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PubMed2004

Lymph node metastasis as a significant prognostic factor in gastric cancer: a multiple logistic regression analysis.

BACKGROUND: In Japan, the standard treatment policy for all potentially curable patients with gastric cancer is radical resection including extensive lymphadenectomy. This treatment strategy has been used for both early and advanced gastric cancers, and substantial increases in survival time have been reported. In advanced gastric cancer, lymphatic spread is reported to be one of the most relevant prognostic factors for gastric cancer resected for cure. The purpose of this study was to determine the factors affecting lymph node involvement and to establish guidelines for the extent of lymph node dissection most appropriate for the treatment of gastric cancer. METHODS: The clinicopathological features of 926 patients with gastric cancer were reviewed. Information on the clinicopathological features was obtained from the database of gastric cancer at the Department of Gastroenterological Surgery, Sendai National Hospital. Univariate and multivariate analyses of data for patients with gastric cancer tumors were performed to evaluate the prognostic significance of clinicopathological features. The independent risk factors influencing lymph node metastasis were determined by multiple logistic regression analysis. RESULTS: The following clinicopathologic factors were found to be correlated with prognosis of gastric cancer: (1) macroscopic type, (2) depth of invasion, (3) cancer-stromal relationship, (4) histological growth pattern, (5) lymph node involvement, (6) lymphatic invasion, (7) vascular invasion and (8) tumor site. However, a multivariate analysis revealed that macroscopic type, depth of invasion, lymph node involvement and tumor site are independent risk factors for the prognosis of gastric cancer patients. Among these factors, the prognosis of patients with gastric cancer was most strongly influenced by lymph node involvement (odds ratio, 4.632). According to a multiple logistic regression model, depth of cancer invasion and lymphatic invasion was significantly correlated with lymph node metastases. CONCLUSIONS: Lymph node involvement has the strongest influence on the prognosis of gastric cancer. Among the clinicopathological factors, depth of invasion and microscopically lymphatic invasion are important factors in predicting lymph node metastases. Thus, the ability to perform gastrectomy with dissection of lymph nodes is a basic requirement for gastric cancer surgeons.

Adenocarcinoma↗
PubMed1997

Outcome after severe head injury: an analysis of prediction based upon comparison of neural network versus logistic regression analysis.

More reliable prediction of outcome would be helpful for clinicians who treat severely head-injured patients. To determine if neural network modeling would improve outcome prediction compared with standard logistic regression analysis and to determine if data available 24 h after severe head injury allows better prediction than data obtained within 6 h, we tested the ability of both techniques at these two times to predict outcome (dead versus alive) at 6 months. One thousand sixty-six consecutive patients with Glasgow Coma Scale scores of 8 or less during the first 24 h after injury were randomly divided into two groups. Data from the first group (n = 799) were used to develop the models; data from the second group (n = 267) were used to test the accuracy, sensitivity, and specificity of the models by comparing predicted and actual outcomes. The 6-month mortality rate was 63.5%. Our findings confirm the importance of age, Glasgow Coma Scale scores, and hypotension in predicting outcome. Using data available at 24 h improved the predictive power of both models compared with admission data; at both time points, however, the differences in the results obtained with the two models were negligible. We conclude that outcome (dead versus alive) at 6 months after severe head injury can be predicted with logistic regression or neural network models based on data available at 24 h. Critical therapeutic decisions, such as cessation of therapy, should be based on the patient's status 1 day after injury and only rarely on admission status alone.

Adolescent↗
PubMed1997

Characterization of sonographically indeterminate ovarian tumors with MR imaging. A logistic regression analysis.

PURPOSE: The goal of this study was to maximize the discrimination between benign and malignant masses in patients with sonographically indeterminate ovarian lesions by means of unenhanced and contrast-enhanced MR imaging, and to develop a computer-assisted diagnosis system. MATERIAL AND METHODS: Findings in precontrast and Gd-DTPA contrast-enhanced MR images of 104 patients with 115 sonographically indeterminate ovarian masses were analyzed, and the results were correlated with histopathological findings. Of 115 lesions, 65 were benign (23 cystadenomas, 13 complex cysts, 11 teratomas, 6 fibrothecomas, 12 others) and 50 were malignant (32 ovarian carcinomas, 7 metastatic tumors of the ovary, 4 carcinomas of the fallopian tubes, 7 others). A logistic regression analysis was performed to discriminate between benign and malignant lesions, and a model of a computer-assisted diagnosis was developed. This model was prospectively tested in 75 cases of ovarian tumors found at other institutions. RESULTS: From the univariate analysis, the following parameters were selected as significant for predicting malignancy (p< or =0.05): a solid or cystic mass with a large solid component or wall thickness greater than 3 mm; complex internal architecture; ascites; and bilaterality. Based on these parameters, a model of a computer-assisted diagnosis system was developed with the logistic regression analysis. To distinguish benign from malignant lesions, the maximum cut-off point was obtained between 0.47 and 0.51. In a prospective application of this model, 87% of the lesions were accurately identified as benign or malignant. CONCLUSION: Benign and malignant ovarian lesions can be distinguished in most sonographically indeterminate lesions by means of parameters obtained from contrast-enhanced MR imaging.

