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PubMed1982

Vasopressin and the regulation of evaporative water loss and body temperature in the cat.

The role of vasopressin as a possible mediator of the inhibition of evaporative water loss (EWL) in dehydrated, heat-stressed cats has been examined by intravenous (i.v.) and intracerebroventricular (i.c.v.) injections of arginine vasopressin (AVP). In normally hydrated cats exposed to an ambient temperature (Ta) of 38 degrees C, neither EWL nor body temperature (Tb), measured in the hypothalamus, was significantly altered by i.v. AVP infusion. Measurements of plasma osmolality (pOsm), pAVP and cerebrospinal fluid AVP (csfAVP) were made in normally hydrated cats at Tas of 25 and 38 degrees C and after dehydration for 1-4 days at these temperatures. The relationship between pOsm and pAVP can be described equally well by either a linear model or a log-linear model (r = 0.81 for both models). The pOsm-csfAVP relationship is best described by a log-linear model (r = 0.80). A possible role for intracranially released AVP in body temperature regulation and control of EWL was examined by injecting various doses of AVP into the lateral ventricles of normally hydrated cats. No effect of AVP injection on Tb was observed at either a Ta of 23 degrees C or 38 degrees C. EWL was also unaffected by i.c.v. AVP administration at a Ta of 38 degrees C. To confirm further that intracranial AVP is not responsible for elevation of Tb and reduction of EWL during dehydration and heat-stress, specific antiserum to AVP was injected into the ventricles of dehydrated animals at a Ta of 38 degrees C. No significant effect on either Tb or EWL was measured subsequent to antiserum infusion. These negative findings indicate that AVP does not suppress EWL by either a peripheral or a central action and is therefore not responsible for lowered EWL and elevated Tb seen in dehydrated heat-stressed cats.

Animals↗
PubMed2004

Biologically valid linear factor models of gene expression.

MOTIVATION: The identification of physiological processes underlying and generating the expression pattern observed in microarray experiments is a major challenge. Principal component analysis (PCA) is a linear multivariate statistical method that is regularly employed for that purpose as it provides a reduced-dimensional representation for subsequent study of possible biological processes responding to the particular experimental conditions. Making explicit the data assumptions underlying PCA highlights their lack of biological validity thus making biological interpretation of the principal components problematic. A microarray data representation which enables clear biological interpretation is a desirable analysis tool. RESULTS: We address this issue by employing the probabilistic interpretation of PCA and proposing alternative linear factor models which are based on refined biological assumptions. A practical study on two well-understood microarray datasets highlights the weakness of PCA and the greater biological interpretability of the linear models we have developed.

Algorithms↗
PubMed2003

Linear system models for ultrasonic imaging: application to signal statistics.

Linear equations for modeling echo signals from shift-variant systems forming ultrasonic B-mode, Doppler, and strain images are analyzed and extended. The approach is based on a solution to the homogeneous wave equation for random inhomogeneous media. When the system is shift-variant, the spatial sensitivity function--defined as a spatial weighting function that determines the scattering volume for a fixed point of time--has advantages over the point-spread function traditionally used to analyze ultrasound systems. Spatial sensitivity functions are necessary for determining statistical moments in the context of rigorous image quality assessment, and they are time-reversed copies of point-spread functions for shift variant systems. A criterion is proposed to assess the validity of a local shift-invariance assumption. The analysis reveals realistic situations in which in-phase signals are correlated to the corresponding quadrature signals, which has strong implications for assessing lesion detectability. Also revealed is an opportunity to enhance near- and far-field spatial resolution by matched filtering unfocused beams. The analysis connects several well-known approaches to modeling ultrasonic echo signals.

Computer Simulation↗
PubMed2002

Ranitidine and omeprazole as adjuvant therapy to pancrelipase to improve fat absorption in patients with cystic fibrosis.

