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PubMed1993

On the efficacy of the rank transformation in stepwise logistic and discriminant analysis.

We have evaluated the performance of four stepwise variable selection procedures commonly used in medical and epidemiologic research. The four procedures are discriminant and logistic regression and their rank transformed versions, where the independent variables are replaced by their ranks. We generated, by computer, data for two groups from several distributions with a variety of sample sizes and covariance matrices. The two ranking procedures each increased the chance of correctly selecting those variables related to group membership for data generated from log-normal or contaminated distributions. For normally distributed data the ranking procedure had little effect on variable selection. Rank transformed discriminant analysis and rank transformed logistic regression were equally effective in selecting variables when sample sizes exceeded 100. Rank transformed discriminant analysis was superior for smaller data sets. We discuss the implications of the results of this study for clinical and epidemiologic research.

Case-Control Studies↗
PubMed1998

A multivariate logistic regression analysis in predicting malignancy for patients with ovarian tumors.

OBJECTIVE: Our objective was to improve the preoperative diagnosis of ovarian malignancy using a multivariate logistic regression analysis on the basis of demographic, serologic, gray-scale morphological, and Doppler variables. METHODS: One hundred seventy-one patients with ovarian tumors (120 benign, 51 malignant including 9 tumors of low malignant potential) were studied with transvaginal B-mode, color, and pulsed Doppler ultrasonography before surgery. Based on the gray-scale ultrasound imaging, each tumor was classified as a unilocular cyst, multilocular cyst, unilocular cyst with solid parts, multilocular cyst with solid parts, or solid tumor. Intratumoral blood flow velocity waveforms were recorded on all tumors except unilocular cyst and were evaluated for resistance index (RI) and peak systolic velocity (PSV). Serum CA 125 levels were also measured. RESULTS: Twenty tumors were unilocular cysts and were all benign. Seventy tumors including all unilocular cysts which showed no flows were all benign. The remaining 101 tumors (50 benign, 51 malignant including 9 tumors of low malignant potential) presented intratumoral blood flows. Univariate and multivariate logistic regression analyses were conducted to identify variables predictive of ovarian malignancy in these 101 tumors. The variables included age, menstrual state, serum CA 125 levels, B-mode classification, RI, and PSV. In univariate analysis, menopause, the positivity of CA 125 (> or = 35 U/ml), and PSV larger than or equal to 10.4 cm/s were found to be significantly associated with malignant tumors. The PSV value of 10.4 cm/s was the median in benign tumors. Multivariate analysis showed that serum CA 125 levels (> or = 35 U/ml) (P = 0.002) and PSV (> or = 10.4 cm/s) (P < 0.001) were to be independent predictors of malignancy. CONCLUSION: These results suggest that intratumoral PSV is the strongest means of differentiating benign from malignant ovarian tumors with suspicious gray-scale ultrasonographic findings.

Adolescent↗
PubMed1987

Equilibrium and local stability in a logistic matrix model for age-structured populations.

A logistic matrix model for age-structured population dynamics is constructed. This model discretizes a continuous, density-dependent model with age structure, i.e. it is an extension of the logistic model to the case of age-dependence. We prove the existence and uniqueness of its equilibrium and give a necessary and sufficient condition for the local stability of the equilibrium.

Aging↗
PubMed2006

The logistic organ dysfunction score as a tool for making ethical decisions.

PURPOSE: We examined whether the change of the logistic organ dysfunction score (LOD) between the first and the fourth day in the intensive care unit (ICU) could be predictive of death in the ICU. The LOD could then be used to help make decisions concerning therapeutic limitations (TL). METHODS: One hundred fifty-four patients were included. Exclusion criteria were: discharge from the ICU or TL before the 72nd hr. Ninety-three patients remained for evaluation. The LOD was calculated on the day of admission (LOD1) and between the 72nd and 96th hr (LOD4). The DeltaLOD = LOD4-LOD1 index was calculated for survivors and non-survivors; sensitivity, specificity, positive predictive value (PPV) and negative predictive value (NPV) were calculated. RESULTS: Sixteen patients died in the ICU, they had a higher DeltaLOD (0 vs -2; P = 0.0046) than the survivors. After logistic regression, a high DeltaLOD was associated with a higher risk of death in the ICU independent of the initial severity of disease. The PPV concerning death in the ICU was 0.66 for a DeltaLOD > or = 4 cut-off. The NPV was 0.89 for a cut-off of > or = 1. CONCLUSION: DeltaLOD appears to be a predictor of death in the ICU, independent of the initial severity of disease. The PPV is not high enough to assist with making individual TL decisions. The NPV can help to identify patients at low risk of death. The DeltaLOD deserves to be evaluated in a population exhibiting greater severity of disease.

