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PubMed2003

[A logistic cellular automaton for simulating tumor growth].

This paper focuses on a differential equation logistic model simulating tumor growth. We design a kind of tumor dynamic growth model with one-dimensional cellular automata. A discrete logistic model is developed from the continuous logistic model. Based on others' work, we design discrete mathematical growth dynamic model with cellular automaton. In terms of discrete model, we design stochastic evolving rules of cellular automaton. And this paper simulates the tumor growth dynamic model with cellular automata. The theoretic analysis and results of cellular automaton model are in agreement with data from the ideal differential equation logistic growth of cancer.

Algorithms↗

PubMed1989

[Study of logistic curve fitting for primary liver cancer death rate in Chengdu].

Logistic curve was used for fitting primary liver cancer (PLC) age-specific death rate in Chengdu. The results showed that the age-specific death rate from 1981 to 1986 in Chengdu (population about 4,000,000) was satisfactorily fitted by logistic curve in male, female and total (P less than 0.01). The R2s were 0.9885, 0.9912 and 0.9974, respectively. Velocity analysis of death rate showed that the increasing peak was in the group of age 40-60 for male and 50-65 for female. Male's velocity and slope of death rate were higher and steeper than female's. These results are consistent with the feature of logistic curve and parameters obtained from logistic curve fitting in this study. The age-specific death rate by sex for every year from 1981 to 1986 was fitted very well (P less than 0.01). R2s for male and female were 0.9415 +/- 0.044 and 0.9056 +/- 0.048, respectively.

Age Factors↗

PubMed1997

[Use of a logistic regression model at two levels in the analysis of medical practice variations: the prophylactic cesarean].

We show the use of a hierarchical logistic model to study the variations of the prophylactic cesarean section rate between the maternity hospitals of the Rhône-Alpes region. These variations are analyzed according to the women characteristics at first level, and the maternity hospital characteristics at second level. We present the two-level hierarchical logistic model and the method of estimation of the fixed and random parameters. Then, we compare and discuss the results obtained with those of the usual logistic model. The usual logistic model underestimates the standard error of the regression parameters. In our example however, the results obtained with the hierarchical model do not modify the conclusions concerning the effect of the women characteristics. All the women characteristics increase significantly the probability for a woman to have a prophylactic cesarean section. Nevertheless, the hierarchical model reveals the effect of the maternity hospital characteristics and shows that the maternity hospitals which receive many "at risk" women tend to perform fewer prophylactic cesarean sections than the others, in women with the same characteristics. It permits to estimate the residual variance of second level linked to the unobserved characteristics of the maternity hospitals. It permits to show that the effect of the main characteristics of the women (previous cesarean section, dystocia, chronic fetal distress) vary between maternity hospitals.

Bias↗

PubMedDate not supplied

Ordinal logistic regression in medical research.

Medical research workers are making increasing use of logistic regression analysis for binary and ordinal data. The purpose of this paper is to give a non-technical introduction to logistic regression models for ordinal response variables. We address issues such as the global concept and interpretation of logistic models, the model building procedure from a practical point of view, and the assessment of the model adequacy. For illustrative purposes we apply these methods to real data of a study investigating the association between glycosylated haemoglobin and retinopathy. We give some recommendations for the use and assessment of ordinal logistic regression models in medical research.

Analysis of Variance↗

PubMed1998

Generation of correlated logistic-normal random variates for medical decision trees.

A Logistic-Normal random variable (Y) is obtained from a Normal random variable (X) by the relation Y = (ex)/(1 + ex). In Monte-Carlo analysis of decision trees, Logistic-Normal random variates may be used to model the branching probabilities. In some cases, the probabilities to be modeled may not be independent, and a method for generating correlated Logistic-Normal random variates would be useful. A technique for generating correlated Normal random variates has been previously described. Using Taylor Series approximations and the algebraic definitions of variance and covariance, we describe methods for estimating the means, variances, and covariances of Normal random variates which, after translation using the above formula, will result in Logistic-Normal random variates having approximately the desired means, variances, and covariances. Multiple simulations of the method using the Mathematica computer algebra system show satisfactory agreement with the theoretical results.

Algorithms↗

PubMedDate not supplied

Selecting risk factors: a comparison of discriminant analysis, logistic regression and Cox's regression model using data from the Tromsø Heart Study.

For comparative evaluation, discriminant analysis, logistic regression and Cox's model were used to select risk factors for total and coronary deaths among 6595 men aged 20-49 followed for 9 years. Groups with mortality between 5 and 93 per 1000 were considered. Discriminant analysis selected variable sets only marginally different from the logistic and Cox methods which always selected the same sets. A time-saving option, offered for both the logistic and Cox selection, showed no advantage compared with discriminant analysis. Analysing more than 3800 subjects, the logistic and Cox methods consumed, respectively, 80 and 10 times more computer time than discriminant analysis. When including the same set of variables in non-stepwise analyses, all methods estimated coefficients that in most cases were almost identical. In conclusion, discriminant analysis is advocated for preliminary or stepwise analysis, otherwise Cox's method should be used.

