancer was significantly increased compared to the U.S. white male population. For those workers more than 20 years since hire, the standard mortality rate (SMR) for lung cancer (ICDA 162-163) was 84.7, 225.1, 109.3, and 671.3 for less than 50, 50-99, 100-399, and more than 399 fiber-years respectively. Corresponding results for NMRD (ICDA 460-519) were 327.8, 283.5, 0, and 278.4. Based on a linear model for greater than 20 years since hire, the estimated percentage increase in lung cancer mortality risk was 0.6% for each fiber-year of exposure. At 5 fiber-years, the estimated percentage was 2.9% from an unrestricted (nonthreshold) linear model and 0.6% from a survival model.

Aluminum Silicates↗

PubMed2002

Marginalized transition models and likelihood inference for longitudinal categorical data.

Marginal generalized linear models are now frequently used for the analysis of longitudinal data. Semiparametric inference for marginal models was introduced by Liang and Zeger (1986, Biometrics 73, 13-22). This article develops a general parametric class of serial dependence models that permits likelihood-based marginal regression analysis of binary response data. The methods naturally extend the first-order Markov models of Azzalini (1994, Biometrika 81, 767-775) and prove computationally feasible for long series.

Biometry↗

PubMed1989

Linear programming models for cost reimbursement.

Tamura, Lauer, and Sanborn (1985) reported a multiple regression approach to the problem of determining a cost reimbursement (rate-setting) formula for facilities providing long-term care (nursing homes). In this article we propose an alternative approach to this problem, using an absolute-error criterion instead of the least-squares criterion used in regression, with a variety of side constraints incorporated in the derivation of the formula. The mathematical tool for implementation of this approach is linear programming (LP). The article begins with a discussion of the desirable characteristics of a rate-setting formula. The development of a formula with these properties can be easily achieved, in terms of modeling as well as computation, using LP. Specifically, LP provides an efficient computational algorithm to minimize absolute error deviation, thus protecting rates from the effects of unusual observations in the data base. LP also offers modeling flexibility to impose a variety of policy controls. These features are not readily available if a least-squares criterion is used. Examples based on actual data are used to illustrate alternative LP models for rate setting.

Computer Simulation↗

PubMed2007

Assessing observer agreement when describing and classifying functioning with the International Classification of Functioning, Disability and Health.

OBJECTIVE: The International Classification of Functioning, Disability and Health (ICF) is used increasingly to describe and classify functioning in medicine without being a psychometrically sound measure. All categories of the ICF are quantified using the same generic 0-4 scale. The objective of this study was to assess observer agreement when describing and classifying functioning with the ICF. DESIGN: A second-level category of the ICF, d430 lifting and carrying objects, was used as an example. To the qualifiers of this category, clinically meaningful definitions were assigned. Data were collected in a cross-sectional survey with repeated measurement. We report raw, specific and chance-corrected measures or agreement, a graphical method and the results of log-linear models for ordinal agreement. SUBJECTS/PATIENTS: A convenience sample of patients requiring physical therapy in an acute hospital. RESULTS: Twenty-five patients were assessed twice by 2 observers. Raw agreement was 0.52. Kappa was 0.36, indicating fair agreement. Different hierarchical log-linear models indicated that the strength of agreement was not homogeneous over all categories. CONCLUSION: Observer agreement has to be evaluated when describing and classifying functioning using the ICF Qualifiers'scale. When assessing inter-observer reliability, the first step is to calculate a summary statistic. Modelling agreement yields valuable insight into the structure of a contingency table, which can lead to further improvement of the scale.

Cross-Sectional Studies↗

PubMed1995

Unit-price analysis of opioid consumption by monkeys responding under a progressive-ratio schedule of drug injection.

Several reports have indicated that drug consumption in self-administration procedures is a function of the ratio of the instrumental requirement to the dose of drug, a quantity termed unit price. We evaluated three predictions from this unit-price model in a reanalysis of data on opioid self-administration in rhesus monkeys responding under a progressive-ratio schedule (Hoffmeister, 1979). We evaluated whether consumption was inversely related to unit price, and compared the goodness of fit of an equation devised by Hursh, Raslear, Shurtleff, Bauman, and Simmons (1988) to that of a linear model predicting consumption as a function of dose. We also tested whether consumption was constant when the same unit price was comprised of different combinations of dose and instrumental requirement. Consumption declined overall as unit price increased. The equation devised by Hursh et al. and the linear model based on dose fit the data equally well. Drug consumption was not uniform at a given unit price. The analyses suggest limits on the unit-price model as a characterization of drug consumption.

Animals↗

PubMed1999

Non-linear pharmacokinetic modelling of intravenous elgodipine.

