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Results for “Logistic Models”

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PubMed2006

Ordinal regression model and the linear regression model were superior to the logistic regression models.

OBJECTIVE: Ordinal scales often generate scores with skewed data distributions. The optimal method of analyzing such data is not entirely clear. The objective was to compare four statistical multivariable strategies for analyzing skewed health-related quality of life (HRQOL) outcome data. HRQOL data were collected at 1 year following catheterization using the Seattle Angina Questionnaire (SAQ), a disease-specific quality of life and symptom rating scale. STUDY DESIGN AND SETTING: In this methodological study, four regression models were constructed. The first model used linear regression. The second and third models used logistic regression with two different cutpoints and the fourth model used ordinal regression. To compare the results of these four models, odds ratios, 95% confidence intervals, and 95% confidence interval widths (i.e., ratios of upper to lower confidence interval endpoints) were assessed. RESULTS: Relative to the two logistic regression analysis, the linear regression model and the ordinal regression model produced more stable parameter estimates with smaller confidence interval widths. CONCLUSION: A combination of analysis results from both of these models (adjusted SAQ scores and odds ratios) provides the most comprehensive interpretation of the data.

Adolescent↗

PubMed2002

Predicting amphipod toxicity from sediment chemistry using logistic regression models.

Individual chemical logistic regression models were developed for 37 chemicals of potential concern in contaminated sediments to predict the probability of toxicity, based on the standard 10-d survival test for the marine amphipods Ampelisca abdita and Rhepoxynius abronius. These models were derived from a large database of matching sediment chemistry and toxicity data, which includes contaminant gradients from a variety of habitats in coastal North America. Chemical concentrations corresponding to a 20, 50, and 80% probability of observing sediment toxicity (T20, T50, and T80 values) were calculated to illustrate the potential for deriving application-specific sediment effect concentrations and to provide probability ranges for evaluating the reliability of the models. The individual chemical regression models were combined into a single model, using either the maximum (P(Max) model) or average (P(Avg) model) probability predicted from the chemicals analyzed in a sample, to estimate the probability of toxicity for a sample. The average predicted probability of toxicity (from the P(Max) model) within probability quartiles closely matched the incidence of toxicity within the same ranges, demonstrating the overall reliability of the P(Max) model for the database that was used to derive the model. The magnitude of the toxic effect (decreased survival) in the amphipod test increased as the predicted probability of toxicity increased. Users have a number of options for applying the logistic models, including estimating the probability of observing acute toxicity to estuarine and marine amphipods in 10-d toxicity tests at any given chemical concentration or estimating the chemical concentrations that correspond to specific probabilities of observing sediment toxicity.

Amphipoda↗

PubMed1994

Alternative models for ordinal logistic regression.

Armstrong and Sloan have reviewed two types of ordinal logistic models for epidemiologic data: the cumulative-odds model and the continuation-ratio model. I review here certain aspects of these models not emphasized previously, and describe a third type, the stereotype model, which in certain situations offers greater flexibility coupled with interpretational advantages. I illustrate the models in an analysis of pneumoconiosis among coal miners.

Epidemiologic Methods↗

PubMed2003

Correlated noise in a logistic growth model.

The logistic differential equation is used to analyze cancer cell population, in the presence of a correlated Gaussian white noise. We study the steady state properties of tumor cell growth and discuss the effects of the correlated noise. It is found that the degree of correlation of the noise can cause tumor cell extinction.

Journal Article↗

PubMed2004

Application of likelihood ratio and logistic regression models to landslide susceptibility mapping using GIS.

For landslide susceptibility mapping, this study applied and verified a Bayesian probability model, a likelihood ratio and statistical model, and logistic regression to Janghung, Korea, using a Geographic Information System (GIS). Landslide locations were identified in the study area from interpretation of IRS satellite imagery and field surveys; and a spatial database was constructed from topographic maps, soil type, forest cover, geology and land cover. The factors that influence landslide occurrence, such as slope gradient, slope aspect, and curvature of topography, were calculated from the topographic database. Soil texture, material, drainage, and effective depth were extracted from the soil database, while forest type, diameter, and density were extracted from the forest database. Land cover was classified from Landsat TM satellite imagery using unsupervised classification. The likelihood ratio and logistic regression coefficient were overlaid to determine each factor's rating for landslide susceptibility mapping. Then the landslide susceptibility map was verified and compared with known landslide locations. The logistic regression model had higher prediction accuracy than the likelihood ratio model. The method can be used to reduce hazards associated with landslides and to land cover planning.

Databases, Factual↗

PubMed1996

Repopulation in the SCCVII squamous cell carcinoma assessed by an in vivo-in vitro excision assay.