BACKGROUND: Inadequate treatment of pancreatic insufficiency in patients with cystic fibrosis (CF) causes malabsorption of nutrients with significant sequelae. The objective of this study was to measure the effect of acid suppressant therapy on fat absorption in patients with CF who received a pH-sensitive, enteric-coated microtablet enzyme product. METHODS: A double-blind, placebo-controlled crossover study of 12 children and 10 adults with pancreatic insufficient CF was performed. All subjects were receiving pancrelipase therapy (Pancrease MT10 and MT16; Ortho-McNeil, Springhouse, PA, U.S.A.) and for the study also received either placebo or ranitidine (Zantac; Glaxo-Wellcome, Research Triangle Park, NC U.S.A.) 5 mg/kg or 10 mg/kg daily. The adult subjects also received omeprazole therapy (Prilosec; AstraZeneca/Merck, Wilmington, DE, U.S.A.), 20 mg daily, as adjuvant therapy to pancreatic enzymes. Serial 3-day fat-balance studies were performed in the Clinical Research Center. The data were analyzed using individual paired t tests that compared each treatment with placebo and two repeated-measures, general linear model F tests. RESULTS: The linear model for all subjects showed no overall adjuvant drug effect on fat absorption, P = 0.32. A second linear model F test analysis of adult subjects, comparing all four drug treatments (placebo, ranitidine 5 and 10 mg/kg daily and omeprazole), also showed no difference in fat absorption, P = 0.15. Paired t test subgroup analysis of the adults showed an improvement of 4.97% (P = 0.003) in mean fat absorption comparing low-dose ranitidine to placebo. All other t test analyses showed no significant change in fat absorption between placebo and acid suppressant treatment. There was marked intersubject and intrasubject variability in fat absorption. CONCLUSIONS: No overall significant improvement in fat absorption could be demonstrated with adjuvant therapy. Fat absorption measured by 3-day fat-balance studies varied greatly even when comparing the same subject for placebo and baseline treatments, despite identical dietary fat and enzyme intakes. The large variability limited our ability to test for a difference in fat absorption and has significant implication for the use of this test, considered the gold standard, for determining enzyme dosage adequacy.

Adolescent↗
PubMed2005

Survival analysis applied to genetic evaluation for female fertility in dairy cattle.

The objective of this research was to study whether survival analysis results in a more accurate genetic evaluation for female fertility traits compared with the usual methodology based on linear models. The fertility trait studied was interval between calving and last insemination. A stochastic simulation describing the reproductive cycle of first-parity cows was done, in which true breeding values for conception rate were created. A model containing effects of sire and herd was used both with survival analysis and with mixed linear model analysis to predict sire breeding values. Correlations between true breeding values for conception rate and breeding values for calving to last insemination predicted by the best survival analysis model or the best linear model were 0.77 and 0.68, respectively. The results showed that when pregnancy status is known, survival analysis is a better method than linear models for genetic evaluation of conception rate when using observations on the interval between calving and last insemination.

Animals↗
PubMed2003

A heuristic for the degrees of freedom of statistics based on multiple variance parameters.

In neuroimaging, data are often modeled using general linear models. Here, we focus on GLMs with error covariances which are modeled as a linear combination of multiple variance/covariance components. Each of these components is weighted by one variance parameter. In many analyses variance parameters are estimated using restricted maximum likelihood (ReML). Most classical approaches assume the error covariance matrix can be factorized into a single variance parameter and a nonspherical correlation matrix. In this context, the F test based on a single variance parameter, with a suitable correction to the degrees of freedom, is the standard inference tool. This correction can also be adapted to models with multiple variance parameters. However, this extension overlooks the uncertainty about the variance parameter estimates and P values tend to be underestimated. Here, we show how one can overcome this problem to render the F test more exact. This issue is important, because serial correlations in fMRI time series are generally modeled using multiple variance parameters. Another application is to hierarchical linear models, which are used for modeling multisubject data. To illustrate our approach, we apply it to some typical modeling scenarios in fMRI data analysis.

Algorithms↗
PubMed2006

PLASQ: a generalized linear model-based procedure to determine allelic dosage in cancer cells from SNP array data.

