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PubMed2002

Generalised additive models and hierarchical logistic regression of lameness in dairy cows.

We examined the relationship between lameness (defined by locomotion score) and four time-related variables using data collected from a study of cattle lameness conducted in the UK from 1998 to 1992. The data were 19,667 locomotion scores for 1790 cows from 27 dairy herds; the four variables were time-from-calving, time of year, parity and time spent in the study. The shape of the relationships between calving and temporal variables and lameness were assessed using loess smoothed terms in a multivariable logistic generalised additive model (GAM). Polynomial relationships derived from the GAM then were included in a Bayesian hierarchical logistic-regression model incorporating between-herd, between-cow and within-cow random effects. The final hierarchical multivariable model showed that the most important variable influencing the probability of lameness was the time of scoring in the study; but, parity, time of year and time-from-calving also were significant. Between-herd and between-cow effects were of roughly equal importance.

Animals↗
PubMed2003

Comparing the importance of prognostic factors in Cox and logistic regression using SAS.

Two SAS macro programs are presented that evaluate the relative importance of prognostic factors in the proportional hazards regression model and in the logistic regression model. The importance of a prognostic factor is quantified by the proportion of variation in the outcome attributable to this factor. For proportional hazards regression, the program %RELIMPCR uses the recently proposed measure V to calculate the proportion of explained variation (PEV). For the logistic model, the R(2) measure based on squared raw residuals is used by the program %RELIMPLR. Both programs are able to compute marginal and partial PEV, to compare PEVs of factors, of groups of factors, and even to compare PEVs of different models. The programs use a bootstrap resampling scheme to test differences of the PEVs of different factors. Confidence limits for P-values are provided. The programs further allow to base the computation of PEV on models with shrinked or bias-corrected parameter estimates. The SAS macros are freely available at www.akh-wien.ac.at/imc/biometrie/relimp

Data Interpretation, Statistical↗
PubMed2003

Fixing the nonconvergence bug in logistic regression with SPLUS and SAS.

When analyzing clinical data with binary outcomes, the parameter estimates and consequently the odds ratio estimates of a logistic model sometimes do not converge to finite values. This phenomenon is due to special conditions in a data set and known as 'separation'. Statistical software packages for logistic regression using the maximum likelihood method cannot appropriately deal with this problem. A new procedure to solve the problem has been proposed by Heinze and Schemper (Stat. Med. 21 (2002) pp. 2409-3419). It has been shown that unlike the standard maximum likelihood method, this method always leads to finite parameter estimates. We developed a SAS macro and an SPLUS library to make this method available from within one of these widely used statistical software packages. Our programs are also capable of performing interval estimation based on profile penalized log likelihood (PPL) and of plotting the PPL function as was suggested by Heinze and Schemper (Stat. Med. 21 (2002) pp. 2409-3419).

Likelihood Functions↗
PubMed1999

Computing measures of explained variation for logistic regression models.

The proportion of explained variation (R2) is frequently used in the general linear model but in logistic regression no standard definition of R2 exists. We present a SAS macro which calculates two R2-measures based on Pearson and on deviance residuals for logistic regression. Also, adjusted versions for both measures are given, which should prevent the inflation of R2 in small samples.

Computer Simulation↗
PubMed2003

A multiple logistic regression analysis of in-hospital factors related to survival at six months in patients resuscitated from out-of-hospital ventricular fibrillation.

