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PubMed1999

Complementary nonparametric analysis of covariance for logistic regression in a randomized clinical trial setting.

In the randomized clinical trial setting, controlling for covariates is expected to produce variance reduction for the treatment parameter estimate and to adjust for random imbalances of covariates between the treatment groups. However, for the logistic regression model, variance reduction is not obviously obtained. This can lead to concerns about the assumptions of the logistic model. We introduce a complementary nonparametric method for covariate adjustment. It provides results that are usually compatible with expectations for analysis of covariance. The only assumptions required are based on randomization and sampling arguments. The resulting treatment parameter is a (unconditional) population average log-odds ratio that has been adjusted for random imbalance of covariates. Data from a randomized clinical trial are used to compare results from the traditional maximum likelihood logistic method with those from the nonparametric logistic method. We examine treatment parameter estimates, corresponding standard errors, and significance levels in models with and without covariate adjustment. In addition, we discuss differences between unconditional population average treatment parameters and conditional subpopulation average treatment parameters. Additional features of the nonparametric method, including stratified (multicenter) and multivariate (multivisit) analyses, are illustrated. Extensions of this methodology to the proportional odds model are also made.

Humans↗
PubMed1998

Use of two-segmented logistic regression to estimate change-points in epidemiologic studies.

In many epidemiologic data, the dose-response relation between a continuous exposure and the risk of disease abruptly changes when the exposure variable reaches an unknown threshold level, the so-called change-point. Although several methods are available for dose-response assessment with dichotomous outcomes, none of them provide inferential procedures to estimate change-points. In this paper, we describe a two-segmented logistic regression model, in which the linear term associated with a continuous exposure in standard logistic regression is replaced by a two-segmented polynomial function with unknown change-point, which is also estimated. A modified, iteratively reweighted least squares algorithm is presented to obtain parameter estimates and confidence intervals, and the performance of this model is explored through simulation. Finally, a two-segmented logistic regression model is applied to a case-control study of the association of alcohol intake with the risk of myocardial infarction and compared with alternative analyses. The ability of two-segmented logistic regression to estimate and provide inferences for the location of change-points and for the magnitude of other parameters of effect will make this model a useful complement to other methods of dose-response analysis in epidemiologic studies.

Alcohol Drinking↗
PubMed2004

Comparison of the missing-indicator method and conditional logistic regression in 1:m matched case-control studies with missing exposure values.

The missing-indicator method and conditional logistic regression have been recommended as alternative approaches for data analysis in matched case-control studies with missing exposure values. The authors evaluated the performance of the two methods using Monte Carlo simulation. Data were generated from a 1:m matched design based on McNemar's 2 x 2 tables with four scenarios for missing values: completely-at-random, case-dependent, exposure-dependent, and case/exposure-dependent. In their analysis, the authors used conditional logistic regression for complete pairs and the missing-indicator method for all pairs. For 1:1 matched studies, given no confounding between exposure and disease, the two methods yielded unbiased estimates. Otherwise, conditional logistic regression produced unbiased estimates with empirical confidence interval coverage similar to nominal coverage under the first three missing-value scenarios, whereas the missing-indicator method produced slightly more bias and lower confidence interval coverage. An increased number of matched controls was associated with slightly more bias and lower confidence interval coverage. Under the case/exposure-dependent missing-value scenario, neither method performed satisfactorily; this indicates the need for more sophisticated statistical methods for handling such missing values. Overall, compared with the missing-indicator method, conditional logistic regression provided a slight advantage in terms of bias and coverage probability, at the cost of slightly reduced statistical power and efficiency.

Bias↗
PubMed2005

Appropriate assessment of neighborhood effects on individual health: integrating random and fixed effects in multilevel logistic regression.