APACHE↗
PubMed1997

Prevalence of delta F508 cystic fibrosis carriers in The Netherlands: logistic regression on sex, age, region of residence and number of offspring.

An average cystic fibrosis (CF) carrier frequency of 1 in 25 in Europe is cited in numerous reports, although a great variability in estimated prevalences has been found in different European populations. The estimates of these frequencies were based on numbers of CF patients before identification of the gene in 1989. Here we report the results of a study to determine the carrier frequency of the delta F508 mutation in The Netherlands by analyzing mouthwashes and matched blood samples from 11654 blood donors all over the country. We analyzed possible relationships between a number of theoretically explanatory variables and the delta F508 carrier frequency by means of univariate and multivariate logistic regression. These variables were: distance of the blood banks from the northeastern part of the country (distance); whether the blood donors knew that we were looking for a CF mutation; sex and age of the donor; and number of children of the donor (family size). We detected a delta F508 carrier frequency of 1 in 42 (95% CI 1/37-1/47) in The Netherlands. If we assume that the relative frequency of the delta F508 mutation among carriers and patients is comparable in The Netherlands, this gives an estimated overall CF carrier frequency of 1 in 32 (95% CI 1/28-1/36), significantly less than 1 in 25. The univariate logistic regression analysis of the effects of the explanatory variables on the carrier frequency revealed no significant relationships, except for an increase in carrier frequency with increasing distance from the northeastern region. In the multivariate analysis with all five independent variables, distance, age and family size were significantly related to the carrier frequency, but sex and CF information were not. There was a significant interaction between age and family size. In our final model, distance, age and family size were positively related to the carrier frequency, while the interaction of age with family size showed a negative relation. These results confirm that there is a gradient in gene frequency with low frequencies in the northeastern part of the country and high frequencies in the southern part. They also suggest a relation of age and family size with carrier frequency. This relation, however, is too complex to be explained by heterozygote advantage.

Adolescent↗
PubMed1986

Logistic analysis of risk factors in acute retinopathy of prematurity.

In a prospective study of 328 high-risk neonates, we used computer-assisted logistic regression of 47 potential risk factors to study acute retinopathy of prematurity. Only four factors were significant in the logistic regression equation: ventilator hours, xanthine administration, birthweight, and maternal bleeding. Xanthine administration was identified as a new independent and significant (P less than .0001) predictor of acute retinopathy of prematurity.

Female↗
PubMed1990

Computerized estimation of size of nucleic acid fragments using the four-parameter logistic model.

We have developed improved methods for statistical estimation of the size of linear duplex DNA after continuous- or pulsed-field electrophoresis in agarose and polyacrylamide gels. We employ the four-parameter logistic model to describe the smooth, symmetrical, sigmoidal relationship between electrophoretic mobility (distance migrated) and log of molecular size (kb): distance = a - d/1 + (size/c)b + d. The four parameters (a,b,c,d) are estimated by nonlinear least-squares curve fitting using the Marquardt-Levenberg algorithm, where a represents an upper plateau, b a slope factor, c the midpoint, and d the lower plateau. Estimates of size for unknown species are accompanied by estimates of the standard error (SE) or coefficient of variation (%CV). A plot of SE and %CV versus size results in a "precision profile" which objectively defines the useful range of the calibration curve. This logistic relationship is more general than the rectangular hyperbola or linear methods, provides excellent goodness of fit, and can be used as a "global" method for the entire calibration curve, rather than as a "local" method for small segments of the curve.(ABSTRACT TRUNCATED AT 250 WORDS)

Calibration↗
PubMed1993

Use of logistic regression in comparing multiple limiting dilution analyses of antigen-reactive T cells.

