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PubMed1999

[Logistic regression vs other generalized linear models to estimate prevalence rate ratios].

In cross-sectional studies, to quantify the association between a risk factor and a disease (possibly adjusted for confounders), in the framework of the multiplicative model, the more obvious effect measure is a prevalence rate ratio with an associated confidence interval. The validity of this confidence interval requires an unbiased estimator and an appropriate estimate of the variance. In numerous epidemiological studies however, routine use is made of odds ratios and logistic regression. As the odds ratio per se is difficult to understand, prevalence odds ratios are often interpreted as prevalence rate ratios. But this latter approximation is valid only under the rare disease assumption. Moreover, in the logistic regression model, the variance of the estimates is based on the assumption of binomial variability, which is not always supported by the data; in the frequent case of overdispersion, this leads to under-estimation of the type I error rate. Yet, within the generalized linear model, it is easy to choose a link function other than the logit. For example, the log link (log-binomial model) is appropriate to directly estimate adjusted prevalence rate ratios. In case of overdispersion, it is also possible to achieve a better fit of the model, either by choosing another distribution in the exponential family or by estimating a dispersion parameter for the binomial distribution. Thus, there are no valid reasons for the systematic choice of odds ratio and of the logistic regression model to estimate prevalence rate ratios, unless the type of study imperatively requires their use.

Humans↗
PubMed2001

Application of a sigmapolycyclic aromatic hydrocarbon model and a logistic regression model to sediment toxicity data based on a species-specific, water-only LC50 toxic unit for Hyalella azteca.

Two models, a sigmapolycyclic aromatic hydrocarbon (PAH) model based on equilibrium partitioning theory and a logistic-regression model, were developed and evaluated to predict sediment-associated PAH toxicity to Hyalella azteca. A sigmaPAH model was applied to freshwater sediments. This study is the first attempt to use a sigmaPAH model based on water-only, median lethal concentration (LC50) toxic unit (TU) values for sediment-associated PAH mixtures and its application to freshwater sediments. To predict the toxicity (i.e., mortality) from contaminated sediments to H. azteca, an interstitial water TU, calculated as the ambient interstitial water concentration divided by the water-only LC50 in which the interstitial water concentrations were predicted by equilibrium partitioning theory, was used. Assuming additive toxicity for PAH, the sum of TUs was calculated to predict the total toxicity of PAH mixtures in sediments. The sigmaPAH model was developed from 10- and 14-d H. azteca water-only LC50 values. To obtain estimates of LC50 values for a wide range of PAHs, a quantitative structure-activity relationship (QSAR) model (log LC50 - log Kow) with a constant slope was derived using the time-variable LC50 values for four PAH congeners. The logistic-regression model was derived to assess the concentration-response relationship for field sediments, which showed that 1.3 (0.6-3.9) TU were required for a 50% probability that a sediment was toxic. The logistic-regression model reflects both the effects of co-occurring contaminants (i.e., nonmeasured PAH and unknown pollutants) and the overestimation of exposure to sediment-associated PAH. An apparent site-specific bioavailability limitation of sediment-associated PAH was found for a site contaminated by creosote. At this site, no toxic samples were less than 3.9 TU. Finally, the predictability of the sigmaPAH model can be affected by species-specific responses (Hyalella vs Rhepoxynius); chemical specific (PAH vs DDT in H. azteca) biases, which are not incorporated in the equilibrium partitioning model; and the uncertainty from site-specific effects (creosote vs other sources of PAH contamination) on the bioavailability of sediment-associated PAH mixtures.

Animals↗
PubMed2002

Prediction of early and delayed postoperative deaths after coronary artery bypass surgery alone in Italy. Multivariate predictions based on Cox and logistic models and a chart based on the accelerated failure time model.

