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PubMed2003

A mixed-effects multinomial logistic regression model.

A mixed-effects multinomial logistic regression model is described for analysis of clustered or longitudinal nominal or ordinal response data. The model is parameterized to allow flexibility in the choice of contrasts used to represent comparisons across the response categories. Estimation is achieved using a maximum marginal likelihood (MML) solution that uses quadrature to numerically integrate over the distribution of random effects. An analysis of a psychiatric data set, in which homeless adults with serious mental illness are repeatedly classified in terms of their living arrangement, is used to illustrate features of the model.

Adult↗
PubMed2004

A tree based lack-of-fit test for multiple logistic regression.

Several omnibus tests have been developed to assess the fit of a regression model. But many of these lack-of-fit tests focus on the simple regression setting. Here, we focus on multiple logistic regression. Pearson's well-known chi-square test statistic and the deviance statistic are no longer valid in the case that the model contains one or more continuous covariates. To overcome this difficulty, Hosmer and Lemeshow proposed a Pearson type statistic based on groups defined by the so-called deciles of risk. We propose a test statistic that is similar in approach to the Hosmer and Lemeshow statistic in that the observations are classified into distinct groups. In the procedure proposed here however, the grouping is not according to probabilities fitted under the null model. We use a recursive partitioning algorithm to divide the sample space into different groups. This generally allows for a more powerful assessment of the model fit. Simulations are carried out to compare the results of the proposed test to that of Hosmer and Lemeshow. Three data examples illustrate the performance of the tree based lack-of-fit test, in comparison to several other tests.

Adult↗
PubMed2004

Validation and updating of predictive logistic regression models: a study on sample size and shrinkage.

A logistic regression model may be used to provide predictions of outcome for individual patients at another centre than where the model was developed. When empirical data are available from this centre, the validity of predictions can be assessed by comparing observed outcomes and predicted probabilities. Subsequently, the model may be updated to improve predictions for future patients. As an example, we analysed 30-day mortality after acute myocardial infarction in a large data set (GUSTO-I, n = 40 830). We validated and updated a previously published model from another study (TIMI-II, n = 3339) in validation samples ranging from small (200 patients, 14 deaths) to large (10,000 patients, 700 deaths). Updated models were tested on independent patients. Updating methods included re-calibration (re-estimation of the intercept or slope of the linear predictor) and more structural model revisions (re-estimation of some or all regression coefficients, model extension with more predictors). We applied heuristic shrinkage approaches in the model revision methods, such that regression coefficients were shrunken towards their re-calibrated values. Parsimonious updating methods were found preferable to more extensive model revisions, which should only be attempted with relatively large validation samples in combination with shrinkage.

Computer Simulation↗
PubMed2004

Statistical assessment of mediational effects for logistic mediational models.

The concept of mediation has broad applications in medical health studies. Although the statistical assessment of a mediational effect under the normal assumption has been well established in linear structural equation models (SEM), it has not been extended to the general case where normality is not a usual assumption. In this paper, we propose to extend the definition of mediational effects through causal inference. The new definition is consistent with that in linear SEM and does not rely on the assumption of normality. Here, we focus our attention on the logistic mediation model, where all variables involved are binary. Three approaches to the estimation of mediational effects-Delta method, bootstrap, and Bayesian modelling via Monte Carlo simulation are investigated. Simulation studies are used to examine the behaviour of the three approaches. Measured by 95 per cent confidence interval (CI) coverage rate and root mean square error (RMSE) criteria, it was found that the Bayesian method using a non-informative prior outperformed both bootstrap and the Delta methods, particularly for small sample sizes. Case studies are presented to demonstrate the application of the proposed method to public health research using a nationally representative database. Extending the proposed method to other types of mediational model and to multiple mediators are also discussed.

Adolescent↗
PubMed2005

Testing goodness-of-fit of the logistic regression model in case-control studies using sample reweighting.

A new goodness-of-fit test for the logistic regression model is proposed. It exploits the property of this model that when it is correct, i.e. not misspecified, the parameter estimates are (asymptotically) invariant under reweighting the observations by weights wi that are a function of the binary (0/1) outcomes yi. Misspecification of the model can thus be concluded when parameter estimates change under reweighting. A local test, considering weights of the form wi=(1 + epsilonyi) is explored. The test is especially suitable for case-control studies but may be used in other contexts as well.

Adult↗
PubMed2005

Does it always help to adjust for misclassification of a binary outcome in logistic regression?

It is well known that in logistic regression, where the outcome is measured with error, a biased estimate of the association between the outcome and a risk factor may result if no proper adjustment is made. Hence, it seems tempting to always adjust for possible misclassification of the outcome. Here we show that it is not always beneficial to do so because, though the adjustment reduces the bias, it also inflates the variance, leading to a possibly larger mean squared error of the estimate. In the context of a data set on agricultural injuries, numerical evidence is provided through simulation studies.

Accidents, Occupational↗
PubMed2006

Multilevel logistic regression modelling with correlated random effects: application to the Smoking Cessation for Youth study.

