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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↗
PubMed2007

A weighted logistic regression model for estimation of recurrence of adenomas.

In a colorectal polyp prevention trial, some participants might have their follow-up colonoscopy conducted before the scheduled time (i.e. at the end of the trial). This results in variable follow-up lengths for participants and the data of recurrence status at the end of the trial can be considered as current status data. In this paper, we use a weighted logistic regression model to estimate recurrence rate of adenoma data at the end of the trial. The weights are used to adjust for variable follow-up. We show that logistic regression tends to underestimate recurrence rate. In a simulation study, we show that Kaplan-Meier estimator derived from the right endpoint of the current status data tends to overestimate recurrence rate in contrast to logistic regression and the weighted logistic regression method can produce reasonable estimates of recurrence rate even under a high non-compliance rate compared to conventional logistic regression and Kaplan-Meier estimator. The method described here is illustrated with an example from a colon cancer study.

Adenoma↗
PubMed2005

Public health application comparing multilevel analysis with logistic regression: immunization coverage among long-term care facility residents.

PURPOSE: Public health studies often sample populations using nested sampling plans. When the variance of the residual errors is correlated between individual observations as a result of these nested structures, traditional logistic regression is inappropriate. We used nested nursing home patient data to show that one-level logistic regression and hierarchical multilevel regression can yield different results. METHODS: We performed logistic and multilevel regression to determine nursing home resident characteristics associated with receiving pneumococcal immunizations. Nursing home characteristics such as type of ownership, immunization program type, and certification were collected from a sample of 249 nursing homes in 14 selected states. Nursing home resident data including demographics, receipt of immunizations, cognitive patterns, and physical functioning were collected on 100 randomly selected residents from each facility. RESULTS: Factors associated with receipt of pneumococcal vaccination using logistic regression were similar to those found using multilevel regression model with some exceptions. Predictors using logistic regression that were not significant using multilevel regression included race, speech problems, infections, renal failure, legal responsibility for oneself, and affiliation with a chain. Unstable health conditions were significant only in the multilevel model. CONCLUSIONS: When correlation of resident outcomes within nursing home facilities was not considered, statistically significant associations were likely due to residual correlation effects. To control the probability of type I error, epidemiologists evaluating public health data on nested populations should use methods that account for correlation among observations.

Aged↗
PubMed2005

An alternative formulation for a delayed logistic equation.

We derive an alternative expression for a delayed logistic equation, assuming that the rate of change of the population depends on three components: growth, death, and intraspecific competition, with the delay in the growth component. In our formulation, we incorporate the delay in the growth term in a manner consistent with the rate of instantaneous decline in the population given by the model. We provide a complete global analysis, showing that, unlike the dynamics of the classical logistic delay differential equation (DDE) model, no sustained oscillations are possible. Just as for the classical logistic ordinary differential equation (ODE) growth model, all solutions approach a globally asymptotically stable equilibrium. However, unlike both the logistic ODE and DDE growth models, the value of this equilibrium depends on all of the parameters, including the delay, and there is a threshold that determines whether the population survives or dies out. In particular, if the delay is too long, the population dies out. When the population survives, i.e., the attracting equilibrium has a positive value, we explore how this value depends on the parameters. When this value is positive, solutions of our DDE model seem to be well approximated by solutions of the logistic ODE growth model with this carrying capacity and an appropriate choice for the intrinsic growth rate that is independent of the initial conditions.

Animals↗
PubMed1997

Value of logistic discriminant analysis for interpreting initial visual field defects.

