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PubMed1998

Intersection accident estimation: the role of intersection location and non-collision flows.

This paper reviews models used in practice to relate accidents to traffic flows, with particular emphasis on the appropriateness of the model form and the statistical analysis technique employed for parameter estimation. The development of generalised linear models for predicting individual accident types at intersections in New Zealand is then described. The use of covariate analysis to identify the effect of intersection location, an investigation of the effect of non-collision flows, and the use of the models for predicting intersection accidents in three networks, are also described. It is concluded that generalised linear models for estimating different accident types (based on the conflicting flows) are better than models for estimating total accidents (based on the approach flows), especially when the cost of different accident types is known. It is also found that intersection location affects the number of different accident types, that it is important to consider the interactions between turning flows (to take better account of the mechanisms of accident occurrence), and that non-collision flows are sometimes important. Comparison of the predicted and observed numbers of accidents has shown that there is poor agreement for individual intersections, but fairly good agreement for networks.

Accidents, Traffic↗

PubMed1993

Multiphasic allometry.

A multiphasic linear model is presented that describes the allometric relation between body components and permits a smooth transition from one linear segment to the next. Three applications of a diphasic linear model to allometric growth problems were used to illustrate the model. The data sets were selected because a breakpoint exists in the allometric relation. Relations between growth of the alimentary tract and of empty body weight in rabbits, growth of length and of body weight in larval-carp and growth of protein and of fat in pullets were described by a diphasic allometric model. For rabbits and larval-carp, relations were described significantly better by a diphasic instead of a monophasic (simple) allometric model. For situations where response is expected to consist of more than one linear segment, the multiphasic model is recommended.

Animals↗

PubMed2002

ADME evaluation in drug discovery. 1. Applications of genetic algorithms to the prediction of blood-brain partitioning of a large set of drugs.

In this study, the relationships between the brain-blood concentration ratio of 96 structurally diverse compounds with a large number of structurally derived descriptors were investigated. The linear models were based on molecular descriptors that can be calculated for any compound simply from a knowledge of its molecular structure. The linear correlation coefficients of the models were optimized by genetic algorithms (GAs), and the descriptors used in the linear models were automatically selected from 27 structurally derived descriptors. The GA optimizations resulted in a group of linear models with three or four molecular descriptors with good statistical significance. The change of descriptor use as the evolution proceeds demonstrates that the octane/water partition coefficient and the partial negative solvent-accessible surface area multiplied by the negative charge are crucial to brain-blood barrier permeability. Moreover, we found that the predictions using multiple QSPR models from GA optimization gave quite good results in spite of the diversity of structures, which was better than the predictions using the best single model. The predictions for the two external sets with 37 diverse compounds using multiple QSPR models indicate that the best linear models with four descriptors are sufficiently effective for predictive use. Considering the ease of computation of the descriptors, the linear models may be used as general utilities to screen the blood-brain barrier partitioning of drugs in a high-throughput fashion.

Algorithms↗

PubMed1984

Physical activity and osteoporosis in post-menopausal women.

Osteoporosis is an accepted fact of the female's aging process. This decrease in bone mass is most often linked to a lack of estrogen; however, prolonged inactivity is also known to cause atrophy in both muscle and bone. The purpose of this study was to investigate the relationship between the degree of osteoporosis and the physical activity levels of a group of post-menopausal women. Forty women between the ages of 60-69 yr were selected at random from a group of volunteers. The possible existence of a correlation between cortical diameter and activity level was investigated by using linear-model analysis. The width of the cortex may be related to many factors in addition to activity level. Some of the more important factors also considered were height, weight, ponderal index, age, years since taking estrogen, and total metacarpal diameter. The inclusion of these terms in the linear-model analysis allowed for an accounting of variability as associated with variables that could not be held constant. The variables showing the most significant relationships with the cortical diameter were the activity level and the use of estrogen. The relationships investigated through the linear-model analysis do not need to be independent. It is possible that combinations of these variables act to retard or enhance osteoporosis. Therefore, because the primary concern of the investigators was the relationship between physical activity and osteoporosis, a t-test was performed comparing the 10 most active women with the 10 most sedentary.(ABSTRACT TRUNCATED AT 250 WORDS)

Age Factors↗

PubMed2006

Modelling predictions of cancer deaths in Northern Ireland.