The logistic regression model is frequently used in epidemiologic studies, yielding odds ratio or relative risk interpretations. Inspired by the theory of linear normal models, the logistic regression model has been extended to allow for correlated responses by introducing random effects. However, the model does not inherit the interpretational features of the normal model. In this paper, the authors argue that the existing measures are unsatisfactory (and some of them are even improper) when quantifying results from multilevel logistic regression analyses. The authors suggest a measure of heterogeneity, the median odds ratio, that quantifies cluster heterogeneity and facilitates a direct comparison between covariate effects and the magnitude of heterogeneity in terms of well-known odds ratios. Quantifying cluster-level covariates in a meaningful way is a challenge in multilevel logistic regression. For this purpose, the authors propose an odds ratio measure, the interval odds ratio, that takes these difficulties into account. The authors demonstrate the two measures by investigating heterogeneity between neighborhoods and effects of neighborhood-level covariates in two examples--public physician visits and ischemic heart disease hospitalizations--using 1999 data on 11,312 men aged 45-85 years in Malmo, Sweden.

Aged↗
PubMed1996

Estimating relative risk functions in case-control studies using a nonparametric logistic regression.

The authors describe an approach to the analysis of case-control studies in which the exposure variables are continuous, i.e., quantitative variables, and one wishes neither to categorize levels of the exposure variable nor to assume a log-linear relation between level of exposure and disease risk. A dose-response association of an exposure variable with a disease outcome can be depicted by estimated relative risks at various exposure levels, and the functional relation between exposure dose and disease risk is here termed a relative risk function (RRF). A RRF takes values that are greater than zero: Values less than one imply lower risk; the value one implies no risk, and values greater than one imply increased risk, when compared with a reference value. The authors describe how a nonparametric logistic regression can be used to estimate and display these RRFs. Using data from a previously published case-control study of diet and colon cancer, RRFs for total energy, dietary fiber, and alcohol intakes are compared with the original results obtained from using categorized levels of exposure variables. For total energy and alcohol intakes, there were meaningful differences in study results based on the two analytic approaches. For energy, the nonparametric logistic regression detected a significant protective effect of low intakes, which was not found in the original analysis. For alcohol, the nonparametric logistic regression suggested that there were two underlying populations, non- or very light drinkers and moderate to heavy drinkers, with different relation of dose to disease risk. In contrast, the original analysis found a nonlinear increase in risk across intake categories and did not detect the complex, bimodal nature of the exposure distribution. These results demonstrate that nonparametric logistic regression can be a useful approach to displaying and interpreting results of case-control studies.

Adult↗
PubMed2006

Growth characteristics of pearl gray guinea fowl as predicted by the Richards, Gompertz, and logistic models.

This study was undertaken to describe the growth pattern of the pearl gray Guinea fowl. Using BW data from hatch to 22 wk, 3 nonlinear mathematical functions (Richards, Gompertz, and logistic) were used to estimate growth patterns of the pearl gray guinea fowl. The logistic and Gompertz models are a special case of the Richards model, which has a variable point of inflection defined by the shape or growth trajectory parameter, m. The shape parameter m was 1.08 and 0.98 in males and females, respectively, suggesting that the growth pattern of the pearl gray female guinea fowl is Gompertz. The pearl gray guinea fowl exhibited sexual dimorphism for their growth characteristics. From the Gompertz model, the asymptotic BW, growth rate, and age at maximum growth were 1.62 kg, 0.22 kg/wk, and 6.65 wk in males, respectively, and 1.70 kg, 0.19 kg/wk, and 6.70 wk in females, respectively. The ages at maximum growth were 6.65, 6.47, and 8.12 wk for the Richards, Gompertz, and logistic models, respectively. The pearl gray guinea fowl females have a higher asymptotic BW compared with the males. The average asymptotic BW of about 1.57 kg for both sexes predicted by the logistic model was below the average predicted BW from the Richards (1.66 kg) and Gompertz (1.67 kg) models, respectively, at 22 wk of age. The inverse relationship between the asymptotic weight and both relative growth and age at maximum growth of the pearl gray guinea fowl is similar to that of chickens, quail, and ducks. Success in studying the growth characteristics of guinea fowl will contribute to the efforts of genetically improving this least-studied avian species.

Aging↗
PubMed1999

Classification trees and logistic regression applied to prognostic studies: a comparison using meningococcal disease as an example.

