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Prospective evaluation of logistic regression models for the diagnosis of ovarian cancer.

OBJECTIVE: To test the accuracy of three logistic regression models in diagnosing malignancy in women with adnexal masses. METHODS: This was a prospective collaborative study. Women were recruited from three hospitals and all assessments were performed at the Gynaecology Ultrasound Unit, King's College Hospital. One hundred women with known adnexal masses were examined preoperatively. The demographic, biochemical, and sonographic data recorded for each patient included age, menopausal status, CA 125 levels, ultrasound morphology, and Doppler blood flow analysis. The diagnosis of malignancy was made for each woman using three logistic regression models previously described by Alcazar et al, Tailor et al, and Timmerman et al. Variables used in these models were then combined to form a new model. The results were compared with the final histopathologic diagnosis. RESULTS: Sixty-seven women had benign tumors and 33 had ovarian cancer. Women with malignant tumors were older than those with benign masses. There were significant differences in CA 125 levels, presence of papillary proliferations, and ascites between the two groups. The sensitivities and specificities achieved respectively by the models were as follows: 45% and 93% with Tailor et al's model, 9% and 99% with Alcazar et al's model, and 73% and 91% with Timmerman et al's model. There was no significant improvement over the performance of Timmerman et al's model and the new combined model. CONCLUSION: All models performed less well than originally reported. Combining the models did not lead to a significant improvement in performance. Larger sample sizes that incorporate all types of ovarian tumors are necessary to design more accurate diagnostic models.

Adult↗

Predictive indicators of deep venous thrombosis and pulmonary arterial thromboembolism in 54 subjects after total knee arthroplasty using multislice computed tomography in logistic regression models.

PURPOSE: To determine predictors of deep venous thrombosis (DVT) in the lower extremities and pulmonary arterial thromboembolism (PE) after total knee arthroplasty (TKA), we evaluated the incidence of these events using multislice computed tomography (CT). METHODS: 54 subjects (10 males, 53-81 years old, the first consecutive 25 receiving anticoagulant therapy) underwent enhanced multislice CT (MSCT) before and one week after TKA. RESULTS: DVT, PE, and both were detected in twelve, twelve, and three subjects, respectively, one week after TKA. Hemoglobin and alveolar-arterial oxygen gradient (AaDO2) on the day after TKA, and total amount of operative bleeding (TAOB) were significantly higher in subjects with DVT or PE (P<0.05). In a logistic model for predicting DVT or PE, hemoglobin and AaDO2 levels on the day after TKA and TAOB were associated with an increased incidence of DVT or PE (relative risks 3.51, 1.19 and 1.01 (P<0.05), respectively). From box and whisker plots, we speculated the significant border to predict DVT or PE as 10.5 g/dl for hemoglobin, 34 Torr for AaDO2, and 1280 ml for TAOB. These factors also predicted DVT or PE (relative risks 5.08 (hemoglobin more than 10.5), 6.25 (AaDO2 more than 34 Torr), and 4.95 (TAOB more than 1280 ml) (P<0.05)). CONCLUSIONS: The incidence of DVT or PE one week after TKA was 39% by MSCT. High levels of TAOB, hemoglobin and AaDO2 on the day after TKA may be predictive indicators of DVT or PE one week after TKA.

Aged↗

Hierarchical logistic regression models for imputation of unresolved enumeration status in undercount estimation.

"In this article we describe a logistic regression modeling approach for nonresponse in the [U.S.] Post-Enumeration Survey (PES) that has desirable theoretical properties and that has performed well in practice.... In the 1990 PES, interviews were not obtained from approximately 1.2% of households in the sample, and approximately 2.1% of the individuals in interviewed households were considered unresolved after follow-up....The missing binary enumeration statuses for these unresolved cases were replaced with probabilities estimated under a statistical model that incorporated covariate information observed for these cases. This article describes an approach to modeling missing binary outcomes when there are a large number of covariates."

