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PubMed2004

[The logistic regression model including interactions between the factor variables demonstrated for the detection of E. coli O157.H7 in artificially contaminated minced beef].

Logistic regression is a powerful tool to analyse data sets with a dichotomous response variable. However, in most situations it is used as a model without interactions between the factor variables. This is done either by presumption or to avoid difficulties in the interpretation of the statistical results. In this article first the model of simple logistic regression without interactions is introduced followed by the expanded model with pairwise interactions between the factors. The application of both models is demonstrated at the present data set concerning the detection of E. coli O157.H7 in artificially contaminated minced beef. The influencing variables are the factors enrichment time, inoculation density, enrichment broth, subculturing medium, and state of samples (fresh vs. deep frozen). The statistical reanalysis displayed strongly differing results emphasizing the importance of interactions in logistic regression models. In particular, the odds ratio for E. coli detection dependant from the enrichment time (24 h vs. 6 h) (OR = 0.41) was strongly overestimated without simultaneous attention of the E. coli inoculation density (OR approximately equal to 0.2 to 0.02). In this context the possible interpretation of the interaction is discussed.

Animals↗
PubMed2004

Predicting blood pressure change caused by rapid injection of propofol during anesthesia induction with a logistic regression model.

BACKGROUND: Propofol is a common intravenous agent for induction and maintenance of anesthesia. The advantage of propofol is rapid recovery of consciousness when the continuous infusion is stopped. Additionally, it has antiemetic effect of reducing postoperative nausea and vomiting. On the other hand, rapid infusion of propofol is painful and may cause hypotension. In this study, we aimed to develop a logistic regression model to accurately predict blood pressure change caused by rapid infusion of propofol. METHODS: Seventeen variables (including demographic data, past medical history, laboratory data, and blood pressure before induction) were assessed in 200 patients who received propofol for induction of anesthesia for routine surgery. A logistic regression model was derived using these values as independent variables to predict whether a patient would suffer a significant blood pressure change (> 30% decrease from baseline). Sensitivity, specificity, and area under the receiver operating characteristic curve (AUC) were calculated to evaluate the performance of our prediction model. RESULTS: A cut-off value of 0.17 in the logistic regression model predicted decreased blood pressure with 90.0% sensitivity and, 67.3% specificity. The area under the receiver operating characteristic curve was 0.855. CONCLUSIONS: Our prediction model predicts propofol-induced hypotension with acceptable accuracy. Because of the straightforward mathematic formula used, our model can be integrated effortlessly into a hospital information system, providing a reliable and useful decision support for clinical anesthesia staff.

Adolescent↗
PubMed2005

Determination of osteoporosis risk factors using a multiple logistic regression model in postmenopausal Turkish women.

OBJECTIVE: To determine the risk factors of osteoporosis using a multiple binary logistic regression method and to assess the risk variables for osteoporosis, which is a major and growing health problem in many countries. METHODS: We presented a case-control study, consisting of 126 postmenopausal healthy women as control group and 225 postmenopausal osteoporotic women as the case group. The study was carried out in the Department of Physical Medicine and Rehabilitation, Dicle University, Diyarbakir, Turkey between 1999-2002. The data from the 351 participants were collected using a standard questionnaire that contains 43 variables. A multiple logistic regression model was then used to evaluate the data and to find the best regression model. RESULTS: We classified 80.1% (281/351) of the participants using the regression model. Furthermore, the specificity value of the model was 67% (84/126) of the control group while the sensitivity value was 88% (197/225) of the case group. We found the distribution of residual values standardized for final model to be exponential using the Kolmogorow-Smirnow test (p=0.193). The receiver operating characteristic curve was found successful to predict patients with risk for osteoporosis. This study suggests that low levels of dietary calcium intake, physical activity, education, and longer duration of menopause are independent predictors of the risk of low bone density in our population. CONCLUSION: Adequate dietary calcium intake in combination with maintaining a daily physical activity, increasing educational level, decreasing birth rate, and duration of breast-feeding may contribute to healthy bones and play a role in practical prevention of osteoporosis in Southeast Anatolia. In addition, the findings of the present study indicate that the use of multivariate statistical method as a multiple logistic regression in osteoporosis, which maybe influenced by many variables, is better than univariate statistical evaluation.

