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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↗

PubMed1996

Repopulation in the SCCVII squamous cell carcinoma assessed by an in vivo-in vitro excision assay.

An in vivo-in vitro excision assay was used to study repopulation after a single dose of clamped irradiation (40 Gy) in the SCCVII tumour implanted in the foot of C3H/Km mice. The growth pattern of clonogenic cells was analysed by two different mathematical models: the logistic model and the Gompertz model. The logistic model described the data better than the Gompertz model. Accelerated repopulation was found when the regrowth rate after irradiation was compared to the growth rate at the time of treatment, and when it was compared to the growth rate in untreated tumours with a number of cells equivalent to the number that was found after irradiation. The clonogenic doubling time (cDT) was estimated at 15.1 h (95% c.i.: 14.2; 16.0) after irradiation, and 27.8 h (95% c.i.: 16.7; 43.5) in untreated controls of matching size. However, the estimate relies on the mathematical model chosen and on extrapolation below actually measured data. A small cDT points to shortening of the cell cycle time and recruitment of non-cycling clonogenic tumour cells to be the main mechanism behind the accelerated repopulation.

Animals↗

PubMed1998

Mixed effects logistic regression models for longitudinal binary response data with informative drop-out.

A shared parameter model with logistic link is presented for longitudinal binary response data to accommodate informative drop-out. The model consists of observed longitudinal and missing response components that share random effects parameters. To our knowledge, this is the first presentation of such a model for longitudinal binary response data. Comparisons are made to an approximate conditional logit model in terms of a clinical trial dataset and simulations. The naive mixed effects logit model that does not account for informative drop-out is also compared. The simulation-based differences among the models with respect to coverage of confidence intervals, bias, and mean squared error (MSE) depend on at least two factors: whether an effect is a between- or within-subject effect and the amount of between-subject variation as exhibited by variance components of the random effects distributions. When the shared parameter model holds, the approximate conditional model provides confidence intervals with good coverage for within-cluster factors but not for between-cluster factors. The converse is true for the naive model. Under a different drop-out mechanism, when the probability of drop-out is dependent only on the current unobserved observation, all three models behave similarly by providing between-subject confidence intervals with good coverage and comparable MSE and bias but poor within-subject confidence intervals, MSE, and bias. The naive model does more poorly with respect to the within-subject effects than do the shared parameter and approximate conditional models. The data analysis, which entails a comparison of two pain relievers and a placebo with respect to pain relief, conforms to the simulation results based on the shared parameter model but not on the simulation based on the outcome-driven drop-out process. This comparison between the data analysis and simulation results may provide evidence that the shared parameter model holds for the pain data.

Analgesics↗

PubMed1997

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

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

Bias↗

PubMed1998

Incorporation of family history in logistic regression models.

For diseases with a genetic component, logistic regression models are presented that incorporate family history in a quantitative way. In the largest model, every type of relative has their own regression coefficient. The other two models are submodels, which incorporate family history either by the number of cases in the family minus its expectation or by a weighted number of cases in the family minus its expectation. For various genetic effects, namely polygenic and autosomal dominant effects, the performance of these simple logistic models is studied. First, the predictive values of the logistic and true genetic models are computed and compared. Secondly, a simulation study is carried out to investigate the effects of estimation of the parameters in a small data set. Thirdly, the logistic models are fitted to a data set of Von Willebrand Factor responses of target individuals and their families; in these models, family history has a significant effect. The conclusion is that for the genetic effects considered the logistic models perform well.

Female↗

PubMedDate not supplied

The effect of disease-prevalence adjustments on the accuracy of a logistic prediction model.