Contrast Media↗
PubMed1997

Modeling microbial populations with the original and modified versions of the continuous and discrete logistic equations.

The life histories of microbial populations, under favorable and adverse conditions, exhibit a variety of growth, decay, and fluctuation patterns. They have been described by numerous mathematical models that varies considerably in structure and number of constants. The continuous logistic equation alone and combined with itself or with its mirror image, the Fermi function, can produce many of the observed growth patterns. They include those that are traditionally described by the Gompertz equation and peaked curves, with the peak being symmetric or asymmetric narrow or wide. The shape of survival and dose response curves appears to be determined by the distribution of the resistance's to the lethal agent among the individual organisms. Thus, exponential decay and Fermian or Gompertz-type curves can be considered manifestations of skewed to the right, symmetric, and skewed to the left distributions, respectively. Because of the mathematical constraints and determinism, the original discrete logistic equation can rarely be an adequate model of real microbial populations. However, by making its proportionality constant a normal-random variate it can simulate realistic histories of fluctuating microbial populations, including scenarios of aperiodic population explosions of varying intensities of the kind found in food-poisoning episodes.

Food Microbiology↗
PubMed2006

Sequential designs for logistic phase I clinical trials.

Both parametric and nonparametric sequential designs and estimation methods are implemented in phase I clinical trials. In this article, we take a systematic approach, consisting of a start-up design, a follow-on design, a sequential dose-finding design, and an estimation method, to find an efficient estimate of the maximum tolerated dose under the assumption that the dose-response curve has a true underlying logistic distribution. In particular, for the problem of the nonexistence of the maximum likelihood estimates of the logistic parameters, a constraint on the probability of an undetermined maximum likelihood estimator (MLE) is incorporated into the parametric sequential designs. In addition, this approach can also be extended to incorporate ethical considerations, which prohibit an administered dose from exceeding the maximum acceptable dose. Comparison based on simulation studies between the systematic designs and nonparametric designs are described both for continuous dose spaces and discrete dose spaces, respectively.

Algorithms↗
PubMed1998

A note on the small sample behavior of logistic regression in a bioassay setting.

The logistic regression procedure is a popular statistical method used when analyzing quantal dose-response data. However, logistic regression results based on a poorly designed experiment can be seriously compromised. Our results indicate that depending on the spacing of the doses, the number of doses, and the number of replications at each dose, the user can get very misleading results, including ineffective lack-of-fit tests and severely biased coefficient estimates along with biased estimates of response. In addition, variance formulas based on asymptotic theory may be completely inappropriate. Simulation results are used to support these statements.

Dose-Response Relationship, Drug↗
PubMed2006

Clinical symptoms and the odds of human T-cell lymphotropic virus type 1-associated myelopathy/ tropical spastic paraparesis (HAM/TSP) in healthy virus carriers: application of best-fit logistic regression equation based on host genotype, age, and provirus load.

The authors have previously developed a logistic regression equation to predict the odds that a human T-cell lymphotropic virus type 1 (HTLV-1)-infected individual of specified genotype, age, and provirus load has HTLV-1-associated myelopathy/tropical spastic paraparesis (HAM/TSP) in southern Japan. This study evaluated whether this equation is useful predictor for monitoring asymptomatic HTLV-1-seropositive carriers (HCs) in the same population. The authors genotyped 181 HCs for each HAM/TSP-associated gene (tumor necrosis factor [TNF]-alpha-863A/C, stromal cell-derived factor 1 (SDF-1) +801G/A, human leukocyte antigen [HLA]-A*02, HLA-Cw*08, HTLV-1 tax subgroup) and measured HTLV-1 provirus load in peripheral blood mononuclear cells using real-time polymerase chain reaction (PCR). Finally, the odds of HAM/TSP for each subject were calculated by using the equation and compared the results with clinical symptoms and laboratory findings. Although no clear difference was seen between the odds of HAM/TSP and either sex, family history of HAM/TSP or adult T-cell lenkemia (ATL), history of blood transfusion, it was found that brisk patellar deep tendon reflexes, which suggest latent central nervous system compromise, and flower cell-like abnormal lymphocytes, which is the morphological characteristic of ATL cells, were associated with a higher odds of HAM/TSP. The best-fit logistic regression equation may be useful for detecting subclinical abnormalities in HCs in southern Japan.

