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PubMed2006

Establishing the change in antibiotic resistance of Enterococcus faecium strains isolated from Dutch broilers by logistic regression and survival analysis.

In this study, we investigated the change in the resistance of Enterococcus faecium strains isolated from Dutch broilers against erythromycin and virginiamycin in 1998, 1999 and 2001 by logistic regression analysis and survival analysis. The E. faecium strains were isolated from caecal samples that had been randomly collected from six slaughterhouses. Moreover, between the sample collection in 1998 and the sample collection in 1999, virginiamycin and the macrolide antibiotics (of which erythromycin is a member) have been banned in The Netherlands from use in broiler feeds as growth promoter. In the logistic regression analysis we used the internationally accepted cut-off values to determine whether bacteria were resistant or not. In the survival analysis, inhibition of bacterial growth was the event and time to event was replaced by concentration of antibiotic to event. As a consequence, changes in the growth of bacteria can be tested over an entire range of concentrations and no cut-off value for resistance has to be determined. We performed the survival analysis by use of a Cox logistic model with an odds ratio (OR) for the increase of the odds of the basic hazard rate as outcome. Both the logistic regression and the survival analyses showed that resistance to erythromycin and virginiamycin decreased during the study period. In the logistic regression model the ORs associated with the fraction of bacteria inhibited by the antibiotics in 2001 as compared to 1998 were 3.76 (2.57-5.49) for erythromycin and 11.65 (7.68-17.66) for virginiamycin. The corresponding ORs from the survival analysis were lower; 2.88 (2.21-3.76) and 2.11 (1.80-2.49), respectively. The reason for the differences between the ORs of the survival analysis and the logistic regression analysis is probably because most changes in resistance included the cut-off value and logistic regression specifically examines those changes.

Abattoirs↗
PubMed1999

Logistic regression models in obstetrics and gynecology literature.

OBJECTIVE: To evaluate the reporting of multivariable logistic regression analyses and assess variations in quality over time in the obstetrics and gynecology literature. METHODS: Methodologic criteria for reporting logistic regression analyses were developed to identify problems affecting accuracy, precision, and interpretation of this approach to multivariable statistical analysis. These criteria were applied to 193 articles that reported multivariable logistic regression in the issues of four generic obstetrics and gynecology journals in 1985, 1990, and 1995. Rates of compliance with the methodologic criteria and their time trends were analyzed. RESULTS: The proportion of articles using logistic regression analysis increased over time: 1.7% in 1985, 2.8% in 1990, and 6.5% in 1995 (P < .001 for trend). Violations and omissions of methodologic criteria for reporting logistic models were common. The research question, in terms of dependent and independent variables, was not clearly reported in 32.1%. The process of variable selection was inadequately described in 51.8% of the articles. Among articles with ranked independent variables, 85.1% did not report assessment of conformity to linear gradient. Tests for goodness of fit were not given in 93.2% of articles. The contribution of the independent variables could not be evaluated in 36.2% of the articles because of a lack of coding of the variables. Interactions between variables were not assessed in 86.4% of articles. Analysis of variations in the quality of logistic regression analyses over time showed no increase in reporting of the criteria concerning variable selection and goodness of fit. However, the proportion of articles reporting one quality criterion concerning interpretation of the substantive significance of independent variables showed a trend toward improvement: 42.3% in 1985, 73.6% in 1990, and 75.4% in 1995 (P = .004 for trend). CONCLUSION: The reporting of multivariable logistic regression models in the obstetrics and gynecology literature is poor, and the time trends of improvement in quality of reporting are not particularly encouraging.

Gynecology↗
PubMed2001

The use of neural networks and logistic regression analysis for predicting pathological stage in men undergoing radical prostatectomy: a population based study.