Adult↗

PubMed1996

Human population dynamics revisited with the logistic model: how much can be modeled and predicted?

"We revive the logistic model, which was tested and found wanting in early-20th-century studies of aggregate human populations, and apply it instead to life expectancy (death) and fertility (birth)....For death...the logistic portrays the situation crisply. Human life expectancy is reaching the culmination of a two-hundred year-process that forestalls death until about 80 for men and the mid 80s for women. No breakthroughs in longevity are in sight unless genetic engineering comes to help. For birth, the logistic covers quantitatively its actual morphology. However, because we have not been able to model this essential parameter in a predictive way over long periods, we cannot say whether the future of human population is runaway growth or slow implosion... From a niche point of view, resources are the limits to numbers, and access to resources depends on technologies. The logistic makes clear that for homo faber, the limits to numbers keep shifting. These moving edges may most confound forecasting the long-run size of humanity."

Conservation of Natural Resources↗

PubMed1986

Logistic regression analysis of incidental-tumor data from animal carcinogenicity experiments.

Survival differences can have a substantial impact on the statistical comparison of tumor development in control and treated animals and thus should be taken into account routinely in the analysis of carcinogenicity data from laboratory experiments. However, the appropriate survival adjustment depends on whether the tumor of interest is fatal or incidental. The usual analysis of incidental tumors, which adjusts for survival by stratifying the animals according to age at death, has various shortcomings. Alternatively, logistic regression methods allow a continuous survival adjustment and furnish a convenient framework for solving many of the problems associated with the age-stratified approach of grouping the data into time intervals. Logistic regression substitutes modeling the prevalence function for the arbitrary choice of time intervals, providing a survival adjustment (when the model holds) even when differential mortality might increase the bias or decrease the sensitivity of interval-based methods. The logistic analysis also can incorporate covariables which, if ignored, might confound the interpretation of the data. Several examples illustrate these potential advantages of basing the analysis of incidental tumors on logistic regression techniques.

Aging↗

PubMed2005

Nomographic representation of logistic regression models: a case study using patient self-assessment data.

Logistic regression models are widely used in medicine, but difficult to apply without the aid of electronic devices. In this paper, we present a novel approach to represent logistic regression models as nomograms that can be evaluated by simple line drawings. As a case study, we show how data obtained from a questionnaire-based patient self-assessment study on the risks of developing melanoma can be used to first identify a subset of significant covariates, build a logistic regression model, and finally transform the model to a graphical format. The advantage of the nomogram is that it can easily be mass-produced, distributed and evaluated, while providing the same information as the logistic regression model it represents.

Algorithms↗

PubMed2003

A simple clinical scoring system to improve the sensitivity and standardization of the diagnosis of mycosis fungoides type cutaneous T-cell lymphoma: logistic regression of clinical and laboratory data.

BACKGROUND: The diagnosis of mycosis fungoides (MF) is notoriously difficult to establish because in the early stages, histological features may be nonspecific or merely suggestive. OBJECTIVES: To standardize the diagnosis of MF. METHODS: We studied 138 patients with suspected MF referred over a 7-year period to a university department of a dermatology-based cutaneous lymphoma clinic. Six diagnostic criteria were evaluated: clinical morphology, clinical distribution, skin biopsy T-cell receptor gene rearrangement (TCR-GR), skin biopsy pan T-cell marker loss > or = 2, skin biopsy CD4/CD8 ratio > or = 6, and skin biopsy diffuse epidermal HLA-DR expression. These six clinical and laboratory criteria were compared by logistic regression analysis in patients with histologically diagnosed MF and those with benign disease. RESULTS: Of the 138 patients, 74 had histology of MF, 47 of benign dermatoses and 17 were indeterminate. Close associations were found between a histological diagnosis of MF and TCR-GR (odds ratio 14.4), classical morphology (7.5), classical distribution (2.5) and diffuse epidermal HLA-DR expression (2.8). Logistic regression models were developed depending on the availability of data (either TCR-GR or HLA-DR). Probabilities for correctly diagnosing MF compared with histology as the 'gold standard' were derived from these logistic regression models. A scoring system assigning point values based on these probabilities was then created in order to assist the clinician in making the diagnosis. If using TCR-GR data, a positive TCR-GR = 2.5 points, the presence of classical morphology = 2.0 points, and the presence of classical distribution = 1.5 points. A total score of > or = 3.5 points assigns a high probability (> 85%) of having MF. If using HLA-DR expression, then the presence of classical morphology = 2.5 points, a positive diffuse epidermal HLA-DR expression = 2.0 points, and the presence of classical distribution = 1.5 points. In this case, a total score of > or = 4.0 points assigns a high probability (> 85%) of MF. CONCLUSIONS: The logistic regression models and scoring systems integrate clinical and laboratory assessments, allow rapid probability estimation, and provide a threshold for the diagnosis of MF in an objective, standardized manner.

