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Results for “Logistic Models”

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PubMed1994

[Prognosis of idiopathic interstitial pneumonia].

Idiopathic interstitial pneumonia (IIP) is characterized by chronic inflammation and fibrosis of the lung. It carries a poor prognosis and the treatment for IIP has not yet been established. We evaluated 116 cases of IIP retrospectively, and analyzed possible prognostic factors, such as the mode of detection, clinical symptoms, chest X-ray findings, pulmonary function tests, blood chemistry, bronchoalveolar lavage (BAL), and treatments. The 5-year survival rate from the onset was 39.5% and the 10-year survival rate was only 12.7%. The 5-year survival rate from the appearance of dyspnea on exertion was 23.2% and 10-year survival rate was 9.0%. According to the results of the Kaplan-Meier analysis, patients with low% FVC (< 70%), those with high values of ESR, those with high values of CRP, and those with advanced chest X-ray shadows did not survive as long as other patients. Multivariate analysis with a proportional hazards model revealed that a high percentage of eosinophils in BALF was associated with a poor prognosis. Analysis with a logistic model revealed that being male having a low %DLCO were associated with a poor prognosis.

Female↗

PubMed2000

Estimating the time to extinction in an island population of song sparrows.

We estimated and modelled how uncertainties in stochastic population dynamics and biases in parameter estimates affect the accuracy of the projections of a small island population of song sparrows which was enumerated every spring for 24 years. The estimate of the density regulation in a theta-logistic model (theta = 1.09 suggests that the dynamics are nearly logistic, with specific growth rate r1 = 0.99 and carrying capacity K = 41.54. The song sparrow population was strongly influenced by demographic (ŝigma2(d) = 0.66) and environmental (ŝigma2(d) = 0.41) stochasticity. Bootstrap replicates of the different parameters revealed that the uncertainties in the estimates of the specific growth rate r1 and the density regulation theta were larger than the uncertainties in the environmental variance sigma2(e) and the carrying capacity K. We introduce the concept of the population prediction interval (PPI), which is a stochastic interval which includes the unknown population size with probability (1 - alpha). The width of the PPI increased rapidly with time because of uncertainties in the estimates of density regulation as well as demographic and environmental variance in the stochastic population dynamics. Accepting a 10% probability of extinction within 100 years, neglecting uncertainties in the parameters will lead to a 33% overestimation of the time it takes for the extinction barrier (population size X = 1) to be included into the PPI. This study shows that ignoring uncertainties in population dynamics produces a substantial underestimation of the extinction risk.

Animals↗

PubMed1982

Evaluation of some mathematical models for tumor growth.

A number of mathematical models for tumor growth have been proposed in the past to increase the understanding of the tumor growth process. This study evaluates the exponential, the Gompertz, the Bertalanffy and the logistic models. The data used for the evaluation of the models consists of: the untreated primary carcinoma of the human lung, and induced sarcoma in mice. The non-linear regression method was used for the analysis of the data. The logistic equation gave the best fit in the cases of all seven patients. However, the Bertalanffy equation was the best in seven out of 10 cases of mice. The models were also judged by comparing the percentage error in predicting the volume of a tumor.

Animals↗

PubMed2005

Perceptual interactions in odour mixtures: odour quality in binary mixtures of woody and fruity wine odorants.

The qualitative perceptual interactions in three binary mixtures of wine odorants were studied: isoamyl acetate (fruity note)/whisky lactone (woody note), ethyl butyrate (fruity note)/whisky lactone (woody note) and ethyl butyrate (fruity note)/guaiacol (woody note). For each binary mixture, the perceived quality and intensity of 24 stimuli (four supra-threshold concentration levels of each of the two compounds and their 16 possible combinations) were evaluated in five replications by a trained panel of 13 subjects. The application of the Olsson predictive model for odour intensity and quality perception gave quite a good estimation of the evolution of single component identification in the mixture when the intensity proportion of unmixed components varied. However, this model was unable to account for the odour quality dominance in mixtures of iso-intense components. An alternative linear logistic model was proposed to study the qualitative dominance of the woody note in the three mixtures when the perceived intensities of each unmixed compound were equal.

