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PubMed1992

Development and validation of a logistic regression-derived algorithm for estimating the incremental probability of coronary artery disease before and after exercise testing.

OBJECTIVES: Our goals were to develop and validate a multivariate algorithm for estimating the incremental probability of the presence of coronary artery disease. BACKGROUND: Multivariate methods, including logistic regression analysis, have been extensively applied to diagnostic exercise testing. However, few previous studies have included both an incremental design and external validation. METHODS: A retrospective collection of clinical, exercise test and catheterization data was performed involving four U.S. referral medical centers. All patients had no prior history of coronary disease and had undergone coronary angiography < or = 3 months after exercise stress testing. An algorithm was developed in one center (590 patients with a 41% prevalence of coronary artery disease) with the use of logistic regression analysis and was validated in the other three centers (1,234 patients, 70% prevalence). The algorithm incorporated pretest variables (age, gender, symptoms, diabetes, cholesterol), exercise electrocardiographic (ECG) variables (mm of ST segment depression, ST slope, peak heart rate, metabolic equivalents [METs], exercise angina) and one thallium variable. Discrimination was measured with receiver operating characteristic curve analysis. Calibration (that is, reliability) was assessed from a comparison of probability estimates and the actual prevalence of disease. RESULTS: The overall incremental receiver operating characteristic curve areas for the validation group were pretest, -0.738 +/- 0.016; postexercise ECG, 0.78 (SE 0.017); and postthallium, 0.82 (SE 0.016); p < 0.01 for both increments. Within the three validation institutions, the institution with a disease prevalence closest to that of the derivation institution had the best incremental receiver operating characteristic curve areas. There was a stepwise incremental improvement in calibration especially from exercise ECG to thallium testing. CONCLUSIONS: An incremental multivariate algorithm derived in one center reliably estimated disease probability in patients from three other centers. The incremental value of testing was best demonstrated when the derivation and validation groups had a similar disease prevalence. This algorithm may be useful in decision making that relates to the diagnosis of coronary disease.

Algorithms↗

PubMed2005

Characteristics of rear-end accidents at signalized intersections using multiple logistic regression model.

Multi-vehicle rear-end accidents constitute a substantial portion of the accidents occurring at signalized intersections. To examine the accident characteristics, this study utilized the 2001 Florida traffic accident data to investigate the accident propensity for different vehicle roles (striking or struck) that are involved in the accidents and identify the significant risk factors related to the traffic environment, the driver characteristics, and the vehicle types. The Quasi-induced exposure concept and the multiple logistic regression technique are used to perform this analysis. The results showed that seven road environment factors (number of lanes, divided/undivided highway, accident time, road surface condition, highway character, urban/rural, and speed limit), five factors related to striking role (vehicle type, driver age, alcohol/drug use, driver residence, and gender), and four factors related to struck role (vehicle type, driver age, driver residence, and gender) are significantly associated with the risk of rear-end accidents. Furthermore, the logistic regression technique confirmed several significant interaction effects between those risk factors.

Accidents, Traffic↗

PubMed2004

Combined logistic and Bayesian modeling of cesarean section risk.

OBJECTIVE: This study was undertaken to develop a simple and robust method for predicting risk of cesarean section. STUDY DESIGN: Retrospective cohort study of singleton births at term between 1992 and1999 in 22 Scottish maternity hospitals among primigravid women induced with prostaglandin. The risk of emergency cesarean section was modeled by using multivariate logistic regression in a development sample (n = 14,968). The output of this model was converted into adjusted likelihood ratios by using a novel method and tested in a validation sample (n = 12,638). RESULTS: Maternal age, height, gestational age, and fetal sex were all predictive of the risk of emergency cesarean section after prostaglandin induction of labor (all P < .001). The area under the receiver operator characteristic (ROC) curve in the development group was 0.677. The derived Bayesian model was comparably predictive of cesarean section risk in the validation sample: ROC of 0.673 (95% CI 0.662-0.684). Among the 994 women (8%) with a predicted cesarean section risk of more than 40%, the expected proportion was 48.2% and the observed proportion was 47.2%. Among the 1439 (11.4%) with a predicted cesarean risk of less than 10%, the expected proportion was 7.9% and the actual proportion 8.6%. CONCLUSION: Women at low or high risk of cesarean section after prostaglandin induction of labor can be identified with the use a novel combination of logistic regression and Bayesian modeling. The method is simple, robust, and may be generally applicable for clinical estimation of risk.