PURPOSE: The authors evaluate logistic discriminant analysis as a method for interpreting visual field results in initial stages of several ophthalmic diseases. METHODS: The authors retrospectively studied the visual field defects of 96 patients with early glaucomatous damage and prospectively studied 84 subjects with normal eyes (n = 28), cataracts (n = 27), diabetic retinopathy (n = 14), or hypertensive retinopathy (n = 15). The visual fields were examined at least twice with program G1 of Octopus 500 (Interzeag AG, Schlieren, Switzerland). Only one eye per patient was randomly selected and included in the study. The authors created a database with all visual field information provided by Octopus and applied logistic discriminant analysis (SAS Logistic Procedures, SAS Institute, Cary, NC) to obtain classification rules capable of qualifying visual field defects as glaucomatous or nonglaucomatous. The rules were tested with an independent sample. RESULTS: There were significant differences between the groups in the distribution of visual field defects tested by program G1. Logistic discriminant analysis correctly identified the glaucomatous or nonglaucomatous origin of the defects with a sensitivity of 65% to 85% and a specificity of 60% to 92%. CONCLUSIONS: Logistic discriminant analysis is a useful tool to aid in the interpretation of early glaucomatous and nonglaucomatous visual field defects.

Data Interpretation, Statistical↗
PubMed2001

Comparison of logistic regression and neural networks to predict rehospitalization in patients with stroke.

CONTEXT: Rehospitalization following inpatient medical rehabilitation has important health and economic implications for patients who have experienced a stroke. OBJECTIVE: Compare logistic regression and neural networks in predicting rehospitalization at 3-6-month follow-up for patients with stroke discharged from medical rehabilitation. DESIGN: The study was retrospective using information from a national database representative of medical rehabilitation patients across the US. SETTING: Information submitted to the Uniform Data System for Medical Rehabilitation from 1997 and 1998 by 167 hospital and rehabilitation facilities from 40 states was examined. PARTICIPANTS: 9584 patient records were included in the sample. The mean age was 70.74 years (SD = 12.87). The sample included 51.6% females and was 77.6% non-Hispanic White with an average length of stay of 21.47 days (SD = 15.47). MAIN OUTCOME MEASURES: Hospital readmission from 80 to 180 days following discharge. RESULTS: Statistically significant variables (P <.05) in the logistic model included sphincter control, self-care ability, age, marital status, ethnicity and length of stay. Area under the ROC curves were 0.68 and 0.74 for logistic regression and neural network analysis, respectively. The Hosmer-Lemeshow goodness-of-fit chi-square was 11.32 (df = 8, P = 0.22) for neural network analysis and 16.33 (df = 8, P = 0.11) for logistic regression. Calibration curves indicated a slightly better fit for the neural network model. CONCLUSION: There was no statistically significant or practical advantage in predicting hospital readmission using neural network analysis in comparison to logistic regression for persons who experienced a stroke and received medical rehabilitation during the period of the study.

Aged↗
PubMed2002

Comparison of prediction models for adverse outcome in pediatric meningococcal disease using artificial neural network and logistic regression analyses.

The objective of this study was to compare artificial neural network (ANN) and multivariable logistic regression analyses for prediction modeling of adverse outcome in pediatric meningococcal disease. We analyzed a previously constructed database of children younger than 20 years of age with meningococcal disease at four pediatric referral hospitals from 1985-1996. Patients were randomly divided into derivation and validation datasets. Adverse outcome was defined as death or limb amputation. ANN and multivariable logistic regression models were developed using the derivation set, and were tested on the validation set. Eight variables associated with adverse outcome in previous studies of meningococcal disease were considered in both the ANN and logistic regression analyses. Accuracies of these models were then compared. There were 381 patients with meningococcal disease in the database, of whom 50 had adverse outcomes. When applied to the validation data set, the sensitivities for both the ANN and logistic regressions models were 75% and the specificities were both 91%. There were no significant differences in any of the performance parameters between the two models. ANN analysis is an effective tool for developing prediction models for adverse outcome of meningococcal disease in children, and has similar accuracy as logistic regression modeling. With larger, more complete databases, and with advanced ANN algorithms, this technology may become increasingly useful for real-time prediction of patient outcome.

Adolescent↗
PubMed1998

Using binary logistic regression models for ordinal data with non-proportional odds.

