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PubMed2006

[Preload and ventricular lusitropism; logistic and monoexponential function fittings].

A logistic function has been found to fit the isovolumic left ventricular (LV) relaxation pressure curve and the isometric relaxation force curve of the papillary muscle much more precisely than the conventional monoexponential function. Therefore, the logistic time constant (tauL) has been proposed as a better index of the rate of cardiac relaxation or lusitropism than the conventional monoexponential time constant (tauE). Many investigators have reported that tauE changes with preloading. We analysed and compared the effect of LV volume (LVV) loading on both logistic and monoexponential fittings and their time constants of the isovolumic LV relaxation pressure curve in the excised, cross-circulated canine hearts. We found that the logistic fitting was superior to the monoexponential fitting at any LVV. LVV loading did not affect tauL at all but affected tauE slightly. The logistic fitting more reliably characterises the lusitropism than the monoexponential fitting, and tauL, serving as a more reliable ventricular lusitropism index, is independent of changes in LVV loading or the Frank-Starling effect.

Anesthesia↗
PubMed1991

Age-dependent logistic regression model and its application.

In the present paper we introduce the theory and algorithm of the unconditional and conditional age-dependent logistic regression model, which combines logistic regression analysis of case-control study with survival analysis of cases in the data, thus facilitating simultaneous comparison analysis between cases and controls and among cases with different ages of disease onset under study. In age-dependent logistic regression analysis, estimated compound relative risk (CRR) and compound attributable risk (CAR) comprise the variance contributions of risk factors to disease occurrence and the time of disease onset, thereby the role played by various risk factors in etiology and etiopathology can be objectively evaluated. The current logistic regression model is only a particular case of age-dependent logistic regression theory neglecting the variations in onset age of diseases.

Age Factors↗
PubMed1993

Modeling mortality in the intensive care unit: comparing the performance of a back-propagation, associative-learning neural network with multivariate logistic regression.

The objective of this study was to compare and contrast two techniques of modeling mortality in a 30 bed multi-disciplinary ICU; neural networks and logistic regression. Fifteen physiological variables were recorded on day 3 for 422 consecutive patients whose duration of stay was over 72 hours. Two separate models were built using each technique. First, logistic and neural network models were constructed on the complete 422 patient dataset and discrimination was compared. Second, the database was randomly divided into a 284 patient developmental dataset and a 138 patient validation dataset. The developmental dataset was used to construct logistic and neural net models and the predictive power of these models was verified on the validation dataset. On the complete dataset, the neural network clearly outperformed the logistic model (sensitivity and specificity of 1 and .997 vs. .525 and .966, area under ROC curve .9993 vs. .9259), while both performed equally well on the validation dataset (area under ROC of .82). The excellent performance of the neural net on the complete dataset reveals that the problem is classifiable. Since our dataset only contained 40 mortality events, it is highly likely that the validation dataset was not representative of the developmental dataset, which led to a decreased predictive performance by both the neural net and the logistic regression models. Theoretically, given an extensive dataset, the neural network should be able to perform mortality prediction with a sensitivity and a specificity approaching 95%. Clinically, this would be an extremely important achievement.(ABSTRACT TRUNCATED AT 250 WORDS)

Hospital Mortality↗
PubMed1996

Logistic character of myocardial twitch force curve: simulation.

We found that the isovolumic pressure-time curve of the canine left ventricle closely fitted the difference of two logistic function curves and that the isovolumic relaxation-pressure curve segment was more reliably characterized by a logistic time constant than by the conventional exponential time constant. We therefore hypothesized that the calcium (Ca) transient and the Ca-troponin (Tn) binding and crossbridge (CB) kinetics underlay the logistic character of the ventricular isovolumic pressure curve. We tested this hypothesis with a computer simulation of a simple Ca and CB kinetics model of myocardial isometric twitch force development. We assumed the instantaneous number of attached CBs that was theoretically given as the difference between the cumulative CB attachment and detachment curves. We radically changed the Ca transient, Ca-Tn binding, and CB kinetic parameters. We always found that both the cumulative CB attachment and detachment curves closely fitted logistic functions. The difference curve of these two best-fit logistic functions closely fitted the theoretical F curve with certain combinations of the Ca transient, the Ca-Tn binding, and the CB kinetic parameters. These results seem to support our hypothesis.

Animals↗
PubMed1990

Robust logistic discriminant functions in diagnosing chronic obstructive airways disease.