Adult↗

PubMed2003

[Contribution to the logistic theory of growth: temporal structure and growth potential].

The analysis of a structured population according to three (juvenile, mature and senescent) cellular states is carried out within the framework of Delattre's transformation systems theory. Growth in number, with the dissymmetry of cell divisions, is determined by an autocatalysis process under the constraint of the availability of a source. Two models are presented: their dynamics results in a growth of the exponential type or of the sigmoidal type, respectively. In the sigmoidal case, the logistic equation (Richards-Nelder's function with adjunction of a lower asymptote Y not equal to 0) fits satisfactorily the simulated data of the total cell number Y. The growth potential is defined as the instantaneous capacity of autocatalysis, which is expressed in relation to the present 'mitotic resources' (source + non-senescing mature cells). The acceleration variations d2Y/dt2 are in close agreement with the growth potential gradient. The analysis is then generalized to other population structuring. As a result, the logistic equation can be interpreted in terms of a formal model of growth of a structured population submitted to autocatalysis and competition.

Animals↗

PubMed2006

[The notion of the internal and external limitations of monotonic growth functions. A reformulation of the logistic equation].

The boundary value (plateau) of non-periodic growth functions constitutes one of the parameters of various usual models such as the logistic equation. Its double interpretation involves either a limit of an internal or endogenous nature or an external environment-dependent limit. Using the autocatalytic model of structured cell populations (Buis, model II, 2003), a reformulation of the logistic equation is put forward and illustrated in the case of three cell classes (juvenile, mature, senescing). The agonistic component corresponds exactly to the only active fraction of the population (non-senescing mature cells), whereas the antagonistic component is interpreted in terms of an external limit (available substrate or source). The occurrence and properties of an external limit are investigated using the same autocatalytic model with two major modifications: the absence of competition (non-limiting source) and the occurrence of a maximum number of mitoses per cell filiation (Lück and Lück, 1978). The analysis, which is carried out according to the principle of deterministic cell automata (L-systems), shows the flexibility of the model, which exhibits a diversity of kinetic properties: shifts from the sigmoidal form, number and position of growth rate extremums, number of phases of the temporal structure. These characteristics correspond to the diversity of the experimental growth curves where the singularities of the growth rate gradient are often not accounted for satisfactorily by the usual global models.

Algorithms↗

PubMed2026

The incidence and descriptive factors of calcaneal malunion after surgical fixation of intra-articular calcaneal fractures using the sinus tarsi approach: A retrospective cohort study with binary logistic regression analysis.

BACKGROUND: This study evaluated the incidence of calcaneal malunion after minimally invasive sinus tarsi approach (MIS-STA) in displaced intra-articular calcaneal fractures (I-ACFs) and identified related descriptive factors of calcaneal malunion. METHODS: A retrospective review of 99 displaced I-ACFs treated with MIS-STA was conducted. Demographic data, pre-operative radiographs, and operative details were analyzed. Outcomes included numerical rating scale (NRS) pain scores at rest and during activities of daily living (ADL), Foot and Ankle Ability Measure (FAAM) for ADL and radiographic parameters. Logistic regression was used to identify descriptive factors associated with malunion. RESULTS: Malunion occurred in 33/99 cases (33.3%). The significant descriptive factors were the initial Böhler angle < 0.5 °, time to surgery > 12.5 days, and Sanders type ≥ III. Malunion patients had significantly worse NRS and FAAM scores (p ≤ 0.001). CONCLUSION: Calcaneal malunion after MIS-STA occurred in one-third of cases, with three descriptive factors identified and poorer outcomes observed. LEVEL OF EVIDENCE: III, Comparative retrospective study with binary logistic regression analysis.