An in vivo-in vitro excision assay was used to study repopulation after a single dose of clamped irradiation (40 Gy) in the SCCVII tumour implanted in the foot of C3H/Km mice. The growth pattern of clonogenic cells was analysed by two different mathematical models: the logistic model and the Gompertz model. The logistic model described the data better than the Gompertz model. Accelerated repopulation was found when the regrowth rate after irradiation was compared to the growth rate at the time of treatment, and when it was compared to the growth rate in untreated tumours with a number of cells equivalent to the number that was found after irradiation. The clonogenic doubling time (cDT) was estimated at 15.1 h (95% c.i.: 14.2; 16.0) after irradiation, and 27.8 h (95% c.i.: 16.7; 43.5) in untreated controls of matching size. However, the estimate relies on the mathematical model chosen and on extrapolation below actually measured data. A small cDT points to shortening of the cell cycle time and recruitment of non-cycling clonogenic tumour cells to be the main mechanism behind the accelerated repopulation.

Animals↗

PubMedDate not supplied

Prognostic modeling with logistic regression analysis: in search of a sensible strategy in small data sets.

Clinical decision making often requires estimates of the likelihood of a dichotomous outcome in individual patients. When empirical data are available, these estimates may well be obtained from a logistic regression model. Several strategies may be followed in the development of such a model. In this study, the authors compare alternative strategies in 23 small subsamples from a large data set of patients with an acute myocardial infarction, where they developed predictive models for 30-day mortality. Evaluations were performed in an independent part of the data set. Specifically, the authors studied the effect of coding of covariables and stepwise selection on discriminative ability of the resulting model, and the effect of statistical "shrinkage" techniques on calibration. As expected, dichotomization of continuous covariables implied a loss of information. Remarkably, stepwise selection resulted in less discriminating models compared to full models including all available covariables, even when more than half of these were randomly associated with the outcome. Using qualitative information on the sign of the effect of predictors slightly improved the predictive ability. Calibration improved when shrinkage was applied on the standard maximum likelihood estimates of the regression coefficients. In conclusion, a sensible strategy in small data sets is to apply shrinkage methods in full models that include well-coded predictors that are selected based on external information.

Aged↗

PubMed1996

Gauss or Bernoulli? A Monte Carlo comparison of the performance of the linear mixed-model and the logistic mixed-model analyses in simulated community trials with a dichotomous outcome variable at the individual level.

This Monte Carlo study compares performance of the linear and the logistic mixed-model analyses of simulated community trials having event rates of 37%, 13%, or 5%, intraclass correlations between 0.01 and 0.05, and 17 or 5 denominator degrees of freedom. Type I or Type II error rates showed no essential difference between the two analysis methods. They showed depressed error rates when the event rate or the denominator degrees of freedom were small. The authors conclude that in studies with adequate denominator degrees of freedom, the researcher may use either method of analysis but should accept negative estimates of components of variance to avoid depression of error rates.

Analysis of Variance↗

PubMed2005

From data to knowledge: a method for modeling hospital logistic processes.

When modeling or redesigning a process, the knowledge-management perspective is seldomly used. Using the knowledge categorization developed by van Heusden and Jorna, we propose a knowledge-management perspective to provide a strategy for modeling and redesigning a business process. As an illustration of our approach, we use hospital data of multidisciplinary patients. This specific group of patients requires the involvement of different specialisms for their medical treatment that leads to more efforts regarding the coordination of care for these patients. In order to increase the care efficiency, knowledge that supports the reorganization of care for multidisciplinary patients should be provided. We use the above-mentioned knowledge-management perspective for creating new multidisciplinary units, in which different specialisms coordinate the treatment of specific groups of patients.

Artificial Intelligence↗

PubMed2006

Modeling the effect of temperature on growth of Salmonella in chicken.

Growth data of Salmonella in chicken were collected at several isothermal conditions (10, 15, 20, 25, 28, 32, 35, 37, 42, and 45 degrees C) and were then fitted into primary models, namely the logistic model, modified Gompertz model and Baranyi model. Measures of goodness-of-fit such as mean square error, pseudo-R(2), -2 log likelihood, Akaike's information, and Sawa's Bayesian information criteria were used for comparison for these primary models. Based on these criteria, modified Gompertz model described growth data the best, followed by the Baranyi model, and then the logistic model. The maximum growth rates obtained from each primary model were then modeled as a function of temperature using the modified Ratkowsky model. Pseudo-R(2) values for this secondary model describing growth rate obtained from Baranyi, modified Gompertz, and logistic models were 0.999, 0.980, and 0.990, respectively. Mean square error values for corresponding models were 0.0002, 0.0008, and 0.0009, respectively. Both measures clearly show that the Baranyi model performed better than the modified Gompertz model or the logistic model.

Animals↗

PubMed1999

Fitting logistic IRT models: small wonder.