Adult↗
PubMed2005

A two-stage logistic model based on the measurement of pro-inflammatory cytokines in bronchial secretions for assessing bacterial, viral, and non-infectious origin of COPD exacerbations.

UNLABELLED: Exacerbations often complicate the progressive course of chronic obstructive pulmonary disease (COPD), mainly due to infectious agents. The precise role of bacterial infections in the course and the pathogenesis of COPD has been a source of controversy for decades. Also viruses and other non-infectious causes of exacerbation play a relevant role and also contribute to persisting airway inflammation. Usually, the etiologic identification of the infective causes of COPD require considerable time and costs. The development of more rapid, reliable, and widely applicable methods to promptly define the etiology of COPD exacerbations should represent a relevant issue in devising earlier and more specific strategies for their effective therapeutic control. AIM: Of the study was to assess the predictive role of some pro-inflammatory cytokines measured in spontaneous bronchial secretions in discriminating the main infectious causes of COPD exacerbations. METHODS: 124 subjects with moderate COPD (51-79 y; mean basal FEV1 = 49.6% pred. +/- 4.6 sd; FEV1 reversibility +3.9% from baseline +/- 4.8 sd after salbutamol 200 mcg) were studied during acute exacerbation. Respiratory viruses were isolated from bronchial secretions in 21 cases; common bacteria (CFU > or = 10(6)/ml) in 28 cases; Pseudomonas Aeruginosa (Ps.Ae.; CFU > or = 10(6)/ml) in 20 cases. The cytokines IL1beta, IL8, and TNFalpha (pg/ml; Immulite; Diagnostic Product Corp, Los Angeles, CA, USA), and neutrophils (% total count) were measured in bronchial secretions of all patients. STATISTICS: A two-stage logistic model was chosen for discriminating the different causes of COPD exacerbations (such as: non-infectious, or viral, bacterial, or due to Ps.Ae.). RESULTS: At the first decisional step, the two-stage logistic model proved that TNFalpha levels in bronchial secretions recognise clearly patients belonging to the Ps.Ae. group from those of all other groups (Area under ROC curve = 0.96; 95% CI = 0.91-0.99), and that, at the second decisional step, IL8 + IL10 levels discriminate patients with bacterial causes (such as all bacteria) from the non-infected ones and from those with a viral cause of exacerbation (Area under ROC curve = 0.87; 95% CI = 0.77-0.94). Neutrophil percent count did not support any contribution in discriminating the different subgroups of COPD subjects. CONCLUSIONS: When exacerbated, COPD subjects express different patterns of pro-inflammatory mediators in bronchial secretions, which appear modulated according to the etiological cause of the exacerbation. In particular, TNFalpha concentration per se enables recognition of COPD exacerbations due to Ps.Ae., while IL8 + IL1beta levels prove helpful in discriminating those to common bacteria from those to viral agents and to non-infectious causes. When present data are further confirmed, the use of a decisional rule based on cytokine measurements might be regarded as a helpful predictive tool. As measures of pro-inflammatory cytokines are low-cost, simple, and faster to perform, they could support rapid clinical decision making at the bedside regarding therapeutic strategy for COPD exacerbations, in particular when they are needed for severe COPD patients.

Aged↗
PubMed2006

Gene selection in cancer classification using sparse logistic regression with Bayesian regularization.