Age Distribution↗
PubMed1991

[Logistics regression in epidemiology. II].

The logistic regression is used in epidemiology to study the relationships between a disease in two modalities (diseased or disease free) and risk factors Xi which may be qualitative as quantitative variables. According to this model, the probability of disease knowing Xi's values is written: [formula: see text]. The coefficients satisfy to the equation: ORi = exp(beta i) where ORi is the odds-ratio linked to the variable Xi adjusted on the other variables of the model. The second part of this paper is devoted to the tests of hypothesis in the logistic model and to the choice of the variables to be included in the model. The way of using tests to decide how to code variables is explained. Analysis strategy (choice and selection of variables) is discussed. The rational of goodness of fit tests is shown. At least, we indicate how to use the logistic model in case-controls studies and in studies with matched samples.

Case-Control Studies↗
PubMed1995

Enzymatic markers of gallstone-induced pancreatitis identified by ROC curve analysis, discriminant analysis, logistic regression, likelihood ratios, and information theory.

We investigated the diagnostic utility of frequent serial determinations of aspartate aminotransferase, alanine aminotransferase (ALT), lipase, amylase, and the lipase/amylase (L/A) ratio for distinguishing patients with acute pancreatitis due to biliary obstruction from those with acute pancreatitis due to other pathogenesis. Analyzed were enzyme activities obtained at admission and peak enzyme activities identified retrospectively from serial measurements in 53 patients with acute pancreatitis due to various causes. We evaluated the data with multiple statistical tools. Discriminant analysis and logistic regression revealed the diagnostic significance of ALT at initial and peak values, and the maximum information provided by peak ALT was confirmed by both logistic regression and stratum-specific likelihood ratios. Stratum-specific likelihood ratios showed peak ALT > 150 U/L was highly diagnostic of biliary pancreatitis. The L/A ratio, either at admission or at peak, was the only other significant variable for identifying patients with acute pancreatitis due to biliary obstruction. A multivariate logistic discriminant function including ALT and the L/A ratio significantly discriminated biliary acute pancreatitis from pancreatitis due to other causes. Evaluation of initial and peak enzyme data by information theory revealed that the optimal test depended on disease prevalence. Initial ALT activities were the test of choice for identifying biliary pancreatitis, up to a disease prevalence of approximately 0.75. At disease prevalence > 0.75, the initial L/A ratio provided the greatest amount of diagnostic information.

Acute Disease↗
PubMed1994

The use of logistic discrimination and receiver operating characteristics (ROC) analysis in dentistry.

Logistic regression is a statistical method which allows an investigator to 'explain' or 'predict' a binary response variable from a set of independent variables. In particular, it may be used to classify persons for example, as diseased or healthy, high risk or low risk etc. (logistic discrimination). During recent years this method has been of increasing interest and importance in dentistry. Since this demanding statistical method may not be easily accessible to dentists, a description is provided of its basic characteristics in an introductory and condensed form. A worked example, 'identification of children with high caries risk', is presented in order to demonstrate the application and use of the method. Following the presentation of the logistic model, evaluation of the performance of a classification model by means of 'receiver operating characteristic (ROC) analysis' is demonstrated. The presentation of these statistical tools here, puts more weight on verbal explanation and on graphical representations than on mathematical details. This statistical tools here, puts more weight on verbal explanation and on graphical representations than on mathematical details. This may help to make the methods accessible to readers who have insufficient time to study a more comprehensive discourse.

Child↗
PubMed1996

Logistic regression model of fotemustine toxicity combining independent phase II studies.