State-of-the-art item response theory (IRT) models use logistic functions exclusively as their item response functions (IRFs). Logistic functions meet the requirements that their range is the unit interval and that they are monotonically increasing, but they impose a parameter space whose dimensions can only be assigned a metaphorical interpretation in the context of testing. Applications of IRT models require obtaining the set of values for logistic function parameters that best fit an empirical data set. However, success in obtaining such set of values does not guarantee that the constructs they represent actually exist, for the adequacy of a model is not sustained by the possibility of estimating parameters. This article illustrates how mechanical adoption of off-the-shelf logistic functions as IRFs for IRT models can result in off-the-shelf parameter estimates and fits to data. The results of a simulation study are presented, which show that logistic IRT models can fit a set of data generated by IRFs other than logistic functions just as well as they fit logistic data, even though the response processes and parameter spaces involved in each case are substantially different. An explanation of why logistic functions work as they do is offered, the theoretical and practical consequences of their behavior are discussed, and a testable alternative to logistic IRFs is commented upon.

Humans↗

PubMed1998

Mixed effects logistic regression models for longitudinal binary response data with informative drop-out.

A shared parameter model with logistic link is presented for longitudinal binary response data to accommodate informative drop-out. The model consists of observed longitudinal and missing response components that share random effects parameters. To our knowledge, this is the first presentation of such a model for longitudinal binary response data. Comparisons are made to an approximate conditional logit model in terms of a clinical trial dataset and simulations. The naive mixed effects logit model that does not account for informative drop-out is also compared. The simulation-based differences among the models with respect to coverage of confidence intervals, bias, and mean squared error (MSE) depend on at least two factors: whether an effect is a between- or within-subject effect and the amount of between-subject variation as exhibited by variance components of the random effects distributions. When the shared parameter model holds, the approximate conditional model provides confidence intervals with good coverage for within-cluster factors but not for between-cluster factors. The converse is true for the naive model. Under a different drop-out mechanism, when the probability of drop-out is dependent only on the current unobserved observation, all three models behave similarly by providing between-subject confidence intervals with good coverage and comparable MSE and bias but poor within-subject confidence intervals, MSE, and bias. The naive model does more poorly with respect to the within-subject effects than do the shared parameter and approximate conditional models. The data analysis, which entails a comparison of two pain relievers and a placebo with respect to pain relief, conforms to the simulation results based on the shared parameter model but not on the simulation based on the outcome-driven drop-out process. This comparison between the data analysis and simulation results may provide evidence that the shared parameter model holds for the pain data.

Analgesics↗

PubMed1997

[Use of a logistic regression model at two levels in the analysis of medical practice variations: the prophylactic cesarean].

We show the use of a hierarchical logistic model to study the variations of the prophylactic cesarean section rate between the maternity hospitals of the Rhône-Alpes region. These variations are analyzed according to the women characteristics at first level, and the maternity hospital characteristics at second level. We present the two-level hierarchical logistic model and the method of estimation of the fixed and random parameters. Then, we compare and discuss the results obtained with those of the usual logistic model. The usual logistic model underestimates the standard error of the regression parameters. In our example however, the results obtained with the hierarchical model do not modify the conclusions concerning the effect of the women characteristics. All the women characteristics increase significantly the probability for a woman to have a prophylactic cesarean section. Nevertheless, the hierarchical model reveals the effect of the maternity hospital characteristics and shows that the maternity hospitals which receive many "at risk" women tend to perform fewer prophylactic cesarean sections than the others, in women with the same characteristics. It permits to estimate the residual variance of second level linked to the unobserved characteristics of the maternity hospitals. It permits to show that the effect of the main characteristics of the women (previous cesarean section, dystocia, chronic fetal distress) vary between maternity hospitals.

Bias↗

PubMed1998

Incorporation of family history in logistic regression models.

For diseases with a genetic component, logistic regression models are presented that incorporate family history in a quantitative way. In the largest model, every type of relative has their own regression coefficient. The other two models are submodels, which incorporate family history either by the number of cases in the family minus its expectation or by a weighted number of cases in the family minus its expectation. For various genetic effects, namely polygenic and autosomal dominant effects, the performance of these simple logistic models is studied. First, the predictive values of the logistic and true genetic models are computed and compared. Secondly, a simulation study is carried out to investigate the effects of estimation of the parameters in a small data set. Thirdly, the logistic models are fitted to a data set of Von Willebrand Factor responses of target individuals and their families; in these models, family history has a significant effect. The conclusion is that for the genetic effects considered the logistic models perform well.

Female↗

PubMedDate not supplied

The effect of disease-prevalence adjustments on the accuracy of a logistic prediction model.