The paper gives a comparison of the classical logistic discriminant function, the alpha-trimmed logistic discriminant function and the L1-logistic discriminant function as used for assistance of medical diagnosis in chronic obstructive airways disease. The robustified logistic discriminant functions enable one to obtain higher rates of correctly classified individuals, especially the L1-logistic discriminant function should be recommended.

Discriminant Analysis↗
PubMed1990

Association of logistic and Poisson models of infection with some physical characteristics of a single component plant virus.

A logistic model was recently formulated to describe the relationship between concentration of a single component plant virus and infections produced by inoculation to a local lesion host. In this paper the logistic is combined with a Poisson model. The logistic makes accurate fitting possible for a variety of infection-dilution series; and the Poisson acts as a base line, indicating whether lesion numbers are compatible with the hypothesis that random infection of similar infection sites has occurred. A logarithmic form of the logistic equation gives a straight line with negative slope (logit slope) which is useful in characterizing dilution series to which the logistic is fitted. A modified Poisson equation can also be fitted to a range of dilution series; it provides an independent estimate of slope for curves not widely divergent from the standard Poisson. Models have also been developed to define the limits of concentration within which single virions are likely to be randomly dispersed in inoculum without immediate contact with other virions, and are therefore more likely to enter inoculated tissue independently and cause random infections. Models are formulated for aggregation of tobacco mosaic virus in monolayers, crystals, and lenticular aggregates. Published and unpublished data are fitted and analyzed using some of these models.

Models, Statistical↗
PubMed2004

Predicted quantitative effect of logistic slaughter on microbial prevalence.

Logistic slaughter is an intervention measure intended to reduce cross-contamination during slaughter by slaughtering contaminated units (=(groups of) animals) last. This paper describes a simple mathematical model which predicts the prevalences of contaminated units after logistic and random-order slaughter. The effect of logistic slaughter is the difference between these prevalences. The model assumes that uncontaminated units can become contaminated by contaminated units that were slaughtered before them; the contributions of contaminated units are independent. It also assumes that a slaughterhouse is uncontaminated at the start of the day and that a unit that is contaminated before slaughter also is contaminated after slaughter. The model was analysed using numerical simulations; for a selection of cases, analytical formulas can be derived and are presented. Contamination of broiler flocks with Salmonella was used as a case study. Even for this simple model, data availability is a problem leading to uncertain parameter estimates. An average cross-contamination scenario predicts that the beneficial effect of logistic slaughter is as low as 9.1%, which casts doubt on its usefulness as an intervention measure. The case study produced these general model results: the effect of logistic slaughter increases with the probability of cross-contamination between units; with the length of the slaughter queue; and with sensitivity (the probability of a positive test from a unit contaminated at the start of slaughter). However, the effect is small if the prevalence of contaminated units before slaughter is low or high.

Abattoirs↗
PubMed1998

Analysis of blood pressure responses during exercise by logistic function curve in hypertension: effects of age, gender and physical training.

During exercise blood pressure fluctuates from minute to minute and does not rise linearly with time. Blood pressure responses were evaluated during exercise by a logistic function curve. Thirty-nine hypertensive patients underwent exercise testing with an ergometer, employing a multistage method (25 watts increment, every 3 min). We plotted the exercise duration on the X-coordinate and systolic blood pressure on the Y-coordinate and blood pressure was assumed to form a logistic curve for exercise duration. The relationship of systolic blood pressure vs. exercise duration was better fitted into a logistic function curve than a linear regression model. The logistic curve was defined by lower plateau, upper plateau, SPX (the X-coordinate at the shift point) and df (SPX), the maximal slope at the shift point. The effects of aging, gender and physical training were then analyzed on the curve. Aging did not affect lower plateau, upper plateau and SPX but augmented df (SPX), indicating greater blood pressure responses in older subjects during exercise. In females the curve was shifted to the left compared to males (SPX: 4.9 vs. 8.3 min, P < 0.05) without changes in plateaux and df (SPX), indicating greater blood pressure responses than males. Physical training for 3 weeks decreased the lower plateau from 157 to 144 mmHg (P < 0.05) and shifted the curve to the right (SPX: 7.1 vs. 8.6 min, P < 0.05), indicating unchanged blood pressure responses after training because of the opposite effects by decreases in the lower plateau vs. the curve shift to the right. In conclusion, blood pressure during exercise is better delineated by a logistic function curve than a linear regression model. The biological or physiological significance of df (SPX) is not clear at present and needs further investigations.