BACKGROUND: An ageing population has service planners concerned about future levels of disease which are age dependent. Predictions of mortality for colorectal, lung and breast cancers, which account for 30% of cancer cases and 40% of cancers deaths, were calculated for 2010 and 2015, based on trends in death rates and the predicted change in the demography of the Northern Ireland population. METHODS: The U.S. National Cancer Institute's "Joinpoint" program was used to check for structural breaks in the time series of cancer death rates from 1984 to 2004. The prediction models applied to the data allowed variations in trends across age groups to be taken into account. A linear model was used for increasing or constant trends and a log linear model was used where the trend was decreasing. The models assume the number of deaths in each stratum, defined by age-sex and time-period, is Poisson distributed, with the average value determined by a log or linear function. RESULTS: Recent trends in rates of cancers studied were downwards except for female lung. Predictions include decreased colorectal cancer deaths in females and lung cancer deaths in males. In females, lung cancer deaths are predicted to more than double by the year 2015 (473 deaths), based on the 1984 level. Colorectal death rates in males are predicted to drop, but the number of deaths will increase by more than 10%, due to demographic change. Numbers of breast cancer deaths are likely to rise slightly, despite falling age standardised death rates, due to an ageing population. CONCLUSIONS: This work has provided estimates of early future trends, useful to service planners, and highlights the need for tobacco control, to reduce numbers of lung cancer deaths in females. The recently announced control of environmental tobacco legislation is one welcome development which should reduce lung cancer mortality in Northern Ireland.

Adolescent↗

PubMedDate not supplied

Variations in clinical estimates of tumor volume regression parameters and time factor during external radiotherapy in cancer cervix: does it mimic the linear-quadratic model of cell survival?

BACKGROUND: Tumor regression parameters and time factor during external radiotherapy (EXTRT) are of paramount importance. AIMS: To quantify the parameters of tumor regression and time factor during EXTRT in cancer cervix. SETTINGS AND DESIGN: Patients, treated solely with radiotherapy and enrolled for other prospective studies having weekly tumor regressions recorded were considered. MATERIALS AND METHODS: Seventy-seven patients received 50 Gy of EXTRT followed by intracavitary brachytherapy. Loco-regional regressions were assessed clinically and regression fraction (RF) was represented as RF=c + a 1D + a 2 D2 sub - a 3T, with c, D and T as constant, cumulative EXTRT dose and treatment time respectively. STATISTICAL ANALYSIS USED: Step wise linear regression was performed for RF. Scatter plots were fitted using linear-quadratic fit. RESULTS: Coefficients of parameters D, D2 sub and T were computed for various dose intervals, namely 0--20 Gy, 0--30 Gy, 0--40 Gy and 0--50 Gy. At 0--20 Gy and 0--30 Gy, only the coefficient of D2 was significant (P 2 sub and T turned significant (P 2 sub and T showed significance, leading to an estimate of 26 Gy for a1/a2 and 0.96 Gy/day for a3/a1. CONCLUSIONS: As with alpha/beta and gamma/alpha of post-irradiation cell survival curves, a1/a2 and a3/a1 represents the cumulative effect of various radiobiological factors influencing clinical regression of tumor during the course of EXTRT. The dynamic changes in the coefficients of D, D2 sub and T, indicate their relative importance during various phases of EXTRT.

Adenocarcinoma↗

PubMed2000

Analysis of genotype frequencies and interlocus association for the PM, DQA1, and D1S80 loci in four populations.