Humans↗

PubMed2006

Use of linear, Weibull, and log-logistic functions to model pressure inactivation of seven foodborne pathogens in milk.

Survival curves of six foodborne pathogens suspended in ultra high-temperature (UHT) whole milk and exposed to high hydrostatic pressure at 21.5 degrees C were obtained. Vibrio parahaemolyticus was treated at 300 MPa and other pathogens, Listeria monocytogenes, Escherichia coli O157:H7, Salmonella enterica serovar Enteritidis, Salmonella enterica serovar Typhimurium, and Staphylococcus aureus were treated at 600 MPa. All the survival curves showed a rapid initial drop in bacterial counts followed by tailing caused by a diminishing inactivation rate. A linear model and two nonlinear models were fitted to these data and the performances of these models were compared using mean square error (MSE) values. The log-logistic and Weibull models consistently produced better fits to the inactivation data than the linear model. The mean MSE value of the linear model was 6.1, while the mean MSE values were 0.7 for the Weibull model and 0.3 for the log-logistic model. There was no correlation between pressure resistance and the taxonomic group the bacteria belong to. The order, most to least pressure-sensitive, of the single strains tested was: V. parahaemolyticus (gram negative)<L. monocytogenes (gram positive)<Salmonella Typhimurium (gram negative) approximately = Salmonella Enteritidis (gram negative)<E. coli O157:H7 approximately = Staphylocollus aureus (gram positive)<Shigella flexneri (gram negative). The most pressure-resistant gram-negative bacterium, Shigella flexneri, and most pressure resistant gram-positive bacterium, Staphylocollus aureus, were pressurized at 50 degrees C. Staphylocollus aureus was treated at 500 MPa and Shigella flexneri at 600 MPa. Elevated temperature considerably enhanced pressure inactivation of these two pathogens, but did not affect the overall shape of the survival curves. Pressure level (250 MPa) and substrate (1% peptone water plus 3% NaCl) in which V. parahaemolyticus was suspended affected the shape of survival curves of V. parahaemolyticus.

Animals↗

PubMed2006

Epidemiology of fat replacement of the right ventricular myocardium determined by multislice computed tomography using a logistic regression model.

PURPOSE: We frequently observe fat replacement (FR) of the anterior wall of the right ventricular myocardium (RVM), but its epidemiological significance is not clear. METHODS AND MATERIALS: 49 consecutive subjects (28 males, 36-83 years old, median 67) underwent enhanced ECG-gated multislice CT (Light speed ultra 16, General Electrics, WI) and we retrospectively analyzed the presence of FR of RVM. A logistic model for predicting FR of RVM was constructed using age, sex, hypertension [HT], diabetes mellitus [DM], hyperlipidemia [HL] smoking, obesity (body mass index >25.0) and calcified and non-calcified plaques of coronary arteries (CA). RESULTS: FR of RVM was detected in 21 subjects (12 males, 51-78 years old, median 67), 76% of whom had HT, 38% DM, 43% HL, 48% smoking history, 52% were obese, and 76% had calcified and 24% had non-calcified plaques of CA. Only obesity was significantly higher in FR (p<0.05). A logistic regression model showed, although there was a close association between obesity and an increased incidence of FR, it did not reach statistical significance (p=0.0515, relative risk 5.11). CONCLUSIONS: Obesity is significantly more common in cases of FR, and despite a negative multivariable analysis, may influence FR in the RVM. FR in obesity may occur independently of clinically-significant arrhythmia, which is different from ARVC. Thus, even with FR, obesity must be considered as a diagnosis before ARVC.

Adult↗

PubMed2004

Predicting polymorphic transformation curves using a logistic equation.