Americas↗

Logistic regression model to predict outcome after in-hospital cardiac arrest: validation, accuracy, sensitivity and specificity.

OBJECTIVE: To develop and validate a logistic regression model to identify predictors of death before hospital discharge after in-hospital cardiac arrest. DESIGN: Retrospective derivation and validation cohorts over two 1 year periods. Data from all in-hospital cardiac arrests in 1986-87 were used to derive a logistic regression model in which the estimated probability of death before hospital discharge was a function of patient and arrest descriptors, major underlying diagnosis, initial cardiac rhythm, and time of year. This model was validated in a separate data set from 1989-90 in the same hospital. Calculated for each case was 95% confidence limits (C.L.) about the estimated probability of death. In addition, accuracy, sensitivity, and specificity of estimated probability of death and lower 95% C.L. of the estimated probability of death in the derivation and validation data sets were calculated. SETTING: 560-bed university teaching hospital. PATIENTS: The derivation data set described 270 cardiac arrests in 197 inpatients. The validation data set described 158 cardiac arrests in 120 inpatients. INTERVENTIONS: none. MEASUREMENTS AND RESULTS: Death before hospital discharge was the main outcome measure. Age, female gender, number of previous cardiac arrests, and electrical mechanical dissociation were significant variables associated with a higher probability of death. Underlying coronary artery disease or valvular heart disease, ventricular tachycardia, and cardiac arrest during the period July-September were significant variables associated with a lower probability of death. Optimal sensitivity and specificity in the validation set were achieved at a cut-off probability of 0.85. CONCLUSIONS: Performance of this logistic regression model depends on the cut-off probability chosen to discriminate between predicted survival and predicted death and on whether the estimated probability or the lower 95% C.L. of the estimated probability is used. This model may inform the development of clinical practice guidelines for patients who are at risk of or who experience in-hospital cardiac arrest.

Confidence Intervals↗

[A logistic cellular automaton for simulating tumor growth].

This paper focuses on a differential equation logistic model simulating tumor growth. We design a kind of tumor dynamic growth model with one-dimensional cellular automata. A discrete logistic model is developed from the continuous logistic model. Based on others' work, we design discrete mathematical growth dynamic model with cellular automaton. In terms of discrete model, we design stochastic evolving rules of cellular automaton. And this paper simulates the tumor growth dynamic model with cellular automata. The theoretic analysis and results of cellular automaton model are in agreement with data from the ideal differential equation logistic growth of cancer.

Algorithms↗

The use of a new logistic regression model for predicting the outcome of pregnancies of unknown location.

BACKGROUND: The aim of this study was to generate and evaluate new logistic regression models from simple demographic and hormonal data to predict the outcome of pregnancies of unknown location (PULs). METHODS: Data were collected prospectively from 185 consecutive women classified as having a PUL by transvaginal scan; blood was taken at presentation and 48 h later to measure serum progesterone and HCG. These women were followed-up until the outcome was established: an intrauterine pregnancy (IUP), an ectopic pregnancy (EP) or a failing PUL. Three multi-categorical logistic regression models were tested. M1 was based on the HCG ratio (rate of change in HCG over 48 h), M2 was based on the average progesterone level (the mean of the progesterone level at 0 and 48 h) and M3 was based on the patient's age. RESULTS: A total of 102 failing PULs, 63 IUPs and 20 EPs were used in the training set to develop the new models. The best of these models, M3, gave a retrospective area under the receiver operating characteristic (ROC) curve of 0.984 for failing PUL, 0.995 for IUP and 0.920 for EP. All three models were tested prospectively on the test set of 196 cases. M1 outperformed M2 and M3 when tested prospectively. The area under the ROC curve (AUC) was 0.975 for failing PUL, 0.966 for IUP and 0.885 for EP. M1, for the detection of EP, had a sensitivity of 91.7%, a specificity of 84.2%, a positive likelihood ratio of 5.8, a positive predictive value of 27.5% and a negative predictive value of 99.4%. CONCLUSIONS: The logistic regression model M1, can predict which PULs will become failing PULs, IUPs and, most importantly, EPs based on the patient's HCG ratio alone.