Allele frequencies of the LDLR, HBGG, GYPA, D7S8, GC, DQA1, and D1S80 loci are presented and genotypes are analyzed for each of four ethnic groups: African Americans (n = 200), US Caucasians (n = 200), US Hispanics (n = 200), and Japanese (n = 89). Hardy-Weinberg genotypic proportions were observed in all but two of the 28 population-locus tests undertaken. Those two instances are attributable to type I statistical error. Gametic equilibrium among loci is an assumption invoked for application of the product rule to utilize the discriminatory power from two or more loci simultaneously. Two statistical methods, a genotype matching statistic and log-linear modeling, were used to evaluate gametic disequilibrium. The match statistic, comparing observed to expected likelihood of genotypic identity for seven loci among pairs of individuals within the database, revealed only one statistically significant deviation among 20 tests. As expected, the probability of match was generally lowest in the test on all ethnic groups combined, indicating that allele frequencies differ among ethnic groups for some of the loci. This was confirmed with the statistic theta to measure ethnic stratification, in which about 0.10 of the genetic variation is apportioned among the four ethnic groups for four of the structural loci (LDLR, HBGG, GC, and DQA1), while for GYPA, D7S8, and D1S80, variation is more uniformly distributed among ethnic groups. Log-linear modeling was also applied to the five PM loci. The most parsimonious log-linear model included only three higher order terms: the two-way interactions of three of the PM loci with ethnic group. These three instances (LDLR, HBGG, and GC) indicated differences in allele frequencies between ethnic groups. No two or higher way interaction (disequilibrium) was observed among loci. In summary, the assumptions of Hardy-Weinberg and gametic equilibrium that facilitate the use of the five PM loci, DQA1 and D1S80 in forensic applications are consistent with the allele and genotype frequencies observed in these populations.

Asian People↗

PubMed2005

An investigation of the relationship between air emissions of volatile organic compounds and the incidence of cancer in Indiana counties.

Cancer is a health endpoint influenced by a multitude of factors, including genetic history, individual behavior, and environmental insults. The ubiquity of toxicants in the environment has raised questions about the extent of their role in causing cancer in humans. More specifically, it is desirable to understand the cancer incidence due to airborne toxicants in anthropogenic pollution. One particular class of such pollutants is volatile organic compounds (VOCs). This paper reports an epidemiological investigation of the incidence of cancer in the 92 counties of Indiana. We evaluated the relationship between the amount of VOCs released in each county, as reported by the Toxic Release Inventory, and the county-by-county incidence of various types of cancer, especially those of less common organ systems not directly associated with the absorption or distribution of toxicants. Our evaluation considered chlorinated versus nonchlorinated emissions as well as stack versus fugitive emissions. We evaluated three models: linear, quadratic, and polynomial. Of these, the quadratic model appeared to be the best predictor (highest r2) for most endpoints for which there was a positive correlation. However, the linear model was the most sensitive (lowest P-value) for skin, melanoma, and endocrine-related cancers, including female genital system cancers. Our results indicate a relationship between emissions of VOCs and the incidence of some types of cancers. Most notable were strong correlations between VOC emissions and cancers of the brain, nervous system, endocrine system, and skin.

Air Pollutants↗

PubMed2004

Regression models for relative survival.

Four approaches to estimating a regression model for relative survival using the method of maximum likelihood are described and compared. The underlying model is an additive hazards model where the total hazard is written as the sum of the known baseline hazard and the excess hazard associated with a diagnosis of cancer. The excess hazards are assumed to be constant within pre-specified bands of follow-up. The likelihood can be maximized directly or in the framework of generalized linear models. Minor differences exist due to, for example, the way the data are presented (individual, aggregated or grouped), and in some assumptions (e.g. distributional assumptions). The four approaches are applied to two real data sets and produce very similar estimates even when the assumption of proportional excess hazards is violated. The choice of approach to use in practice can, therefore, be guided by ease of use and availability of software. We recommend using a generalized linear model with a Poisson error structure based on collapsed data using exact survival times. The model can be estimated in any software package that estimates GLMs with user-defined link functions (including SAS, Stata, S-plus, and R) and utilizes the theory of generalized linear models for assessing goodness-of-fit and studying regression diagnostics.