A multilevel logistic regression model is presented for the analysis of clustered and repeated binary response data. At the subject level, serial dependence is expected between repeated measures recorded on the same individual. At the cluster level, correlations of observations within the same subgroup are present due to the inherent hierarchical setting. Two random components are therefore incorporated explicitly within the linear predictor to account for the simultaneous heterogeneity and autoregressive structure. Application to analyse a set of longitudinal data from an adolescent smoking cessation intervention that motivated this study is illustrated.

Adolescent↗
PubMed1994

Non-hierarchical logistic models and case-only designs for assessing susceptibility in population-based case-control studies.

This article describes how genetic components of disease susceptibility can be evaluated in case-control studies, where cases and controls are sampled independently from the population at large. Subjects are assumed unrelated, in contrast to studies of familial aggregation and linkage. The logistic model can be used to test collapsibility over phenotypes or genotypes, and to estimate interactions between environmental and genetic factors. Such interactions provide an example of a context where non-hierarchical models make sense biologically. Also, if the exposure and genetic categories occur independently and the disease is rare, then analyses based only on cases are valid, and offer better precision for estimating gene-environment interactions than those based on the full data.

Biomarkers↗
PubMed1994

Alternative models for ordinal logistic regression.

Armstrong and Sloan have reviewed two types of ordinal logistic models for epidemiologic data: the cumulative-odds model and the continuation-ratio model. I review here certain aspects of these models not emphasized previously, and describe a third type, the stereotype model, which in certain situations offers greater flexibility coupled with interpretational advantages. I illustrate the models in an analysis of pneumoconiosis among coal miners.

Epidemiologic Methods↗
PubMed1995

Logistic regression in case-control studies: the effect of using independent as dependent variables.

In case-control studies, cases are sampled separately from controls. In such studies the primary analysis concerns the estimation of the effect of covariables on being a case or a control. To explore causal pathways, further secondary analysis could concern the relationships among the covariables. In this paper the validity of such secondary analysis is addressed. In particular, the use of multiple logistic regression in case-control studies where the dependent variable is not the case/control indicator is explored. It is shown that only under very restrictive conditions will sample regression coefficients correctly estimate their true value. In many situations, it may be valid to regress one covariable on others in the control group, but not in the case group or the combined sample. This principle is illustrated by a study of sexually transmitted disease in Kenya.

Case-Control Studies↗
PubMed1995

Exact logistic regression: theory and examples.

We provide an alternative to the maximum likelihood method for making inferences about the parameters of the logistic regression model. The method is based appropriate permutational distributions of sufficient statistics. It is useful for analysing small or unbalanced binary data with covariates. It also applies to small-sample clustered binary data. We illustrate the method by analysing several biomedical data sets.

Algorithms↗
PubMed2001

Correction of the P-value after multiple coding of an explanatory variable in logistic regression.

We propose a method and a program to determine a significance level for a series of codings of an explanatory variable in logistic regression. Dichotomous and Box-Cox transformations are considered. Three methods of correcting the significance level are studied: the Bonferroni method; Efron's method, which uses the correlation between successive tests, and the exact calculation by numerical integration using all correlations. A simulation study has led to a strategy for the choice and number of the different codings of the variable. This method is illustrated using the data of a study of the relation between cholesterol and dementia.

Aged↗
PubMed2001

Bayesian analysis of logistic regression with an unknown change point and covariate measurement error.

We discuss Bayesian estimation of a logistic regression model with an unknown threshold limiting value (TLV). In these models it is assumed that there is no effect of a covariate on the response under a certain unknown TLV. The estimation of these models in a Bayesian context by Markov chain Monte Carlo (MCMC) methods is considered with focus on the TLV. We extend the model by accounting for measurement error in the covariate. The Bayesian solution is compared with the likelihood solution proposed by Küchenhoff and Carroll using a data set concerning the relationship between dust concentration in the working place and the occurrence of chronic bronchitis.

Bayes Theorem↗
PubMed2002

Two goodness-of-fit tests for logistic regression models with continuous covariates.

Assessing goodness-of-fit in logistic regression models can be problematic, in that commonly used deviance or Pearson chi-square statistics do not have approximate chi-square distributions, under the null hypothesis of no lack of fit, when continuous covariates are modelled. We present two easy to implement test statistics similar to the deviance and Pearson chi-square tests that are appropriate when continuous covariates are present. The methodology uses an approach similar to that incorporated by the Hosmer and Lemeshow goodness-of-fit test in that observations are classified into distinct groups according to fitted probabilities, allowing sufficient cell sizes for chi-square testing. The major difference is that the proposed tests perform this grouping within the cross-classification of all categorical covariates in the model and, in some situations, allow for a more powerful assessment of where model predicted and observed counts may differ. A variety of simulations are performed comparing the proposed tests to the Hosmer-Lemeshow test.

Aortic Aneurysm, Abdominal↗
PubMed1999

A comparison of logistic regression to decision tree induction in the diagnosis of carpal tunnel syndrome.

