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PubMed1995

Spatial interaction between neighbouring counties: cancer mortality data in Valencia Spain.

The statistical analysis of geographical mortality data has usually been approached via regression models that include appropriate covariates. These models assume stochastic independence of mortality counts for neighbouring sites, a questionable assumption that spatial automodels (Besag, 1974, Journal of the Royal Statistical Society, Series B 36, 192-236) make unnecessary. This paper presents the use of the autopoisson distribution in order to detect spatial interaction between neighbouring sites. If this interaction results in being nonsignificant, the auto-Poisson distribution reduces to a usual Poisson regression model, a particular case of generalized linear models (McCullagh and Nelder, 1989, Generalized Linear Models, 2nd edition. London: Chapman and Hall) which can be analyzed with the GLIM package.

Colonic Neoplasms↗

PubMed2005

Comparison of different mathematical models to analyze diminution kinetics of ultrasound contrast enhancement in a flow phantom.

Ultrasound (US) energy leads to intensity- and frequency-dependent destruction of US contrast agent (UCA) microbubbles. When applying repeated US pulses, this phenomenon can be detected as contrast diminution over time. Contrast diminution kinetics depend on the replenishment of UCA into the sample volume. Thus, it is related to organ perfusion. To analyze the contrast diminution kinetics following pulsed harmonic US application (SONOS 5500, 1.8-3.6 MHz, MI: 1.6, frame rates: 2, 4, and 6.67 Hz), we performed an in vitro study using SonoVue continuous infusion. Seven flow rates (4.5, 9, 13.5, 18, 22.5, 27 and 36 mL/min) were tested. Based on our results, three mathematical models (linear intensity decrease, exponential decay, and an exponential destruction/reperfusion model) describing diminution kinetics were compared. In 113 (89.7%) of 126 trials, a signal decrease was observed after US application. At higher flow rates (18 to 36 mL/min), curve fitting was not possible for the exponential models. For the linear model, intensity decrease depended significantly on the flow rate (p < or = 0.005, n = 7). A logistic model was fitted to the data, defining the slope in the dynamic range of quasilinear dependence for the different frame rates, as well as the inflection point: The higher the frame rate, the higher the flow rate at the point of inflection. For the exponential model, the contrast half-life was dependent on the flow rate (r = 0.95, p = 0.03, n = 6) only at the highest frame rate (6.67 Hz). The perfusion coefficient derived from the destruction/reperfusion model was not significantly related to the flow rate. In conclusion, the linear intensity decrease correlates well with the flow rate (i.e., flow velocity) and defines optimum frame rates for diminution imaging at different flow velocities. The exponential models, which required curve-fitting procedures, were determined to be inappropriate to describe flow in our phantom.

Contrast Media↗

PubMed2000

Use of linear mixed models to detect irregular fetal growth.

Ultrasonographic fetal biometry data can be used to estimate fetal weights repeatedly over time. Different types of reference bands have been presented to judge such data. But relevant aspects of an individual growth curve are not taken in to account. How can individual growth curves be used efficiently to detect irregular fetal growth? Linear mixed model analysis of a sample of 167 uncomplicated pregnancies with 304 ultrasonic measurements revealed that a random intercept model is sufficient and heterogeneity in slopes is negligible. Hence irregularity of a sequence of weights can be captured by three quantities' residual level, trend and mean squared error' for which reference ranges are derived from the fitted model. After standardization they are independently normal and chi-square distributed in the reference population. Regularity of fetal growth may then be reported in terms of level and trend either in the form of Z-scores or as percentile indices. A sample of 97 pregnancies diagnosed as cases of chronic placental insufficiency postnatally is analysed to validate the ability to detected abnormal growth. Only the mean level and slope revealed to be able to detect IUGR. MSE was not discriminative. The sensitivity of the method depends on the number and placement of observation times, which opens the possibility of a model-based cost-effectiveness analysis. The derived scores make efficient use of available information and are easily implementable into any computer based monitoring device.