UNLABELLED: OBJECTIVE, SUBJECTS AND METHODS: The 1,4-dihydropyridine elgodipine was given as continuous infusion at various rates (5, 10, 15, 20, 40 microg/kg/h for 48, 48, 48, 24, or 6 h, respectively) to five groups of 6-12 healthy male subjects (total 42). Elgodipine plasma concentrations were measured with HPLC in 20-24 samples from each subject. Concentrations increased overproportionally with dose. Non-compartmental and compartmental evaluations were made. A two-compartment model with lag time and Michaelis-Menten term for elimination was found to be appropriate. RESULTS: Based on Michaelis-Menten parameters and concentration time courses during infusions, the elimination appeared to be saturated already at low dosages. There appeared to be two distinct subpopulations with two-fold differences in the maximal elimination velocity. In 9/42 subjects, more frequently in the groups with lower infusion rates, the model failed and the Michaelis-Menten term had to be replaced with a constant rate to fit. A dose-dependent increase in the volume of distribution and differences in and difficulties with estimations of the Michaelis-Menten constant KM might indicate a non-linear plasma protein binding. The transfer rate constants to or from the peripheral compartment correlated with blood hemoglobin or creatinine and bilirubin concentrations, respectively. CONCLUSION: The results indicated that tissue distribution and protein binding had marked influence on the plasma concentrations and, thus, attenuated the impact of saturation in the elimination.

Adult↗

PubMed2002

An adaptive test of significance for a subset of regression coefficients.

An F-test for a subset of regression coefficients is often used in order to compare two nested linear models. An adaptive test is proposed that has higher power than this F-test for many non-normal distributions of error terms. The adaptive test uses a weighted least squares procedure with weights determined from the Studentized deleted residuals from a linear model. A permutation method is then used so that the resulting test maintains its size near the nominal value. Results from several simulation studies are used to compare the power of the adaptive test to the F-test. The adaptive test is recommended as a way of increasing the power of many common tests when used with models that have few parameters whenever the distribution of errors is non-normal and the number of observations exceeds 20.

Computer Simulation↗

PubMed1990

Twin concordance for a binary trait: III. A bivariate analysis of hay fever and asthma.

Self-reported histories of hay fever and asthma were obtained from 3,808 pairs of adult twins 18 years and over registered with the Australian National Health Medical Research Council Twin Registry (1232 MZF, 567 MZM, 751 DZF, 352 DZM, 906 DZO). The prevalence of hay fever and asthma was 0.32 and 0.13, respectively, with little variation with zygosity, sex, and age. The associations between twin pairs for these two traits were analysed, under the assumption of constant prevalences, as a special case of a log-linear model for binary traits in pedigrees using the statistical package GLIM. The model assumption that there are no second- or higher-order interactions was tested in the 2 X 2 X 2 X 2 table of twin by disease outcomes without revealing strong evidence of departure, even in this large data set. The log-linear modelling showed that only three first-order interactions, namely 1) between hay fever in a twin pair, 2) asthma in a twin pair, and 3) hay fever and asthma in the same twin, were necessary to describe the data. The first two interaction terms were significantly larger in identical pairs; the third was independent of zygosity. Under this parsimonious model, there was a significant difference between identical and fraternal pairs in marginal correlation, both in asthma and hay fever, and in the cross-correlation between hay fever in one twin and asthma in the other. This suggests that genetic factors are implicated in both hay fever and asthma and that some of these genetic factors are common (at least among a subgroup of individuals) to both traits.

Adolescent↗

PubMed2002

Rate-limited desorption of volatile organic compounds from soils and implications for the remediation of a Louisiana Superfund site.

The rates of desorption of trichloroethylene (TCE) and 1,3-dichlorobenzene (DCB) from a silty soil at a Superfund site and a silty-clayey soil from an uncontaminated bottomland hardwood swamp in Baton Rouge, Louisiana were studied in laboratory batch systems. The effect of the age of soil contamination was studied using a laboratory-spiked soil incubated for 3 days, 3 months and 5 months. An empirical non-linear model was used to describe the bi-phasic nature of desorption with one fraction (labile) being released in relatively short periods of time (typically 24-100 hr) and a second fraction (non-labile or irreversible) being resistant to desorption. The non-linear model parameters, viz., the fraction of the chemical released rapidly (F), and the first order desorption rate coefficients, k1 and k2 respectively for the labile and slowly released fractions were determined by fitting the experimental data to the model. The data fit the model well as indicated by the high r2 values. The estimate of k1 was good. However, the values of k2 are known with less precision due to the limited duration of the experiment and number of samples taken at long times. In addition, desorption kinetics of 3 and 5-month old contaminated soils showed that progressively less amount of contaminant was available for facile desorption (lower F) compared to freshly contaminated soil. The labile fraction had desorption rate constants of the order of 10(-1) h(-1), whereas the slowly released fraction had rate constants of the order of 10(-4) h(-1) in accord with literature reported values for a variety of other compounds and soils. Possible mechanisms describing these rates and implications for the site clean up are discussed.