The authors used logistic regression and classification trees to develop prediction models for fatal outcomes in meningococcal disease in a cohort of 829 children hospitalized for meningococcal disease during 1989-1990 in Rio de Janeiro. The area under the receiver operator characteristic (ROC) curve was 92 per cent for logistic regression and 88 per cent for classification trees. Logistic regression may be preferred when the main objective is to obtain explicit measures for statistical inference and measures of the force of the association between each variable and the outcome. However, estimation of the probability of dying for each patient involves manipulation of the logistic regression formula, which would not easily be done in an emergency room. Classification trees provided comparable discrimination between fatal and non-fatal outcomes, and yielded a graphical display of the results that is easier to understand and is straightforward to apply in clinical settings.

Adolescent↗
PubMed2006

Differential item functioning analysis with ordinal logistic regression techniques. DIFdetect and difwithpar.

INTRODUCTION: We present an ordinal logistic regression model for identification of items with differential item functioning (DIF) and apply this model to a Mini-Mental State Examination (MMSE) dataset. We employ item response theory ability estimation in our models. Three nested ordinal logistic regression models are applied to each item. Model testing begins with examination of the statistical significance of the interaction term between ability and the group indicator, consistent with nonuniform DIF. Then we turn our attention to the coefficient of the ability term in models with and without the group term. If including the group term has a marked effect on that coefficient, we declare that it has uniform DIF. We examined DIF related to language of test administration in addition to self-reported race, Hispanic ethnicity, age, years of education, and sex. METHODS: We used PARSCALE for IRT analyses and STATA for ordinal logistic regression approaches. We used an iterative technique for adjusting IRT ability estimates on the basis of DIF findings. RESULTS: Five items were found to have DIF related to language. These same items also had DIF related to other covariates. DISCUSSION: The ordinal logistic regression approach to DIF detection, when combined with IRT ability estimates, provides a reasonable alternative for DIF detection. There appear to be several items with significant DIF related to language of test administration in the MMSE. More attention needs to be paid to the specific criteria used to determine whether an item has DIF, not just the technique used to identify DIF.

Bias↗
PubMed1990

Using logistic regression in perinatal epidemiology: an introduction for clinical researchers. Part 1: Basic concepts.

Logistic regression is a statistical modelling technique which may be applied to estimate the simultaneous effect of a set of predictors (e.g. gestational age, birthweight) on the risk of a certain outcome variable (e.g. neonatal death) which can take either one of two possible values (yes/no, alive/dead) or in the situation where one wants to estimate the effect of a particular risk factor (e.g. sex) while adjusting (correcting) for the effect of other risk factors (e.g. gestational age). Since this situation often occurs both in medical or epidemiological research and in daily practice it is important to have a flexible and readily interpretable technique to predict risk of mortality and morbidity. Since the logistic regression technique is a powerful and widely applicable tool which is appearing more and more often in the epidemiological literature, a basic understanding of this technique becomes necessary for the clinical researcher. In this paper we explain logistic regression to medical researchers who do not have any particular statistical background. Part 1 covers the basic concepts. Part 2 will describe the actual representation of the basic concepts in a logistic framework.

Epidemiologic Methods↗
PubMed1996

Using a logistic model to identify women with first-trimester spontaneous abortion suitable for expectant management.

OBJECTIVE: To design a method to identify women with first trimester spontaneous abortion suitable for expectant management. DESIGN: A stepwise logistic regression analysis based on retrospective analysis of clinical and biochemical variables. SETTING: Department of Obstetrics and Gynaecology, Sahlgrenska University Hospital, Gothenburg, Sweden. PARTICIPANTS: One hundred and three women with inevitable or incomplete spontaneous abortion at < 13 weeks of gestation were chosen for expectant management. Eighty-one women with complete spontaneous abortion (i.e. complete expulsion and/or resolution of pregnancy products within three days of expectant management) were compared with those (n = 22) who underwent surgical evacuation of the uterus, most commonly owing to retained products of conception after three days. RESULTS: Employing a stepwise logistic regression procedure, five diagnostic variables possessing prognostic power were identified: serum progesterone, daily serum hCG change, serum CA125, serum alpha fetoprotein and intrauterine diameter. The logistic regression analysis was also applied to three diagnostic variables chosen for routine clinical use: serum progesterone, serum hCG and intrauterine diameter. The probability of complete spontaneous abortion within three days of expectant management in each woman could be calculated. CONCLUSION: We have used a logistic model to calculate the probability of complete spontaneous abortion within three days in women with first trimester miscarriages. Such information may be of clinical use in caring for women, as well as for development of management guidelines for those with miscarriages.