MOTIVATION: Gene selection algorithms for cancer classification, based on the expression of a small number of biomarker genes, have been the subject of considerable research in recent years. Shevade and Keerthi propose a gene selection algorithm based on sparse logistic regression (SLogReg) incorporating a Laplace prior to promote sparsity in the model parameters, and provide a simple but efficient training procedure. The degree of sparsity obtained is determined by the value of a regularization parameter, which must be carefully tuned in order to optimize performance. This normally involves a model selection stage, based on a computationally intensive search for the minimizer of the cross-validation error. In this paper, we demonstrate that a simple Bayesian approach can be taken to eliminate this regularization parameter entirely, by integrating it out analytically using an uninformative Jeffrey's prior. The improved algorithm (BLogReg) is then typically two or three orders of magnitude faster than the original algorithm, as there is no longer a need for a model selection step. The BLogReg algorithm is also free from selection bias in performance estimation, a common pitfall in the application of machine learning algorithms in cancer classification. RESULTS: The SLogReg, BLogReg and Relevance Vector Machine (RVM) gene selection algorithms are evaluated over the well-studied colon cancer and leukaemia benchmark datasets. The leave-one-out estimates of the probability of test error and cross-entropy of the BLogReg and SLogReg algorithms are very similar, however the BlogReg algorithm is found to be considerably faster than the original SLogReg algorithm. Using nested cross-validation to avoid selection bias, performance estimation for SLogReg on the leukaemia dataset takes almost 48 h, whereas the corresponding result for BLogReg is obtained in only 1 min 24 s, making BLogReg by far the more practical algorithm. BLogReg also demonstrates better estimates of conditional probability than the RVM, which are of great importance in medical applications, with similar computational expense. AVAILABILITY: A MATLAB implementation of the sparse logistic regression algorithm with Bayesian regularization (BLogReg) is available from http://theoval.cmp.uea.ac.uk/~gcc/cbl/blogreg/

Algorithms↗
PubMed1998

A logistic regression model including DNA status and morphology of spermatozoa for prediction of fertilization in vitro.

To determine predictive values of routine semen analysis, sperm morphology evaluation using strict criteria and DNA status for in-vitro fertilization (IVF), 66 consecutive couples undergoing IVF in a university hospital IVF programme were prospectively investigated. Semen samples from 66 men were evaluated by routine semen analysis, morphology evaluation using strict criteria and acridine orange staining for determination of DNA status. A new technique is described for acridine orange scoring which consisted of evaluation of two smears per case, with and without heat treatment. Resistance to heat-provoked denaturation was determined by the difference between two evaluations. A logistic regression model was built and receiver operating characteristic curves were constructed to determine the threshold values and to compare diagnostic properties. Morphology evaluation using strict criteria and concentration of progressively motile spermatozoa were found to be the principal parameters determining the sperm fertilizing capacity in vitro. The logistic regression model composed of morphology evaluation using strict criteria and acridine orange score had a powerful diagnostic capability for prediction of fertilization in vitro.

Acridine Orange↗
PubMed1990

Correction of logistic regression relative risk estimates and confidence intervals for measurement error: the case of multiple covariates measured with error.

If several risk factors for disease are considered in the same multiple logistic regression model, and some of these risk factors are measured with error, the point and interval estimates of relative risk corresponding to any of these factors may be biased either toward or away from the null value. A method is provided for correcting point and interval estimates of relative risk obtained from logistic regression for measurement error in one or more continuous variables. The method requires a separate validation study to estimate the coefficients from the multivariate linear regression model relating the surrogate variables to the vector of true risk factors. Similar methods have been suggested by other authors, but none provides a means of correcting the confidence intervals which include a component of variability due to estimation of the measurement error parameters from a validation study. An example is provided from a prospective study of dietary fat, calories, and alcohol in relation to breast cancer, and from a validation study of the questionnaire used to assess these nutrients. Before correcting for measurement error, the age-adjusted relative risk for a 25 g increment in alcohol intake was 1.33 (95% confidence interval (CI) 1.14-1.55); after correcting for measurement error, the relative risk increased to 1.62 (95% CI 1.23-2.12). Similarly, for a 10 g increment in saturated fat intake, the age-adjusted relative risk was 0.94 (95% CI 0.83-1.06); after correcting for measurement error, the relative risk was 0.84 (95% CI 0.59-1.20). These results indicate that the failure to find a substantial positive association between breast cancer risk and saturated fat intake cannot be explained by measurement error in fat, calories, or alcohol.

Bias↗
PubMed1993

Sample size and power determination for a binary outcome and an ordinal exposure when logistic regression analysis is planned.

General methods of sample size determination for logistic regression analyses are now available, but these will often require substantial information for their application. The author presents methods useful in the special case of a binary outcome and a three-level quantitative exposure, which includes application to a three-level ordinal exposure for a specified scaling. The computationally simple methods were developed in planning an investigation of the prognostic value of multidrug resistance gene (mdr1) expression in sarcoma. Because logistic regression was planned for the analysis, calculations were based on the ability to detect a linear trend in the log odds of tumor response to chemotherapy associated with increases in the level of mdr1 expression from negative to low positive to high positive. Closed form expressions were used to assess sensitivity to the ordinal scaling and the distribution of the mdr1 levels, and to the assumption of a linear trend in the log odds versus a linear trend in the proportions.

Case-Control Studies↗
PubMed1991

Using logistic regression to estimate the adjusted attributable risk of low birthweight in an unmatched case-control study.