Adult↗
PubMed2003

The spatial logistic map as a simple prototype for spatiotemporal chaos.

A spatial extension of the logistic map-termed spatial logistic map-is found to display the same basic universality classes as the commonly studied diffusively coupled logistic lattice despite being vastly simpler. By analyzing the escape rates and the Lyapunov spectra it is shown that the main attractors of the spatial logistic map are stable and hence that it is a good candidate for serving as a prototype for the class of coupled map lattices which it is a part of. The spatial logistic map is then employed to provide an analytical derivation for the recently discovered linear scaling of the wavelength under increasing coupling ranges.

Journal Article↗
PubMed1978

A critical analysis of the double and triple logistic growth curves.

Recently a model of human growth from the age of one year to maturity, based on two logistic terms, has been proposed. The originators of the model claim that it provides biologically meaningful parameters, and allows total growth to be partitioned into a pre-pubertal and an adolescent component. More recently, they have suggested an improved model, with three logistic terms, which gives a better fit. While the double logistic model gives an adequate fit to the observed height curve, differentiating it leads to a height velocity curve which differs considerably from the observed velocity curve. The triple logistic model gives an excellent fit to both the attained height and height velocity curves. Both models, however, imply a considerable time interval during which both the pre-pubertal and adolescent components are simultaneously contributing to growth, a situation that is difficult to justify biologically. The double model should therefore be discarded, and the triple logistic model considered to be of descriptive, rather than of interpretative, value.

Adolescent↗
PubMed2001

Conditional logistic analysis of case-control studies with complex sampling.

Methods for the analysis of unmatched case-control data based on a finite population sampling model are developed. Under this model, and the prospective logistic model for disease probabilities, a likelihood for case-control data that accommodates very general sampling of controls is derived. This likelihood has the form of a weighted conditional logistic likelihood. The flexibility of the methods is illustrated by providing a number of control sampling designs and a general scheme for their analyses. These include frequency matching, counter-matching, case-base, randomized recruitment, and quota sampling. A study of risk factors for childhood asthma illustrates an application of the counter-matching design. Some asymptotic efficiency results are presented and computational methods discussed. Further, it is shown that a 'marginal' likelihood provides a link to unconditional logistic methods. The methods are examined in a simulation study that compares frequency and counter-matching using conditional and unconditional logistic analyses and indicate that the conditional logistic likelihood has superior efficiency. Extensions that accommodate sampling of cases and multistage designs are presented. Finally, we compare the analysis methods presented here to other approaches, compare counter-matching and two-stage designs, and suggest areas for further research.To whom correspondence should be addressed.

Journal Article↗
PubMed1986

An insight on the use of multiple logistic regression analysis to estimate association between risk factor and disease occurrence.

Multiple logistic regression is an accepted statistical method for assessing association between an anticedant characteristic (risk factor) and a quantal outcome (probability of disease occurrence), statistically adjusting for potential confounding effects of other covariates. Yet the method has potential drawbacks which are not generally recognized. This article considers one important drawback of logistic regression. Specifically the so-called main effect logistic model assumes that the probability of developing disease is linearly and additively related to the risk factors on the logistic scale. This assumption stipulates that for each risk factor, the odds ratio is constant over all reference exposure levels, and that the odds ratio exposed to two or more factors is equal to the product of individual risk factor odds ratios. If the observed odds ratios in the data follow this pattern, the model-predicted odds ratios will be accurate, and the meaning of the odds ratio for each risk factor will be straightforward. But if the observed odds ratios deviate from the model assumption, the model will not fit the data accurately, and the model-predicted odds ratios will not reflect those in the data. Although satisfactory fit can always be achieved by adding to the model polynomial and product terms derived from the original risk factors, the odds ratios estimated by such an interaction logistic model are difficult to interpret, viz., the odds ratio for each risk factor depends not only on the reference exposure levels of that factor, but also on the exposure level in other factors.(ABSTRACT TRUNCATED AT 250 WORDS)

Environmental Exposure↗
PubMed1984

Interpreting multiple logistic regression coefficients in prospective observational studies.

Multiple logistic models are frequently used in observational studies to assess the contribution of a risk factor to disease while controlling for one or more covariates. Often, the covariates are correlated with the risk factor, resulting in multiple logistic coefficients that are difficult to interpret. This paper highlights the problem of assessing the magnitude of a multiple logistic coefficient and proposes a supplemental procedure to the usual logistic analysis for describing the relationship between a risk factor and disease. An example is given, along with results that are not apparent when the multiple logistic coefficient is considered alone. Conclusions that are presented are important in biologic studies if describing the effect of a risk factor is influenced by correlation with a covariate.