BACKGROUND: The aim of the multicenter OP-RISK (OPerative RISK) study was to investigate the early (28 days) and delayed (365 days) death rates following coronary artery bypass grafting (CABG) among patients representing a nationwide distribution [Centers in Northern (2), Central (1) and Southern (1) Italy] and further to define the multivariate risk factors for the early and delayed mortality after CABG. METHODS: Data were collected from 1126 patients undergoing CABG alone. Data were analyzed using Cox and logistic regression models, to accurately assess the major factors influencing survival over time after CABG. Having defined the significant factors, we constructed a chart of the absolute early risk of mortality using the accelerated failure time model. RESULTS: Using the Cox proportional hazards model and logistic regression we have demonstrated that age, preoperative ejection fraction and heart rate, and the duration of aortic cross-clamping are multivariate risk factors in the short and long term. The role of one arterial conduit was also assessed. CONCLUSIONS: The OP-RISK study produced relevant information for risk assessment and control in CABG and the results may form the basis for the objective quality assurance and accreditation of cardiac surgical institutions in Italy. Incidentally, Cox model appeared more adequate than logistic model for the assessment of the major factors influencing survival over time after CABG. The risk factors so assessed were used to construct a chart for practical predictive purposes.

Adult↗
PubMed1992

Combining logistic regression and neural networks to create predictive models.

Neural networks are being used widely in medicine and other areas to create predictive models from data. The statistical method that most closely parallels neural networks is logistic regression. This paper outlines some ways in which neural networks and logistic regression are similar, shows how a small modification of logistic regression can be used in the training of neural network models, and illustrates the use of this modification for variable selection and predictive model building with neural networks.

Algorithms↗
PubMed1987

A comparison of discriminant analysis and logistic regression for the prediction of coliform mastitis in dairy cows.

Results from discriminant analysis and logistic regression were compared using two data sets from a study on predictors of coliform mastitis in dairy cows. Both techniques selected the same set of variables as important predictors and were of nearly equal value in classifying cows as having, or not having mastitis. The logistic regression model made fewer classification errors. The magnitudes of the effects were considerably different for some variables. Given the failure to meet the underlying assumptions of discriminant analysis, the coefficients from logistic regression are preferable.

Animals↗
PubMed1979

[The description of growth course using a generalized logistic growth function].

For a quantitative description of measured growth courses the generalized logistic function will be used which is derived on the basis of the well-known logistic function of VERHULST. Numerical properties of this expression and possibilities for its computerized adjustment to measured courses are discussed. Examples of growth processes and their mathematical description by adjusted generalized logistic functions demonstrate the effectiveness of an ALGOL-program system for nonlinear approximation which is specialized to this function type. Especially the numerical improvement of approximation quality is demonstrated for expressions containing an absolute term in form of an also adjustable parameter.

Body Height↗
PubMed1983

Comparison of a logistic and a mass-action curve for radioimmunoassay data.

This paper compares a logistic curve and a mass-action curve in their ability to represent radioimmunoassay standard curves. A data base from 10 different assays is used in this comparison. Six of the 10 assays could be modeled equally well by either the logistic or the mass-action curve. In one case the mass-action curve gave a slightly better fit, though the practical distinction was negligible. In the remaining three assays the mass-action curve performed very much worse than the logistic curve. It is shown that the mass-action curve can assume only a very limited range of shapes, which explains its difficulty with these three assays. In particular, the mass-action curve cannot represent assays where the standard curve slope is less than a specified value. The paper also discusses the extension of each of these curves to more complicated equations, and their application to immunoassay data.

Computers↗
PubMedDate not supplied

[Control of onchocerciasis vectors in West Africa: description of the logistics adapted for a large-scale public health program].