The commonly used solid-state reaction models (for example-Prout-Tompkins, Avrami-Erofe'ev) describe the polymorphic transformation data only over a certain range, alpha from 10% to 90%. Predictions based on a fit to a fraction of the data are inadequate because we ignore the early induction phase of the reaction, which is important for predictive purposes. A four-parameter logistic equation describes the data over the entire curve for polymorphic transformation at high temperatures. We use the parameters of the logistic equation to predict the transformation curves. The predicted curves agree with the experimental data.

Algorithms↗

PubMed2005

Comparing logistic models based on modified GCS motor component with other prognostic tools in prediction of mortality: results of study in 7226 trauma patients.

A simple reproducible and sensitive prognostic trauma tool is still needed. In this article we have introduced modified GCS motor response (MGMR) and evaluated the performance of logistic models based on this variable. The records of 8452 trauma patients admitted to major hospitals of Tehran from 1999 to 2000 were analysed. 7226 records with known outcome were included in our study. Logistic models based on outcome (death versus survival) as a dependent variable and Injury Severity Score (ISS), Revised Trauma Score (RTS), Glasgow Coma Scale (GCS), GCS motor component (GMR) and MGMR (following command [=2], movement but not following [=1] command and without movement [=0]) were compared based on their accuracy and area under the Receiver Operating Characteristic (ROC) curve. The accuracy of the Trauma and Injury Severity Score (TRISS), RTS, GCS, GMR and MGMR models were almost the same. Considering both the area under the ROC curve and accuracy, the age included MGMR model was also comparable with other age included models (RTS+age, GCS+age, GMR+age). We concluded that although in some situations we need more sophisticated models, should our results be reproducible in other populations, MGMR (with or without age added) model may be of considerable practical value.

Adolescent↗

PubMed2004

Automated variable selection methods for logistic regression produced unstable models for predicting acute myocardial infarction mortality.

OBJECTIVES: Automated variable selection methods are frequently used to determine the independent predictors of an outcome. The objective of this study was to determine the reproducibility of logistic regression models developed using automated variable selection methods. STUDY DESIGN AND SETTING: An initial set of 29 candidate variables were considered for predicting mortality after acute myocardial infarction (AMI). We drew 1,000 bootstrap samples from a dataset consisting of 4,911 patients admitted to hospital with an AMI. Using each bootstrap sample, logistic regression models predicting 30-day mortality were obtained using backward elimination, forward selection, and stepwise selection. The agreement between the different model selection methods and the agreement across the 1,000 bootstrap samples were compared. RESULTS: Using 1,000 bootstrap samples, backward elimination identified 940 unique models for predicting mortality. Similar results were obtained for forward and stepwise selection. Three variables were identified as independent predictors of mortality among all bootstrap samples. Over half the candidate prognostic variables were identified as independent predictors in less than half of the bootstrap samples. CONCLUSION: Automated variable selection methods result in models that are unstable and not reproducible. The variables selected as independent predictors are sensitive to random fluctuations in the data.

Aged↗

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↗

PubMed2005

The role of logistic constraints in termite construction of chambers and tunnels.

In previous models of the building behaviour of termites, physical and logistic constraints that limit the movement of termites and pheromones have been neglected. Here, we present an individual-based model of termite construction that includes idealized constraints on the diffusion of pheromones, the movement of termites, and the integrity of the architecture that they construct. The model allows us to explore the extent to which the results of previous idealized models (typically realised in one or two dimensions via a set of coupled partial differential equations) generalize to a physical, 3-D environment. Moreover we are able to investigate new processes and architectures that rely upon these features. We explore the role of stigmergic recruitment in pillar formation, wall building, and the construction of royal chambers, tunnels and intersections. In addition, for the first time, we demonstrate the way in which the physicality of partially built structures can help termites to achieve efficient tunnel structures and to establish and maintain entrances in royal chambers. As such we show that, in at least some cases, logistic constraints can be important or even necessary in order for termites to achieve efficient, effective constructions.