Traditionally, statistical analyses of multiple limiting dilution analyses have used linear regression in comparing the fit of each analysis to a single-hit Poisson model. Multiple analyses can, however, result in an inflated type I error leading to spurious rejection of the null hypothesis. Logistic regression was used as an umbrella statistic to analyze eight limiting dilution analyses for antigen-reactive T cells from two mouse strains (SJL/J; B10.S), at two priming doses of antigen, for each of two antigens (porcine myelin basic protein, PMBP; purified protein derivative of M. tuberculosis, PPD) used to induce experimental allergic encephalomyelitis (EAE). This proved superior to traditional methods: six of the eight strain/dose/antigen combinations were consistent with a viable model, whereas only three of eight were consistent with the Poisson single-hit model. Moreover, only three of the resultant 32 standardized residual values (four per group times eight groups) fell outside the 95% confidence interval. Logistic regression, therefore, is recommended when nominal dependent measures can be structured as a function of more than one independent variable.

Animals↗
PubMed1994

Extension of the four-parameter logistic model for ELISA to multianalyte analysis.

The standard implementation of enzyme-linked immunosorbent assay (ELISA) for single analytes can lead to false conclusions if cross reacting compounds are present in the sample. This paper discusses the extension of the usual four-parameter logistic model for ELISA to the case of multiple cross-reacting analytes. The use of the extended model in multianalyte analysis (MELISA) is illustrated and compared with a more simplistic approach. Data on the analysis of a binary mixture of s-triazines suggests the superiority of the proposed model. This model is also suitable for other forms of immunoassay that use the four-parameter logistic curve.

Cross Reactions↗
PubMedDate not supplied

The logistic equation revisited: the two-sex case.

The goal of this article is to formulate and analyze the simplest logistic pair-formation model and to contrast its dynamics to that of the corresponding Malthusian pair-formation model, that is, a generalization of the Kendall-Keyfitz model. The Malthusian pair-formation model supports a unique nontrivial stable exponential solution, and it is shown that the logistic pair-formation model supports a unique stable nontrivial bounded solution.

Animals↗
PubMed1989

Logistic regression model for the assessment of microalbuminuria and microproteinuria in insulin-dependent diabetic patients at risk.

Diabetic microalbuminuria, which predisposes to the irreversible macroproteinuria and terminal renal failure, has been shown to be reversible by stringent metabolic control. In this study, using logistic regression, 23 patients with insulin-dependent diabetes mellitus were evaluated. Basing on the reported biochemical changes in patients with diabetes mellitus, the relationship between microalbuminuria and serum biochemistries was assessed. Four biochemical parameters were shown to be significantly related to the amount of microalbuminuria and microproteinuria. The microalbuminuria as assayed by rocket immunoelectrophoresis is closely correlated with the microproteinuria as measured by the Coomassie dye binding method and both have a significant relationship with plasma creatinine, bicarbonate, albumin and globulin as assessed by the Minitab computer program and the Biomedical Data Package--Logistic Regression computer program. The relationship with bicarbonate and creatinine can be due to a decrease in glomerular filtration rate associated with more advanced microproteinuria. The relationship with albumin and globulin is the result of impaired albumin synthesis by the liver in diabetes mellitus. From these data, two simple equations which can provide a relative risk factor with rough quantitative assessment for microproteinuria and microalbuminuria are derived. Thus, from these four parameters available from relatively simple blood biochemistries, assessment can be made of the severity of coexisting diabetic proteinuria. The measurement of the latter is not readily available and is more costly and tedious. This assessment together with the finding of a decrease in albumin, slight increase in creatinine and decrease in bicarbonate associated with the more severe microalbuminuria can be used to alert the diabetologist in implementing tighter metabolic control and other interventional methods before irreversible macroproteinuria develops.

Adult↗
PubMed1990

Estimation of complications for linear accelerator radiosurgery with the integrated logistic formula.