Biopsy↗

PubMed1981

Longitudinal models for chronic disease risk: an evaluation of logistic multiple regression and alternatives.

The logistic multiple regression model is often used in the analysis of the relation between chronic disease risk and selected risk factors in longitudinal data. Unfortunately, the logistic function has certain properties that make it inappropriate as a mode of risk analysis for longitudinal studies. The consequences of applying the logistic function to longitudinal data is that the numerical values of logistic regression coefficients cannot be meaningfully compared between studies of different durations. Sample calculations are presented to illustrate the magnitude of the problem for a range of relative study lengths and levels of risk. Two solutions are offered for the problem. First, a series of approximations are derived which permit such comparisons if the studies are not greatly dissimilar in length. Second, if comparisons of the risk coefficients are to be made across studies of greatly dissimilar duration, it is necessary to model risk via an appropriate statistical model. Criteria for assessing the appropriateness of risk functions for the analysis of longitudinal data are proposed and alternatives evaluated.

Chronic Disease↗

PubMed1985

Logistic regression in survival analysis.

Logistic regression has been applied to numerous investigations that examine the relationship between risk factors and various disease events. Recently, the ability to consider the time element of event occurrences by proportional hazards models has meant that logistic regression has played a less important role in the analysis of survival data. This paper, however, shows that when event times are grouped into intervals, logistic regression can be adapted to the analysis of such data by modeling the interval when an event occurs. Furthermore, it is shown that results from such an adaptation will often lead to parameter estimates close to those obtained by the proportional hazards model in the grouped event time setting. An illustration of the application of logistic regression to survival analysis is based on data from the Framingham Heart Study.

Coronary Disease↗

PubMed2001

Fit of second order thermoluminescence glow peaks using the logistic distribution function.

A new thermoluminescence glow curve deconvolution (GCD) function is introduced which accurately describes second order thermoluminescence (TL) curves. The logistic asymmetric (LA) statistical probability function is used with the function variables being the maximum peak intensity (Im), the temperature of the maximum peak intensity (Tm) and the LA width parameter a2. An analytical expression is derived from which the activation energy E can be calculated as a function of Tm and the LA width parameter a2 with an accuracy of 2% or better. The accuracy of the fit was tested for E values ranging from 0.7 to 2.5 eV, for s values between 10(5) and 10(25) s(-1), and for trap occupation numbers no/N between 1 and 10(-6). The goodness of fit of the logistic asymmetric function is described by the Figure of Merit (FOM) which is found to be of the order of 10(-2). Preliminary results show that the GCD described here can easily be extended to the description of general order TL glow curves by varying the asymmetry parameter of the logistic asymmetric function. It is concluded that the TL kinetic analysis of first, second and general order TL glow curves can be performed with high accuracy and speed by using commercially available statistical packages that incorporate the Weibull and logistic asymmetric functions.

Computer Simulation↗

PubMed2006

A brief conceptual tutorial of multilevel analysis in social epidemiology: using measures of clustering in multilevel logistic regression to investigate contextual phenomena.

STUDY OBJECTIVE: In social epidemiology, it is easy to compute and interpret measures of variation in multilevel linear regression, but technical difficulties exist in the case of logistic regression. The aim of this study was to present measures of variation appropriate for the logistic case in a didactic rather than a mathematical way. DESIGN AND PARTICIPANTS: Data were used from the health survey conducted in 2000 in the county of Scania, Sweden, that comprised 10 723 persons aged 18-80 years living in 60 areas. Conducting multilevel logistic regression different techniques were applied to investigate whether the individual propensity to consult private physicians was statistically dependent on the area of residence (that is, intraclass correlation (ICC), median odds ratio (MOR)), the 80% interval odds ratio (IOR-80), and the sorting out index). RESULTS: The MOR provided more interpretable information than the ICC on the relevance of the residential area for understanding the individual propensity of consulting private physicians. The MOR showed that the unexplained heterogeneity between areas was of greater relevance than the individual variables considered in the analysis (age, sex, and education) for understanding the individual propensity of visiting private physicians. Residing in a high education area increased the probability of visiting a private physician. However, the IOR showed that the unexplained variability between areas did not allow to clearly distinguishing low from high propensity areas with the area educational level. The sorting out index was equal to 82%. CONCLUSION: Measures of variation in logistic regression should be promoted in social epidemiological and public health research as efficient means of quantifying the importance of the context of residence for understanding disparities in health and health related behaviour.