Coronary Disease↗
PubMed1975

Comparison of logistic equations for population growth.

Two different forms of the logistic equation for population growth appear in the ecological literature. In the form of the logistic equation that appears in recent ecology textbooks the parameters are the instantaneous rate of natural increase per individual and the carrying capacity of the environment. In the form of the logistic equation that appears in some older literature the parameters are the instantaneous birth rate per individual and the carrying capacity. The decision whether to use one form or the other depends on which form of the equation is biologically more realistic. In this study the form of the logistic equation in which the instantaneous birth rate per individual is a parameter is shown to be more realistic in terms of the birth and death processes of population growth. Application of the logistic equation to calculate yield from an exploited fish population also shows that the parameters must be the instantaneous birth rate per individual and the carrying capacity.

Mathematics↗
PubMed1988

A modified logistic model applied to human populations.

"The use of the logistic curve for forecasting human populations [in the United Kingdom] considered by Leach is re-examined. A modification of the use of the logistic curve is suggested, which changes the emphasis from fitting a logistic trend to providing a forecast logistic trend. The assumption, used by Leach, that the variance of the additive disturbance term is constant is replaced by a more realistic supposition that the variance of the proportional disturbance is constant. The forecasting performance of the modified logistic model is shown to be superior to that of the model used by Leach." A reply by Leach (pp. 496-7) and a response by the author (p. 498) are included.

Developed Countries↗
PubMed1987

The use of the logistic model in space motion sickness prediction.

The one-equation and the two-equation logistic models were used to predict tested subjects' susceptibility to motion sickness in KC-135 parabolic flights using data from other ground-based motion sickness tests. A data set containing data from 6 provocative tests, 2 vestibular function tests, and 1 motion sickness experience questionnaire from 162 subjects was used in this study. The prediction results from the logistic models were compared with those from the previously-used Bayes linear discriminant analysis procedures. The results based on this data set show that the logistic models correctly predicted substantially more cases (an average of 13%) in the data subset used for model building. In the data subset used for model cross-validation, the logistic models correctly predicted 4% and 5% more cases in the prediction of vomit or nonvomit, and of degree of susceptibility, respectively. Overall, the logistic models ranged from 53 to 65% predictions of the three endpoint parameters, whereas the Bayes linear discriminant procedure ranged from 48 to 65% correct for the cross validation sample.

Adult↗
PubMed1996

Understanding logistic regression analysis through example.

Logistic regression is a valuable statistical tool that is often used in primary care research. When researchers explore the association between a possible risk factor and a disease, they attempt to control the effects of extraneous factors (confounders) that can obscure the true association. Using logistic regression, researchers can simultaneously control for the effects of multiple confounders. When investigators use logistic regression, they make subjective decisions about which factors to include in the analysis and in the final predictive model. Critical readers must understand basic concepts of logistic regression and potential problems with its use before they can accurately interpret study results. This article uses a familiar example to explain the principles of logistic regression to make it understandable to nonstatisticians.

Coffee↗
PubMed1998

Using logistic regression to describe the length of breastfeeding: a study in Guadalajara, Mexico.

This study seeks, through a logistic regression model, to describe the pattern of breastfeeding duration in Guadalajara, Mexico, during 1993. A multistage random sample of children under 1 year of age (n = 1036) was studied; observational data regarding breastfeeding duration, obtained through a "status quo" procedure, were compared with prevalence rates obtained from the logistic regression model. Modeling the duration of breastfeeding during the first year of life rather than only analyzing observational data helps researchers to understand this process in a dynamic and quantitative way. For example, uncommon indicators of breastfeeding were derived from the model. These indicators are impossible to obtain from observational data. The prevalence curve estimated through the logistic model was adequately fitted to observed data: there were no significant differences between the number or distribution of breastfed infants observed and those predicted by the model. Moreover, the model revealed that less than 40% of the children were breastfed in the fourth month of life; the median age for weaning was 39.3 days; 55% of the potential breastfeeding in the first 4 months did not occur; and the greatest abandonment of breastfeeding in the first 4 months was observed in the first 60 days. Thus, logistic regression seems a suitable option to construct a population-based model that describes breastfeeding duration during the first year of life. The indicators derived from the model offer health care providers valuable information for developing programs that promote breastfeeding.

Adult↗