Adsorption↗

PubMed1983

Assessment of cerebrospinal fluid compliance and outflow resistance: analysis of steady-state response to sinusoidal input.

Cerebrospinal fluid dynamics have been studied in the past by analyses of responses to bolus, constant rate or constant pressure inputs. In this study, we present a method for analyzing CSF pressure responses to sinusoidal variation in the infusion rate. Infusion of artificial CSF into the cisterna magna of adult rats was modulated sinusoidally between 0 and 30 microliter/min. The resulting sinusoidal variation in intracranial pressure was recorded on a strip chart recorder simultaneously with the infusion rate signal. The two signals were analyzed for peak-to-peak variation, mean value, and phase shift for input frequencies in the range of 0.0015 to 0.01 HZ (0.00942 to 0.0628 radians/sec). The system was analyzed at each mean infusion rate as a parallel resistance and compliance with a first order linear model. The resistance to CSF outflow was determined as the change in mean steady-state pressure divided by the change in mean infusion rate. The compliance was then obtained from the frequency dependent phase shift between input and output using the first-order linear model. Resistance values were lower for higher average infusion rates consistent with our previous work, while compliance remained constant over the measured pressure range.

Animals↗

PubMed1992

Airway calibre as a confounder in interpreting bronchial responsiveness in asthma.

BACKGROUND: The relation between airway responsiveness to constrictor agents and forced expiratory volume in one second (FEV1) is important when interpreting change in airway responsiveness after an intervention. The aim of the study was to analyse the relation between FEV1 as a percentage of predicted values (% predicted) and airway responsiveness between and within asthmatic subjects. METHODS: Results of non-specific bronchial challenge tests were pooled from two randomised crossover studies comparing the effect of a non-sedative antihistamine with placebo in 35 patients with moderate asthma. The design of the two studies was similar: the provocative concentration of either histamine (first study) or methacholine (second study) resulting in a 20% decrease in ventilatory capacity (PC20) was repeated at two week intervals while patients were treated with the antihistamine or placebo. The dose of inhaled corticosteroid was gradually reduced during the study. Data were analysed with PC20 as the dependent variable in a general linear model so that the influence on PC20 of inhaled corticosteroid dose, antihistamine, and choice of bronchoconstricting agent could be separated from the influence of FEV1% predicted. RESULTS: The correlation coefficient between mean PC20 and mean prechallenge FEV1 for each patient was 0.45. In the general linear model two thirds (65%) of the variation in PC20 was due to variation between subjects. One third of the within subject variation in PC20 could be explained by variation in prechallenge FEV1% predicted (a change in FEV1 of 27% predicted was associated with one doubling or halving of PC20). Treatment with the antihistamine had no influence on PC20, except when histamine was used as the bronchoconstricting agent. The dose of inhaled corticosteroid had a small but significant effect. CONCLUSIONS: The variation in a patient's PC20 over time (several months) is related to changes in FEV1% predicted. Variation in FEV1% predicted explains less of the variation in bronchial responsiveness between subjects where a patient specific factor, which is probably related to the pathogenesis of bronchial asthma, seems to dominate.

Adrenal Cortex Hormones↗

PubMed2026

PGS-GS: a framework integrating polygenic scores and genomic selection in animal breeding.

Genomic prediction has become a central paradigm in biology, enabling quantitative inference of genetic contributions to complex traits across humans, animals, and plants. Although genomic research in human genetics and animal breeding shares a highly homologous methodological foundation, significant barriers persist in their analytical paradigms and application scenarios. This study aims to promote cross-disciplinary integration by introducing human-derived polygenic scores (PGS) algorithms into animal genomic selection (GS) and proposing a PGS-GS framework with a preliminary weighting-based implementation. We systematically benchmarked the predictive performance and computational efficiency of 20 algorithms, including classical linear models, machine learning, PGS, and PGS-GS using both array and whole-genome sequencing (WGS) data across four major agricultural species: beef cattle, sheep, pigs, and chickens. Our results demonstrate that PGS and PGS-GS algorithms achieve predictive accuracy competitive with genomic best linear unbiased prediction (GBLUP) while offering markedly higher computational efficiency. Moreover, incorporating PGS-derived prior information into weighted linear and non-linear models outperformed conventional weighted GBLUP. The results provide empirical evidence to inform algorithm selection and highlight the potential of integrating human-derived PGS methodologies into animal genomic prediction frameworks.

Animals↗