Butyrates↗

PubMed1998

Statistical models for predicting a beneficial response to interferon-alpha in patients with chronic hepatitis B.

Therapy with interferon-alpha has been reported to induce remissions in 35% of patients with chronic hepatitis B. The ability to identify patients likely to respond would be helpful in making recommendations for treatment. In this statistical analysis we included 82 patients with chronic hepatitis B who received interferon-alpha in clinical trials at the National Institutes of Health between 1984 and 1991. A response was defined as the loss of hepatitis B virus (HBV) DNA and hepatitis B e antigen (HBeAg) within 1 year of therapy. Multiple clinical parameters measured at pretreatment (month 0) and after the first month (month 1) of therapy were selected by stepwise regression to support the development of the prognostic models: the two-stage logistic regression model and a neural network that utilized higher-order non-linear interactions between variables. Among the 82 patients, 24 (29%) were responders. The two-stage logistic model using pretreatment variables: sex, hepatic fibrosis and alanine aminotransferase (ALT) levels correctly identified 61% of responders and 76% of non-responders. When HBV DNA at month 1 along with sex, initial ALT and fibrosis was included, the resultant model correctly identified 69% of responders and 77% of non-responders. The neural network, by incorporating interactions between variables, correctly identified 77% and 86% of responders, and 87% and 92% of non-responders, using pretreatment factors alone and the combination of pretreatment and month 1 factors respectively. Hence, the neural network was more accurate than the simple logistic regression model in predicting a response to interferon-alpha in chronic hepatitis B. The universality of these models needs to be further verified.

Antiviral Agents↗

PubMed2004

On stochastic logistic population growth models with immigration and multiple births.

This paper develops a stochastic logistic population growth model with immigration and multiple births. The differential equations for the low-order cumulant functions (i.e., mean, variance, and skewness) of the single birth model are reviewed, and the corresponding equations for the multiple birth model are derived. Accurate approximate solutions for the cumulant functions are obtained using moment closure methods for two families of model parameterizations, one for badger and the other for fox population growth. For both model families, the equilibrium size distribution may be approximated well using the Normal approximation, and even more accurately using the saddlepoint approximation. It is shown that in comparison with the corresponding single birth model, the multiple birth mechanism increases the skewness and the variance of the equilibrium distribution, but slightly reduces its mean. Moreover, the type of density-dependent population control is shown to influence the sign of the skewness and the size of the variance.

Animal Migration↗

PubMed1997

Tumor control probability of nasopharyngeal carcinoma: a comparison of different mathematical models.

PURPOSE: Radiation dose and tumor volume are factors known to affect the local control of a given type of tumor. Local tumor control is a major factor to consider when a treatment plan is evaluated. This article reports the correlation between tumor control probability, dose, and volume in a retrospective study of 142 patients with nasopharyngeal carcinoma (NPC). METHODS AND MATERIALS: The tumor volume was outlined and calculated from a computed tomographic scan. Patients were categorized according to tumor volume and radiation dose received in treatment. Local control rate was calculated for each category by the Kaplan-Meier method. Mathematical models were fitted to correlate the local control rate, dose, and volume. Both empirical and mechanistic approaches were attempted; the former included logistic models with two and three parameters, and the latter, the formulation from Brenner and Bentzen with a radiobiological basis. RESULTS: Brenner's model estimated alpha at 0.041 Gy(-1) with 95% confidence limits (-0.032, 0.113) Gy(-1). The volume dependent constant h was estimated at 0.160 cm(-3) with 95% confidence limits (-0.729, 1.048) cm(-3). The Pearson correlation coefficient was 0.64. The magnitude and sign of the fitted parameters were reasonable and consistent with reported clinical experience. The other models were fitted with slightly better goodness of fit (r = 0.65 - 0.68), but with less interpretable parameters. CONCLUSION: Brenner's model is considered appropriate for a description of the dose and volume effect on the local control of the NPC. It could be used in combination with normal tissue complication probability for treatment plan evaluation to optimize treatment results.