Adolescent↗

PubMed2006

Eigengene-based linear discriminant model for tumor classification using gene expression microarray data.

MOTIVATION: The nearest shrunken centroids classifier has become a popular algorithm in tumor classification problems using gene expression microarray data. Feature selection is an embedded part of the method to select top-ranking genes based on a univariate distance statistic calculated for each gene individually. The univariate statistics summarize gene expression profiles outside of the gene co-regulation network context, leading to redundant information being included in the selection procedure. RESULTS: We propose an Eigengene-based Linear Discriminant Analysis (ELDA) to address gene selection in a multivariate framework. The algorithm uses a modified rotated Spectral Decomposition (SpD) technique to select 'hub' genes that associate with the most important eigenvectors. Using three benchmark cancer microarray datasets, we show that ELDA selects the most characteristic genes, leading to substantially smaller classifiers than the univariate feature selection based analogues. The resulting de-correlated expression profiles make the gene-wise independence assumption more realistic and applicable for the shrunken centroids classifier and other diagonal linear discriminant type of models. Our algorithm further incorporates a misclassification cost matrix, allowing differential penalization of one type of error over another. In the breast cancer data, we show false negative prognosis can be controlled via a cost-adjusted discriminant function. AVAILABILITY: R code for the ELDA algorithm is available from author upon request.

Artificial Intelligence↗

PubMed1993

Modeling simple-cell direction selectivity with normalized, half-squared, linear operators.

1. A longstanding view of simple cells is that they sum their inputs linearly. However, the linear model falls short of a complete account of simple-cell direction selectivity. We have developed a nonlinear model of simple-cell responses (hereafter referred to as the normalization model) to explain a larger body of physiological data. 2. The normalization model consists of an underlying linear stage along with two additional nonlinear stages. The first is a half-squaring nonlinearity; half-squaring is half-wave rectification followed by squaring. The second is a divisive normalization non-linearity in which each model cell is suppressed by the pooled activity of a large number of cells. 3. By comparing responses with counterphase (flickering) gratings and drifting gratings, researchers have demonstrated that there is a nonlinear contribution to simple-cell responses. Specifically they found 1) that the linear prediction from counterphase grating responses underestimates a direction index computed from drifting grating responses, 2) that the linear prediction correctly estimates responses to gratings drifting in the preferred direction, and 3) that the linear prediction overestimates responses to gratings drifting in the nonpreferred direction. 4. We have simulated model cell responses and derived mathematical expressions to demonstrate that the normalization model accounts for this empirical data. Specifically the model behaves as follows. 1) The linear prediction from counterphase data underestimates the direction index computed from drifting grating responses. 2) The linear prediction from counterphase data overestimates the response to gratings drifting in the nonpreferred direction. The discrepancy between the linear prediction and the actual response is greater when using higher contrast stimuli. 3) For an appropriate choice of contrast, the linear prediction from counterphase data correctly estimates the response to gratings drifting in the preferred direction. For higher contrasts the linear prediction overestimates the actual response, and for lower contrasts the linear prediction underestimates the actual response. 5. In addition, the normalization model is qualitatively consistent with data on the dynamics of simple-cell responses. Tolhurst et al. found that simple cells respond with an initial transient burst of activity when a stimulus first appears. The normalization model behaves similarly; it takes some time after a stimulus first appears before the model cells are fully normalized. We derived the dynamics of the model and found that the transient burst of activity in model cells depends in a particular way on stimulus contrast. The burst is short for high-contrast stimuli and longer for low-contrast stimuli.(ABSTRACT TRUNCATED AT 400 WORDS)

Animals↗

PubMed2004

Linearized kinetic model of Listeria monocytogenes biofilm growth.