The accuracy of a logistic prediction model is degraded when it is transported to populations with outcome prevalences different from that of the population used to derive the model. The resultant errors can have major clinical implications. Accordingly, the authors developed a logistic prediction model with respect to the noninvasive diagnosis of coronary disease based on 1,824 patients who underwent exercise testing and coronary angiography, varied the prevalence of disease in various "test" populations by random sampling of the original "derivation" population, and determined the accuracy of the logistic prediction model before and after the application of a mathematical algorithm designed to adjust only for these differences in prevalence. The accuracy of each prediction model was quantified in terms of receiver operating characteristic (ROC) curve area (discrimination) and chi-square goodness-of-fit (calibration). As the prevalence of the test population diverged from the prevalence of the derivation population, discrimination improved (ROC-curve areas increased from 0.82 +/- 0.02 to 0.87 +/- 0.03; p < 0.05), and calibration deteriorated (chi-square goodness-of-fit statistics increased from 9 to 154; p < 0.05). Following adjustment of the logistic intercept for differences in prevalence, discrimination was unchanged and calibration improved (maximum chi-square goodness-of-fit fell from 154 to 16). When the adjusted algorithm was applied to three geographically remote populations with prevalences that differed from that of the derivation population, calibration improved 87%, while discrimination fell by 1%. Thus, prevalence differences produce statistically significant and potentially clinically important errors in the accuracy of logistic prediction models. These errors can potentially be mitigated by use of a relatively simple mathematical correction algorithm.

Adult↗

PubMed1991

The importance of assessing the fit of logistic regression models: a case study.

BACKGROUND: The logistic regression model is being used with increasing frequency in all areas of public health research. In the calendar year 1989, over 30% of the articles published in the American Journal of Public Health employed some form of logistic regression modeling. In spite of this increase, there has been no commensurate increase in the use of commonly available methods for assessing model adequacy. METHODS: We review the current status of the use of logistic regression modeling in the American Journal of Public Health. We present a brief overview of currently available and easily used methods for assessing the adequacy of a fitted logistic regression model. RESULTS: An example is used to demonstrate the methods as well as a few of the adverse consequences of failing to assess the fit of the model. One important adverse consequence illustrated in the example is the inclusion of variables in the model as a result of the influence of one subject. CONCLUSIONS: Failure to address model adequacy may lead to misleading or incorrect inferences. Recommendations are made for the use of methods for assessing model adequacy and for future editorial policy in regard to the review of articles using logistic regression.

Bias↗

PubMed1987

Equilibrium and local stability in a logistic matrix model for age-structured populations.

A logistic matrix model for age-structured population dynamics is constructed. This model discretizes a continuous, density-dependent model with age structure, i.e. it is an extension of the logistic model to the case of age-dependence. We prove the existence and uniqueness of its equilibrium and give a necessary and sufficient condition for the local stability of the equilibrium.

Aging↗

PubMed1997

Regression models for ordinal responses: a review of methods and applications.

BACKGROUND: Epidemiologists are often interested in estimating the risk of several related diseases as well as adverse outcomes, which have a natural ordering of severity or certainty. While most investigators choose to model several dichotomous outcomes (such as very low birthweight versus normal and moderately low birthweight versus normal), this approach does not fully utilize the available information. Several statistical models for ordinal responses have been proposed, but have been underutilized. In this paper, we describe statistical methods for modelling ordinal response data, and illustrate the fit of these models to a large database from a perinatal health programme. METHODS: Models considered here include (1) the cumulative logit model, (2) continuation-ratio model, (3) constrained and unconstrained partial proportional odds models, (4) adjacent-category logit model, (5) polytomous logistic model, and (6) stereotype logistic model. We illustrate and compare the fit of these models on a perinatal database, to study the impact of midline episiotomy procedure on perineal lacerations during labour and delivery. Finally, we provide a discussion on graphical methods for the assessment of model assumptions and model constraints, and conclude with a discussion on the choice of an ordinal model. The primary focus in this paper is the formulation of ordinal models, interpretation of model parameters, and their implications for epidemiological research. CONCLUSIONS: This paper presents a synthesized review of generalized linear regression models for analysing ordered responses. We recommend that the analyst performs (i) goodness-of-fit tests and an analysis of residuals, (ii) sensitivity analysis by fitting and comparing different models, and (iii) by graphically examining the model assumptions.

Epidemiologic Methods↗

PubMed1994

Corrections for exposure measurement error in logistic regression models with an application to nutritional data.

Two correction methods are considered for multiple logistic regression models with some covariates measured with error. Both methods are based on approximating the complicated regression model between the response and the observed covariates with simpler models. The first model is the logistic approximation proposed by Rosner et al., and the second is a second-order extension of this model. Only the mean and covariance matrix of the true values of the covariates given the observed values have to be specified, but no distributional assumptions about the measurement error are made. The parameters related to the conditional moments are estimated from a separate validation data set. The correction methods considered here are compared to other methods proposed in the literature. They are also applied to a multiple logistic model describing the effect of nutrient intakes on the ratio of serum HDL cholesterol. The data constitute baseline data from an epidemiological cohort study, in which a separate pilot study has been carried out to obtain validation information. In the example the corrected parameter estimates from the two approximate models are very similar. Both differ considerably from the naive logistic estimates, indicating a large effect of the measurement error. The various assumptions required by the correction methods are also discussed.