Adolescent↗

PubMed2004

Nonsymmetrical double logistic analysis of ambulatory blood pressure recordings.

We developed an asymmetric double logistic curve-fitting procedure for circadian analysis that can determine the rate of change in variables during the day-to-night separately from the night-to-day transition for use in animal studies. We now have applied this procedure to 24-h systolic (SAP) and diastolic arterial pressure (DAP) and heart rate ambulatory recordings from 302 patients. In 292 cases, all parameters showed a pattern of higher day and lower night values. In men there was a similar rate of transition between day and night or from night to day for both SAP and DAP that lasted 3-4 h, indicating a symmetrical diurnal pattern. By contrast, women showed a faster rate of decrease in mean arterial pressure in the evening compared with men (P < 0.05) and therefore showed an asymmetric diurnal SAP pattern. For both men and women, there was a markedly greater rate of morning increase in heart rate compared with the rate of evening decrease (2.2- and 1.9-fold, respectively, P < 0.001). The logistic method provided a better fit than the square-wave or the cosinor method (P < 0.001) and more appropriately detected nondippers. We conclude that analysis of ambulatory recordings by a new logistic curve-fitting method reveals more rapid reductions in evening SAP in women than men but both have two- to threefold more rapid morning rates of tachycardia. The ability of the double logistic method to determine the diurnal blood pressure rates of change independently is key to determining new markers for cardiovascular risk.

Adult↗

PubMed1995

Logistic characterization of left ventricular isovolumic pressure-time curve.

Although some investigators have attempted to express the left ventricular pressure-time curve by mathematical functions such as exponential and sinusoidal functions, none of them reasonably fits the left ventricular pressure-time curve. In the present study, we hypothesized that a ventricular isovolumic pressure-time curve could be expressed as the difference between two S-shaped curves for pressure rising and falling, and proposed a new "hybrid logistic" function to express the left ventricular isovolumic pressure-time curve. We investigated how well this hybrid logistic function fits left ventricular isovolumic pressure curves experimentally observed under physiological preload and contractility in the excised cross-circulated left ventricles of 10 dogs. The new function precisely fitted the isovolumic pressure curves regardless of preload and contractility with correlation coefficients above 0.9996, much better than the previously proposed functions. The observed values characterizing the magnitude and time course of the isovolumic pressure curve such as peak +/- dP/dt also closely correlated with the corresponding theoretical values calculated by the present best-fit function. We conclude that our new hybrid logistic function reasonably characterizes the canine left ventricular isovolumic pressure-time curve within physiological ranges of preload and contractility. The present results indicate that this hybrid logistic function is useful to evaluate left ventricular contraction and relaxation comprehensively.

Animals↗

PubMed2000

Safety of immunization injections in Africa: not simply a problem of logistics.

In 1995, the WHO Regional Office for Africa launched a logistics project to address the four main areas of immunization logistics: the cold chain, transport, vaccine supply and quality, and the safety of injections in the countries of the region. The impact of this logistic approach on immunization injection safety was evaluated through surveys of injection procedures and an analysis of the injection materials (e.g. sterilizable or disposable syringes) chosen by the Expanded Programme on Immunization (EPI) and those actually seen to be used. Re-use of injection materials without sterilization, accidental needle-stick injuries among health care workers, and injection-related abscesses in patients were common in countries in the WHO African Region. Few health centres used time-steam saturation-temperature (TST) indicators to check the quality of sterilization and, in many centres, the injection equipment was boiled instead of being steam sterilized. Facilities for the proper disposal of used materials were rarely present. Although the official EPI choice was to use sterilizable equipment, use of a combination of sterilizable and disposable equipment was observed in the field. Unsafe injection practices in these countries were generally due to a failure to integrate nursing practices and public awareness with injection safety issues, and an absence of the influence of EPI managers on health care service delivery. Holistic rather than logistic approaches should be adopted to achieve safe injections in immunization, in the broader context of promoting safe vaccines and safety of all injections.

Africa↗

PubMed1990

Assessing proportionality in the proportional odds model for ordinal logistic regression.

The proportional odds model for ordinal logistic regression provides a useful extension of the binary logistic model to situations where the response variable takes on values in a set of ordered categories. The model may be represented by a series of logistic regressions for dependent binary variables, with common regression parameters reflecting the proportional odds assumption. Key to the valid application of the model is the assessment of the proportionality assumption. An approach is described arising from comparisons of the separate (correlated) fits to the binary logistic models underlying the overall model. Based on asymptotic distributional results, formal goodness-of-fit measures are constructed to supplement informal comparisons of the different fits. A number of proposals, including application of bootstrap simulation, are discussed and illustrated with a data example.

Biometry↗