PURPOSE: Clinical under staging occurs in 40% to 60% of patients who undergo radical prostatectomy for prostate cancer. To decrease under staging several methods of predicting pathological stage preoperatively have been developed based on statistical logistic regression analysis and neural networks. To our knowledge none has been validated in our homogeneous regional patient population to date. We created logistic regression and neural network models, and implemented and adapted them into our practice. We also compared the 2 methods to determine their value and practicality in daily clinical practice. We present the results of our novel approach for predicting pathological staging of prostate adenocarcinoma. MATERIALS AND METHODS: Between 1986 and 1999, 600 white men from the Aragon region of Spain underwent surgery for prostate cancer; of whom 468 were selected for study. Predictive study variables included patient age, clinical stage, biopsy Gleason score and preoperative prostate specific antigen (PSA). The predicted result included in analysis was organ confined or nonorgan confined disease. Data were analyzed by multivariate logistic regression and a supervised neural network (multilayer perceptron and radial basis function). Results were compared by comparing the areas under the receiver operating characteristics curves. RESULTS: We generated 5 logistic regression models. The model created with clinical staging, Gleason biopsy score and PSA distributed in 5 categories (p <0.001) with an area under the receiver operating characteristics curve of 0.840 proved to be most predictive of pathological stage. Similarly of the 6 neural network models evaluated the radial basis function model, which included age, clinical stage, Gleason biopsy score and preoperative PSA distributed in 5 categories with an area under the curve of 0.882, proved the most predictive but not superior to the logistic regression model. The difference in the area under the curves in the 2 chosen models was 0.042 (p = 0.1). CONCLUSIONS: It is possible to generate useful predictive models of organ confined disease using logistic regression or neural networks with high indexes of clinical and statistical validity. However, using these variables neural networks did not prove to be better than logistic regression analysis. Therefore, better predictive variables must be identified, preferably nonlinear characteristics with respect to the probability of organ confined tumor, to generate better predictive models using neural networks.

Aged↗
PubMed1988

Estimation of probabilities using the logistic model in retrospective studies.

Methods for estimating the parameters of the logistic regression model when the data are collected using a case-control (retrospective) scheme are compared. The regression coefficients are estimated by maximum likelihood methodology. This leaves the constant term parameter to be estimated. Four methods for estimating this parameter are proposed. The comparison of the four estimators is in two parts. First, they are compared for large samples. This is accomplished via the asymptotic distribution of the estimators. Second, the estimators are compared for small samples. This is conducted via stimulation using 11 logistic models. The estimation of the posterior probability of the response variable being a success (Px), as given by the logistic regression model, when the constant parameter is estimated by each of the four proposed methods is the main focus of this paper. A third concern is the comparison of the logistic discriminant procedures when each of the four methods of estimating the constant parameters is used. In addition, the linear discriminant function procedure is included. This comparison is executed only for small samples via simulation. It was found that when estimating Px, method 1 (which is essentially the MLE) minimizes the expected mean square error. The results were not as clear when the parameter of interest was the constant term itself. The results from the classification comparisons implied that when the logistic model contains mostly (or all) binary regression variables the logistic discriminant procedure using method 1 to estimate the constant term gives minimum expected error rate; otherwise the linear discriminant function gives minimum expected error rate. In the latter case the logistic discriminant procedure (method 1 estimator of the constant term) is approximately as good.

Computer Simulation↗
PubMed2005

Comparative analysis of logistic regression and artificial neural network for computer-aided diagnosis of breast masses.

RATIONALE AND OBJECTIVE: To compare logistic regression and artificial neural network for computer-aided diagnosis on breast sonograms. MATERIALS AND METHODS: Ultrasound images of 24 malignant and 30 benign masses were analyzed quantitatively for margin sharpness, margin echogenicity, and angular variation in margin. These features and age of patients were used with two pattern classifiers, logistic regression, and an artificial neural network to differentiate between malignant and benign masses. The performance of two methods was compared by receiver operating characteristic (ROC) analysis. RESULTS: The area under the ROC curve Az (+/-SD) of the logistic regression analysis was 0.853 +/- 0.059 with 95% confidence limit (0.760-0.950). The area under the ROC curve of the artificial neural network analysis was 0.856 +/- 0.058 with 95% confidence limit (0.734-0.936). Although both the logistic regression and the artificial neural network had the same area under the ROC curve, the shapes of two curves were different. At 95% sensitivity, the artificial neural network had 76.5% specificity, whereas logistic regression had 64.7% specificity. CONCLUSION: There was no difference in performance between logistic regression and the artificial neural network as measured by the area under the ROC curve. However, at a fixed 95% sensitivity, the artificial neural network had higher (12%) specificity compared with logistic regression value.

Breast Neoplasms↗
PubMed2005

Repeated split sample validation to assess logistic regression and recursive partitioning: an application to the prediction of cognitive impairment.