Aged↗

PubMed1998

Using binary logistic regression models for ordinal data with non-proportional odds.

The proportional odds model (POM) is the most popular logistic regression model for analyzing ordinal response variables. However, violation of the main model assumption can lead to invalid results. This is demonstrated by application of this method to data of a study investigating the effect of smoking on diabetic retinopathy. Since the proportional odds assumption is not fulfilled, separate binary logistic regression models are used for dichotomized response variables based upon cumulative probabilities. This approach is compared with polytomous logistic regression and the partial proportional odds model. The separate binary logistic regression approach is slightly less efficient than a joint model for the ordinal response. However, model building, investigating goodness-of-fit, and interpretation of the results is much easier for binary responses. The careful application of separate binary logistic regressions represents a simple and adequate tool to analyze ordinal data with non-proportional odds.

Bias↗

PubMed1995

Logistic transmission modeling of simulated data.

A nonparametric method for linkage analysis has been developed and applied to the Problem 1 data set of the Genetic Analysis Workshop 9. Basically, the univariate matched pair strategy of the transmission disequilibrium test has been adapted to multivariate modeling using the conditional logistic function. After setting the critical value for significance at p < or = 0.0001, models at only D5G23 and D1G31 appear to be significant (p < 10(-7)). Logistic transmission modeling is a powerful method for establishing linkage by disequilibrium.

Alleles↗

PubMed1989

Estimating intervention effects in longitudinal studies.

Longitudinal studies aimed at assessing the impact of interventions on disease risk factors often confront several statistical problems. These problems include 1) dependent variables measured by ordered categories, 2) numerous potentially relevant patterns of transition between outcome levels, 3) mixed units of analysis (e.g., assignment by social unit while theorizing in terms of individuals), 4) incomplete randomization, and 5) correlated estimates for successive occasions of longitudinal measurement. Longitudinal data on use of cigarettes, alcohol, and marijuana among adolescents (n = 1,244, complete data) from the Midwestern Prevention Project are used to demonstrate solutions to each of these problems: 1) a proportional odds regression model, 2) conditional logistic models of transitions with interactions between baseline level and intervention effect, 3) a logistic model estimated with linear regression methods on measures aggregated by social unit, 4) conditional and unconditional models of effect magnitude, and 5) a repeated measures logistic regression technique. Panel data fit to the various models yielded the following conclusions concerning intervention effects in the Midwestern Prevention Project: reduction in the prevalence of cigarette users in treatment schools compared with control schools (8% vs. 18% smoked in the last week at one year follow-up), mixed evidence of an effect on marijuana use, and no evidence of an effect on alcohol use.

Adolescent↗

PubMedDate not supplied

The relation of smoking to waist-to-hip ratio and diabetes mellitus among elderly women.

BACKGROUND: Smoking is associated with lower body weight, but an increased risk of diabetes in some studies. Because smoking may increase waist-to-hip ratio (WHR), a risk factor for diabetes, we postulated that the relation between smoking and diabetes may be mediated in part by smoking-associated differences in body fat distribution. METHODS: We conducted a cross-sectional analysis of baseline data from 9,435 elderly nonblack women enrolled in the Study of Osteoporotic Fractures. Data were collected by Self-report and physical examination. Linear and logistic models were used to determine the relation of smoking to WHR and prevalence of self-reported diabetes. RESULTS: Current and past smokers had greater WHRs compared with never smokers. In multivariate models that adjusted for body mass index, the prevalence of diabetes was lower among smokers of < or = 10 cigarettes/day [odds ratio (OR) = 0.57, 95% confidence interval (CI) 0.31-1.03] and higher among smokers of > 10 cigarettes/day (OR = 1.38, 95% CI 0.99-1.92) compared with never smokers. The relation of smoking > 10 cigarettes/day to prevalence of diabetes was slightly attenuated after further adjustment for WHR. CONCLUSIONS: Smoking-associated differences in WHR may mediate, at least in part, the prevalence of diabetes among smokers of > 10 cigarettes/day. The decreased prevalence of diabetes that we observed among smokers of < or = 10 cigarettes/day was not explained by differences in obesity and requires confirmation.