The proportional odds model (POM) is the most popular logistic regression model for analyzing ordinal response variables. However, violation of the main model assumption can lead to invalid results. This is demonstrated by application of this method to data of a study investigating the effect of smoking on diabetic retinopathy. Since the proportional odds assumption is not fulfilled, separate binary logistic regression models are used for dichotomized response variables based upon cumulative probabilities. This approach is compared with polytomous logistic regression and the partial proportional odds model. The separate binary logistic regression approach is slightly less efficient than a joint model for the ordinal response. However, model building, investigating goodness-of-fit, and interpretation of the results is much easier for binary responses. The careful application of separate binary logistic regressions represents a simple and adequate tool to analyze ordinal data with non-proportional odds.

Bias↗
PubMed2004

Bayesian multivariate logistic regression.

Bayesian analyses of multivariate binary or categorical outcomes typically rely on probit or mixed effects logistic regression models that do not have a marginal logistic structure for the individual outcomes. In addition, difficulties arise when simple noninformative priors are chosen for the covariance parameters. Motivated by these problems, we propose a new type of multivariate logistic distribution that can be used to construct a likelihood for multivariate logistic regression analysis of binary and categorical data. The model for individual outcomes has a marginal logistic structure, simplifying interpretation. We follow a Bayesian approach to estimation and inference, developing an efficient data augmentation algorithm for posterior computation. The method is illustrated with application to a neurotoxicology study.

Algorithms↗
PubMed1995

Logistic time constant of isovolumic relaxation pressure-time curve in the canine left ventricle. Better alternative to exponential time constant.

BACKGROUND: The time constant of left ventricular (LV) relaxation derived from a monoexponential model has been widely used as an index of LV relaxation rate or lusitropism, although this model has several well-recognized problems. In the present study, we proposed a logistic model and derived a "logistic" time constant (TL) as a better alternative to the conventional "exponential" time constant (TE). METHODS AND RESULTS: A total of 189 beats (147 isovolumic and 42 ejecting beats) were investigated in seven canine excised cross-circulated heart preparations. We found that the logistic model fitted much more precisely all the observed LV isovolumic relaxation pressure-time [P(t)] curves than the monoexponential model (P < .05). The logistic model also fitted well both the time curve of the first derivative of the observed P(t) (dP/dt) and the dP/dt-P(t) phase-plane curve. Like TE, TL indicated that volume loading depressed LV lusitropism and that increasing heart rate and ejection fraction augmented it. TL was independent of the choice of cutoff point defining the end of isovolumic relaxation; TE was dependent on that choice. CONCLUSIONS: We conclude that the logistic model better fits LV isovolumic relaxation P(t) than the monoexponential model in the present heart preparation. We therefore propose TL as a better alternative to TE for evaluating LV lusitropism.

Animals↗
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↗
PubMed1989

Logistic patterning of brain activity.

Brain activity is a set of electrochemical events in the neural tissue during a specified period of time. Neural networks are the functionally connected and dynamically organized population of neurons and neuroglial cells, serving as a unified interface between environmental input and behavioral output at a specified time. They are patterned dynamically in neural space, time and intensity. It is proposed that 1. the electrophysiological patterning of brain activity follows the laws of logistic growth, decay and impulse response function and 2. that this process of logistic transform (LOGIT) of electrochemical processes is itself the general code of information transfer in the brain. A mathematical model of logistic transformation and new electrophysiological data based on the topographic mapping of event-related potentials (ERP) during selective auditory attentional tasks from nine healthy adults is presented. The N100-P200 and the N200-P300 segments of ERP's were analyzed at 20 ms intervals. Logarithmic latencies and voltages were highly correlated. Significant correlation was found between the mathematically estimated and actual values. The interpeak latencies also followed the logistic growth pattern and could be predicted by the model. A general equation of logistic transformation of brain activity, including variables of cortical voltage and frequency is proposed.