Screening strategies play an important part in the identification and diagnosis of illness. Testing of such strategies in a clinical trial can have important implications for the treatment of such illnesses. Before the clinical trial, however, it is important to develop a practical screening/classification procedure that accurately predicts the presence of the illness in question. Recent published studies have shown a growing preference for classification tree/recursive partitioning procedures.This paper compares the application of logistic regression and recursive partitioning to a neuropsychological data set of 252 patients recruited from four Veterans Affairs Medical Centers. Logistic regression and recursive partitioning was used to predict cognitive impairment in 12 randomly selected exploratory/validation samples. We assessed the effect of sampling on variable selection and predictive accuracy.Predictive accuracy of the logistic regression and recursive partitioning procedures was comparable across the exploratory data samples but varied across the validation samples. Based on shrinkage, both classification procedures performed equally well for the prediction of cognitive impairment across the twelve samples. While logistic regression provided an estimated probability of outcome for each patient, it required several mathematical calculations to do so. However, logistic regression selected one or two less predictors than recursive partitioning with comparable predictive accuracy. Recursive partitioning, on the other hand, readily identified patient characteristics and variable interactions, was easy to interpret clinically and required no mathematical calculations. There was a high degree of overlap of the predictor variables between the two procedures.In the context of neuropsychological screening, logistic regression and recursive partitioning performed equally well and were quite stable in the selection of predictors for the identification of patients with cognitive impairment, although recursive partitioning may be easier to use in a clinical setting because it is based on a simple decision tree.

Cognition Disorders↗
PubMedDate not supplied

Logistic regression when binary predictor variables are highly correlated.

Standard logistic regression can produce estimates having large mean square error when predictor variables are multicollinear. Ridge regression and principal components regression can reduce the impact of multicollinearity in ordinary least squares regression. Generalizations of these, applicable in the logistic regression framework, are alternatives to standard logistic regression. It is shown that estimates obtained via ridge and principal components logistic regression can have smaller mean square error than estimates obtained through standard logistic regression. Recommendations for choosing among standard, ridge and principal components logistic regression are developed. Published in 2001 by John Wiley & Sons, Ltd.

Computer Simulation↗
PubMed2003

Logistic or additive EuroSCORE for high-risk patients?

OBJECTIVES: To assess whether the use of the full logistic European System for Cardiac Operative Risk Evaluation (EuroSCORE) is superior to the standard additive EuroSCORE in predicting mortality in high-risk cardiac surgical patients. METHODS: Both the simple additive EuroSCORE and the full logistic EuroSCORE were applied to 14,799 cardiac surgical patients from across Europe, of whom there were 4293 high-risk patients (additive EuroSCORE of 6 or more). The systems were compared for absolute prediction and discrimination (area under the receiver operating characteristic (ROC) curve). RESULTS: Actual mortality was 4.72%. The logistic model was closer to this than the additive model (4.84% (4.72-4.94) versus 4.21 (4.21-4.26)). Most of this difference was due to high-risk patients where actual mortality was 11.18% and predicted was 7.83% (additive) and 11.23% (logistic). Discrimination was similar in both systems as measured by the area under the ROC curve (additive 0.783, logistic 0.785). CONCLUSIONS: The additive EuroSCORE model remains a simple "gold standard" for risk assessment in European cardiac surgery, usable at the bedside without complex calculations or information technology. The logistic model is a better risk predictor especially in high-risk patients and may be of interest to institutions engaged in the study and development of risk stratification.

Aged↗
PubMed2003

Comparison of logistic regression versus propensity score when the number of events is low and there are multiple confounders.

The aim of this study was to use Monte Carlo simulations to compare logistic regression with propensity scores in terms of bias, precision, empirical coverage probability, empirical power, and robustness when the number of events is low relative to the number of confounders. The authors simulated a cohort study and performed 252,480 trials. In the logistic regression, the bias decreased as the number of events per confounder increased. In the propensity score, the bias decreased as the strength of the association of the exposure with the outcome increased. Propensity scores produced estimates that were less biased, more robust, and more precise than the logistic regression estimates when there were seven or fewer events per confounder. The logistic regression empirical coverage probability increased as the number of events per confounder increased. The propensity score empirical coverage probability decreased after eight or more events per confounder. Overall, the propensity score exhibited more empirical power than logistic regression. Propensity scores are a good alternative to control for imbalances when there are seven or fewer events per confounder; however, empirical power could range from 35% to 60%. Logistic regression is the technique of choice when there are at least eight events per confounder.

Bias↗
PubMed2001

Comparison of logistic regression and linear regression in modeling percentage data.

Percentage is widely used to describe different results in food microbiology, e.g., probability of microbial growth, percent inactivated, and percent of positive samples. Four sets of percentage data, percent-growth-positive, germination extent, probability for one cell to grow, and maximum fraction of positive tubes, were obtained from our own experiments and the literature. These data were modeled using linear and logistic regression. Five methods were used to compare the goodness of fit of the two models: percentage of predictions closer to observations, range of the differences (predicted value minus observed value), deviation of the model, linear regression between the observed and predicted values, and bias and accuracy factors. Logistic regression was a better predictor of at least 78% of the observations in all four data sets. In all cases, the deviation of logistic models was much smaller. The linear correlation between observations and logistic predictions was always stronger. Validation (accomplished using part of one data set) also demonstrated that the logistic model was more accurate in predicting new data points. Bias and accuracy factors were found to be less informative when evaluating models developed for percentage data, since neither of these indices can compare predictions at zero. Model simplification for the logistic model was demonstrated with one data set. The simplified model was as powerful in making predictions as the full linear model, and it also gave clearer insight in determining the key experimental factors.