BACKGROUND: To optimize fotemustine chemotherapy, the authors considered how to combine independent Phase II trials to predict the risk of first occurrence of severe toxicity as a function of initial patient characteristics. METHODS: Clinical data from six Phase II trials were collected. Of the 478 patients enrolled 442 (male/female, 259/183; age range, 15-81 years) were evaluable for toxicity (1384 cycles of chemotherapy), including 221 with malignant malignant melanomas, 138 with primary brain tumors, 29 with lung carcinomas, 8 with head and neck carcinomas, and 46 with miscellaneous cancers. The influence of age, sex, performance status, type of tumor, number and location of metastases, and previous treatment by chemotherapy and/or radiotherapy was studied. The logistic regression method was applied to predict occurrence of leukopenia, thrombocytopenia, anemia, digestive tract, and/or hepatic toxicity. RESULTS: Univariate analysis showed that predictive factors for hematologic toxicity were age (> 50 years), type of tumor (brain < melanoma < others), number of metastatic sites (> 3), location of metastases (nonvisceral), and previous chemotherapy. Performance status and previous radiotherapy did not affect the toxicity of fotemustine Nausea and vomiting were predictable based on the type of tumor (head and neck < lung < brain < melanoma < others), the number of metastatic sites (> three) and visceral metastases. Hepatic disorders occurred preferentially in patients with hepatic metastases and more than three metastatic sites. Individual risk of hematologic and hepatic toxicity for patients with melanoma and primary brain tumors was predicted using logistic regression models. CONCLUSIONS: By combining clinical data from independent Phase II trials, the logistic model developed could predict the probability of fotemustine hematologic and hepatic toxicity.

Adolescent↗
PubMed1997

Prediction of low bone mineral density in postmenopausal women by artificial neural network model compared to logistic regression model.

Measuring bone mineral density (BMD) is currently the best modality to diagnose osteoporosis and predict future fractures. The use of risk factors to predict BMD and fracture risk has been considered to be inadequate for precise diagnostic purpose, but it may be helpful as a screening tool to determine who actually needs BMD assessment. Recently, artificial neural network (ANN), a nonlinear computational model, has been used in clinical diagnosis and classification. In the present study, we evaluated the risk factors associated with low BMD in Thai postmenopausal women and assessed the prediction of low BMD using an ANN model compared to a logistic regression model. The subjects consisted of 129 Thai postmenopausal women divided into 2 groups, 100 subjects in the training set and the remaining 29 subjects in the validation set. The subjects were classified as having either low BMD or normal BMD by using BMD value 1 SD lower than the mean value of young adults as the cutoff point. Decreased body weight, decreased hip circumference and increased years since menopause were found to be associated with low BMD at the lumbar spine by logistic regression. For the femoral neck, increased age and decreased urinary calcium were associated with low BMD. The models had a sensitivity of 85.0 per cent, a specificity of 11.1 per cent and an accuracy of 62.0 per cent for the diagnosis of low BMD at the lumbar spine when tested in the validation group. For the femoral neck, the sensitivity, specificity and accuracy were 90.5 per cent, 12.5 per cent, and 69.0 per cent, respectively. Models based on ANN correctly classified 65.5 per cent of the subjects in the validation group according to BMD at the lumbar spine with a sensitivity of 80.0 per cent and a specificity of 33.3 per cent while it correctly classified 58.6 per cent of the subjects at the femoral neck with a sensitivity of 76.2 per cent and a specificity of 12.5 per cent. There was no significant difference in terms of accuracy, sensitivity and specificity in the prediction of low BMD at the lumbar spine or the femoral neck between ANN model and logistic regression model. We concluded that ANN does not perform better than convention statistical methods in the prediction of low BMD. The less than perfect performance of the prediction rules used in the prediction of low BMD may be due to the lack of adequate association between the commonly used risk factors and BMD rather than the nature of the computational models.

Aged↗
PubMed1998

Artificial neural networks and logistic regression as tools for prediction of survival in patients with Stages I and II non-small cell lung cancer.