Adult↗

PubMed2002

Percutaneous coronary interventions in octogenarians in the American College of Cardiology-National Cardiovascular Data Registry: development of a nomogram predictive of in-hospital mortality.

OBJECTIVES: We sought to evaluate the results of percutaneous coronary intervention (PCI) in elderly patients in contemporary practice. BACKGROUND: Prior studies of PCI in the elderly population demonstrate increased in-hospital mortality, but these studies are limited by small population size. METHODS: Using the American College of Cardiology-National Cardiovascular Data Registry (ACC-NCDR) of 100,253 patients, the in-hospital outcomes in all 8,828 PCI procedures performed on octogenarians were evaluated. Patients underwent PCI between 1998 and 2000 at over 145 participating centers. RESULTS: The mean age was 83.72 +/- 3.02 years, with female preponderance (53%). The PCI was considered angiographically successful in 93%, stents were placed in 75%, and the post-PCI length of stay was 3.3 +/- 5.1 days. Overall in-hospital mortality was 3.77% but was only 1.35% in PCI without recent myocardial infarction (MI) within one week (p < 0.0001). Patients having PCI within 6 h of the onset of their MI had an increase in mortality tenfold (13.79%) compared with patients without a recent MI (p < 0.0001). All groups that were defined based on time of PCI after MI onset up to seven days had increased mortality (all p < 0.0001). Older age (odds ratio [OR] of 1.03 per incremental year), depressed ejection fraction (EF) (OR 0.69 per 10 points for EF <60%), and time of PCI after MI onset (<6 h, OR 6.87; 6 to 24 h, OR 5.66; 24 h to one week, OR 2.93) were most strongly predictive of outcome by multivariate analysis. The predicted mortality from the multivariate model correlated well with the observed in-hospital mortality up to 20% mortality. A 254-point nomogram was constructed employing the logistic model using a weighted point system. CONCLUSIONS: In patients > or = 80 years old, PCI has good success and acceptable mortality. The presence of an acute or recent MI substantially increases the risk of in-hospital death.

Age Factors↗

PubMed2006

Salt, alone or in combination with sucrose, can improve the survival of Escherichia coli O157 (SERL 2) in model acidic sauces.

The commercial production of microbiologically safe and stable sauces containing acetic acid is guided by the Comité des Industries des Mayonnaises et Sauces Condimentaires de la Communauté Economique Européenne's (CIMSCEE) code. The CIMSCEE safety value is calculated using a linear regression equation combining weighted contributions of pH and aqueous-phase concentrations of undissociated acetic acid, NaCl, and sugars. By implication, the CIMSCEE safety equation predicts that increasing concentrations of hurdles will always increase inactivation of the target pathogen. In this study, the time to achieve a 3-log10 reduction of an acid-resistant, acid-adapted, Shiga toxin-producing Escherichia coli (STEC) O157 isolate was determined experimentally for 81 formulations at various pHs and acetic acid, NaCl, and sucrose concentrations in a broth model. The combinations were intended to simulate the aqueous phase of acidic sauces and dressings. Experimental data were fitted to the log logistic model to estimate the time to 3-log10 reduction (t3D). Comparison of fitted t3D estimates with CIMSCEE values showed agreement in predicting safety (as defined by CIMSCEE) for the majority of formulations. However, CIMSCEE safety predictions were "fail dangerous" for 13 of 81 formulations. Among these formulations and others, the observed E. coli t3D initially increased and then decreased with increasing osmolalities (NaCl and sucrose). Relative protection increased with exposure time where the protective effect of NaCl predominated. While commercial acidic sauces are not considered high-risk vehicles for STEC, interactions among hurdles that decrease their combined effectiveness are deserving of further investigation because they may reveal mechanisms of broader relevance in the inactivation of pathogens in foods.