Clostridium botulinum↗
PubMedDate not supplied

Diagnosis of sensorineural hearing loss with neural networks versus logistic regression modeling of distortion product otoacoustic emissions.

We investigated whether modeling with artificial neural networks or logistic regression of distortion product otoacoustic emissions (DPOAE), across diverse frequencies, may achieve an accurate diagnosis of sensorineural hearing loss (SNHL) of cochlear origin. 256 ears (90 with SNHL and 166 with normal hearing) were evaluated with pure-tone audiometry, impedance audiometry, speech audiometry and DPOAE. Ears were split into training (n = 176) and validation (n = 80) sets. Input variables included gender, age, examination time, DPOAE intensity at F(2) frequencies 593, 937, 1906, 3812 and 6031 Hz, and respective values corrected for noise levels. In the validation data set, an average network had an area under the receiver operating characteristic curve (AUC) of 0.86 (accuracy 84%). Logistic regressions including all these variables or those selected by backward elimination had AUC values of 0.91 and 0.92, respectively (accuracy 85% both). Eleven of 12 trained networks had better specificity than the backward elimination logistic regression, and the backward elimination logistic regression had a better sensitivity than 11 of the 12 networks. Both modeling approaches correctly identified all ears with sudden hearing loss, congenital hearing loss, head trauma, nuclear jaundice and ototoxicity, and 2-3 of 5 ears with acoustic trauma, but missed 1-3 of 3 ears with Ménière's disease and 4-6 of 8 ears with abnormal pure-tone thresholds on audiometry which had no accompanying findings. For SNHL exceeding 45 dB HL on a pure-tone threshold, sensitivity was 83% (15/18) by neural networks and 84 or 94% (16/18 or 17/18) by logistic regression. Both neural-network-based analysis and logistic regression modeling of the DPOAE pattern across a range of frequencies offer promising approaches for the objective diagnosis of moderate and severe SNHL.

Adult↗
PubMed1997

Hybrid logistic characterization of isometric twitch force-time curve of intact blood-perfused canine right ventricular papillary muscle.

We previously found that a ventricular isovolumic pressure-time curve could be well fitted by the difference between two S-shaped logistic curves for the pressure rising and falling components, and called it "hybrid logistic" function: P(t)=A/[1+exp[-(4B/A)(t-C)]]-D/[1+exp[-(4E/D)(t-F)]]+G. We reported that the parameters of this hybrid logistic function are useful to characterize left ventricular contraction and relaxation comprehensively. In this study, we investigated how well this hybrid logistic function could fit the isometric twitch force-time curves of cross-circulated right ventricular papillary muscles of 7 dogs. This function precisely fitted the isometric force curves with correlation coefficients above 0.9996, much better than another fitting function (F(t)=C(t/A)(B)exp[1-(t/A)(B)]) proposed by Nwasokwa. The present results indicate that our hybrid logistic function can also reasonably express the canine right ventricular papillary muscle isometric twitch force-time curve. We suggest the possibility that the parameters of this hybrid logistic function are also useful to comprehensively characterize right ventricular papillary muscle twitch contraction and relaxation.

Animals↗
PubMed1999

Hybrid logistic characterization of isometric twitch force curve of isolated ferret right ventricular papillary muscle.

We previously found that the isovolumic pressure curve of the left ventricle and the isometric twitch force curve of the right ventricular in situ papillary muscle, both of the blood-perfused canine heart, were precisely fitted by our newly proposed hybrid logistic function. This function describes the difference between the two S-shaped logistic functions for the rising and falling components: A/[1+exp{-(4B/A)(t-C)}]-D/[1+exp{-(4E/D)(t-F)}]+G. This function characterizes comprehensively both ventricular and in situ papillary muscle contraction and relaxation. In the present study, we hypothesized that this function could also characterize the force curve of the most popular, standard-type, isolated and Tyrode-superfused papillary muscle preparation. To test this hypothesis, we investigated how precisely the hybrid logistic function could fit 112 isometric twitch force curves observed in eight isolated and Tyrode-superfused ferret right ventricular papillary muscles at different muscle lengths and extracellular Ca2+ concentrations. We always obtained a precise curve fitting with a correlation coefficient above 0.9987. This fitting was much more precise than sinusoidal and polynomial exponential function curve fittings. These results supported the present hypothesis. We conclude that our hybrid logistic function reasonably characterizes the force curve of the isolated myocardial preparation. This result broadens the generality of the hybrid logistic characterization of ventricular isovolumic pressure and myocardial isometric twitch force generation. The hybrid logistic characterization seems to be an integrative expression of contractile processes in myocardial twitch contraction.