The prognosis of patients with Stage I and II non-small cell lung cancer (NSCLC) can be estimated but cannot be definitively ascertained by use of current clinicopathologic criteria and tumor marker studies. The potential value of probabilistic neural networks (NNs) with genetic algorithms and multivariate logistic regression to predict the survival of NSCLC patients has not been previously evaluated. Multiple prognostic factors (age, sex, cell type, stage, tumor grade, smoking history, and immunoreactivity to c-erbB-3, bcl-2, Glut1, Glut3, retinoblastoma gene and p53 were correlated with 5-year survival in 63 patients with Stage I or II NSCLC, treated solely by surgical excision at Baylor Medical College, Houston, Texas. Several probabilistic NNs with genetic algorithm models were developed using the prognostic features as input neurons and survival at 5 years (free of disease/dead of disease) as output neurons. The probabilistic NN yielded excellent classification rates for dependent variable survival. The best model was trained with 52 cases and classified all 11 "unknown" test cases correctly. Several statistically significant logistic regression models were fitted using 50 cases to build the models and 13 cases as "hold-out" test cases. These multivariate statistical models provide various cutoff values that predict/classify the probability of survival at 5 years. In conclusion, probabilistic NNs and logistic regression models can be useful in estimating the prognosis of patients with Stage I and II NSCLC using multiple clinicopathologic and molecular variables. These multivariate predictive models need to be validated with much larger groups of patients to assess their potential clinical value.

Adult↗
PubMed1987

Making the most of multiple measurements in estimating carrier probability in Duchenne muscular dystrophy: the Bayesian incorporation of repeated measurements using logistic discrimination.

In carrier detection studies, females-at-risk are usually tested several times if the results are ambiguous, whereas subjects in the control and obligate carrier reference groups may not be tested as often. The question is how to incorporate the multiple measurements most effectively with information in the family pedigree into combined carrier risks. Sets of measurements on individuals are not independent, but are related with the correlation coefficient 0 less than rho less than 1. We have developed a procedure for incorporating repeated measurements on individuals and their a priori chance of having the disease into logistic models. This procedure utilizes the set of measurements and an estimate of rho. We describe application of this procedure to carrier detection in Duchenne muscular dystrophy (DMD) using serum creatine kinase (CK) measurements as the biochemical indicator of carrier status. Estimates of rho for controls and obligate DMD carriers did not differ significantly from 0.5. Repeated testing with use of rho = 0.5 significantly decreased the median logistic carrier probability for controls and increased it for carriers. In some cases four to six rather than the three CK tests conventionally used in genetic counseling were necessary to obtain a stable logistic carrier probability for a subject.

Creatine Kinase↗
PubMed1988

Carrier detection in hemophilia A: ABO blood group, multiple measurements, and application of logistic discrimination.

In healthy 20- to 50-year-old women, the ABO blood group has a significant effect on levels of von Willebrand factor (VWF:Ag, formerly VIIIR:Ag) and on factor VIII activity (F.VIII:C). However, there is no significant effect of ABO group or subject age on the ratio log e(F.VIII:C/VWF:Ag). Multiple measurements of the "ratio" on possible carriers of hemophilia A may be combined with pedigree information using logistic discrimination to yield final risk assessment. To reduce misclassification of carriers as normal women, a lower limit, specified by the logistic model, is set on the logistic carrier probabilities. In this study, the proportion of blood group A for a population of obligate carriers was significantly higher than that expected for the general population (60% vs. 42%); for a population of control women it was lower than expected (22.5 vs. 42%). The effect for the carriers came primarily from daughters of affected fathers, as 81.3% were of blood group A. These observations indicate that a "universal" discriminant should be applied with caution.

ABO Blood-Group System↗
PubMed1993

Logistic regression of inhalation toxicities of perchloroethylene--application in noncancer risk assessment.