Acetic Acid↗

PubMed2005

Modeling surface growth of Escherichia coli on agar plates.

Surface growth of Escherichia coli cells on a membrane filter placed on a nutrient agar plate under various conditions was studied with a mathematical model. The surface growth of bacterial cells showed a sigmoidal curve with time on a semilogarithmic plot. To describe it, a new logistic model that we presented earlier (H. Fujikawa et al., Food Microbiol. 21:501-509, 2004) was modified. Growth curves at various constant temperatures (10 to 34 degrees C) were successfully described with the modified model (model III). Model III gave better predictions of the rate constant of growth and the lag period than a modified Gompertz model and the Baranyi model. Using the parameter values of model III at the constant temperatures, surface growth at various temperatures was successfully predicted. Surface growth curves at various initial cell numbers were also sigmoidal and converged to the same maximum cell numbers at the stationary phase. Surface growth curves at various nutrient levels were also sigmoidal. The maximum cell number and the rate of growth were lower as the nutrient level decreased. The surface growth curve was the same as that in a liquid, except for the large curvature at the deceleration period. These curves were also well described with model III. The pattern of increase in the ATP content of cells grown on a surface was sigmoidal, similar to that for cell growth. We discovered several characteristics of the surface growth of bacterial cells under various growth conditions and examined the applicability of our model to describe these growth curves.

Adenosine Triphosphate↗

PubMedDate not supplied

Longitudinal analysis of the 90K glycoprotein in the Italian HIV-seroconversion study: temporal trend and predictability of the maturity of HIV infection.

OBJECTIVES: To evaluate the level of 90K as a predictor of AIDS; to describe 90K levels over time after HIV serconversion; and to evaluate the 90K level as a marker of the maturity of infection. DESIGN: Prospective incident cohort of HIV-infected individuals with documented dates of seroconversion. METHODS: Cox models were applied to estimate the crude and adjusted relative hazards (RH) of AIDS by level of 90K. Regression models were applied to describe the temporal trend and the correlates of the level of 90K over time after HIV-seroconversion. Logistic models were applied to evaluate the probability of a sample of 90K having been taken within a certain time period after HIV-seroconversion. RESULTS: The study population consisted of 150 participants of the Italian Seroconversion Study. A total of 429 measurements of 90K were taken. Both early and later measurements of 90K were highly predictive of AIDS, also when adjusting for CD4 lymphocyte count and HIV load. The 90K level (U/ml) increased by 10% annually (95% CI: 7%-13%); the increase over time was linear. IDUs had higher 90K levels than heterosexuals and homosexuals over the course of HIV disease. High 90K levels were highly predictive of distant seroconversions (age-adjusted probability, 74%), whereas were poorly predictive of recent seroconversions (age-adjusted probability, 5%); the results were similar for the predictability of CD4 lymphocyte count. CONCLUSIONS: The level of 90K is a useful prognostic tool for clinical purposes. As a marker of the maturity of infection, 90K is similar to the CD4 lymphocyte count, with the advantage of being able to use serum instead of fresh whole blood. It has a good capacity to identify distant infections.

Acquired Immunodeficiency Syndrome↗

PubMed2004

Likelihood-based modelling of age-related normal ranges for ordinal measurements: changes in visual acuity through early childhood.

This paper investigates the construction of age-related standards for ordinal outcome data. Asymmetric logistic models are used to describe the age-related changes in the cumulative probabilities for each ordinal level. Maximum likelihood estimation of model parameters allows the use of likelihood ratio tests to ascertain the appropriate model complexity. In contrast to methodologies for constructing age-related standards where the outcome is continuous, we show how the methodology leads directly to centile estimation for individuals. The method is illustrated using visual acuity measurements collected from 2968 children between 2 and 9 years of age made on a 30-point ordinal scale. We show how, in this instance, smoothing of parameters across ordinal categories leads to reduced validity of the centiles, justifying the need for specialized methodology for non-continuous outcomes.