Abortion, Spontaneous↗
PubMed2006

Starling-effect-independent lusitropism index in canine left ventricle: logistic time constant.

The logistic time constant (tau(L)) has been proposed as a better index of the rate of left ventricular (LV) relaxation or lusitropism than the conventional monoexponential time constant (tau(E)). However, whether and how the Frank-Starling effect influences tau(L) remains to be elucidated. We compared the effect of LV volume (LVV) loading on both logistic and monoexponential fittings. The isovolumic LV relaxation pressure curves from the maximum negative time derivative of pressure (-dP/dt(max)) were analyzed at 3 different end-points at 4 LVVs of 10, 12, 14, and 16 mL in 8 excised, cross-circulated canine hearts. We found that the logistic fitting was superior to the monoexponential fitting at all LVVs and end-points. LVV loading did not affect tau(L) but affected tau(E) slightly. Although the advancing end-point increased both tau(L) and tau(E), the increases were significantly smaller for tau(L) than for tau(E) at all LVVs. Moreover, the changes in both the amplitude constants and nonzero asymptotes with the advancing end-point were significantly smaller for the logistic fitting than for the monoexponential fitting. We conclude that tau(L) served as a more reliable index of lusitropism that is independent of the change in LVV loading or the Frank-Starling effect.

Animals↗
PubMedDate not supplied

The logistic model for predicting the non-gonoactive Aedes aegypti females.

OBJECTIVE: To estimate, using logistic regression, the likelihood of occurrence of a non-gonoactive Aedes aegypti female, previously fed human blood, with relation to body size and collection method. MATERIAL AND METHODS: This study was conducted in Monterrey, Mexico, between 1994 and 1996. Ten samplings of 60 mosquitoes of Ae. aegypti females were carried out in three dengue endemic areas: six of biting females, two of emerging mosquitoes, and two of indoor resting females. Gravid females, as well as those with blood in the gut were removed. Mosquitoes were taken to the laboratory and engorged on human blood. After 48 hours, ovaries were dissected to register whether they were gonoactive or non-gonoactive. Wing-length in mm was an indicator for body size. The logistic regression model was used to assess the likelihood of non-gonoactivity, as a binary variable, in relation to wing-length and collection method. RESULTS: Of the 600 females, 164 (27%) remained non-gonoactive, with a wing-length range of 1.9-3.2 mm, almost equal to that of all females (1.8-3.3 mm). The logistic regression model showed a significant likelihood of a female remaining non-gonoactive (Y=1). The collection method did not influence the binary response, but there was an inverse relationship between non-gonoactivity and wing-length. CONCLUSIONS: Dengue vector populations from Monterrey, Mexico display a wide-range body size. Logistic regression was a useful tool to estimate the likelihood for an engorged female to remain non-gonoactive. The necessity for a second blood meal is present in any female, but small mosquitoes are more likely to bite again within a 2-day interval, in order to attain egg maturation. The English version of this paper is available too at: http://www.insp.mx/salud/index.html.

Aedes↗
PubMed2006

Genetic parameters for calving rate and calf survival from linear, threshold, and logistic models in a multibreed beef cattle population.