Adult↗
PubMed2005

Comparison between logistic regression and neural networks to predict death in patients with suspected sepsis in the emergency room.

INTRODUCTION: Neural networks are new methodological tools based on nonlinear models. They appear to be better at prediction and classification in biological systems than do traditional strategies such as logistic regression. This paper provides a practical example that contrasts both approaches within the setting of suspected sepsis in the emergency room. METHODS: The study population comprised patients with suspected bacterial infection as their main diagnosis for admission to the emergency room at two University-based hospitals. Mortality within the first 28 days from admission was predicted using logistic regression with the following variables: age, immunosuppressive systemic disease, general systemic disease, Shock Index, temperature, respiratory rate, Glasgow Coma Scale score, leucocyte counts, platelet counts and creatinine. Also, with the same input and output variables, a probabilistic neural network was trained with an adaptive genetic algorithm. The network had three neurone layers: 10 neurones in the input layer, 368 in the hidden layer and two in the output layer. Calibration was measured using the Hosmer-Lemeshow goodness-of-fit test and discrimination was determined using receiver operating characteristic curves. RESULTS: A total of 533 patients were recruited and overall 28-day mortality was 19%. The factors chosen by logistic regression (with their score in parentheses) were as follows: immunosuppressive systemic disease or general systemic disease (2), respiratory rate 24-33 breaths/min (1), respiratory rate > or = 34 breaths/min (3), Glasgow Come Scale score < or = 12 (3), Shock Index > or = 1.5 (2) and temperature < 38 degrees C (2). The network included all variables and there were no significant differences in predictive ability between the approaches. The areas under the receiver operating characteristic curves were 0.7517 and 0.8782 for the logistic model and the neural network, respectively (P = 0.037). CONCLUSION: A predictive model would be an extremely useful tool in the setting of suspected sepsis in the emergency room. It could serve both as a guideline in medical decision-making and as a simple way to select or stratify patients in clinical research. Our proposed model and the specific development method -- either logistic regression or neural networks -- must be evaluated and validated in an independent population.

Adolescent↗
PubMed2003

An appraisal of multivariable logistic models in the pulmonary and critical care literature.

OBJECTIVE: Multivariable modeling techniques are appearing in today's medical literature with increasing frequency. Improper reporting of these statistical models can potentially make the results of a study inaccurate, misleading, or difficult to interpret. We performed a manual literature search of five international pulmonary and critical care journals to determine the accuracy in the reporting of logistic regression modeling strategies. DESIGN: We examined all of the published manuscripts for 12 potential limitations in the reporting of important statistical methodologies over a 6-month period from July 1, 2000, until December 31, 2000. RESULTS: Of the 81 articles that included multivariable logistic regression analyses, only 65% (53 analyses) properly reported the coding classification of pertinent independent variables that were included in the final model. An odds ratio and confidence interval were reported for the independent variables included in the final model for 79% (64 analyses) and 74% (60 analyses), respectively. Only 12% (10 articles) referenced whether interaction terms or effect modifications were examined, 1% (1 article) reported testing for collinearity, and only 16% (13 articles) included a goodness-of-fit analysis of the logistic model. The type of statistical package was reported in 69% (56 articles). Finally, approximately 39% of the articles (22 of 57) may have overfit the logistic regression model, leading to potentially unreliable regression coefficients and odds ratios. CONCLUSIONS: Our results indicate that the reporting of multivariable logistic regression analyses in the pulmonary and critical care literature is often incomplete, therefore making it difficult for the reader to accurately interpret the manuscript. We recommend the implementation of adequate guidelines that will lead to overall improvements in the reporting and possibly to the conducting of multivariable analyses in the pulmonary medicine and critical care medicine literature.

Critical Care↗
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

Ransacking the curve of cardiac isovolumic pressure decay by logistic-and-oscillation regression.