Decision Making, Computer-Assisted↗

PubMed2002

Combining fMRI with a pharmacokinetic model to determine which brain areas activated by painful stimulation are specifically modulated by remifentanil.

We present a method for investigating the dynamic pharmacological modulation of pain-related brain activity, measured by BOLD-contrast fMRI. Noxious thermal stimulation was combined with a single infusion and washout of remifentanil, a short-acting opioid analgesic agent. The temporal profile of the effect site concentration of remifentanil, estimated from a pharmacokinetic model, was incorporated into a linear model of the fMRI data. The methodology was tested in nine healthy male subjects. During each imaging session the subjects received noxious thermal stimulation to the back of the left hand, prior to infusion, during infusion to a remifentanil effect site concentration of 1.0 ng/ml, and during washout of the remifentanil. Infusions were repeated with saline. Remifentanil-induced analgesia was confirmed from subjective pain intensity scores. Pain-related brain activity was identified in a matrix of regions using a linear model of the transient BOLD responses to noxious stimulation. Of those regions, there was a significant fractional reduction in the amplitude of the pain-related BOLD response in the insular cortex contralateral to the stimulus, the ipsilateral insular cortex, and the anterior cingulate cortex. Statistical parametric mapping of the component of pain-related BOLD responses that was linearly scaled by remifentanil concentration confirmed the contralateral insular cortex as the pain-processing region most significantly modulated by remifentanil compared to saline. The mapping of specific modulation of pain-related brain activity is directly relevant for understanding pharmacological analgesia. The method of examining time-dependent pharmacological modulation of specific brain activity may be generalized to other drugs that modulate brain activity other than that associated with pain.

Analgesics, Opioid↗

PubMed1992

The analysis of a multiple-dose, combination-drug clinical trial using response surface methodology.

We consider the situation where a multiple-dose, combination-drug clinical trial is conducted to identify one or more combinations that satisfy regulatory requirements. Generally, these requirements involve a compound hypothesis with multiple comparisons. The min test has been shown to be an optimal alpha-level test for testing a single combination drug. Analysis procedures in a multiple-dose, combination-drug study have typically involved classical ANOVA models or multiple regression models in a response surface methodology (RSM) framework. An inferential procedure based on an ANOVA model uses a screening test to address multiple comparison issues and multiple min tests to explicitly identify combinations satisfying regulatory requirements. An exploratory procedure based on RSM modeling is used to build a segmented linear model and a stairstep linear model to describe dose-response relationships. The two procedures are mutually supportive of one another in providing a broader assurance in the identification of effective combinations.

Analysis of Variance↗

PubMed1988

General treatment of mean residence time, clearance, and volume parameters in linear mammillary models with elimination from any compartment.

A general treatment for mean residence time, clearance, and volume parameters in linear mammillary models which includes the possibility of first-order elimination from compartments other than the central compartment is presented. The interrelationship between noncompartmentally derived parameters and compartmentally derived pharmacokinetic microconstants is described. The concept of exit site dependent and exit site independent parameters is introduced in the development of these treatments. Explications of mean residence time in terms of elimination rate, amount eliminated, and amount in the body are presented together with demonstrations of their utility.

Humans↗

PubMed2005

Judging the significance of multiple linear regression models.

It is common practice to calculate large numbers of molecular descriptors, apply variable selection procedures to reduce the numbers, and then construct multiple linear regression (MLR) models with biological activity. The significance of these models is judged using the usual statistical tests. Unfortunately, these tests are not appropriate under these circumstances since the MLR models suffer from "selection bias". Experiments with regression using random numbers have generated critical values (Fmax) with which to assess significance.

Antimycin A↗

PubMed2003

Formation, modeling and validation of trihalomethanes (THM) in Malaysian drinking water: a case study in the districts of Tampin, Negeri Sembilan and Sabak Bernam, Selangor, Malaysia.