Human cancer is largely driven by the acquisition of mutations. One class of such mutations is copy number polymorphisms, comprised of deviations from the normal diploid two copies of each autosomal chromosome per cell. We describe a probe-level allele-specific quantitation (PLASQ) procedure to determine copy number contributions from each of the parental chromosomes in cancer cells from single-nucleotide polymorphism (SNP) microarray data. Our approach is based upon a generalized linear model that takes advantage of a novel classification of probes on the array. As a result of this classification, we are able to fit the model to the data using an expectation-maximization algorithm designed for the purpose. We demonstrate a strong model fit to data from a variety of cell types. In normal diploid samples, PLASQ is able to genotype with very high accuracy. Moreover, we are able to provide a generalized genotype in cancer samples (e.g. CCCCT at an amplified SNP). Our approach is illustrated on a variety of lung cancer cell lines and tumors, and a number of events are validated by independent computational and experimental means. An R software package containing the methods is freely available.

Algorithms↗
PubMed2005

Estimation of linear mixed models with a mixture of distribution for the random effects.

The aim of this paper is to propose an algorithm to estimate linear mixed model when random effect distribution is a mixture of Gaussians. This heterogeneous linear mixed model relaxes the classical Gaussian assumption for the random effects and, when used for longitudinal data, can highlight distinct patterns of evolution. The observed likelihood is maximized using a Marquardt algorithm instead of the EM algorithm which is frequently used for mixture models. Indeed, the EM algorithm is computationally expensive and does not provide good convergence criteria nor direct estimates of the variance of the parameters. The proposed method also allows to classify subjects according to the estimated profiles by computing posterior probabilities of belonging to each component. The use of heterogeneous linear mixed model is illustrated through a study of the different patterns of cognitive evolution in the elderly. HETMIXLIN is a free Fortran90 program available on the web site: http://www.isped.u-bordeaux2.fr.

Aged↗
PubMed2005

Mathematical models use varying parameter strategies to represent paralyzed muscle force properties: a sensitivity analysis.

BACKGROUND: Mathematical muscle models may be useful for the determination of appropriate musculoskeletal stresses that will safely maintain the integrity of muscle and bone following spinal cord injury. Several models have been proposed to represent paralyzed muscle, but there have not been any systematic comparisons of modelling approaches to better understand the relationships between model parameters and muscle contractile properties. This sensitivity analysis of simulated muscle forces using three currently available mathematical models provides insight into the differences in modelling strategies as well as any direct parameter associations with simulated muscle force properties. METHODS: Three mathematical muscle models were compared: a traditional linear model with 3 parameters and two contemporary nonlinear models each with 6 parameters. Simulated muscle forces were calculated for two stimulation patterns (constant frequency and initial doublet trains) at three frequencies (5, 10, and 20 Hz). A sensitivity analysis of each model was performed by altering a single parameter through a range of 8 values, while the remaining parameters were kept at baseline values. Specific simulated force characteristics were determined for each stimulation pattern and each parameter increment. Significant parameter influences for each simulated force property were determined using ANOVA and Tukey's follow-up tests (alpha <or= 0.05), and compared to previously reported parameter definitions. RESULTS: Each of the 3 linear model's parameters most clearly influence either simulated force magnitude or speed properties, consistent with previous parameter definitions. The nonlinear models' parameters displayed greater redundancy between force magnitude and speed properties. Further, previous parameter definitions for one of the nonlinear models were consistently supported, while the other was only partially supported by this analysis. CONCLUSION: These three mathematical models use substantially different strategies to represent simulated muscle force. The two contemporary nonlinear models' parameters have the least distinct associations with simulated muscle force properties, and the greatest parameter role redundancy compared to the traditional linear model.

Journal Article↗
PubMed1997

Energy cost of treadmill walking.