In this study the dynamics of biofilm formation on aluminum has been investigated. The process of cell growth has been observed using fluorescence microscopy. It has been confirmed that the process of biofilm formation can be represented as a sum of two separate processes: cell adhesion and colony proliferation. The derived set of equations describes kinetics of surface population growth and characteristic times for adsorption and combined growth processes, including characteristic time for the nutrient supply depletion. All equations contain variables based on the fundamental characteristics of bacterial population and can be easily determined from the experimental data or estimated theoretically. The developed theoretical model allows obtaining realistic values for population growth time and characteristic time for nutrient limitation occurrence during the biofilm development. Resulting equations qualitatively describe the biofilm formation process, and allow predicting microbial kinetics in the batch reactor system and determining critical values of the process parameters.

Aluminum↗

PubMed2001

A comparison of generalized linear mixed model procedures with estimating equations for variance and covariance parameter estimation in longitudinal studies and group randomized trials.

Response data in longitudinal studies and group randomized trials are gathered on units that belong to clusters, within which data are usually positively correlated. Therefore, estimates and confidence intervals for intraclass correlation or variance components are helpful when designing a longitudinal study or group randomized trial. Data simulated from both study designs are used to investigate the estimation of variance and covariance parameters from the following procedures: for continuous outcomes, restricted maximum likelihood (REML) and estimating equations (EE); for binary outcomes, restricted pseudo-likelihood (REPL) and estimating equations (EE). We evaluate these procedures to see which provide valid and precise estimates as well as correct standard errors for the intraclass correlation coefficient or variance components. REML seems the better choice for estimating terms related to correlation for models with normal outcomes, especially in group randomized trial situations. Results for REML and EE are mixed when outcomes are continuous and non-normal. With binary outcomes neither REPL nor EE provides satisfactory estimation or inference in longitudinal study situations, while REPL is preferable for group randomized trials.

Cluster Analysis↗

PubMed1993

The methodology of studying decline in Alzheimer's disease.

OBJECTIVE: To present a new model for analyzing longitudinal data. The trilinear model is superior to the commonly used linear model that includes the flawed assumption that decline is uniform throughout the course of disease--an assumption that does not correspond to clinical observations. DESIGN: A longitudinal cohort sample was used to compare the linear and trilinear models. Simulated longitudinal data were generated to assess classification errors with the trilinear model. SUBJECTS AND SETTING: The subjects were 80 patients with Alzheimer's disease tested in a hospital out-patient clinic. METHODS: The trilinear model describes Alzheimer's disease as proceeding through three periods: An initial period of stability before detectable decline, a period of decline, and a final period of stability during which there is no further detectable decline. A program for the Apple Macintosh computer is available at no charge to apply the model to data. FINDINGS: The analyses indicated that the trilinear model provides a better reflection of decline in Alzheimer's disease than does the linear model. This advantage is present whether the periods of stability reflect a "true" lack of decline or insensitivity of a measurement instrument. CONCLUSIONS: The trilinear model provides not only a more accurate estimate of the average rate of change, but also (when possible) estimates of the point at which decline begins and ends. Also, more detailed comparisons of tests could be made by using the trilinear parameters. The trilinear model would benefit researchers engaged in longitudinal research of progressive disorders.

Aged↗

PubMedDate not supplied

Revising regulatory networks: from expression data to linear causal models.

Discovering the complex regulatory networks that govern mRNA expression is an important but difficult problem. Many current approaches use only expression data from microarrays to infer the likely network structure. However, this ignores much existing knowledge because for a given organism and system under study, a biologist may already have a partial model of gene regulation. We propose a method for revising and improving these initial models, which may be incomplete or partially incorrect, with expression data. We demonstrate our approach by revising a model of photosynthesis regulation proposed by a biologist for Cyanobacteria. Applied to wild type expression data, our system suggested several modifications consistent with biological knowledge. Applied to a mutant strain, our system correctly modified the disabled gene. Power experiments with synthetic data that indicate that reliable revision is feasible even with a small number of samples.