Age Factors↗

PubMed2005

Prognostic variables for high titres in a fluorescent antibody test to diagnose tuberculosis.

SETTING: The four hospitals and a tuberculosis clinic in the province of Zeeland, The Netherlands. OBJECTIVE: To assess the usefulness of PPD antibody measurement in the diagnosis of tuberculosis in patients admitted to hospital. PATIENTS AND METHODS: Sixty-one patients presenting with active tuberculosis, and 215 control patients were included in the study. Initial serum PPD antibody titres were determined with a macrophage uptake Fluorescent antibody test (MuFat) to construct a discrimination model between Tuberculosis (TB) and non-TB. We also retrospectively collected clinical parameters of the TB patients at presentation. Univariate and multivariate logistic regression are used to identify variables predicting high antibody titres. RESULTS: In TB patients, the presence of clinical symptoms (OR=10.63) and the presence of at least two concurrent non-lymph node disease localizations outside thorax and abdomen (OR=13.94) are necessary and sufficient to predict high titres. The logistic model shows a significant contribution of the 2log (titre) to the discrimination between TB and non-TB patients. At a cut-off value of 128, a specificity, sensitivity, and positive predictive and negative predictive values of 97%, 39%, 80% and 85%, respectively, are calculated in the study cohort. CONCLUSION: Our data suggest an application of the test at high cut-off values for timely diagnosis of difficult-to-diagnose TB patients. The results of this retrospective study will have to be confirmed in further prospective studies.

Adolescent↗

PubMed2006

On parameter estimation in population models.

We describe methods for estimating the parameters of Markovian population processes in continuous time, thus increasing their utility in modelling real biological systems. A general approach, applicable to any finite-state continuous-time Markovian model, is presented, and this is specialised to a computationally more efficient method applicable to a class of models called density-dependent Markov population processes. We illustrate the versatility of both approaches by estimating the parameters of the stochastic SIS logistic model from simulated data. This model is also fitted to data from a population of Bay checkerspot butterfly (Euphydryas editha bayensis), allowing us to assess the viability of this population.

Animals↗

PubMedDate not supplied

Measuring decision sensitivity: a combined Monte Carlo-logistic regression approach.

Modeling of the uncertainty of multiple input variables for a complex decision problem complicates sensitivity analysis. A method of analysis comprising stochastic simulation of the model and logistic regression of the simulated dichotomous decision variable against all of the input variables yields a direct measure of the importance of input variables to the decision. This method is demonstrated on a previously analyzed clinical decision either to continue observation or to immediately treat with anticoagulants a woman presenting with deep vein thrombosis in the first trimester of pregnancy. A relative measure of the importance of each input variable in causing a change of decision is estimated by calculating the change in the log odds attributable to variation of each input variable over its range of uncertain values compared with the total change of log odds from variation of all input variables. This method is compared with alternative measures of input variable importance, and is found to be a simple yet powerful tool for gaining quantitative insight into the nuances of a decision model.

Analysis of Variance↗

PubMed1997

Evaluation of logistic versus linear regression models for predicting pulmonary hypertension syndrome (ascites) using cold exposure or pulmonary artery clamp models in broilers.