The Onchocerciasis Control Programme (OCP) in West Africa, launched in 1974, includes 11 participating countries and covers more than one million square kilometres. The aim of the OCP is to control blinding onchocerciasis (river blindness) which is caused by the savannah strain of Onchocerca volvulus transmitted by the Simulium damnosum complex. There is no effective macrofilaricide, so vector control to prevent the transmission of the parasite remains the method of choice, despite the availability of ivermectin, a drug which controls ocular morbidity. The potential value of vector control has been demonstrated by the original programme: 14 years activity has eliminated the disease as a public health problem in the areas included. This strategy requires adapted logistical support involving (i) widespread insecticide coverage (27,000 km of river are treated by the OCP during the rainy season), (ii) frequent (weekly) application of larvicide and (iii) prolonged intervention due to the life-span of the worm in the human reservoir, estimated to be approximately 14 years. We describe the vector control operations and their organisation 20 years after the initiation of the OCP. The OCP can be divided into 5 areas of logistic activity. The first covers activities involving insecticide and fuel management for the OCP as a whole: assessment of the requirements for the following year, ordering from insecticide and petrol suppliers, stocking fuel and insecticide at the depots covering the area. The second activity is the treatment of rivers with insecticide. This includes treating the ground with larvicide, the aerial operations run by an independent company supplying 12 helicopters on contract to the OCP, and use of satellite beacons for retransmitting of hydrological data. The third activity is monitoring the impact of larvicides on both the target (adult and larval S. damnosum) and on other fauna (fish, crustaceans and other insects). The fourth activity is field data collection and its processing. This involves a data transmission network to facilitate stock management insecticide application and entomological and hydrological surveillance using computer systems. The fifth activity is the coordination of vector control operations, technical and administrative staff and estimations of the funds available to the Vector Control Unit. The logistic aspects of other large-scale-insect-control programmes world-wide are considered, and the possibility of using the OCP as a model for such programmes (both public health and agricultural) is assessed.

Africa, Western↗
PubMed1994

Current logistics of acute burn care in Singapore.

OBJECTIVE: To study logistic requirements in acute burn care in Singapore and to correlate statistics on fire, unnatural deaths and burns. DESIGN: Fire data (from Singapore Fire Safety Bureau), mortality data (from Institute of Science & Forensic Medicine) and burn data (from Burns Centre, Singapore General Hospital) were studied. SETTING: Severe burn victims often require prolonged treatment. Useful data was obtained in a 1,500-bed restructured government hospital. PARTICIPANTS: All reported and investigated fire incidents, coroner enquiries of unnatural deaths and admitted burn patients. INTERVENTION: General burn data obtained retrospectively from 398 burn admissions in 1988 and logistic burn data from 41 patients requiring fluid replacement regime. RESULTS: Fire data showed one burn admission in every 12 fires (398/4718), one burn death in every 314 fires (15/4174) or 55 unnatural deaths (15/828). Mortality data showed 15 burn deaths, two prior to admission, 7/13 admitted died of suicidal injuries and mortality rate was 3.3% (national annual average is 1.9%). General burn data showed adults 76% and children 24%, 3:1 male predominance; scalds (46%), fire (32%), explosions (11%) and others (11%). Seventy-eight patients (adults 58, children 20) required fluid resuscitation. Logistic burn data (average burn 35%, 28 partial thickness and 13 full thickness burns) were: ALOS 19.5 days, 2.4 major operations per patient (range 2-7), 56 minor procedures and 2.9 L blood transfusion per patient (those who were operated required 3.8 L and those not operated, 1 L per patient). Blood investigations increased with severity and pattern of injury, Acinetobacter species was commonest microorganisms, antibiotics were used in 66% of patients and commonest burn dressings were tullegra (T/G), followed by T/G with silverzine. CONCLUSION: Data presented useful for correlation of fire, mortality and burn statistics, resource allocation and new burn facility establishment.

Blood Transfusion↗
PubMed1996

The Logistic Organ Dysfunction system. A new way to assess organ dysfunction in the intensive care unit. ICU Scoring Group.

OBJECTIVE: To develop an objective method for assessing organ dysfunction among intensive care unit (ICU) patients on the first day of the ICU stay. DESIGN AND SETTING: Physiological variables defined dysfunction in 6 organ systems. Logistic regression techniques were used to determine severity levels and relative weights for the Logistic Organ Dysfunction (LOD) score and for conversion of the LOD score to a probability of mortality. PATIENTS: A total of 13 152 consecutive admission to 137 adult medical/surgical ICUs in 12 countries from the European/North American Study of Severity Systems. OUTCOME MEASURES: Patient vital status at hospital discharge. RESULTS: The LOD System identified from 1 to 3 levels of organ dysfunction for 6 organ systems: neurologic, cardiovascular, renal, pulmonary, hematologic, and hepatic. From 1 to 5 LOD points were assigned to the levels of severity, and the resulting LOD scores ranged from 0 to 22 points. Model calibration was very good in the developmental and validation samples (P=.21 and P=.50, respectively), as was model discrimination (area under the receiver operating characteristic curves of 0.843 and 0.850, respectively). CONCLUSION: The LOD System provides an objective tool for assessing severity levels for organ dysfunction in the ICU, a critical component in the conduct of clinical trials. Neurologic, cardiovascular, and renal dysfunction were the most severe organ dysfunctions, followed by pulmonary and hematologic dysfunction, with hepatic dysfunction the least severe. The LOD System takes into account both the relative severity among organ systems and the degree of severity within an organ system.