Generalized mixed linear, threshold, and logistic sire models and Markov chain, Monte Carlo simulation procedures were used to estimate genetic parameters for calving rate and calf survival in a multibreed beef cattle population. Data were obtained from a 5-generation rotational crossbreeding study involving Angus, Brahman, Charolais, and Hereford (1969 to 1995). Gelbvieh and Simmental bulls sired terminal-cross calves from a sample of generation 5 cows. A total of 1,458 cows sired by 158 bulls had a mean calving rate of 78% based on 4,808 calving records. Ninety-one percent of 5,015 calves sired by 260 bulls survived to weaning. Mean heritability estimates and standard deviations for daughter calving rate from posterior distributions were 0.063 +/- 0.024, 0.150 +/- 0.049, and 0.130 +/- 0.047 for linear, threshold, and logistic models, respectively. For calf survival, mean heritability estimates and standard deviations from posterior distributions were 0.049 +/- 0.022, 0.160 +/- 0.058, and 0.190 +/- 0.078 from linear, threshold, and logistic models, respectively. When transformed to an underlying normal scale, linear sire, mixed model, heritability estimates were similar to threshold and logistic sire mixed model estimates. Posterior density distributions of estimated heritabilities from all models were normal. Spearman rank correlations between sire EPD across statistical models were greater than 0.97 for daughter calving rate and for calf survival. Sire EPD had similar ranges across statistical models for daughter calving rate and for calf survival.

Animals↗
PubMed2002

Predicting recovery in patients suffering from traumatic brain injury by using admission variables and physiological data: a comparison between decision tree analysis and logistic regression.

OBJECT: Decision tree analysis highlights patient subgroups and critical values in variables assessed. Importantly, the results are visually informative and often present clear clinical interpretation about risk factors faced by patients in these subgroups. The aim of this prospective study was to compare results of logistic regression with those of decision tree analysis of an observational, head-injury data set, including a wide range of secondary insults and 12-month outcomes. METHODS: One hundred twenty-four adult head-injured patients were studied during their stay in an intensive care unit by using a computerized data collection system. Verified values falling outside threshold limits were analyzed according to insult grade and duration with the aid of logistic regression. A decision tree was automatically produced from root node to target classes (Glasgow Outcome Scale [GOS] score). Among 69 patients, in whom eight insult categories could be assessed, outcome at 12 months was analyzed using logistic regression to determine the relative influence of patient age, admission Glasgow Coma Scale score, Injury Severity Score (ISS), pupillary response on admission, and insult duration. The most significant predictors of mortality in this patient set were duration of hypotensive, pyrexic, and hypoxemic insults. When good and poor outcomes were compared, hypotensive insults and pupillary response on admission were significant. Using decision tree analysis, the authors found that hypotension and low cerebral perfusion pressure (CPP) are the best predictors of death, with a 9.2% improvement in predictive accuracy (PA) over that obtained by simply predicting the largest outcome category as the outcome for each patient. Hypotension was a significant predictor of poor outcome (GOS Score 1-3). Low CPP, patient age, hypocarbia, and pupillary response were also good predictors of outcome (good/poor), with a 5.1% improvement in PA. In certain subgroups of patients pyrexia was a predictor of good outcome. CONCLUSIONS: Decision tree analysis confirmed some of the results of logistic regression and challenged others. This investigation shows that there is knowledge to be gained from analyzing observational data with the aid of decision tree analysis.

Adult↗
PubMed2000

Prediction on lengths of stay in the postanesthesia care unit following general anesthesia: preliminary study of the neural network and logistic regression modelling.

The length of stay in the postanesthesia care unit (PACU) following general anesthesia in adults is an important issue. A model, which can predict the results of PACU stays, could improve the utilization of PACU and operating room resources through a more efficient arrangement. The purpose of study was to compare the performance of neural network to logistic regression analysis using clinical sets of data from adult patients undergoing general anesthesia. An artificial neural network was trained with 409 clinical sets using backward error propagation and validated through independent testing of 183 records. Twenty-two inputs were used to find determinants and to predict categorical values. Logistic regression analysis was performed to provide a comparison. The neural network correctly predicted in 81.4% of situations and identified discriminating variables (intubated state, sex, neuromuscular blocker and intraoperative use of opioid), whereas the figure was 65.0% in logistic regression analysis. We concluded that the neural network could provide a useful predictive model for the optimization of limited resources. The neural network is a new alternative classifying method for developing a predictive paradigm, and it has a higher classifying performance compared to the logistic regression model.