Radiosurgery techniques permit high doses of single fraction irradiation to be administered to small volumes of tumor with relative sparing of surrounding brain tissue. The tolerance of surrounding normal brain tissue to dose distributions from linear accelerator radiosurgery with different collimator sizes is an important factor that must be estimated by anyone using these treatment techniques. The exponential and linear quadratic versions of the integrated logistic formula were used to estimate the probability of brain necrosis at different doses for radiosurgical dose distributions administered by a 6 MV linear accelerator with a 5 arc technique for collimator sizes from 12.5 to 30 mm in diameter. Dose-volume isoeffect curves for a 3% risk of brain necrosis from linear accelerator radiosurgery were then calculated. These curves approximate those calculated for gamma knife radiosurgery and a published 1% dose-volume isoeffect line predicted for proton beam irradiation. Similar dose-volume isoeffect curves were calculated for single fraction radiosurgery boosts administered after 30 Gy of whole brain irradiation in 12 fractions. The integrated logistic formula appears to be a useful tool for estimating tolerance and providing guidelines for prescribing radiation doses for linear accelerator radiosurgery.

Brain Diseases↗
PubMed1990

An analysis of gestational age, neonatal size and neonatal death using nonparametric logistic regression.

The relationship between gestational age, neonatal size and neonatal death is complex. To date, most authors have used birth weight as a proxy for neonatal size and have neglected to examine head circumference and crown heel length. In addition, they have assumed the size and gestational age were linearly related to neonatal death. In this study we use nonparametric multiple logistic regression to examine the relationship between gestational age, neonatal size and neonatal death. On its own, gestational age was nonlinearly associated with neonatal death. This nonlinearity disappeared with the addition of birth weight, crown heel length and head circumference. Birth weight, head circumference and crown heel length all had significant nonlinear associations with neonatal death in univariate analysis. With all factors in the model, birth weight and head circumference were nonlinearly associated with neonatal death and crown heel length was linearly associated with neonatal death. The complex relations between gestational age, neonatal size and neonatal death were explored with greater ease with nonparametric logistic regression.

Birth Weight↗
PubMed1992

The validity of estimating heart disease reduction from a Framingham logistic equation.

We compared two ways in which a logistic equation could be used to estimate the number of heart disease events prevented after lowering blood cholesterol levels. Men were selected from an Australian population survey who met the entry criteria of the Lipid Research Clinics Coronary Primary Prevention Trial (LRC-CPPT). The numbers of heart disease events expected over 7.4 years were calculated from the logistic equation after reducing the men's blood cholesterol by the amounts achieved in the LRC-CPPT placebo and treatment groups (our simulated placebo and treatment groups). The number of events prevented was calculated as the absolute difference between the simulated groups (9.48 per 1000 men per 7.4 years) and the percentage difference of the simulated groups multiplied by the observed incidence rate in the LRC-CPPT placebo group (13.66 per 1000 men per 7.4 years). The second estimate was closer to that observed in the LRC-CPPT (17.10 per 1000 men per 7.4 years), and we recommend this approach in cost-effectiveness studies.

Australia↗
PubMed1999

A comparison of methods for preoperative discrimination between malignant and benign adnexal masses: the development of a new logistic regression model.

OBJECTIVE: The aim of this study was to assess the complementary use of ultrasonographic end points with the level of circulating CA 125 antigen by multivariate logistic regression analysis algorithms to distinguish malignant from benign adnexal masses before operation. STUDY DESIGN: One hundred ninety-one patients aged 18 to 93 years with overt adnexal masses were examined by transvaginal ultrasonography with color Doppler imaging and 31 variables were recorded. The end points were the histologic classification of the tumor and the areas under the receiver-operator characteristic curves of alternative algorithms. RESULTS: One hundred forty patients had benign tumors and 51 (26.7%) had malignant tumors: 31 primary invasive tumors (37% International Federation of Gynecology and Obstetrics stage I), 5 tumors of borderline malignancy (100% International Federation of Gynecology and Obstetrics stage I), and 15 tumors were metastatic and invasive. The most useful variables for the logistic regression analysis were the menopausal status, the serum CA 125 level, the presence of >/=1 papillary growth (>3 mm in length), and a color score indicative of tumor vascularity and blood flow. The optimized procedure had a sensitivity of 95.9% and a specificity of 87.1%. The area under the receiver-operator characteristic curve was significantly higher (P <.01) than the corresponding values from the independent use of serum CA 125 levels or indexes of tumor form or vascularity. CONCLUSION: Regression analysis of a few complementary variables can be used to accurately discriminate between malignant and benign adnexal masses before operation.