INTRODUCTION: The impact of the immediate in-hospital post-resuscitation care after out-hospital cardiac arrest is not well known. Based on treatment variables and laboratory findings a multiple logistic regression model was created for the prediction of survival at 6 months from the event. MATERIALS AND METHODS: A retrospective study of the hospital charts of patients successfully resuscitated and treated in one of three community hospitals from 1998 to 2000. In addition to several pre-hospital variables, the mean 72 h values of clinical features such as blood pressure, blood glucose concentration and initiated treatment used, were included in a forward multiple logistic regression model predicting survival at 6 months from the event. RESULTS: The charts of 98 out of a total of 102 patients were sufficiently complete and included in the analysis. Variables independently associated with survival were age, delay before a return of spontaneous circulation, mean blood glucose and serum potassium, and the use of beta-blocking agents during post-resuscitation care. When those patients who were assigned a 'do not attempt to resuscitate' (DNAR) order during the first 72 h of treatment were excluded from the analysis blood glucose, blood potassium and the use beta-blocking agents remained independently associated with survival. CONCLUSION: This study suggests that in-hospital factors are associated with survival from out-of-hospital cardiac arrest. The mean blood glucose and serum potassium during the first 72 h of treatment and the use of beta-blocking agents were significantly and independently associated with survival.

Adrenergic beta-Antagonists↗
PubMed2001

Internal validation of predictive models: efficiency of some procedures for logistic regression analysis.

The performance of a predictive model is overestimated when simply determined on the sample of subjects that was used to construct the model. Several internal validation methods are available that aim to provide a more accurate estimate of model performance in new subjects. We evaluated several variants of split-sample, cross-validation and bootstrapping methods with a logistic regression model that included eight predictors for 30-day mortality after an acute myocardial infarction. Random samples with a size between n = 572 and n = 9165 were drawn from a large data set (GUSTO-I; n = 40,830; 2851 deaths) to reflect modeling in data sets with between 5 and 80 events per variable. Independent performance was determined on the remaining subjects. Performance measures included discriminative ability, calibration and overall accuracy. We found that split-sample analyses gave overly pessimistic estimates of performance, with large variability. Cross-validation on 10% of the sample had low bias and low variability, but was not suitable for all performance measures. Internal validity could best be estimated with bootstrapping, which provided stable estimates with low bias. We conclude that split-sample validation is inefficient, and recommend bootstrapping for estimation of internal validity of a predictive logistic regression model.

Aged↗
PubMed2003

External validity of predictive models: a comparison of logistic regression, classification trees, and neural networks.

BACKGROUND AND OBJECTIVE: The utility of predictive models depends on their external validity, that is, their ability to maintain accuracy when applied to patients and settings different from those on which the models were developed. We report a simulation study that compared the external validity of standard logistic regression (LR1), logistic regression with piecewise-linear and quadratic terms (LR2), classification trees, and neural networks (NNETs). METHODS: We developed predictive models on data simulated from a specified population and on data from perturbed forms of the population not representative of the original distribution. All models were tested on new data generated from the population. RESULTS: The performance of LR2 was superior to that of the other model types when the models were developed on data sampled from the population (mean receiver operating characteristic [ROC] areas 0.769, 0.741, 0.724, and 0.682, for LR2, LR1, NNETs, and trees, respectively) and when they were developed on nonrepresentative data (mean ROC areas 0.734, 0.713, 0.703, and 0.667). However, when the models developed using nonrepresentative data were compared with models developed from data sampled from the population, LR2 had the greatest loss in performance. CONCLUSION: Our results highlight the necessity of external validation to test the transportability of predictive models.

Classification↗
PubMed1996

Advantages and disadvantages of using artificial neural networks versus logistic regression for predicting medical outcomes.

Artificial neural networks are algorithms that can be used to perform nonlinear statistical modeling and provide a new alternative to logistic regression, the most commonly used method for developing predictive models for dichotomous outcomes in medicine. Neural networks offer a number of advantages, including requiring less formal statistical training, ability to implicitly detect complex nonlinear relationships between dependent and independent variables, ability to detect all possible interactions between predictor variables, and the availability of multiple training algorithms. Disadvantages include its "black box" nature, greater computational burden, proneness to overfitting, and the empirical nature of model development. An overview of the features of neural networks and logistic regression is presented, and the advantages and disadvantages of using this modeling technique are discussed.

Algorithms↗
PubMed1999

Validation of logistic regression models in small samples: application to calvarial lesions diagnosis.