A modeling procedure that predicts trihalomethane (THM) formation from field sampling at the treatment plant and along its distribution system using Tampin district, Negeri Sembilan and Sabak Bernam district, Selangor as sources of data were studied and developed. Using Pearson method of correlation, the organic matter measured as TOC showed a positive correlation with formation of THM (r=0.380,P=0.0001 for Tampin and r=0.478,P=0.0001 for Sabak Bernam). Similar positive correlation was also obtained for pH in both districts with Tampin (r=0.362,P=0.0010) and Sabak Bernam (r=0.215,P=0.0010). Chlorine dosage was also found to have low correlation with formation of THM for the two districts with Tampin (r=0.233,P=0.0230) and Sabak Bernam (r=0.505,P=0.0001). Distance from treatment plant was found to have correlation with formation of THM for Tampin district with r=0.353 and P=0.0010. Other parameters such as turbidity, ammonia, temperature and residue chlorine were found to have no correlation with formation of THM. Linear and non-linear models were developed for these two districts. The results obtained were validated using three different sets of field data obtained from own source and district of Seremban (Pantai and Sg. Terip), Negeri Sembilan. Validation results indicated that there was significant difference in the predictive and determined values of THM when two sets of data from districts of Seremban were used with an exception of field data of Sg. Terip for non-linear model developed for district of Tampin. It was found that a non-linear model is slightly better than linear model in terms of percentage prediction errors. The models developed were site specific and the predictive capabilities in the distribution systems vary with different environmental conditions.

Chlorine↗

PubMed1998

Evaluating the burst hypothesis at a site-specific level using the lack-of-fit test.

It has been hypothesized that periodontal disease progresses by means of sudden losses of periodontal attachment surface area. Obtaining reliable tests of this burst hypothesis has proven to be difficult; the signal (true model of disease progression) often gets lost in the noise. The purpose of this study was to determine how reliably we could distinguish sudden changes from linear disease progression at a site using a time series of clinical attachment levels. Specifically, the following question was investigated: If, in reality, disease progresses by means of sudden changes in clinical attachment level (bursts), and a linear model is fitted to these data, what is the likelihood of rejecting the linear model using the lack-of-fit test? This likelihood was determined as a function of the probing measurement error (range: 0.2 to 1.0 mm) and the number of clinical examinations over time. The results suggested that bursts of 2 mm or smaller cannot be reliably distinguished from linear disease progression using the lack-of-fit test, except under unusual clinical circumstances. Under typical clinical circumstances, burst sizes needed to be 3 to 5 mm in order to be reliably distinguished from linear disease progression. These results are probably overly optimistic. The ability to verify the burst hypothesis at the site level is likely to be even less than our results indicate because of various assumptions that were required. We conclude that the lack-of-fit test will reliably reject the linear model at a site-specific level only if true disease progresses in such a fashion that a handful of sudden changes leads to a tooth mortality event.

Algorithms↗

PubMed2001

Interviewers' and respondents' effects on self-reported alcohol consumption in a Swiss health survey.

OBJECTIVE: Characteristics of interviewers and respondents have been shown to influence the quality of data from survey research in various domains. There is little evidence for such effects in alcohol research, however. The purpose of the study reported here was to examine effects of gender and age of interviewers and respondents simultaneously This was done using hierarchical linear modeling, the advantage of which is that it can account for the clustering effects of respondents being nested within interviewers. METHOD: Data were obtained from the first wave of an ongoing randomized longitudinal study on changes in alcohol consumption in Switzerland. The response rate was 77.9%. Analyses were based on 2,746 (1,749 male) subjects with an average of at least monthly consumption in the 6 months before the telephone interview. Consumption was assessed by means of a graduated frequency measure. Five different hierarchical linear models of increasing complexity were used to test several hypotheses of interviewer and respondent effects. Findings from hierarchical linear modeling were compared with those from "classical" analysis of variance. RESULTS: A theoretical design effect of 1.89 attributable to interviewers was found. Both analyses of variance and hierarchical linear modeling provide support for a structure with a main effect for gender of respondents, as well as a main effect for age of respondents and an interaction effect between interviewers' and respondents' ages. CONCLUSIONS: Interviewer effects affect the estimation of statistics in survey research and must be adjusted for either by means of multilevel analysis or by the use of specialized sample survey software.