Adnexal Diseases↗
PubMed1985

Risk factors for severe bacterial infections after valve replacement and aortocoronary bypass operations: analysis of 246 cases by logistic regression.

Risk factors for severe bacterial infections, that is, deep sternal wound infection, pneumonia, septicemia, and prosthetic valve endocarditis, were evaluated in 246 consecutive patients undergoing valve replacement (N = 84) or aortocoronary bypass operation (N = 162). Multiple logistic regression analysis was applied to determine the ability of putative risk factors to predict infection. The risk factors considered were age, sex, diabetes mellitus, duration of cardiopulmonary bypass (CPB), duration of operation, amount of blood restored on the day of operation, repeat thoracotomy for bleeding, intraaortic balloon pumping, reoperation, emergency operation, and the professional status of the surgeon. Severe infections occurred in similar frequency after valve replacement (8/84; 9.5%) and aortocoronary bypass (11/162; 6.8%). For patients who had a bypass procedure, repeat thoracotomy was the only factor significantly associated with infection (p = 0.0004). However, the classification analysis revealed that this variable alone is too unspecific for a reliable prediction. Univariate analysis indicated that restoration of more than 2,500 ml of blood (p = 0.0001), reoperation (p = 0.0821), duration of operation (p = 0.0061), duration of CPB (p = 0.0318), and intraaortic balloon pumping (p = 0.0281) were associated with infection following valve replacement. A model with three variables emerged from the multiple logistic regression: after correction for blood restoration, reoperation, and duration of CPB, no other variable was of additional predictive value. For patients who underwent valve replacement, the model performed well in predicting complications. The classification analysis revealed a high correspondence between observed and predicted instances of infection: it correctly predicted 75% of the patients with infection and 96% of those without infection.(ABSTRACT TRUNCATED AT 250 WORDS)

Adolescent↗
PubMed1987

Comparison of multigroup logistic and linear discriminant ECG and VCG classification.

The performance of logistic (LOG) and linear discriminant analysis (LDA) has been studied, both for the conventional 12-lead electrocardiogram (ECG) and the orthogonal Frank 3-lead electrocardiogram (VCG), using a large validated data base. Classification rules were derived form a learning set (N = 2446) and applied to a test set (N = 820) to differentiate between normal, left, right and biventricular hypertrophy, anterior, inferior and combined myocardial infarction (MI). Total accuracy of LOG, assuming no normal distribution and using population proportions as prior probabilities, was up to 3% higher than that of LDA, depending on the number of variables used. The 12- and 3-lead LOG and LDA formulas resulted in very similar accuracy rates, i.e., between 67 and 70% for the seven-group and between 77 and 84% for the five-group analysis. LDA posterior probabilities were systematically more extreme than LOG ones. Correct classification of normals' specificity by LDA was 5 to 9% higher, but sensitivity for different groups was 1.5 to 10% lower than by LOG, with sample size proportions as priors. Specificity could be improved by changing the priors at the cost of lower sensitivity and vice versa, both for the LDA and LOG models. Classification results at 95% specificity were only slightly different, except for anterior MI where LOG scored 6% better. Other measures of performance demonstrated that the LDA model was overconfident and that the LOG model fitted better the real class membership of the patients. In conclusion, logistic ECG and VCG models improve the total accuracy of classification by about 1 to 3% when compared to LDA. More importantly, reliability of classification represents the improvement we want to emphasize. These methods may enhance the diagnostic utility of the ECG and VCG in routine practice.

Analysis of Variance↗
PubMed1990

Logistic analysis of the defense reaction induced by electrical stimulation of the rat mesencephalic tectum.

Subliminal and threshold functions of behavioral output to electrical stimulation of the rat mesencephalic tectum were fitted using the logistic model. The results suggest the existence of isotopic albeit anisotropic freezing and flight mechanisms in the dorsal periaqueductal gray and deep layers of the superior colliculus. Moreover, the marked parallelism of immobility and running threshold functions indicates the probable coupling of these mechanisms through a kind of negative feedback. Finally, the good fitting to the model suggests that the behavioral output to electrical stimulation of these areas follows a logistic function of the logarithm of the stimulus intensity.

Aggression↗