Animals↗

PubMed2006

Evaluation of magnetic resonance imaging criteria for cavernous sinus invasion in patients with pituitary adenomas: logistic regression analysis and correlation with surgical findings.

BACKGROUND: This study used high-resolution magnetic resonance (MR) imaging (1.5 T) to define and evaluate preoperative imaging criteria for cavernous sinus invasion (CSI) by pituitary adenoma (PA). METHODS: Magnetic resonance images obtained from 103 patients with PA submitted to surgery (48 with CSI) were retrospectively reviewed. The following MR signs were studied and compared with intraoperative findings: (1) presence of normal pituitary gland between the adenoma and cavernous sinus (CS), (2) status of the CS venous compartments, (3) CS size, (4) CS lateral wall bulging, (5) displacement of the intracavernous internal carotid artery (ICA) by adenoma, (6) grade of parasellar extension (Knosp-Steiner classification), and (7) percentage of intracavernous ICA encased by the tumor. Statistical analysis was performed using chi2 testing, and sensitivity, specificity, positive predictive value (PPV), and negative predictive value (NPV) were obtained for each MR finding. The odds ratio of the most significant criteria was also obtained, and the multiple logistic regression test was used to compare the criteria altogether. RESULTS: The following signs have been found to represent accurate criteria for noninvasion of the CS: (1) normal pituitary gland interposed between the adenoma and the CS (PPV, 100.0%), (2) intact medial venous compartment (PPV, 100.0%), and (3) percentage of encasement of the intracavernous ICA lower than 25% (NPV, 100.0%). Cavernous sinus invasion was certain if the percentage of encasement of the intracavernous ICA was higher than 45% and 3 or more CS venous compartments were not depicted. The most valuable criterion of CSI by logistic regression analysis was the percentage of encasement of intracavernous ICA of 30% or more, with an odds ratio of 49.25. CONCLUSION: The preoperative diagnosis of CSI by PA is extremely important because endocrinologic remission is rarely obtained after microsurgery alone in patients with invasive tumors. The aforementioned MR imaging criteria may be useful in patient's management and in advising most of the patients preoperatively on the potential need for complimentary therapy after surgery.

Adenoma↗

PubMed2006

Logistic regression analysis of pregnancy rate following transfer of Bos indicus embryos into Bos indicus x Bos taurus heifers.

Factors affecting pregnancy rate of 5627 Zebu embryos in crossbred females with unknown proportions of Holstein and Zebu breeding were examined. After evaluation for developmental stage, quality, and viability, embryos were immediately transferred to recipients. Pregnancy diagnosis was conducted approximately 53 d after transfer; pregnancy rate was coded as a binomial event and analyzed using logistic regression models. Maximum likelihood methodology and the likelihood ratio statistic were used to estimate regression coefficients and test hypotheses. Explanatory variables were year of transfer (1992-1999), season of transfer (summer, autumn, winter and spring), breed of the embryo (Guzerat, Gyr or Nellore), stage of the embryo (morula, early blastocyst, blastocyst, expanded blastocyst, and hatching blastocyst), quality of the embryo (excellent, good or regular), and donor-recipient synchrony (estrus in the recipient occurred 2-3 d before, 1 d before, the day of, 1 d after, or 2-3 d after estrus in the donor). Average pregnancy rate was 63.7%. Pregnancy rates were not significantly affected by breed of embryo. The best multiple-logistic model to explain the pregnancy result included the effects of year and season of transfer, embryo stage and quality, and estrous synchrony between donor and recipient (P<or=.01). High pregnancy rates occurred when transfers occurred in autumn, early blastocysts or morulae were transferred, and excellent quality embryos were chosen. In addition, pregnancy rates were highest when estrus in the recipient began 1 d earlier than that of the donor.

Animals↗

PubMed2003

Population pharmacokinetic and pharmacodynamic modeling of etanercept using logistic regression analysis.