Chorionic Gonadotropin↗

Logistic regression model of fotemustine toxicity combining independent phase II studies.

BACKGROUND: To optimize fotemustine chemotherapy, the authors considered how to combine independent Phase II trials to predict the risk of first occurrence of severe toxicity as a function of initial patient characteristics. METHODS: Clinical data from six Phase II trials were collected. Of the 478 patients enrolled 442 (male/female, 259/183; age range, 15-81 years) were evaluable for toxicity (1384 cycles of chemotherapy), including 221 with malignant malignant melanomas, 138 with primary brain tumors, 29 with lung carcinomas, 8 with head and neck carcinomas, and 46 with miscellaneous cancers. The influence of age, sex, performance status, type of tumor, number and location of metastases, and previous treatment by chemotherapy and/or radiotherapy was studied. The logistic regression method was applied to predict occurrence of leukopenia, thrombocytopenia, anemia, digestive tract, and/or hepatic toxicity. RESULTS: Univariate analysis showed that predictive factors for hematologic toxicity were age (> 50 years), type of tumor (brain < melanoma < others), number of metastatic sites (> 3), location of metastases (nonvisceral), and previous chemotherapy. Performance status and previous radiotherapy did not affect the toxicity of fotemustine Nausea and vomiting were predictable based on the type of tumor (head and neck < lung < brain < melanoma < others), the number of metastatic sites (> three) and visceral metastases. Hepatic disorders occurred preferentially in patients with hepatic metastases and more than three metastatic sites. Individual risk of hematologic and hepatic toxicity for patients with melanoma and primary brain tumors was predicted using logistic regression models. CONCLUSIONS: By combining clinical data from independent Phase II trials, the logistic model developed could predict the probability of fotemustine hematologic and hepatic toxicity.

Adolescent↗

A developmental transition in prehension modeled as a cusp catastrophe.

The purpose of the study was to show that the change from reaching without grasping to reaching with grasping during the first 6 months of life carried the characteristics of a discontinuous phase transition (catastrophe). A cross-sectional study was carried out with 58 infants between 60 and 408 days old. The infants were seated in a specially designed seat, and presented with nine detachable balls on a black curved board within reaching distance at shoulder height. The number of reaches without and with grasping were scored from video. A cusp catastrophe model was fitted to the data. A Likelihood-Ratio test indicated that the likelihood of the cusp model was significantly higher, p < .001, than a linear regression model. The cusp model was also compared with a logistic model. Akaike's Information criterion for the cusp catastrophe exceeded the logistic model, thus indicating a general better fit. Based on prior research, the following potential control parameters were chosen: crown-heel length, total body weight, arm length, arm circumference, ponderal index, arm volume, arm weight, and body position relative to the horizontal. The cusp model predicted that arm weight and arm circumference significantly contributed to the control parameters. It was found that these two variables had their largest contribution to the asymmetry control parameters.

Anthropometry↗

A Bayesian approach to logistic regression models having measurement error following a mixture distribution.

To estimate the parameters in a logistic regression model when the predictors are subject to random or systematic measurement error, we take a Bayesian approach and average the true logistic probability over the conditional posterior distribution of the true value of the predictor given its observed value. We allow this posterior distribution to consist of a mixture when the measurement error distribution changes form with observed exposure. We apply the method to study the risk of alcohol consumption on breast cancer using the Nurses Health Study data. We estimate measurement error from a small subsample where we compare true with reported consumption. Some of the self-reported non-drinkers truly do not drink. The resulting risk estimates differ sharply from those computed by standard logistic regression that ignores measurement error.

Age Factors↗

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

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

Black or African American↗

Assessing proportionality in the proportional odds model for ordinal logistic regression.