Adolescent↗

PubMed2001

Statistical measures of foetal growth using linear mixed models applied to the foetal origins hypothesis.

Statistical models of the relationship between the distribution of each of five foetal dimensions and gestational age are developed based on serial ultrasound biometric data from a prospective longitudinal study in Perth, Western Australia. Both the response variable and the gestational age timescale are transformed to establish an approximately linear relationship within subjects. This relationship is modelled using a linear mixed effects model that accounts for between-subject heterogeneity by incorporating subject specific random effects for both intercept and gradient. These models are used to motivate three measures of foetal growth: the conditional centile or z-score of a current measurement given an earlier value for the same measurement; the best linear unbiased predictor (BLUP) of the subject specific random effect gradient (which is shown to be invariant to transformations of location and scale), and the standardized residual at a given gestational age, which characterizes departures from the modelled growth trajectory. We illustrate how these three measures of growth might be applied to subsequent health outcomes in later life by relating growth in foetal abdominal circumference to blood pressure in children from the same cohort at six years of age. Foetuses whose summary measures indicate poor growth in abdominal circumference have higher blood pressure in early childhood, supporting the 'foetal origins' hypothesis that many chronic diseases of adulthood have their origins before birth.

Anthropometry↗

PubMed2005

Marginal regression of multivariate event times based on linear transformation models.

Multivariate event time data are common in medical studies and have received much attention recently. In such data, each study subject may potentially experience several types of events or recurrences of the same type of event, or event times may be clustered. Marginal distributions are specified for the multivariate event times in multiple events and clustered events data, and for the gap times in recurrent events data, using the semiparametric linear transformation models while leaving the dependence structures for related events unspecified. We propose several estimating equations for simultaneous estimation of the regression parameters and the transformation function. It is shown that the resulting regression estimators are asymptotically normal, with variance-covariance matrix that has a closed form and can be consistently estimated by the usual plug-in method. Simulation studies show that the proposed approach is appropriate for practical use. An application to the well-known bladder cancer tumor recurrences data is also given to illustrate the methodology.

Biomedical Research↗

PubMed1995

General linear compartment model with zero input: III. First passage residence time of enzyme systems.

In this paper, we present an alternative procedure to derive the residence times of enzyme and compartment systems. This procedure allows to express the residence time by a general, symbolic and simplified formula relating it directly with the rate constants. It is applicable to any enzyme reaction scheme which can be formulated as a set of first-order or pseudo-first order interconversions, without any other restriction. A computer program has been developed that greatly facilitates the task of the residence time derivations. The above analysis was extrapolated to any linear compartment model.

Computer Simulation↗

PubMed1994

Social and environmental factors and life expectancy, infant mortality, and maternal mortality rates: results of a cross-national comparison.

Using data from United Nations sources we conducted an international comparison study of infant and maternal mortality rates and life expectancy at birth. We examined these three dependent variables in relation to a range of independent variables including dietary factors, medical resource availability, gross national product (GNP/capita), literacy rates, growth in the labor force, and provision of sanitation facilities and safe water. Based on exploratory stepwise regression models, we fitted a series of general linear models for each of the three dependent variables. For the models with the highest explanatory ability, the percent of households without sanitation facilities showed the strongest association with all three dependent variables: life expectancy at birth (R2 = 0.83, B = -0.088, P = 0.0007); infant mortality rate (R2 = 0.87, B = +0.611, P < 0.0001); and maternal mortality rate (R2 = 0.54, B = +8.297, P = 0.002). Additional significant predictors of life expectancy at birth and infant mortality rate included the quantity of animal products consumed, the percent of households without safe water, excess calories consumed as fat, and the total literacy level. Maternal mortality rate was significantly associated with total energy consumption and excess energy consumed as fat. Using residuals from the general linear models we chose three outlying countries: Costa Rica, Sri Lanka and Egypt, on which to do case studies. These country case studies are discussed briefly in regard to characteristics that could account for their differing statistical relationships.