Aged↗

PubMed1994

Thyroid diseases among atomic bomb survivors in Nagasaki.

OBJECTIVE: To elucidate the current thyroid disease status for the Nagasaki Adult Health Study cohort of the Radiation Effects Research Foundation. DESIGN: Survey study. SETTING: Nagasaki, Japan. PARTICIPANTS: Cohort members of the Nagasaki Adult Health Study who received biennial health examinations from October 1984 to April 1987 (n = 2856). A total of 2587 subjects remained after exclusion of persons exposed in Hiroshima or in utero and those who were not in Nagasaki at the time of the bombing. Thyroid radiation dose by the dosimetry system established in 1986 was available for 1978 of the 2587 subjects. MAIN OUTCOME MEASURES: Thyroid diseases were diagnosed using uniform procedures including ultrasonic scanning. The relationship of the prevalence of each thyroid disease with thyroid radiation dose, sex, and age was analyzed using logistic models. RESULTS: A significant dose-response relationship was observed for solid nodules, which include cancer, adenoma, adenomatous goiter, and nodules without histological diagnosis, and for antibody-positive spontaneous hypothyroidism (autoimmune hypothyroidism) but not for other diseases. The prevalence of solid nodules showed a monotonic dose-response relationship, yet that of autoimmune hypothyroidism displayed a concave dose-response relationship reaching a maximum (+/- SE) level of 0.7 +/- 0.2 Sv. CONCLUSIONS: The present study confirmed the results of previous studies by showing a significant increase in solid nodules with dose to the thyroid and demonstrated for the first time a significant increase in autoimmune disease among atomic bomb survivors. A concave dose-response relationship indicates the necessity for further studies on the effects of relatively low doses of radiation on thyroid disease.

Cohort Studies↗

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↗

PubMed1996

A computer program using BALF-analysis results as a diagnostic tool in interstitial lung diseases.

Recently, we showed that it is possible to distinguish between three common interstitial lung diseases (ILD) with similarities in clinical presentation by using a number of selected variables derived from bronchoalveolar lavage fluid (BALF) analysis. The aim of this study was to develop a more general discriminant model, based on polychotomous logistic regression analysis. The 277 patients involved in the study belonged to diagnostic groups with sarcoidosis (n = 193), extrinsic allergic alveolitis (EAA; n = 39), and idiopathic pulmonary fibrosis (IPF; n = 45). The diagnosis had been established independently of the BALF-analysis results. The variables used to discriminate among these patient groups were the yield of recovered BALF, total cell count, and percentages of alveolar macrophages, lymphocytes, neutrophils, and eosinophils. In order to test the predictive power of the logistic model, we used 128 patients having sarcoidosis (n = 91), EAA (n = 5), or IPF (n = 32) from another hospital. In this test set the agreement of predicted with actual diagnostic-group membership was the same as in the learning set in which the logistic model was fitted: 94.5% of the cases were correctly classified. A validated computer program based on the polychotomous logistic regression model can be used to predict the diagnosis for an arbitrary patient with information provided by BALF analysis, and is thought to be of diagnostic value in patients suspected of having ILD.

Adolescent↗

PubMed1996

Prediction of postoperative nausea and vomiting using a logistic regression model.

In a previous study, logistic regression analysis was used to determine the association of independent fixed patient factors with the incidence of postoperative nausea and vomiting (PONV). Female sex, previous history of PONV, use of postoperative opioids, previous history of motion sickness and an interaction between male sex and previous history of PONV were combined in an equation from which risk of PONV could be estimated. The present study was designed to test this equation in a group of patients with wide selection criteria. Data on 400 patients were collected in relation to pre-, per- and postoperative factors which may influence the incidence of PONV. The equation was used to predict PONV, and actual outcome was compared with that predicted. The overall incidence of PONV was 36%. The equation predicted an overall probability of PONV of 27.4%. If the model was used to define individual patients as predicted to have or not to have PONV, it was correct only 71% of the time. However, there was good agreement between the actual incidences of PONV and those predicted among the 16 risk groups created by the model.

Analgesics, Opioid↗