Adult↗
PubMed2004

Using logistic regression to estimate delay-discounting functions.

The monetary choice questionnaire (MCQ) and similar computer tasks ask preference questions in order to ascertain indifference, the perceived equivalence of immediate versus larger delayed rewards. Indifference data are then fitted with a hyperbolic function, summarizing the decline in perceived value with delay time. We present a fitting method that estimates the hyperbolic parameter k directly from survey responses. Binary preferences are modeled as a function of time (X2) and a transformed reward ratio (X1), yielding logistic regression coefficients beta 2 and beta 1. The hyperbolic parameter emerges as k = beta 2/beta 1, where the logistic predicted p = .5 (the definition of indifference). The MCQ was administered to 1,073 adolescents and was scored using both standard and logistic methods. The means for In(k) were similar (standard, -4.53; logistic, -4.51), and the results were highly correlated (rho = .973). Simulated MCQ data showed that k was unbiased, except where beta 1 > or = -1, indicating a vague survey response. Jackknife standard errors provided excellent coverage.

Algorithms↗
PubMed1997

Determinants of infection with schistosomiasis haematobia using logistic regression.

A population-based stratified random sample of 10,039 inhabitants of rural communities in Minya Governorate, Egypt, were evaluated for risk factors for Schistosoma haematobium infection using multivariate analysis. Data were obtained by personal interview recording demographics, information on exposure to canal water, history of infection, and other risk factors for infection and examining urine samples for S. haematobium ova. Logistic regression analysis was used to adjust for confounders while assessing the role of each risk factor for infection. Using logistic regression allowed detection of several confounders and interactions which influenced other independent variables. Differences in exposure patterns to canal water among age and gender subgroups explained only a small portion of the variation in infection rates, thus favoring the alternative explanation: development of age-acquired immunity. The association of age with reduced prevalence of S. haematobium was the only relationship increasing (odds ratio [OR] = 2.95-4.30) with logistic regression. Male gender was a risk factor for infection but did not increase with logistic regression (OR = 2.33-2.03). The protective effects of education, only noted in schoolage children (OR = 0.59-0.51), were believed to be due to a school-based screening and treatment program.

Adolescent↗
PubMed1999

Reasoning with uncertainty in pathology: artificial neural networks and logistic regression as tools for prediction of lymph node status in breast cancer patients.

Axillary lymph node status is an important prognostic feature for patients with breast cancer, but the therapeutic value of axillary lymphadenectomy is controversial. It would be useful to be able to predict the status of axillary lymph nodes before lymphadenectomy from prognostic features evaluated in a previous breast biopsy. This prediction would be useful to optimize the treatment of patients with breast cancer who are unlikely to have nodal metastases. We studied 279 patients with invasive breast carcinoma treated with modified radical mastectomy or with lumpectomy combined with axillary lymph node dissection. Prognostic factors evaluated were age, histologic type of invasive tumor, presence of associated ductal and/or lobular carcinoma in situ, lesion size, histologic and nuclear grades, DNA index, presence of multiploidy by flow cytometric analysis, and immunocytochemical expression of estrogen and progesterone receptors, proliferating nuclear cell antigen, and HER-2/neu oncogene. Several probabilistic neural networks (NNs) with genetic algorithms were developed using prognostic features as input neurons and lymph node status (positive or negative) as output neurons. The data were also studied with multiple regression and logistic regression analysis. The best NN model trained with 224 cases using 19 input neurons. It classified correctly 49 (89.0%) of 55 unknown cases (specificity, 97.2%; sensitivity, 80.0%; positive predictive value, 93.8%; negative predictive value, 87.5%). Several statistically significant models could be fitted with both multiple regression and logistic regression. The logistic regression model fitted with 240 cases using 6 independent variables estimated correctly 26 (66%) of 39 holdout cases. NNs and logistic regression models offer potentially useful tools to estimate the status of axillary lymph nodes of breast cancer patients before axillary lymphadenectomy. Future prospective studies with larger groups of patients and perhaps better prognostic markers are needed before these predictive multivariate models become ready for clinical use.

Adult↗