Adult↗

PubMed1986

The application of the linear-quadratic model to fractionated radiotherapy when there is incomplete normal tissue recovery between fractions, and possible implications for treatments involving multiple fractions per day.

By extending a previously developed mathematical model based on the linear-quadratic dose-effect relationship, it is possible to examine the consequences of performing fractionated treatments for which there is insufficient time between fractions to allow complete damage repair. Equations are derived which give the relative effectiveness of such treatments in terms of tissue-repair constants (mu values) and alpha/beta ratios, and these are then applied to some examples of treatments involving multiple fractions per day. The interplay of the various mechanisms involved (including repopulation effects) and their possible influence on treatments involving closely spaced fractions are examined. If current indications of the differences in recovery rates between early- and late-reacting normal tissues are representative, then it is shown that such differences may limit the clinical potential of accelerated fractionation regimes, where several fractions per day are given in a relatively short overall time.

Cell Survival↗

PubMed2004

Estimation of standard liver volume for liver transplantation in the Korean population.

The standard liver volume (LV) of a recipient is estimated in liver transplantation to determine the minimum LV necessary for the recipient. Simple linear formulas of LV estimation were developed for the Japanese and Caucasian populations. The present study examined the applicability of the reported formulas to the Korean population. Liver density (LD) was determined by analyzing 24 healthy livers. Data of liver weight (LW), body weight (BW), body height (BH), body surface area (BSA), and age were obtained from 652 postmortem examination reports (age, 42.4 +/- 16.5 years) showing normal livers. The LV of each subject was estimated by LW / LD and the relationships between LV, BW, BSA, and age were analyzed. LD was 1.04 +/- 0.07 kg/L. LV / BW decreased as age increased in the children but leveled off in the adults; the rate of increase in LV along with BSA in individuals with BSA <1.2 m(2) appeared less than the corresponding rate in individuals with BSA >/=1.2 m(2). The Japanese formula produced underestimates for the Korean population (226.9 +/- 289.4 mL), while the Caucasian formula produced random errors (-30.64 +/- 281.5 mL). A better LV estimation formula was established: LV (mL) = 21.585 x BW (kg)(0.732) x BH (cm)(0.225) (adjusted R(2) = 0.59; SE = 275.8 mL). In conclusion, this study indicates that a nonlinear or piecewise linear model is more desirable than a simple linear model for LV estimation in children and adults, because LV / BW and LV / BSA are not constant with age and BSA.

Adolescent↗

PubMed2001

Use of generalized linear mixed models in the spatial analysis of small-area malaria incidence rates in Kwazulu Natal, South Africa.

Spatial statistical analysis of 1994-1995 small-area malaria incidence rates in the population of the northernmost districts of KwaZulu Natal, South Africa, was undertaken to identify factors that might explain very strong heterogeneity in the rates. In this paper, the authors describe a method of adjusting the regression analysis results for strong spatial correlation in the rates by using generalized linear mixed models and variograms. The results of the spatially adjusted, multiple regression analysis showed that malaria incidence was significantly positively associated with higher winter rainfall and a higher average maximum temperature and was significantly negatively associated with increasing distance from water bodies. The statistical model was used to produce a map of predicted malaria incidence in the area, taking into account local variation from the model prediction if this variation was supported by the data. The predictor variables showed that even small differences in climate can have very marked effects on the intensity of malaria transmission, even in areas subject to malaria control for many years. The results of this study have important implications for malaria control programs in the area.

Climate↗

PubMed2003

The linear interaction model of personality effects in health communication.

The recent growth of research in message tailoring has opened up new avenues for researchers to use personality variables for message delivery. This article builds on research on idiocentrism and self-monitoring to propose a framework for message appeal construction. Based on a scheme for appeal categorization borrowed from commercial marketing, the article suggests that low and high idiocentrics differ from each other in the way they respond to appeal types. Similarly, significant differences are demonstrated between low and high self-monitors in the realm of their response to message appeals. A linear interaction model is proposed to document the combined effects of self-monitoring and idiocentrism.

Acquired Immunodeficiency Syndrome↗