BACKGROUND: The purpose of this study was to determine if energy cost of walking (VO2) could be accurately predicted with the simple models which analyze relationship oxygen uptake-speed of walking. A model to predict energy cost of treadmill walking was published firstly 29 years ago. METHODS: Employing the new modification of this model from 1986 to analyze VO2-speed of walking relationship leads to the elaboration of a simple linear model, two-compartment linear model, polynomial model of second order and monoexponential model of the metabolic cost of treadmill walking. To verify and compare these models 87 males, age ranged from 19 to 62 years, were evaluated on a motor driven treadmill. They walked at 0% grade at various velocities ranged from 3 to 12 km.h-1. RESULTS: The linear model has in range of intensities 3-12 km.h-1 a form of VO2.kg-1 (ml.kg-1.min-1) = 5.228*v (km.h-1)-11.158, r = 0.812, S(EE) = 4.16 ml.kg-1.min-1. The two-compartment linear model has in range of intensities of 3-7 km.h-1 a form of VO2.kg-1 = 3.207*v(km.h-1)-1.777, r = 0.932, and S(EE) = 1.5. In the range of 7.1-12 km.VO2.kg-1 = 7.120*v-29.168, r = 0.901, S(EE) = 3.78. In the range of intensities from 3 to 12 km.h-1 a polynomial model was found in the form VO2.kg-1 = 4.501-0.108*v + 0.379*v2, r = 0.891, S(EE) = 4.43, and the exponential model had a form VO2.kg-1 = 4.360*exp(0.223*v), r = 0.861, S(EE) = 6.84. All these correlation coefficients were highly significant (p < 0.001 in all cases). CONCLUSIONS: It was concluded that when applied to adult population, the models provide reasonable estimate of the actual requirement for treadmill walking provided the subjects in a oxygen uptake steady-state. As other researches for VO2/step we have found U-shaped curves of coefficient energy cost of walking. The minimum was at speed about 4 km.h-1. This finding support the speculation that does exists the "optimal" speed of moving which reflects the minimal energy expenditure during the walking.

Adult↗
PubMed2006

Multilevel modeling was a convenient alternative to common regression designs in longitudinal suicide research.

BACKGROUND AND OBJECTIVE: The prospective investigation of repetitive nonfatal suicidal behavior is associated with two methodological problems. Due to the commonly used definitions of nonfatal suicidal behavior, clinical samples usually consist of patients with a considerable between-person variability. Second, repeated nonfatal suicidal episodes of the same subjects are likely to be correlated. We examined three regression techniques to comparatively evaluate their efficiency in addressing the given methodological problems. STUDY DESIGN AND SETTING: Repeated episodes of nonfatal suicidal behavior were assessed in two independent patient samples during a 2-year follow-up period. The first regression design modeled repetitive nonfatal suicidal behavior as a summary measure. The second regression model treated repeated episodes of the same subject as independent events. The third regression model represented a hierarchical linear model. RESULTS: The estimated mean effects of the first model were likely to be nonrepresentative for a considerable part of the study subjects. The second regression design overemphasized the impact of the predictor variables. The hierarchical linear model most appropriately accounted for the heterogeneity of the samples and the correlated data structure. CONCLUSION: The nonhierarchical regression designs did not provide appropriate statistical models for the prospective investigation of repetitive nonfatal suicidal behavior. Multilevel modeling provides a convenient alternative.

Adolescent↗
PubMed1995

A convenient extension of the linear-quadratic model to include redistribution and reoxygenation.

PURPOSE: At present, the linear-quadratic model for cellular response to radiation can incorporate sublethal damage repair and repopulation. We suggest an extension, termed LQR, to include also the other two "Rs" of radiobiology, cell cycle redistribution, and reoxygenation. METHODS AND MATERIALS: In this approach, redistribution and reoxygenation are both regarded as aspects of a single phenomenon, which we term resensitization. After the first portion of a radiation exposure has decreased the average radiosensitivity of a diverse cell population by preferentially sparing less sensitive cells, resensitization gradually restores the average sensitivity of the population towards its previous value. The proposed LQR formula is of the same form as the original LQ formula, but with two extra parameters, an overall resensitization magnitude and a characteristic resensitization time. The LQR model assumes that resensitization is monotonic rather than oscillatory in time, i.e., always tends to increase average cellular sensitivity as overall time increases. We argue that this monotonicity assumption is likely to hold in clinical situations, though a possible extension is discussed to account for oscillatory decay of resensitization effects. RESULTS: The LQR model gives reasonable fits to relevant experimental data in the literature, reproducing an initial rise in cell survival, due to repair, as the treatment time is increased, followed by a resensitization-related decrease in survival due to redistribution and/or reoxygenation for treatment times of the order of the cell cycle time, and a final survival increase due to repopulation as the treatment time is increased still further. CONCLUSION: The LQR model is a simple and potentially useful extension of the LQ model for computing more realistic isoeffect relations for early responding tissues, including tumors, when comparing different radiotherapeutic protocols.