The decelerative part of the left ventricular isovolumic pressure decay is an important phase to make the heart ready for diastolic refill (lusitropy). Its widely used characterization by an exponential regression with zero pressure asymptote or coestimated asymptote provides empirically biased time constant estimates because of significant deviations of the pressure decay from exponentiality. We systematically analyzed the regression residua of these pressure decays in isolated ejecting rat, guinea pig, and ferret hearts. A four-parametric logistic (tangens hyperbolicus) function, together with a superimposed acustomechanic oscillation, yields normally distributed residua with standard regression error typically less than one per cent of the initial pressure; this is the first model with proved unbiased and statistically complete regressive extraction of the information provided by the time course of pressure decay. Equal values of the lusitropic parameters (logistic time constant and pressure asymptote) were estimated even after the oscillatory component was removed from the regression model. Reliable estimates of the frequency, but not of the amplitude, can be obtained by fitting the oscillation model to the residua provided by the logistic; this two-step method is statistically weaker than the full one-step model, but it reduces computational effort. In conclusion, the four-parametric logistic, but not a three-parametric exponential or logistic model, suffices to obtain unbiased lusitropic parameters characterizing the left ventricular isovolumic pressure decay of small animal hearts.

Animals↗
PubMed2001

Assessment of a new logistic model in the preoperative evaluation of adnexal masses.

OBJECTIVE: To assess a new logistic regression model developed to predict malignancy in adnexal masses. METHODS: In the first part of this study, we developed a logistic model by applying logistic regression analysis in a series of 268 adnexal masses (203 benign and 65 malignant lesions) in 248 patients (mean age, 43.6 years; SD, 14.2 years) evaluated and treated at our institution. Eleven parameters were entered in the logistic regression analysis in a forward stepwise way. In the second part of the study, we evaluated the model's diagnostic performance in a further set of 135 adnexal masses (103 benign and 32 malignant tumors) in 129 patients (mean age, 44.4 years; SD, 14.6 years). This diagnostic performance was compared with that of age, tumor volume, Sassone's and Ferrazzi's B-mode ultrasonographic morphologic scoring systems, serum cancer antigen 125 level, and the tumor's lowest resistive index. Comparison was done by calculating the area under the receiver operating characteristic curve. RESULTS: In logistic analysis, only menopausal status, the presence of papillary projections, the logarithm of the cancer antigen 125 value, tumor blood flow location, and the lowest resistive index were retained in the model. The model had the best area under the curve (0.97), significantly higher than patient age (area under the curve, 0.78; P = .001), tumor volume (area under the curve, 0.68; P < .0001), cancer antigen 125 (area under the curve, 0.88; P = .008), lowest resistive index (area under the curve, 0.85; P = .011), Ferrazzi's scoring system (area under the curve, 0.89; P = .01), and maximal peak systolic velocity (area under the curve, 0.71; P< .0001). Comparison with Sassone's scoring system (area under the curve, 0.91) did not reach statistical significance, but a clear trend was found (P = .116). CONCLUSIONS: The model had the best diagnostic performance for discriminating between benign and malignant adnexal masses. A clinical prospective evaluation is needed to confirm its actual value.

Adnexal Diseases↗
PubMed1998

Diagnosing breast cancer from FNAs: variable relevance in neural network and logistic regression models.

We compared the selection of variables for building a classification model for the diagnosis of breast cancer using neural networks and logistic regression. A set of 460 cases was used to build neural network and logistic regression models that classify cell samples obtained by fine-needle aspiration (FNA) as malignant or benign, depending on nine pathology features. Variables selected by a step down logistic regression model were compared to those selected by a measure of relevance derived from neural network weights. Since both types of models resulted in similar predictive accuracy, we expected approximately the same variables to be selected. The variables with the highest relevance values for the neural network models corresponded to those of high significance in univariate logistic regression models, but were not the ones selected in the step down procedure of multivariate models. Variable relevance based on weights for neural network models does not seem to be a consistent index of the importance of that variable for multivariate models such as logistic regression.

Analysis of Variance↗