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PubMed2000

Linear regression models of methyl mercury exposure during prenatal and early postnatal life among riverside people along the upper Madeira river, Amazon.

This research is focused on prenatal and early postnatal mercury (Hg) exposure among the riverside people along the Upper Madeira river in the Amazon. Linear regression models were developed to predict the hair Hg concentration in infants. The independent variables included in the model of Group 1 (87 pairs of mothers and their infants) were the average maternal hair Hg concentration and maternal age. Group 2 (31 pairs) included maternal segmental hair Hg concentrations. For the segmental hair Hg analysis over time, it was assumed that hair grows at a rate of 11 cm per month. Thus, information on the timing of the dates of pregnancy and breast feeding from the birth history was used to cut the hair strands into segments, making them correspond to the mother's reproductive stage of life (31 pairs of mothers and their infants). Breast milk Hg concentration results were included with segmental and average maternal hair Hg concentration values (22 and 44 pairs of mothers and their infants, respectively). The models including the breast milk Hg concentration indicated that 61 and 55% of the variability of the infant hair Hg concentrations were due to the independent variables: segmental maternal hair Hg with breast milk Hg and average maternal hair Hg with breast milk Hg, respectively. The regression coefficients were in the range of 0.19 to 0.90, and P values were in the range of 0.0001 to 0.1490. Further recommendations include fish advisories to prevent critical Hg exposures during reproductive life and investigation of neurobehavioral performance of this study population.

Adult↗
PubMed1993

Influences upon attendance at out-patient facilities--the contribution of linear-logistic modelling.

The research on attendance at out-patient psychiatric facilities has produced conflicting evidence that provides little guidance for the practitioner. It is suggested that inadequate data exploration could explain some of the discrepant findings. Analyses of multi-way tables using linear-logistic models were undertaken to demonstrate patterns of association that cannot be revealed through the use of simple chi-square tests on two-way contingency tables. The variables chosen for these analyses were those that have produced conflicting findings in the literature on children's attendance at child guidance facilities.

Adolescent↗
PubMed2000

Is modelling dental caries a 'normal' thing to do?

OBJECTIVE: To introduce and encourage the use of generalised linear models (GLMs) in analysing caries data that do not require the response to be treated necessarily as a sample from a normal distribution. BASIC RESEARCH DESIGN: At the present time, it is most likely that the sampling distribution of dmf/DMF in industrialised countries will not approximate normality. Generalised linear modelling can be conducted assuming many underlying distributions which, in fact, includes the normal distribution. In this paper three GLMs are employed (normal, Poisson, negative binomial) for modelling an example caries data set. In addition, a binomial model is used to model the dichotomous outcome of caries-free/caries-present. CLINICAL SETTING: The data comprised 871 Old Trafford, Manchester primary school children aged between 4 years 0 months and 5 years 11 months. RESULTS: The effect of one study covariate was prominent in a normal model applied to all available dmf data but not in two non-normal models which used dmf > 0 data only. Furthermore, the same covariate was significant at the 5% level in a binomial model indicating that it influenced whether or not caries was present and not the level of dmf. CONCLUSION: A suitable modelling approach for caries data is to employ a Poisson or a negative binomial model for the dmf/DMF response and a binomial model for the caries-free/caries-present outcome. This allows separate estimation of those factors which influence the magnitude of caries and those factors which influence whether caries is actually present or not.

Binomial Distribution↗
PubMed2006

Linear quadratic modeling of increased late normal-tissue effects in special clinical situations.

PURPOSE: To extend linear quadratic theory to allow changes in normal-tissue radiation tolerance after exposure to cytotoxic chemotherapy, after surgery, and in elderly patients. METHODS: Examples of these situations are analyzed by use of the biologic effective dose (BED) concept. Changes in tolerance can be allowed for by: estimation of either the contribution of the additional factor as an equivalent BED or the equivalent dose in 2-Gy fractions or by the degree of radiosensitization by a mean dose-modifying factor (x). RESULTS: The estimated x value is 1.063 (95% confidence limits for the mean, 1.056 to 1.070) for subcutaneous fibrosis after cyclophosphamide, methotrexate, and fluorouracil (CMF) chemotherapy and radiotherapy in breast cancer. The point estimate of x is 1.18 for the additional risk of gastrointestinal late-radiation effects after abdominal surgery in lymphoma patients (or 10.62 Gy at 2 Gy per fraction). For shoulder fibrosis in patients older than 60 years after breast and nodal irradiation, x is estimated to be 1.033 (95% confidence limits for the mean, 1.028 to 1.0385). The equivalent BED values were CMF chemotherapy (6.48 Gy3), surgery (17.73 Gy3), and age (3.61 Gy3). CONCLUSIONS: The LQ model can, in principle, be extended to quantify reduced normal-tissue tolerance in special clinical situations.