Gene Expression Profiling↗

PubMed1999

Simple linear QSAR models based on quantum similarity measures.

A novel QSAR approach based on quantum similarity measures was developed and tested in this paper. This approach consists of replacing the usual physicochemical parameters employed in QSAR analysis, such as octanol-water partition coefficient or Hammett sigma constant, by appropriate quantum chemical descriptors. The methodological basis for this substitution is found in recent theoretical studies [J. Comput. Chem. 1998, 19, 1575-1583, J. Comput. -Aided Mol. Des. 1999, 13, 259-270], in which it was demonstrated that both molecular hydrophobic character and electronic substituent effect can be modeled by appropriately chosen quantum self-similarity measures (QS-SM). The most important aim of this study was to prove that selected QS-SM descriptors can be advantageously used in empirical QSAR analysis instead of classical descriptors. For this purpose several QSAR correlations are proposed, in which empirical descriptors such as Hammett sigma constants or log P values are replaced by the appropriate QS-SM. These examples involve: (i) a set of benzenesulfonamides which bind to human carbonic anhydrase, (ii) a set of benzylamines as competitive inhibitors of the enzyme trypsin, and (iii) a set of indole derivatives which are benzodiazepine receptor inverse agonist site ligands. Simple linear QSAR models were developed in order to obtain mathematical relationships between the biological activity and the pertinent quantum chemical descriptors. The validity of the obtained QSAR models is supported by comparison of the observed and predicted values of the biological activity and by a statistical analysis based on a randomization test.

Benzylamines↗

PubMed2004

A generalized linear mixed models approach for detecting incident clusters of disease in small areas, with an application to biological terrorism.

Since the intentional dissemination of anthrax through the US postal system in the fall of 2001, there has been increased interest in surveillance for detection of biological terrorism. More generally, this could be described as the detection of incident disease clusters. In addition, the advent of affordable and quick geocoding allows for surveillance on a finer spatial scale than has been possible in the past. Surveillance for incident clusters of disease in both time and space is a relatively undeveloped arena of statistical methodology. Surveillance for bioterrorism detection, in particular, raises unique issues with methodological relevance. For example, the bioterrorism agents of greatest concern cause initial symptoms that may be difficult to distinguish from those of naturally occurring disease. In this paper, the authors propose a general approach to evaluating whether observed counts in relatively small areas are larger than would be expected on the basis of a history of naturally occurring disease. They implement the approach using generalized linear mixed models. The approach is illustrated using data on health-care visits (1996-1999) from a large Massachusetts managed care organization/multispecialty practice group in the context of syndromic surveillance for anthrax. The authors argue that there is great value in using the geographic data.

Bioterrorism↗

PubMed1999

Generalised linear mixed models analysis of risk factors for contamination of Danish broiler flocks with Salmonella typhimurium.

We present a retrospective observational study of risk factors associated with the occurrence of Salmonella typhimurium (ST) in Danish broiler flocks. The study is based on recordings from 1994 in the ante-mortem database maintained by the Danish Poultry Council. The epidemiological units are the broiler flocks (about 4000 flocks) which are clustered within producers. Broiler flocks with ST-infected parent stocks show increased risk of salmonella infection, and also the hatchery affects the salmonella status significantly. Among the rearing factors, only the use of medicine as well as the time of rearing, and the sampling method are significant. Epidemiological control would seem most efficient on starting at the top levels of the production hierarchy from which a major part of the ST contamination is derived. A secondary purpose of the study is to evaluate different statistical approaches and software for the analysis of a moderately-sized data set of veterinary origin. We compare the results from five analyses of the generalised linear mixed model (GLMM) type. The first observation is that the results agree reasonably well and lead to similar conclusions. A closer look reveals certain patterns of bias and estimation accuracy that correspond well with theoretical findings and practical experience reported in the statistical literature.

Animal Husbandry↗