Other authors have shown how to estimate attributable risk based on stratification. In this paper, we show how to estimate adjusted attributable risks, standard errors, and confidence intervals from an unmatched case-control study that has population-based controls and uses the logistic regression model to estimate relative risk. We apply the method to data from a case-control study of low birthweight. The method is conceptually simple, has no assumptions beyond those of the logistic model, makes use of computer-intensive statistical techniques (the bootstrap), and extends to interactions. A Fortran computer program to carry out the computations is available from the authors upon request.

Case-Control Studies↗
PubMedDate not supplied

Logistic regression: a nontechnical review.

Medical rehabilitation researchers are increasingly interested in investigating complex, multivariate problems. Logistic regression analysis is a statistical tool that may be useful in exploring the relationship between multiple explanatory factors and a categorical outcome. The purpose of this article is to describe logistic regression analysis in nontechnical terms.

Activities of Daily Living↗
PubMedDate not supplied

Dimension reduction-based penalized logistic regression for cancer classification using microarray data.

The use of penalized logistic regression for cancer classification using microarray expression data is presented. Two dimension reduction methods are respectively combined with the penalized logistic regression so that both the classification accuracy and computational speed are enhanced. Two other machine-learning methods, support vector machines and least-squares regression, have been chosen for comparison. It is shown that our methods have achieved at least equal or better results. They also have the advantage that the output probability can be explicitly given and the regression coefficients are easier to interpret. Several other aspects, such as the selection of penalty parameters and components, pertinent to the application of our methods for cancer classification are also discussed.

Algorithms↗
PubMed1999

Optimum experimental designs for multinomial logistic models.

Multinomial responses frequently occur in dose level experiments. For example, in a study of the influence of gamma radiation on the emergence of house flies (Musca domestica L., 1758), three disjoint outcomes occurred: death before the pupae opened, death during emergence, and life after emergence. Although the flies are easy to breed, this sort of bioassay is, in general, very expensive since it requires the use of a gamma radiation source. Experiments therefore need to be designed to involve the minimum number of different doses. Here the theory of optimum experimental design is applied to provide efficient experiments to estimate the parameters of those multinomial logistic models that are a special case of the multivariate logistic models of Glonek and McCullagh (1995, Journal of the Royal Statistical Society, Series B 57, 533-546). The purpose is to reduce the overall experimental cost. The general equivalence theorem (Fedorov, 1972, Theory of Optimal Experiments) is adapted to this class of models, providing an effective method of generating and checking the optimality of designs. One example on flies demonstrates the method, which can be easily implemented.

Animals↗
PubMed2000

Conditional-cumulant-of-exposure method in logistic missing covariate regression.

We consider estimation in logistic regression where some covariate variables may be missing at random. Satten and Kupper (1993, Journal of the American Statistical Association 88, 200-208) proposed estimating odds ratio parameters using methods based on the probability of exposure. By approximating a partial likelihood, we extend their idea and propose a method that estimates the cumulant-generating function of the missing covariate given observed covariates and surrogates in the controls. Our proposed method first estimates some lower order cumulants of the conditional distribution of the unobserved data and then solves a resulting estimating equation for the logistic regression parameter. A simple version of the proposed method is to replace a missing covariate by the summation of its conditional mean and conditional variance given observed data in the controls. We note that one important property of the proposed method is that, when the validation is only on controls, a class of inverse selection probability weighted semiparametric estimators cannot be applied because selection probabilities on cases are zeroes. The proposed estimator performs well unless the relative risk parameters are large, even though it is technically inconsistent. Small-sample simulations are conducted. We illustrate the method by an example of real data analysis.

Biometry↗
PubMed2006

Comparing the predictive value of neural network models to logistic regression models on the risk of death for small-cell lung cancer patients.

Cancer is one of the leading causes of mortality in the developed world, and prognostic assessment of cancer patients is indispensable in medical care. Medical researchers are accustomed to using regression models to predict patient outcomes. Neural networks have been proposed as an alternative with great potential. Nonetheless, empirical evidence remains lacking to support the application of this technique as the appropriate method to investigate cancer prognosis. Utilizing data on patients from two National Cancer Institute of Canada clinical trials, we compared predictive accuracy of neural network models and logistic regression models on risk of death of limited-stage small-cell lung cancer patients. Our results suggest that neural network and logistic regression models have similar predictive accuracy. The distributions of individual predicted probabilities are very similar. On occasion, however, the prediction pairs are quite different, suggesting that they do not always give the same interpretations of the same variables.

Adult↗