Aged↗
PubMed1990

Frequency of micronuclei in hepatocytes following X and fast-neutron irradiations--an analysis by a linear-quadratic model.

The usefulness of the micronucleus assay for investigating the radiation response of hepatocytes was examined. The frequency was defined as the ratio of the total number of micronuclei to the number of hepatocytes examined. The dose-response curves were curvilinear after X rays and linear after neutrons. These dose-response curves were analyzed by a linear-quadratic model, frequency = aD + bD2 + c. The a/b ratio was 3.03 +/- 1.26 Gy following X irradiation. This value is within the range of the alpha/beta ratios reported by others using the clonogenic assay of hepatocytes. While the a/b value for neutrons was 24.3 +/- 11.7 Gy, the maximum relative biological effectiveness of neutrons was 6.30 +/- 2.53. Since the micronucleus assay is simple and rapid, it may be a good tool for evaluating the radiation response of hepatocytes in vivo.

Animals↗
PubMed1999

Solution of the inverse problem for a linear cochlear model: a tonotopic cochlear amplifier.

The extraordinary fine-tuning characteristic of normal mammalian hearing is attributed to physiological mechanisms collectively known as the cochlear amplifier (CA), which amplifies and sharpens the basilar membrane (BM) vibration response to incoming acoustic pressure oscillations. Electromechanical properties of outer hair cells (OHCs) are believed to be the critical component of the CA, but its "circuitry" as yet remains unknown. Here, the required frequency-space response characteristics of the CA are computationally determined when typical in vivo tuning data are introduced as input to a linear hydroelastic cochlear model whose cross-sectional dynamics are represented by two coupled vibrational degrees of freedom. It is assumed that the CA senses motion at the tectorial membrane (TM) reticular lamina (RL) and applies proportional, equal, and opposite forces to the BM and the RL. The results show the CA to be tonotopically tuned, meaning it conforms to a space-frequency similarity principle like other cochlear dynamical responses. This requires that the active mechanism use information distributed along the cochlear partition. The physiological mechanism responsible for such behavior remains unknown, but here the computed CA characteristics can be qualitatively reproduced by a circuit spanning the length of the cochlea. This does not preclude other mechanisms, but is intended to motivate closer experimental investigation of extracellular and intercellular ionic flow pathways.

Animals↗
PubMed2005

Modelling the extra and intracellular uptake and discharge of heavy metals in Fontinalis antipyretica transplanted along a heavy metal and pH contamination gradient.

Samples of the aquatic bryophyte Fontinalis antipyretica Hedw. were transplanted to different sites with the aim of characterizing the kinetics of the uptake and discharge of heavy metals in the extra and intracellular compartments. The accumulation of metals in extracellular compartments, characterized by an initial rapid accumulation, then a gradual slowing down over time, fitted perfectly to a Michaelis-Menten model. The discharge of metals from the same compartment followed an inverse linear model or an inverse Michaelis-Menten model, depending on the metal. In intracellular sites both uptake and discharge occurred more slowly and progressively, following a linear model. We also observed that the acidity of the environment greatly affected metal accumulation in extracellular sites, even when the metals were present at relatively high concentrations, whereas the uptake of metals within cells was much less affected by pH.

Aluminum↗
PubMed2003

Spatial dependence of the nonlinear BOLD response at short stimulus duration.

Most functional magnetic resonance imaging studies use linear models to predict the measured response by convolution of an impulse response with the stimulus profile. Using very short visual presentation times (<2 s), deviation from the linear model in the measured BOLD data from the human brain was found for the response integral, amplitude, and width. In this study, high temporal and spatial resolution were used to quantify nonlinear effects and investigate the spatial dependence. Data at 4 Tesla showed at short stimulus duration a nonlinearity, i.e., deviation from a linear model, with an index up to 400%, whereas data at 7 Tesla exhibited a nonlinearity index up to 40%. The effect was more pronounced for response amplitude than for response area. A reduced width and sharpening of responses at shorter stimulus duration was also found. A voxel-based analysis of 7 Tesla data with 1.2 x 1.2 x 2 mm(3) resolution revealed a correlation between response onset and nonlinearity index. This suggests that the nonlinearity effects are a tissue-specific phenomenon and are likely to be more localized to the site of neuronal activity. The observed magnetic field dependence and the demonstrated nonlinearity in the response width support the hypothesis that the source of the nonlinearity at short stimulus duration has a considerable hemodynamic contribution. The nonlinearity was modeled as a "switch"-type initial hemodynamic response onset. Understanding these nonlinearities in the BOLD response is important for design and the analysis of rapid event-related fMRI experiments with brief stimulus presentations.