Syndromes such as ascites (pulmonary hypertension syndrome) present difficulties both in the interpretation of associated physiological observations and in their analyses. The ability to predict which physiological variables have the greatest influence on survival or, more importantly, which individuals are most susceptible or resistant to ascites would be very useful selection tools. When addressed in this manner, ascites data become binary data sets (healthy or affected). Binary data can be problematic in that they do not meet all of the assumptions necessary for more traditional analyses such as ANOVA and linear regression. Binary data are discrete and do not have normally distributed errors, which violates a fundamental assumption of linear models. The predictive abilities of linear and logistic regression were evaluated in two replicated experiments using two methods to induce ascites, cold exposure (COLD) and surgical clamping of one pulmonary artery (PAC). The logistic and linear predictive models were derived using the same data and variables. The first data set from PAC and COLD were used to develop the predictive models and the replicate data sets of PAC and COLD were used as "test data sets" for the prediction of ascites. The linear models developed were complex, using four or five variables and requiring up to seven different measurements. On average, the linear models predicted ascites correctly 87.6% of the time. The logistic models were simple (single variable) models that predicted ascites correctly 92.0% of the time. The variables used in the logistic models were derivations of the ratio of right ventricular weight to total ventricular weight, either corrected for age or the body weight of the bird. Although linear regression predicted the incidence of ascites almost as well as logistic regression did, logistic regression is the more appropriate test statistic to use.

Analysis of Variance↗

PubMed1995

Dose-response assessments for developmental toxicity. IV. Benchmark doses for fetal weight changes.

Recently, most attention on the application of benchmark dose (BMD) techniques to toxicology data has focused on quantal measures of response. Before the advantages of the BMD approach can be exploited in the risk assessment process, it is important that continuous measures of response also be modeled appropriately. In this study, we examined a variety of approaches to estimating BMDs for a change in fetal weight following chemical exposure from a total of 85 developmental toxicity experiments. We modeled the change in the mean fetal weight of a litter in response to treatment using a continuous power model, as well as reductions in the weight of individual fetuses within litters (defined as falling below a preset level) using a log-logistic model which incorporates litter size as a covariable and considers intralitter correlations. For the litter-based approach, several methods of defining a benchmark effect (BME) were considered, including a percentage change in mean litter weight, a change in mean litter weight relative to variability in the control group, and a reduction in the mean litter weight to some point on the control group distribution curve. For the fetus-based approach, we examined several BME options on the cumulative frequency distribution of the control fetuses for defining a low weight fetus and calculated several levels of additional risk. BMDs for four litter-based BMEs (a difference of 5% in mean fetal weight, a decrease to the 25th percentile mean weight of control litters, a decrease in the mean weight by 2 standard errors, and a decrease of 0.5 standard deviation units) and two fetus-based BMEs (a 5% added risk of weighing less than the 5th percentile of control weights and a 10% added risk of weighing less than the 10th percentile) showed strong similarities to each other and to statistically derived NOAELs. In addition to providing comparison with the NOAEL as a reference value, these analyses provided confirmation of the advantages of the BMD approach over the NOAEL in terms of the influence of dose spacing and dose selection. Combined with our previous analyses of quantal endpoints of fetal effects, this information provides a firm basis upon which to implement the benchmark dose concept in developmental toxicity risk assessments.

Animals↗

PubMed2002

On the probability model for asthma attacks.

In environmental epidemiology, the impact of environmental agents on symptoms or health status is of interest. This influence is described quantitatively in the theory of Whittemore & Keller (1979). They formulated a logistic model for individuals that is useful in evaluation of panel studies in which each participant protocols whether he does or does not have a certain symptom each day. In the present paper an equation for the prevalence of symptoms in the study population that is defined as the fraction of symptomatic subjects is deduced from the model for individuals. The model for the aggregated quantity depends on the individuals' parameters in a nonlinear manner. The relationship between the individual-based model and the corresponding population-based model is illustrated by means of a simulated panel. Bayesian estimates of the parameters are calculated and compared for both approaches. Bayesian inference enables to apply the prevalence model to a population of non-identical individuals. For such a heterogeneous population, we observe an attenuation of environmental effects on the aggregated symptom prevalence in comparison to the individual-based approach. The presented theory is applicable not only to panel studies but also in time-series analysis of prevalences and incidences.

Asthma↗