Animals↗
PubMed1996

The linearized multistage model and the future of quantitative risk assessment.

The linearized multistage (LMS) model has for over 15 years been the default dose-response model used by the U.S. Environmental Protection Agency (USEPA) and other federal and state regulatory agencies in the United States for calculating quantitative estimates of low-dose carcinogenic risks from animal data. The LMS model is in essence a flexible statistical model that can describe both linear and non-linear dose-response patterns, and that produces an upper confidence bound on the linear low-dose slope of the dose-response curve. Unlike its namesake, the Armitage-Doll multistage model, the parameters of the LMS do not correspond to actual physiological phenomena. Thus the LMS is 'biological' only to the extent that the true biological dose response is linear at low dose and that low-dose slope is reflected in the experimental data. If the true dose response is non-linear the LMS upper bound may overestimate the true risk by many orders of magnitude. However, competing low-dose extrapolation models, including those derived from 'biologically-based models' that are capable of incorporating additional biological information, have not shown evidence to date of being able to produce quantitative estimates of low-dose risks that are any more accurate than those obtained from the LMS model. Further, even if these attempts were successful, the extent to which more accurate estimates of low-dose risks in a test animal species would translate into improved estimates of human risk is questionable. Thus, it does not appear possible at present to develop a quantitative approach that would be generally applicable and that would offer significant improvements upon the crude bounding estimates of the type provided by the LMS model. Draft USEPA guidelines for cancer risk assessment incorporate an approach similar to the LMS for carcinogens having a linear mode of action. However, under these guidelines quantitative estimates of low-dose risks would not be developed for carcinogens having a non-linear mode of action; instead dose-response modelling would be used in the experimental range to calculate an LED10* (a statistical lower bound on the dose corresponding to a 10% increase in risk), and safety factors would be applied to the LED10* to determine acceptable exposure levels for humans. This approach is very similar to the one presently used by USEPA for non-carcinogens. Rather than using one approach for carcinogens believed to have a linear mode of action and a different approach for all other health effects, it is suggested herein that it would be more appropriate to use an approach conceptually similar to the 'LED10*-safety factor' approach for all health effects, and not to routinely develop quantitative risk estimates from animal data.

Animals↗
PubMed1997

Using the general linear mixed model to analyse unbalanced repeated measures and longitudinal data.

The general linear mixed model provides a useful approach for analysing a wide variety of data structures which practising statisticians often encounter. Two such data structures which can be problematic to analyse are unbalanced repeated measures data and longitudinal data. Owing to recent advances in methods and software, the mixed model analysis is now readily available to data analysts. The model is similar in many respects to ordinary multiple regression, but because it allows correlation between the observations, it requires additional work to specify models and to assess goodness-of-fit. The extra complexity involved is compensated for by the additional flexibility it provides in model fitting. The purpose of this tutorial is to provide readers with a sufficient introduction to the theory to understand the method and a more extensive discussion of model fitting and checking in order to provide guidelines for its use. We provide two detailed case studies, one a clinical trial with repeated measures and dropouts, and one an epidemiological survey with longitudinal follow-up.

Adolescent↗
PubMed2005

Tutorial in biostatistics: spline smoothing with linear mixed models.