The accuracy of a logistic prediction model is degraded when it is transported to populations with outcome prevalences different from that of the population used to derive the model. The resultant errors can have major clinical implications. Accordingly, the authors developed a logistic prediction model with respect to the noninvasive diagnosis of coronary disease based on 1,824 patients who underwent exercise testing and coronary angiography, varied the prevalence of disease in various "test" populations by random sampling of the original "derivation" population, and determined the accuracy of the logistic prediction model before and after the application of a mathematical algorithm designed to adjust only for these differences in prevalence. The accuracy of each prediction model was quantified in terms of receiver operating characteristic (ROC) curve area (discrimination) and chi-square goodness-of-fit (calibration). As the prevalence of the test population diverged from the prevalence of the derivation population, discrimination improved (ROC-curve areas increased from 0.82 +/- 0.02 to 0.87 +/- 0.03; p < 0.05), and calibration deteriorated (chi-square goodness-of-fit statistics increased from 9 to 154; p < 0.05). Following adjustment of the logistic intercept for differences in prevalence, discrimination was unchanged and calibration improved (maximum chi-square goodness-of-fit fell from 154 to 16). When the adjusted algorithm was applied to three geographically remote populations with prevalences that differed from that of the derivation population, calibration improved 87%, while discrimination fell by 1%. Thus, prevalence differences produce statistically significant and potentially clinically important errors in the accuracy of logistic prediction models. These errors can potentially be mitigated by use of a relatively simple mathematical correction algorithm.

Adult↗

PubMed2007

Tree-based model checking for logistic regression.

A tree procedure is proposed to check the adequacy of a fitted logistic regression model. The proposed method not only makes natural assessment for the logistic model, but also provides clues to amend its lack-of-fit. The resulting tree-augmented logistic model facilitates a refined model with meaningful interpretation. We demonstrate its use via simulation studies and an application to the Pima Indians diabetes data.

Biomedical Research↗

PubMed1991

The importance of assessing the fit of logistic regression models: a case study.

BACKGROUND: The logistic regression model is being used with increasing frequency in all areas of public health research. In the calendar year 1989, over 30% of the articles published in the American Journal of Public Health employed some form of logistic regression modeling. In spite of this increase, there has been no commensurate increase in the use of commonly available methods for assessing model adequacy. METHODS: We review the current status of the use of logistic regression modeling in the American Journal of Public Health. We present a brief overview of currently available and easily used methods for assessing the adequacy of a fitted logistic regression model. RESULTS: An example is used to demonstrate the methods as well as a few of the adverse consequences of failing to assess the fit of the model. One important adverse consequence illustrated in the example is the inclusion of variables in the model as a result of the influence of one subject. CONCLUSIONS: Failure to address model adequacy may lead to misleading or incorrect inferences. Recommendations are made for the use of methods for assessing model adequacy and for future editorial policy in regard to the review of articles using logistic regression.

Bias↗

PubMed2004

Accelerated progression of coronary calcification: four-year follow-up in patients with stable coronary artery disease.

PURPOSE: To prospectively assess the 4-year progression rate of coronary artery calcium (CAC) in patients with clinically stable coronary artery disease (CAD) with multi-detector row computed tomography (CT). MATERIALS AND METHODS: The study group consisted of 382 consecutive patients. All underwent baseline dual-sector spiral CT, and CT was repeated at 2 and 4 years later. Progression of CAC was assessed with measurement of the increase in total calcium score (TCS) and with repeated-measures analysis and multivariate linear regression models. Logistic regression model was used to predict incidence of new lesions. RESULTS: Eighty-seven percent (333 of 382) of the study group were men, with mean age of 65 years +/- 11, and 13% (49 of 382) were women, with mean age of 68 years +/- 11. The average TCS increased after 4 years by sixfold from baseline in the 1st quartile, and by four-, two- and 1.5-fold in the 2nd, 3rd, and 4th quartiles of baseline TCS (P <.01), respectively. Multiple linear regression analysis included age; sex; natural logarithm of baseline TCS; history of hypertension, diabetes mellitus, current smoking, hypercholesterolemia, and lipid-lowering therapy with cholesterol synthesis enzyme inhibitor (statin); and family history of premature CAD. Results demonstrated that natural logarithm of baseline TCS and history of current smoking were independent predictors of the 4th-year natural logarithm of TCS levels (R(2) = 0.85, P <.001). New lesions were diagnosed in 56 (15%) patients. History of statin therapy (odds ratio = 0.35; 95% confidence interval [CI]: 0.16, 0.77; P <.01), age with an increment of 5 years (odds ratio = 0.76; 95% CI: 0.64, 0.90; P =.01), and natural logarithm of baseline TCS (odds ratio = 0.73; 95% CI: 0.62, 0.86; P <.01) were independent predictors for new calcific lesions during 4 years. CONCLUSION: Accelerated progression of CAC during 4 years was found in clinically stable patients with CAD.

Aged↗