Adult↗
PubMed1998

A multivariate logistic model (MLM) for analyzing binary family data.

We consider modeling the familial correlation between 2 related individuals using a multiple logistic regressive model. It is shown that there is a discrepancy in the marginal probability of the second individual. We investigate the conditions under which this discrepancy can be minimized and show how it can have a direct effect on handling missing values and ascertainment. We derive a functional relationship between the parameters in the model that eliminates this discrepancy, hence solving the problems that can arise in the handling of missing values and ascertainment. Because this methodology fails when there are more than 2 related individuals, we present a new model based on a multivariate logistic distribution. Residual familial correlations can be directly related to the parameters of this model. The likelihood for family data under this model is independent of the order in which the family members enter the calculation. The marginal probabilities can be easily computed.

Data Interpretation, Statistical↗
PubMed1997

Jackknife bias reduction for polychotomous logistic regression.

Despite theoretical and empirical evidence that the usual MLEs can be misleading in finite samples and some evidence that bias reduced estimates are less biased and more efficient, they have not seen a wide application in practice. One can obtain bias reduced estimates by jackknife methods, with or without full iteration, or by use of higher order terms in a Taylor series expansion of the log-likelihood to approximate asymptotic bias. We provide details of these methods for polychotomous logistic regression with a nominal categorical response. We conducted a Monte Carlo comparison of the jackknife and Taylor series estimates in moderate sample sizes in a general logistic regression setting, to investigate dichotomous and trichotomous responses and a mixture of correlated and uncorrelated binary and normal covariates. We found an approximate two-step jackknife and the Taylor series methods useful when the ratio of the number of observations to the number of parameters is greater than 15, but we cannot recommend the two-step and the fully iterated jackknife estimates when this ratio is less than 20, especially when there are large effects, binary covariates, or multicollinearity in the covariates.

Bias↗
PubMed1997

A comparison of goodness-of-fit tests for the logistic regression model.

Recent work has shown that there may be disadvantages in the use of the chi-square-like goodness-of-fit tests for the logistic regression model proposed by Hosmer and Lemeshow that use fixed groups of the estimated probabilities. A particular concern with these grouping strategies based on estimated probabilities, fitted values, is that groups may contain subjects with widely different values of the covariates. It is possible to demonstrate situations where one set of fixed groups shows the model fits while the test rejects fit using a different set of fixed groups. We compare the performance by simulation of these tests to tests based on smoothed residuals proposed by le Cessie and Van Houwelingen and Royston, a score test for an extended logistic regression model proposed by Stukel, the Pearson chi-square and the unweighted residual sum-of-squares. These simulations demonstrate that all but one of Royston's tests have the correct size. An examination of the performance of the tests when the correct model has a quadratic term but a model containing only the linear term has been fit shows that the Pearson chi-square, the unweighted sum-of-squares, the Hosmer-Lemeshow decile of risk, the smoothed residual sum-of-squares and Stukel's score test, have power exceeding 50 per cent to detect moderate departures from linearity when the sample size is 100 and have power over 90 per cent for these same alternatives for samples of size 500. All tests had no power when the correct model had an interaction between a dichotomous and continuous covariate but only the continuous covariate model was fit. Power to detect an incorrectly specified link was poor for samples of size 100. For samples of size 500 Stukel's score test had the best power but it only exceeded 50 per cent to detect an asymmetric link function. The power of the unweighted sum-of-squares test to detect an incorrectly specified link function was slightly less than Stukel's score test. We illustrate the tests within the context of a model for factors associated with low birth weight.

Humans↗
PubMed1997

Derivation of the linear-logistic model and Cox's proportional hazard model from a canonical system description.