We have used the leave-one-out (LOO) method and the area under the receiver operating characteristic (ROC) curve to validate logistic models with a sample of 167 patients with calvarial lesions. Seven logistic regression models were developed from 12 clinical and radiological variables to predict the most common diagnoses separately. The LOO method was used to test the validity of the equations. The discriminant power of every model was assessed by means of the area under the ROC curve (Az). The model with the greatest discrimination ability for the whole data set was the osteoma equation (Az = 0.951). The discriminatory ability of the statistical models decreased significantly with the LOO procedure, having the malignancy model the highest value (Az = 0.931). The LOO method can obtain a high benefit from small samples in order to validate prediction rules. In studies with small samples, resampling techniques such as the LOO should be routinely used in predictive modeling. This method may improve the forecast of infrequent diseases, such as calvarial lesions.

Bone Neoplasms↗
PubMed1998

Estimating the incidence rate ratio in cross-sectional studies using a simple alternative to logistic regression.

PURPOSE: Logistic regression is often used for the analysis of cross-sectional studies, and prevalence odds and odds ratios are obtained. Other methods have been proposed for estimating prevalence ratios. An alternative regression method is also available for estimating rate ratios. Its application to cross-sectional studies is discussed. METHODS: When dealing with chronic conditions, it is possible to model binomial data using the complementary log-log link function log(-log(1-pi)), where pi is the prevalence, an option available on many statistical software packages. In effect, these are models for the disease incidence rate lambda, which is assumed to be constant over the underlying follow-up period t. This approach is based on the well-known relationship 1-pi-exp(-lambda t). The cumulative effect of age on prevalence (effectively "time of follow up") can be accounted for in the model, by specifying it as an offset. RESULTS: The regression coefficients associated with the covariates included in the model estimate rate ratios, rather than odds or prevalence ratios. The method is applied to the analysis of the prevalence of respiratory symptoms in 4395 children aged 7-9 years who are residents of Huddersfield (northern England), surveyed in the framework of the SAVIAH (Small Area Variations of Air Quality and Health) study. CONCLUSIONS: By considering saturated models including only sex as a covariate, direct comparison of crude and fitted parameters (odds, prevalence, and rate ratios) shows that, for short follow-up periods, the complementary log-log model is a valid alternative to logistic regression. More complex models including other covariates are also discussed.

Air Pollution↗
PubMed1997

Prevalence and prevention of deafness in the Dalmatian--assessing the effect of parental hearing status and gender using ordinary logistic and generalized random litter effect models.

The Dalmatian dog is susceptible to congenital deafness which is thought to be inherited. The condition cannot be treated or cured, but controlled breeding could prevent or minimize the occurrence. An understanding of the quantitative relationship between the relevant attributes (sex, colour etc.) and the probability of deafness is likely to be of assistance in implementing any breeding programme to eliminate the condition. Most reported studies on Dalmatians have ignored the hearing status of close parental relatives, and none has taken into account the likely positive correlations in dogs from same litters. A composite database, obtained by merging deafness data on 1234 tested Dalmatians with Kennel Club pedigree data on 22,873 Dalmatians in the United Kingdom, has enabled us to include the hearing status of parental relatives and litter effects in our analysis. Contingency tables and ordinary logistic regression were used to obtain preliminary results which could be compared with the findings from other studies based on similar analyses. Further logistic modelling included an additional random effects term for the effect of litters to which the dogs belonged. The preliminary analysis showed that the prevalence of overall deafness in the tested Dalmatians was 18.4%, of which 13.1% were unilaterally deaf, and 5.3% were bilaterally deaf. There was no association between deafness and either testing location or coat colour but prevalence was strongly associated with parental hearing status. In Dalmatians from normal dams the prevalence (15.6%) was significantly lower than in those from untested dams (21.9%). If the parents were both normal or both untested, these figures were 15.3 and 23.6%, respectively, and significantly different. There was a significant gender effect, the prevalence being significantly higher in females (21.1%) than in males (15.5%), and this was seen in all subsets of data partitioned by parental hearing status, by locations, and by dominant coat colours. The use of generalized modelling, which included the random litter effects yielded point estimates of the prevalence of deafness which were smaller, but with wider confidence limits. Breeding from only tested and proven normal dams and sires is therefore recommended, and should reduce overall deafness to below 15% and bilateral deafness to below 4%.