OBJECTIVE: Our objective was to develop a population pharmacokinetic and pharmacodynamic model of etanercept in patients with rheumatoid arthritis, with the American College of Rheumatology response criterion of 20% improvement (ACR20) used as a binary clinical outcome variable. METHODS: Concentration-time profiles from 25 subjects, administered 25 mg subcutaneous etanercept twice weekly for 24 weeks, were pooled with data from 77 subjects, enrolled in a 24-week, randomized, double-blind study comparing 25 mg and 50 mg subcutaneous etanercept twice weekly. The cumulative area under the concentration-time curve (AUC) was used as the exposure variable, and ACR20 was the binomial clinical outcome. ACR20 data from another 80 placebo-treated patients enrolled in a randomized, double-blind phase III study were used to describe the placebo time course of ACR20. A logistic regression analysis with NONMEM was applied to describe the exposure-response relationship, and the 95% confidence intervals (95% CIs) were constructed by bootstrapping 1000 times. RESULTS: The population mean apparent clearance was 0.117 L/h (95% CI, 0.108-0.130 L/h) for white female patients and 0.138 L/h (95% CI, 0.118-0.163 L/h) for white male patients. Interindividual variability and interoccasion variability were 41.1% and 27.6%, respectively. The mean absorption half-life was 20.9 hours, and the elimination half-life was 95.4 hours. An improved response profile in male patients was shown, but the multiplicative factor between slope on cumulative AUC between male and female patients was not statistically significant (1.69; 95% CI, 0.37-9.99). The model-predicted percentage of patients achieving ACR20 at 6 months after dosing of 25 mg subcutaneously twice weekly was 54.9%, comparable to the observed 52.9%. CONCLUSION: The population pharmacokinetic analysis confirmed that etanercept is slowly absorbed and eliminated after subcutaneous administration. The logistic model linking cumulative AUC with ACR20 adequately characterized the time course of clinical improvement in patients with rheumatoid arthritis receiving etanercept.

Area Under Curve↗

PubMed2000

Prospective evaluation of logistic regression models for the diagnosis of ovarian cancer.

OBJECTIVE: To test the accuracy of three logistic regression models in diagnosing malignancy in women with adnexal masses. METHODS: This was a prospective collaborative study. Women were recruited from three hospitals and all assessments were performed at the Gynaecology Ultrasound Unit, King's College Hospital. One hundred women with known adnexal masses were examined preoperatively. The demographic, biochemical, and sonographic data recorded for each patient included age, menopausal status, CA 125 levels, ultrasound morphology, and Doppler blood flow analysis. The diagnosis of malignancy was made for each woman using three logistic regression models previously described by Alcazar et al, Tailor et al, and Timmerman et al. Variables used in these models were then combined to form a new model. The results were compared with the final histopathologic diagnosis. RESULTS: Sixty-seven women had benign tumors and 33 had ovarian cancer. Women with malignant tumors were older than those with benign masses. There were significant differences in CA 125 levels, presence of papillary proliferations, and ascites between the two groups. The sensitivities and specificities achieved respectively by the models were as follows: 45% and 93% with Tailor et al's model, 9% and 99% with Alcazar et al's model, and 73% and 91% with Timmerman et al's model. There was no significant improvement over the performance of Timmerman et al's model and the new combined model. CONCLUSION: All models performed less well than originally reported. Combining the models did not lead to a significant improvement in performance. Larger sample sizes that incorporate all types of ovarian tumors are necessary to design more accurate diagnostic models.

Adult↗

PubMed2002

Calculating sample size bounds for logistic regression.

The calculation of a study's required sample size is one of the most important aspects of the validity of an epidemiological study. Logistic regression often is used in modelling in epidemiology. A simplified method to calculate the sample size for the multiple logistic-regression model was proposed by Hsieh et al. [Stat. Med. 17 (1998) 1623]. The approach for estimating the sample size is described and then applied in the planning of an epidemiological cross-sectional study of the associations of different risk factors with Toxoplasma infection among pregnant women. Although the method demands some additional information which is often difficult to obtain, it is a very useful tool in veterinary epidemiology.

Animals↗