Brain Mapping↗
PubMed1992

Analysis of premature ventricular counts in long term ECG following myocardial infarction.

Frequent and recurrent ventricular premature beats (VPB's) are considered to be associated with a higher risk of sudden cardiac death, particularly for survivors of myocardial infarction (MI). The distribution of VPB's has a large probability mass at zero, and a very heavy right hand tail. In this research, we fitted a model to VPB for patients for which VPB was present. The model was fitted on the basis of a relatively large data set on MI survivors in Israel. The model was fitted by a method which is based on the generalized linear model. This method, which was introduced by Zeger and Liang, is designed for longitudinal data and uses the quasi-likelihood concept. No specific assumptions are required on the shape of the distribution of the dependent variable. The results indicate that the model fits the data quite well but underestimates the very extreme high values. This research demonstrates the applicability of generalized linear models for longitudinal non-Gaussian data. Such data often arise in medical studies. The study also points out the distributional properties of VPB counts. In particular, it shows their associations with simple clinical and epidemiological variables, and with certain time periods during the day.

Cardiac Complexes, Premature↗
PubMed1985

An integer linear programming model of staff retention and termination based on multiattribute utility theory.

An integer linear programming formulation was used to model several staffing alternatives available to the director of a recreation therapy department. The utility function of the decision maker was assessed using two attributes of effectiveness: performance and experience. Two utility approximations were obtained for each staff member based upon the average performance rating and number of years of experience both as a recreation therapist and at the facility. The utility obtained was viewed as a proxy for, and a comparative measure of, effectiveness, which considers the criteria of training and experience. The individuals who comprise the most effective combination of therapists, given staff reductions, were obtained by maximizing the sum of staff values. The first constraint set involved a budgetary constraint, coverage constraints, and an EEOC policy restriction. The coverage restriction and the budget were varied to reflect changes in the department resources. The model was validated with the department supervisor for the case of a one-position, 10% budget decrease.

Employment↗
PubMed1995

General linear compartment model with zero input: II. The computerized derivation of the kinetic equations.

The final equations obtained in the first article of this series describing the concentrations of substances in any of the compartments of a model are here cast in an easily programmable form. A computer program with an easy input method and the ability to expand all of the coefficients in the kinetic equations in terms of the model parameters has been developed. The program has been written in the BASIC language.

Computer Simulation↗
PubMed2006

Linear relationship of valproate serum concentration to response and optimal serum levels for acute mania.

OBJECTIVE: Several studies have shown that achieving adequate serum valproate levels is critical to rapid stabilization of acute mania, but estimates of the target therapeutic level have been imprecise. A post hoc analysis of pooled intent-to-treat data from three randomized, placebo-controlled studies of divalproex treatment for acute mania was performed to test a hypothesized linear relationship between serum concentration and response and to determine optimal blood levels for treatment of acute mania. METHOD: Subjects (N=374) were stratified into seven groups (six valproate serum level ranges and placebo), and effect size was determined for each. Linearity of dose response was tested with both parametric and nonparametric techniques. ANOVA was used to compare the response at each serum level range with that of placebo as well as the lowest valproate level (< =55.0 microg/ml). The mean serum valproate level was then determined for all subjects with an effect size greater than or equal to the maximal effect derived from linear modeling. RESULTS: The fit of blood level and response to a linear model was good. Efficacy was significantly greater than placebo beginning at the 71.4-85.0 microg/ml range and for all higher valproate levels; the 94.1-107.0 and >107.0 microg/ml groups were superior to the lowest valproate serum level group. The effect size associated with highest serum levels (>94 microg/ml) was 1.06 (0.59 after placebo correction). Subjects obtaining this effect or greater (N=84) had a mean serum level of 87.5 microg/ml. Blood levels in the lowest effective range were 60% more effective than placebo and in the higher ranges were 120% more effective. Tolerability appeared similar for all groups. CONCLUSIONS: The results of this study suggest that there is a linear relationship between valproate serum concentration and response and that the target blood level of valproate for best response in acute mania is above 94 microg/ml.

Acute Disease↗
PubMed2003

Geographic variation within the United States in the incidence of hepatocellular carcinoma.