Animals↗
PubMedDate not supplied

Logistic regression and artificial neural network classification models: a methodology review.

Logistic regression and artificial neural networks are the models of choice in many medical data classification tasks. In this review, we summarize the differences and similarities of these models from a technical point of view, and compare them with other machine learning algorithms. We provide considerations useful for critically assessing the quality of the models and the results based on these models. Finally, we summarize our findings on how quality criteria for logistic regression and artificial neural network models are met in a sample of papers from the medical literature.

Classification↗
PubMed1990

Incorporation of twins in the regressive logistic model for pedigree disease data.

Segregation and twin disease concordance analyses have assumed a theoretical underlying liability following a multivariate normal distribution. For reasons of computation, of incorporation of measured explanatory variables, and of testing of fit and assumptions, newer analytical methods are being developed. The regressive logistic model (RLM) relies on expressing the pedigree likelihood as a product of conditional probabilities, one for each individual. In addition to logistic regression modelling of measured epidemiological variables on disease prevalence, there is modelling of vertical transmission, of transmission of unmeasured genotypes and of sibship environment. This paper discusses methods for the analysis of binary traits in twins and in pedigrees. Some extensions to the RLM for pedigrees which include twins are proposed. These enable exploration of twin concordance in the context of the twins' common parenthood, the sibship similarities within the family, and the twins' similarity in age, sex, genes and environment.

Asthma↗
PubMed2002

A logistic mixture model for characterizing genetic determinants causing differentiation in growth trajectories.

The logistic or S-shaped curve of growth is one of the few universal laws in biology. It is certain that there exist specific genes affecting growth curves, but, due to a lack of statistical models, it is unclear how these genes cause phenotypic differentiation in growth and developmental trajectories. In this paper we present a statistical model for detecting major genes responsible for growth trajectories. This model is incorporated with pervasive logistic growth curves under the maximum likelihood framework and, thus, is expected to improve over previous models in both parameter estimation and inference. The power of this model is demonstrated by an example using forest tree data, in which evidence of major genes affecting stem growth processes is successfully detected. The implications for this model and its extensions are discussed.

Crosses, Genetic↗
PubMed1996

Sonography of pregnancies with first-trimester bleeding and a viable embryo: a study of prognostic indicators by logistic regression analysis.

The objective of our study was to investigate the relationship between sonographic findings and the occurrence of abortion in pregnancies complicated by first-trimester bleeding in which fetal cardiac activity was documented upon admission. A prospective study of transvaginal sonography was performed in 270 pregnant patients with bleeding between 5 and 12 weeks' gestation. The study group included 149 cases in which a singleton fetus with cardiac activity was initially documented. The outcome variable was pregnancy loss prior to 20 weeks. The influence of sonographic findings on admission was studied by univariate analysis and logistic regression. The prevalence of abortion was 23/149 (15%). A significant relationship (p < 0.05) was found between the occurrence of abortion and the following: fetal bradycardia (heart rate less than -1.2 SD from the mean), a discrepancy between the diameter of the gestational sac and crown-rump length less than -0.5 SD from the mean, and a discrepancy between menstrual and sonographic age of more than 1 week. According to the logistic regression equation that was obtained, the probability of abortion in first-trimester bleeding with documented fetal cardiac activity upon admission varied between a minimum of 6% when none of the above risk factors were present and a maximum of 84% when all were present. The presence of any of the above factors identified 84% of all subsequent abortions.

Abortion, Spontaneous↗
PubMed2005

Haplotype effects on human survival: logistic regression models applied to unphased genotype data.