Unlike the impressive advancement of cancer risk assessment, the "cutoff approach" based on hazard quotient in noncancer risk assessments recommended by the EPA has crucial deficiencies. Several alternative approaches have been suggested in the literature to modify the noncancer risk characterization based on reference doses. Recent studies have indicated that the effects of perchloroethylene (PERC) on the central nervous system (CNS) is a much more sensitive noncancer endpoint than cancer which is currently the basis for deriving its public health criteria and standards. Studies indicate that 20 ppm of inhaled PERC concentration elicited adverse effects on the CNS in experimental animals and humans. However, the existing EPA oral reference dose (RfD), a noncancer toxicity parameter for PERC (0.01 mg/kg/day), is based on the induction of hepatotoxicity and increased body weight gain induced by PERC in rats. An attempt was made in this paper to examine whether logistic regression of dose-response data could be applied to assess the noncancer risks. In order to perform logistic regression the inhalation toxicity data of PERC were classified according to the severity of toxicity paradigm used in toxicity analysis. Based on the sensitive noncancer endpoints identified from severity classification, a logistic regression analysis of the data was performed and its potential applicability in noncancer risk characterization was described for workers exposure to PERC in dry-cleaning operations.

Administration, Inhalation↗
PubMed2005

Clinic investigation and logistic analysis of risk factors of recurrent hemorrhage after operation in the earlier period of cerebral hemorrhage.

Objective of this study was to investigate the incidence, time, location, prevention, treatment and risk factors of recurrent hemorrhage in the earlier period of cerebral hemorrhage after operation. Three hundred and twenty two patients with operations in the earlier period of cerebral hemorrhage were analyzed retrospectively. The clinical data of hemorrhage and recurrent cerebral hemorrhage groups were compared and statistically analyzed. Logistic regression analysis was applied to evaluate the function of possible factors leading to recurrent hemorrhage after operation. The incidence of recurrent hemorrhage was 21.4% in the earlier period of cerebral hemorrhage after operation. When the operation was performed after cerebral hemorrhage within 6 h, 6-12 h and 12-24 h, the incidence of recurrent hemorrhage after operation were 43.1%, 20.9%, 3.6% respectively. With regard to time of recurrent hemorrhage, the incidence was 3.1% within 12 h after operation, 15.5% between 12-24 h and just 2.8% after 24 h. Site of hemorrhage was in the basal ganglion in 92.6% of the cases. Mono-agent logistic analysis displayed that there is a significant correlation between high diastolic blood pressure, fluctuation of blood pressure after operation, taking anti-coagulant drugs for a long time, site of hemorrhage, difficult or not thorough hemostasis during operation and recurrent hemorrhage (p < 0.01). Multiple linear logistic regression analysis has shown that a remarkable diastolic blood pressure and fluctuation of blood pressure after operation are risk factors for recurrent hemorrhage. Their OR value were 10.32, 7.234. From this it is concluded that the incidence of recurrent cerebral hemorrhage after operation in the earlier period is 21.4%, which must never be ignored. The time period of 24 h after operation is a stage of high risk. Maintaining diastolic blood pressure below 85 mmHg and steadily controlling the pressure after operation are of great importance for prevention of recurrent cerebral hemorrhage.

Adult↗
PubMed1999

Logistic discriminant parametric mapping: a novel method for the pixel-based differential diagnosis of Parkinson's disease.

Positron emission tomography (PET) and single-photon emission tomography (SPET) imaging of the dopaminergic system is a powerful tool for distinguishing groups of patients with neurodegenerative disorders, such as Parkinson's disease (PD). However, the differential diagnosis of individual subjects presenting early in the progress of the disease is much more difficult, particularly using region-of-interest analysis where small localized differences between subjects are diluted. In this paper we present a novel pixel-based technique using logistic discriminant analysis to distinguish between a group of PD patients and age-matched healthy controls. Simulated images of an anthropomorphic head phantom were used to test the sensitivity of the technique to striatal lesions of known size. The methodology was applied to real clinical SPET images of binding of technetium-99m labelled TRODAT-1 to dopamine transporters in PD patients (n=42) and age-matched controls (n=23). The discriminant model was trained on a subset (n=17) of patients for whom the diagnosis was unequivocal. Logistic discriminant parametric maps were obtained for all subjects, showing the probability distribution of pixels classified as being consistent with PD. The probability maps were corrected for correlated multiple comparisons assuming an isotropic Gaussian point spread function. Simulated lesion sizes measured by logistic discriminant parametric mapping (LDPM) gave strong correlations with the known data (r(2)=0. 985, P<0.001). LDPM correctly classified all PD patients (sensitivity 100%) and only misclassified one control (specificity 95%). All patients who had equivocal clinical symptoms associated with early onset PD (n=4) were correctly assigned to the patient group. Statistical parametric mapping (SPM) had a sensitivity of only 24% on the same patient group. LDPM is a powerful pixel-based tool for the differential diagnosis of patients with PD and healthy controls. The diagnosis of disease even before clinical symptoms become apparent may be possible, and ultimately this technique could be most useful in differentiating between several neurodegenerative disorders, incorporating images of multiple neuroreceptor systems.