This paper aims to compare and contrast two types of model (logistic regression and decision tree induction) for the diagnosis of carpal tunnel syndrome using four ordered classification categories. Initially, we present the classification performance results based on more than two covariates (multivariate case). Our results suggest that there is no significant difference between the two methods. Further to this investigation, we present a detailed comparison of the structure of bivariate versions of the models. The first surprising result of this analysis is that the classification accuracy of the bivariate models is slightly higher than that of the multivariate ones. In addition, the bivariate models lend themselves to graphical analysis, where the corresponding decision regions can easily be represented in the two-dimensional covariate space. This analysis reveals important structural differences between the two models.

Algorithms↗
PubMed2000

Combined transvaginal B-mode and color Doppler sonography for differential diagnosis of ovarian tumors: results of a multivariate logistic regression analysis.

OBJECTIVE: Transvaginal sonography is limited in its ability to assess early stage cancers of the ovary as well as in distinguishing benign processes. As a method for characterization of tumor vascularization, color-coded Doppler sonography may be able to improve the diagnostic accuracy of B-mode sonography. METHODS: Preoperative transvaginal B-mode and Doppler sonography was performed in 63 patients with unclear adnexal lesions prior to operation. Using multiple logistic regression, the independent variables of each procedure were selected and combined to yield a diagnostic flow chart. The diagnostic accuracy of this decision matrix was tested on 257 patients with unclear adnexal tumors. RESULTS: In the 63 adnexal tumors investigated, the diagnostic impact of isolated sonomorphological assessment with evidence of a "solid area" was 78%. Using Doppler sonography, the best discrimination was achieved by displaying the vascular distribution ("central vascularization"). Combining these independent significant variables of the two procedures raised the diagnostic accuracy to 90% (sensitivity 86%, specificity 93%). The validity achieved by this combination was confirmed by the independent application of this method to the 257 adnexal tumors with unclear malignancy status (diagnostic accuracy 93%, sensitivity 92%, specificity 94%). CONCLUSIONS: The combination of sonography and Doppler sonography achieves high and reproducible diagnostic accuracy in preoperative malignancy status assessment of adnexal tumors. The additional use of Doppler sonography can thus provide significant aid both for differential diagnostics of adnexal lesions and for the choice of surgical route in the case of an existing indication for operative therapy.

Adnexal Diseases↗
PubMed1998

Impact of resting and ischemic blood flow on infarct probability in ischemic preconditioning--a new approach to infarct size-blood flow data by logistic regression.

The linear regression analysis of infarct size (IS) v ischemic myocardial blood flow (MBF) does not account for the heterogeneity of MBF and infarcted tissue; moreover, it cannot assess a blood flow threshold for infarction (MBFT) accurately, as with ischemic preconditioning (IP) the close relationship between ischemic MBF and IS otherwise observed is lost. Finally, the impact of resting blood flow on myocardial infarction cannot be considered in such analysis. Therefore, in a retrospective data analysis of 32 enflurane-anaesthetized swine undergoing 90 min severe ischemia and 120 min reperfusion without (CON, n = 12) or with IP induced by either 3 (IP3, n = 8) or 10 min ischemia (IP10, n = 12) and 15 min reperfusion, a MBFT was assessed by logistic regression (LR) in individual tissue pieces. MBFT was arbitrarily defined as that ischemic MBF (microspheres) at which infarct probability was 0.2, derived from the ratio of infarcted (n = 141, TTC) to all tissue samples (n = 684). The duration of the preconditioning ischemia and MBF both at rest and during the sustained ischemia were significant predictors of infarct probability. Ischemic MBFT at an infarct probability of 0.2, was 0.089 +/- 0.023 ml/min/g in CON. MBFT was decreased to 0.051 +/- 0.03 ml/min/g with IP3 (P < 0.05 v CON) and further to 0.004 +/- 0.037 ml/min/g with IP10 (P < 0.05 v CON, IP3). Corresponding to the leftward shift of MBFT, the relationships between infarct probability and MBF were shifted in parallel by IP with no change in their slopes.

Animals↗
PubMed1999

Effects of immigration on some stochastic logistic models: a cumulant truncation analysis.

This paper uses a new cumulant truncation methodology to investigate the stochastic power law logistic model with immigration, and illustrates the model with parameter values used to describe the growth of muskrat populations in the Netherlands. This model has a stable equilibrium distribution. The incorporation of immigration into the model, therefore, simplifies the qualitative nature of the stochastic solution. The (unconditional) cumulant functions for the transient and the equilibrium population size distributions are obtained, from which the distributions are shown to be near-normal at all times for the parameter values of interest. Approximating cumulant functions, which are relatively easy to find in practice, are derived and shown to be quite accurate, except for the case of massive immigration. As the level of immigration increases, the mean value rises more rapidly initially, as expected; however, the variance and the skewness of both the transient and the equilibrium distributions are reduced.

Animals↗