Animals↗
PubMed1998

Inference using conditional logistic regression with missing covariates.

When there are many nuisance parameters in a logistic regression model, a popular method for eliminating these nuisance parameters is conditional logistic regression. Unfortunately, another common problem in a logistic regression analysis is missing covariate data. With many nuisance parameters to eliminate and missing covariates, many investigators exclude any subject with missing covariates and then use conditional logistic regression, often called a complete-case analysis. In this article, we derive a modified conditional logistic regression that is appropriate with covariates that are missing at random. Performing a conditional logistic regression with only the complete cases is convenient with existing statistical packages, but it may give bias if missingness is not completely at random.

Bias↗
PubMed1998

Two-parameter logistic and Weibull equations provide better fits to survival data from isogenic populations of Caenorhabditis elegans in axenic culture than does the Gompertz model.

We have fitted Gompertz, Weibull, and two- and three-parameter logistic equations to survival data obtained from 77 cohorts of Caenorhabditis elegans in axenic culture. Statistical analysis showed that the fitting ability was in the order: three-parameter logistic > two-parameter logistic = Weibull > Gompertz. Pooled data were better fit by the logistic equations, which tended to perform equally well as population size increased, suggesting that the third parameter is likely to be biologically irrelevant. Considering restraints imposed by the small population sizes used, we simply conclude that the two-parameter logistic and Weibull mortality models for axenically grown C. elegans generally provided good fits to the data, whereas the Gompertz model was inappropriate in many cases. The survival curves of several short- and long-lived mutant strains could be predicted by adjusting only the logistic curve parameter that defines mean life span. We conclude that life expectancy is genetically determined; the life span-altering mutations reported in this study define a novel mean life span, but do not appear to fundamentally alter the aging process.

Animals↗
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↗
PubMed2006

The logistic EuroSCORE in cardiac surgery: how well does it predict operative risk?

OBJECTIVES: To study the ability of the logistic EuroSCORE to predict operative risk in contemporary cardiac surgery. DESIGN: Retrospective analysis of prospectively collected data. SETTING: All National Health Service centres undertaking adult cardiac surgery in northwest England. PATIENTS: All patients undergoing cardiac surgery between April 2002 and March 2004. MAIN OUTCOME MEASURES: The predictive ability of the logistic EuroSCORE was assessed by analysing how well it discriminates between patients with differing observed risk by using the area under the receiver operating characteristic (ROC) curve and studying how well it is calibrated against observed in-hospital mortality. The performance of the EuroSCORE was examined in the following surgical subgroups: all cardiac surgery, isolated coronary artery surgery, isolated valve surgery, combined valve and coronary surgery, mitral valve surgery, aortic valve surgery and other surgery. RESULTS: 9995 patients underwent surgery. The discrimination of the logistic EuroSCORE was good with a ROC curve area of 0.79 for all cardiac surgery (range 0.71-0.79 in the subgroups). For all operations, the predicted mortality was 5.7% and observed mortality was 3.3%. The logistic EuroSCORE overpredicted observed mortality for all subgroups but by differing degrees (p = 0.02) CONCLUSIONS: The logistic EuroSCORE is a reasonable overall predictor for contemporary cardiac surgery but overestimates observed mortality. Its accuracy at predicting risk in different surgical subgroups varies. The logistic EuroSCORE should be recalibrated before it is used to gain reassurance about outcomes. Caution should be exercised when using it to compare hospitals or surgeons with a different operative case mix.

Cardiac Surgical Procedures↗
PubMed1998

A simple method of sample size calculation for linear and logistic regression.

A sample size calculation for logistic regression involves complicated formulae. This paper suggests use of sample size formulae for comparing means or for comparing proportions in order to calculate the required sample size for a simple logistic regression model. One can then adjust the required sample size for a multiple logistic regression model by a variance inflation factor. This method requires no assumption of low response probability in the logistic model as in a previous publication. One can similarly calculate the sample size for linear regression models. This paper also compares the accuracy of some existing sample-size software for logistic regression with computer power simulations. An example illustrates the methods.

Humans↗