Haplotype based linkage disequilibrium (LD) mapping exhibits higher power than the single locus approach because it makes use of the LD information contained in the flanking markers. New statistical methods have been proposed to help to infer haplotype effects on human diseases using multi-locus genotype data collected from unrelated individuals. In this paper, we introduce a statistical procedure for measuring haplotype effects on human survival using the popular logistic regression model with haplotype based parameterizations. By modeling haplotype frequency as a function of age, our model infers haplotype effects by estimating and testing the slope parameters under different genetic mechanisms (multiplicative, dominant, or recessive). In addition, by estimating the sex-specific slope parameters, our model allows the detection of sex-specific haplotype effects or haplotype-sex interactions. As an example, we apply our model to an empirical dataset on a stress related gene, interleukin-6, to look for haplotypes that affect individual survival and for haplotype-sex interactions. We show that our logistic regression based haplotype model can be a helpful tool for researchers interested in the genetics of human aging and longevity.

Female↗
PubMed2001

A population pharmacokinetic-pharmacodynamic and logistic regression analysis of lotrafiban in patients.

OBJECTIVE: Our objective was to assess the safety, tolerability, pharmacokinetics, and pharmacodynamics of lotrafiban, an oral glycoprotein IIb/IIIa inhibitor, in patients with a recent myocardial infarction, unstable angina, transient ischemic attack, or stroke. METHODS: A 12-week, double-blind, multi-center, placebo-controlled, parallel-group, phase II study of lotrafiban (the Anti-platelet Useful Dose Study) was conducted in patients. Lotrafiban or placebo was administered as a twice daily oral dose at four dose levels (5-100 mg) for 12 weeks with daily doses of aspirin (300-325 mg). The pharmacokinetics of lotrafiban were characterized with the use of a population approach and were described by a two-compartment model with first order absorption and first order elimination. The pharmacodynamic data, ex vivo platelet aggregation, were described with the use of a direct effect inhibitory sigmoidal model with a baseline. The relationship between the severity of bleeding episodes and predicted steady-state lotrafiban exposure was characterized by logistic regression. RESULTS: Pharmacokinetic analysis showed that increasing age and decreasing creatinine clearance resulted in increased exposure to lotrafiban. The concentration-effect relationship was steep, with near complete inhibition of platelet aggregation at lotrafiban concentrations in excess of 20 ng/mL. Logistic regression showed that at exposures that exceeded approximately 835 ng. h/mL, the severity of adverse bleeding events increased considerably; this suggested that dosing recommendations should be generated to minimize the likelihood of patients having an area under the plasma concentration-time curve from 0 to 24 hours in excess of this value. CONCLUSIONS: Patients whose age exceeded 65 years or whose creatinine clearance was less than 60 mL/min should be given a lower dose of lotrafiban than younger patients with good renal function.

Adult↗
PubMedDate not supplied

Dose-response relationship between urinary cadmium concentration and beta2-microglobulinuria using logistic regression analysis.

Logistic regression analysis was used to investigate the dose-response relationship for environmental cadmium exposure and to consider the effect age had on this association. The target population comprised 3178 inhabitants of Japan who were more than 50 y of age and who lived in a cadmium-polluted area and 1134 inhabitants who lived in nonpolluted areas of Japan. Logistic regression analysis was completed on the dose-response relationship between urinary cadmium concentration (i.e., an indicator of cadmium body burden) and beta2-microglobulinuria (i.e., an index of renal tubular dysfunction caused by exposure to cadmium). Both age and urinary cadmium concentration were associated significantly with beta2-microglobulinuria. Based on the relationship that was determined, we calculated, by age and sex, the values of urinary cadmium concentration that corresponded to the prevalence rates of beta2-microglobulinuria in the nonpolluted population. The resulting values were 1.6-3.0 micrograms/g creatinine for men and 2.3-4.6 micrograms/g creatinine for women.

Age Factors↗