The semi-parametric regression achieved via penalized spline smoothing can be expressed in a linear mixed models framework. This allows such models to be fitted using standard mixed models software routines with which many biostatisticians are familiar. Moreover, the analysis of complex correlated data structures that are a hallmark of biostatistics, and which are typically analysed using mixed models, can now incorporate directly smoothing of the relationship between an outcome and covariates. In this paper we provide an introduction to both linear mixed models and penalized spline smoothing, and describe the connection between the two. This is illustrated with three examples, the first using birth data from the U.K., the second relating mammographic density to age in a study of female twin-pairs and the third modelling the relationship between age and bronchial hyperresponsiveness in families. The models are fitted in R (a clone of S-plus) and using Markov chain Monte Carlo (MCMC) implemented in the package WinBUGS.

Adolescent↗
PubMed2006

Scoring and staging systems using cox linear regression modeling and recursive partitioning.

OBJECTIVES: Scoring and staging systems are used to determine the order and class of data according to predictors. Systems used for medical data, such as the Child-Turcotte-Pugh scoring and staging systems for ordering and classifying patients with liver disease, are often derived strictly from physicians' experience and intuition. We construct objective and data-based scoring/staging systems using statistical methods. METHODS: We consider Cox linear regression modeling and recursive partitioning techniques for censored survival data. In particular, to obtain a target number of stages we propose cross-validation and amalgamation algorithms. We also propose an algorithm for constructing scoring and staging systems by integrating local Cox linear regression models into recursive partitioning, so that we can retain the merits of both methods such as superior predictive accuracy, ease of use, and detection of interactions between predictors. The staging system construction algorithms are compared by cross-validation evaluation of real data. RESULTS: The data-based cross-validation comparison shows that Cox linear regression modeling is somewhat better than recursive partitioning when there are only continuous predictors, while recursive partitioning is better when there are significant categorical predictors. The proposed local Cox linear recursive partitioning has better predictive accuracy than Cox linear modeling and simple recursive partitioning. CONCLUSIONS: This study indicates that integrating local linear modeling into recursive partitioning can significantly improve prediction accuracy in constructing scoring and staging systems.

Humans↗
PubMed2000

Graphical approaches to support the analysis of linear-multilevel models of lamb pre-weaning growth in Kolda (Senegal).

Linear-multilevel models (LMM) are mixed-effects models in which several levels of grouping may be specified (village, herd, animal, ellipsis). This study highlighted the usefulness of graphical methods in their analysis through: (1) the choice of the fixed and random effects and their structure, (2) the assessment of goodness-of-fit and (3) distributional assumptions for random effects and residuals. An LMM was developed to study the effect of ewe deworming with morantel on lamb pre-weaning growth in a field experiment involving 182 lambs in 45 herds and 10 villages in Kolda, Senegal. Growth was described as a quadratic polynomial of age. Other covariates were sex, litter-size and treatment. The choice of fixed and random effects relied on three graphs: (1) a trellis display of mean live-weight vs. age, to select main effects and interactions (fixed effects); (2) a trellis display of individual growth curves, to decide which growth-curve terms should be included as random effects and (3) a scatter plot of parameters of lamb-specific regressions (live-weight vs. quadratic polynomial of age) to choose the random-effects covariance structure.Age, litter-size, agexlitter-size, litter-sizextreatment and agexlitter-sizextreatment were selected graphically as fixed effects and were significant (p<0.05) in subsequent statistical models. The selection of random-effect structures was guided by graphical assessment and comparison of the Akaike's information criterion for different models. The final random-effects selected included no random effect at the village level but intercept, age and squared-age at the herd and lamb levels. The structure of the random-effects variance-covariance matrices were blocked-diagonal at the herd level and unstructured at the lamb level. An order-1 autoregressive structure was retained to account for serial correlations of residuals. Smaller residual variance at 90 days than at younger ages was modeled with a dummy variable taking a value of 1 at 90 days and 0 elsewhere.Ewe-deworming with morantel during the rainy season lead to higher lamb live-weights (probably related to a better ewe-nutrition and -health status). A positive correlation was demonstrated between early weight and growth rate at the population level (with important lamb and herd-level random deviations). The persistence of this correlation at older ages should be checked to determine whether early weights are good predictors of mature weights and ewe-reproductive lifetime performance.

Animal Husbandry↗