The linear-logistic regression model and Cox's proportional hazard model are widely used in epidemiology. Their successful application leaves no doubt that they are accurate reflections of observed disease processes and their associated risks or incidence rates. In spite of their prominence, it is not a priori evident why these models work. This article presents a derivation of the two models from the framework of canonical modeling. It begins with a general description of the dynamics between risk sources and disease development, formulates this description in the canonical representation of an S-system, and shows how the linear-logistic model and Cox's proportional hazard model follow naturally from this representation. The article interprets the model parameters in terms of epidemiological concepts as well as in terms of general systems theory and explains the assumptions and limitations generally accepted in the application of these epidemiological models.

Communicable Diseases↗
PubMed1997

Logistic regression models with missing covariate values for complex survey data.

Maximum likelihood methods are used to incorporate partially observed covariate values in fitting logistic regression models. We extend these methods to data collected through complex surveys using the pseudo-likelihood approach. One can obtain parameter estimates of the logistic regression model using standard statistical software and their standard errors by Taylor series expansion or the jackknife method. We apply the approach to data from a two-phase survey screening for dementia in a community sample of African Americans age 65 and older living in Indianapolis. The binary response variable is dementia and the covariate with missing values is a daily functioning score collected from interviews with a relative of the study subject.

Black or African American↗
PubMed1998

Gibbs sampler for the logistic model in the analysis of longitudinal binary data.

Logistic mixed-effects models constitute a natural framework to study longitudinal binary response variables when the question addressed with the data is related to covariate effects within persons. However, the computations of the likelihoods are generally tedious and require the resolution of integrals which have no analytical solution. In this paper, we study a logistic mixed-effects model in a Bayesian framework and use the Gibbs sampler to overcome the current computational limitations. From a study of side-effects occurring during plasma exchanges, we explore the issues of bayesian formulation, model parametrization, choice of the prior distributions, diagnosing convergence, comparison between models and model adequacy. Finally, we show that a Bayesian random-effects model is useful to facilitate prediction.

Bayes Theorem↗
PubMed1999

Bivariate logistic regression: modelling the association of small for gestational age births in twin gestations.

Clustered binary responses, such as disease status in twins, frequently arise in perinatal health and other epidemiologic applications. The scientific objective involves modelling both the marginal mean responses, such as the probability of disease, and the within-cluster association of the multivariate responses. In this regard, bivariate logistic regression is a useful procedure with advantages that include (i) a single maximization of the joint probability distribution of the bivariate binary responses, and (ii) modelling the odds ratio describing the pairwise association between the two binary responses in relation to several covariates. In addition, since the form of the joint distribution of the bivariate binary responses is assumed known, parameters for the regression model can be estimated by the method of maximum likelihood. Hence, statistical inferences may be based on likelihood ratio tests and profile likelihood confidence intervals. We apply bivariate logistic regression to a perinatal database comprising 924 twin foetuses resulting from 462 pregnancies to model obstetric and clinical risk factors for the association of small for gestational age births in twin gestations.

Adolescent↗
PubMed1990

Prediction of mortality by logistic regression analysis in patients with postoperative enterocutaneous fistulae.

The contrasting results of treatment of patients with postoperative enterocutaneous fistulae reflect the heterogeneity of the disease and depend on the patient's condition and the characteristics of the fistulae. For this reason, the use of a prognostic index, which enables such patients to be classified according to their risk of death, could be useful. In this study we propose a prognostic index based on a logistic regression analysis, obtained by using two (APACHE II score and serum albumin concentration) of the eight risk factors that have been retrospectively analysed in a series of 70 patients with postoperative enterocutaneous fistulae treated in our surgical department since 1981. The logistic regression equation indicates that patients with a probability of dying of less than 0.35 have a good prognosis, with a sensitivity of 90 per cent, a specificity of 90 per cent, a negative predictive value of 79 per cent, a positive predictive value of 96 per cent and an accuracy of 90 per cent. The predictive performance of the index has also been evaluated in a group of 17 patients studied prospectively, and this confirms the sensitivity and specificity of the model. This postoperative enterocutaneous fistulae index could be a helpful tool in clinical trials and surgical audit.

Adult↗