Aged↗
PubMed1986

Logistic curve fitting and parameter estimation using nonlinear noniterative least-squares regression analysis.

A microcomputer program has been developed for the fitting of the logistic curve to biological, medical, and other experimental data. In addition to supplying estimates for all of the logistic curve parameters, the program provides the fitted result for each input datum thus allowing for the immediate assessment of the logistic curve and detection of possible outliers.

Biometry↗
PubMed1983

A comparison of the logistic risk function and the proportional hazards model in prospective epidemiologic studies.

The logistic regression and proportional hazards models are each currently being used in the analysis of prospective epidemiologic studies examining risk factors in chronic disease applications. The advantages and disadvantages of each are yet to be fully described. However, a theoretical relationship between the two models has been documented. In this paper the conditions under which results from the two models approximate one another are described. It is shown that where the follow-up period is short and the disease is generally rare, the regression coefficients of the logistic model approximate those of the proportional hazards model with a constant underlying hazard rate. Since under the same conditions the likelihood functions approximate one another, the regression coefficients have similar estimated standard errors. Further, estimation of relative risk with these models is contrasted. These results are illustrated utilizing a previously published data set on metastatic cancer of the breast. With increasing follow-up time, the logistic regression coefficients become uncertain and less reliable.

Epidemiologic Methods↗
PubMed1986

The logistic regression analysis of psychiatric data.

Logistic regression is presented as the statistical method of choice for analyzing the effects of independent variables on a binary dependent variable in terms of the probability of being in one of its two categories vs the other. The method, which must be applied by computer, is illustrated on data from the DSM-III field trials. The dependent variable is treatment with behaviourally-oriented psychotherapy vs treatment with psychoanalytically-oriented psychotherapy, and the independent variables are several patient and clinician characteristics. Like ordinary multiple regression, the method is shown capable of analyzing categorical as well as continuous independent variables. Unlike ordinary multiple regression when applied to binary data, logistic regression analysis necessarily yields estimated probabilities that lie between 0 and 1. The measure of association derived from logistic regression analysis, the odds ratio, is defined. Methods for making inferences about it are presented and illustrated.

Attitude of Health Personnel↗
PubMed1989

Logistic and Poisson models for infection by multicomponent plant viruses.

A model for the relationship between virus concentration and infectivity of multicomponent plant viruses is based on a combination of logistic and Poisson equations. Two separate equations are derived from the Poisson distribution assuming, (i) that infections occur only when a set of components containing the complete multicomponent genome is established at an infection site, but that any excess of components present does not reduce the probability of infection (no interference postulate); and (ii) that infection can occur only if a set of components containing the full genome reaches an infection site before it can be preempted by an incomplete set (competitive interference postulate). Postulate (i) affects the form of a dilution series without affecting N, the maximum possible number of infections (lesions), and postulate (ii) changes the value of N but not the form of the dilution series. There is a close correlation between the logit slope of a logistic dilution series and the form of the corresponding multiple Poisson dilution series for viruses with 2, 3 or 4 components. Calibrated by Poisson equations, the logit slope may thus suggest whether or not the virus components have invaded independently and infected similar infection sites. The methods of fitting the combined logistic-Poisson model are demonstrated by applying it to data for cowpea chlorotic mottle virus.

Models, Theoretical↗