Geographic variation in hepatocellular carcinoma (HCC) has not been previously studied in the United States. Using data collected by the Surveillance, Epidemiology, and End Results registries (SEER) and the 1990 Behavioral Risk Factor Surveillance System (BRFSS), we analyzed incidence and risk factors for HCC in nine geographic regions in the United States. We identified all individuals with HCC during 1975-1998 in five states (Connecticut, Iowa, Utah, New Mexico, and Hawaii) and four metropolitan areas (Detroit-Metropolitan, San Francisco-Oakland, Seattle-Puget Sound, and Atlanta-Metropolitan). Age-adjusted incidence rates were calculated for each geographic region. The association between HCC incidence and geographic regions were examined in Poisson multivariate regression model controlling for age, gender, race, and year of diagnosis. Hierarchical linear modeling was also used to examine these associations while adjusting for potential clustering of persons with similar characteristics within geographic regions, and to assess the effect of the prevalence of smoking, alcohol use, obesity, and diabetes in the underlying population in these geographical regions. A total of 11,547 persons with HCC were examined. Hawaii had the highest age-adjusted incidence rate (4.6), followed by San Francisco-Oakland (3.2), New Mexico (2.0), Detroit-Metropolitan (1.9), Seattle-Puget Sound (1.8), Atlanta-Metropolitan (1.7), Connecticut (1.6), Iowa (1.1), and Utah (1.0); all rates per 100,000. Whites had an age-adjusted incidence rate of 1.5, Blacks 3.2, and other races "Asian, American Indian, Pacific Islander" 7.0. However, Blacks and "other races" in Seattle-Puget Sound had higher age-adjusted incidence rates (4.4 and 8.2, respectively) than Blacks and other races in any other registry, while Whites in Hawaii had a higher rate (2.5) than Whites in any other registry. In general, men had a two to three times higher age-adjusted incidence rate than women. However, Hawaiian men had significantly higher age-adjusted rates (7.0) than men in other regions, while Utah had the lowest rates of HCC in men (1.5). Adjusting for variations in ethnicity, gender, age, and time of diagnosis, the Poisson regression analysis showed persistent geographic differences in HCC as well as a change in the order with New Mexico having the highest HCC incidence followed San Francisco-Oakland. Hierarchical linear modeling confirmed geographic variations in HCC but failed to show a significant effect for the prevalence of smoking, alcohol use, obesity, and diabetes in the underlying population. Significant geographic variation in HCC incidence exist in the United States. These variations are only partly explained by differences in age, gender, race, and year of diagnosis.

Age Distribution↗
PubMed2004

Estimating linear regression models in the presence of a censored independent variable.

The current study examined the impact of a censored independent variable, after adjusting for a second independent variable, when estimating regression coefficients using "naïve" ordinary least squares (OLS), "partial" OLS and full-likelihood models. We used Monte Carlo simulations to determine the bias associated with all three regression methods. We demonstrated that substantial bias was introduced in the estimation of the regression coefficient associated with the variable subject to a ceiling effect when naïve OLS regression was used. Furthermore, minor bias was transmitted to the estimation of the regression coefficient associated with the second independent variable. High correlation between the two independent variables improved estimation of the censored variable's coefficient at the expense of estimation of the other coefficient. The use of "partial" OLS and maximum-likelihood estimation were shown to result in, at most, negligible bias in estimation. Furthermore, we demonstrated that the full-likelihood method was robust under mis-specification of the joint distribution of the independent random variables. Lastly, we provided an empirical example using National Population Health Survey (NPHS) data to demonstrate the practical implications of our main findings and the simple methods available to circumvent the bias identified in the Monte Carlo simulations. Our results suggest that researchers need to be aware of the bias associated with the use of naïve ordinary least-squares estimation when estimating regression models in which at least one independent variable is subject to a ceiling effect.

Confounding Factors, Epidemiologic↗
PubMedDate not supplied

Consistency of sperm morphology classification methods.

The World Health Organization (WHO) recently suggested new morphometric dimensions for normal sperm heads and new sperm head classification rules. These specifications differ from previous WHO methods and from the Kruger method for strict morphology assessment. We analyzed the WHO and Kruger sperm classification rules to determine their appropriateness as predictive linear models. We reviewed the theoretical requirements for allometric modeling, a more traditional approach for specifying the size relationships between phenotypic characters, and developed valid allometric models based on the statistical properties of over 3,700 measurements of individual sperm head dimensions. We implemented the WHO, Kruger, and Allometric methods on the same set of digitized sperm heads to study the empirical consequences of different metric requirements and classification methods. Results show that the WHO and Kruger methods are internally consistent, but specify nonconstant variance. Hence, they are inappropriate linear models. The allometric models were internally consistent and specified constant variance. Hence, they are appropriate linear models. Significant differences were found in the percentage of normal sperm between the methods. On average, the Kruger method produced the lowest value and the Allometric methods produced significantly higher values than the WHO methods, but no average difference was found between WHO methods or between Allometric methods. Nevertheless, the percentage of normal sperm did change significantly for individual specimens. These results indicate that small differences in metric requirements and classification rules can dramatically change the percentage of normal sperm. Until more rigorous definitions of sperm features can be developed, and valid statistical models can be used to describe the population characteristics of fertile sperm, the prognostic value of sperm morphology is limited.

Classification↗