The proportional odds model for ordinal logistic regression provides a useful extension of the binary logistic model to situations where the response variable takes on values in a set of ordered categories. The model may be represented by a series of logistic regressions for dependent binary variables, with common regression parameters reflecting the proportional odds assumption. Key to the valid application of the model is the assessment of the proportionality assumption. An approach is described arising from comparisons of the separate (correlated) fits to the binary logistic models underlying the overall model. Based on asymptotic distributional results, formal goodness-of-fit measures are constructed to supplement informal comparisons of the different fits. A number of proposals, including application of bootstrap simulation, are discussed and illustrated with a data example.

Biometry↗

Alternative parameterization of polychotomous models: theory and application to matched case-control studies.

A method is proposed for transforming a class of models having an outcome variable with more than two levels into an equivalent binary model. The polychotomous logistic model is used to demonstrate the method. The equivalency to a simple logistic regression model after some data transformation (augmentation) is shown. The method is applied to the data from two case-control studies each with two control groups, and further applications are indicated.

Breast Neoplasms↗

A comparison of mixed effects logistic regression models for binary response data with two nested levels of clustering.

We compare mixed effects logistic regression models for binary response data with two nested levels of clustering. The comparison of these models occurs in the context of developmental toxicity data sets, for which multiple types of outcomes (first level) are measured on each rat pup (second level) nested within a litter (third level). Because the nested nature of such data is occasionally accommodated by ignoring one level of clustering, we consider three models: (i) a three-level model adjusting for clustering due to both pup and litter (M1); (ii) a two-level model adjusting for just pup (M2); and (iii) another two-level model adjusting for just litter (M3). The three types of effects of interest are: (i) differences among malformation types (first-level effects); (ii) differences among groups of pups (for example, sex of pup, second-level effects); and (iii) differences among groups of litters (for example, dose, third-level effects). Simulations and data analyses suggest that the M3 model leads to more bias than the M1 or M2 models for all three types of effects. In terms of coverage of confidence intervals for fixed effects log odds ratio parameters, the M1 model achieves nominal coverage, whereas the M2 model reduces coverage for the third-level effects and the M3 model obtains poor coverage for both first- and second-level effects. These reductions in coverage for certain model-parameter combinations worsen as baseline risk increases. The data analyses support these simulation-based conclusions to some extent.

Animals↗

Prediction of remission in adult acute leukemia: development and testing of predictive models.

Logistic regression methods were applied to derive a set of models relating achievement of CR to prognostic characteristics in a group of 300 adult acute leukemia patients treated with cytosine arabinoside, vincristine, and prednisone combined with adriamycin (ADOAP) or rubidazone (ROAP). These models were tested prospectively in an independent group of 107 subsequent patients treated with ADOAP or ROAP therapy, by comparing observed outcomes to predictions of response based on the models. Several models were able to identify subgroups of patients with good, intermediate, and poor prognoses. A model regarded as clinically useful and which provided a good fit to both the population from which it was derived and the test population included the pretreatment factors age, history of an antecedent hematologic disorder, temperature, blood urea nitrogen, hemoglobin, and liver size.

Acute Disease↗

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↗

Diagnosis of sensorineural hearing loss with neural networks versus logistic regression modeling of distortion product otoacoustic emissions.

We investigated whether modeling with artificial neural networks or logistic regression of distortion product otoacoustic emissions (DPOAE), across diverse frequencies, may achieve an accurate diagnosis of sensorineural hearing loss (SNHL) of cochlear origin. 256 ears (90 with SNHL and 166 with normal hearing) were evaluated with pure-tone audiometry, impedance audiometry, speech audiometry and DPOAE. Ears were split into training (n = 176) and validation (n = 80) sets. Input variables included gender, age, examination time, DPOAE intensity at F(2) frequencies 593, 937, 1906, 3812 and 6031 Hz, and respective values corrected for noise levels. In the validation data set, an average network had an area under the receiver operating characteristic curve (AUC) of 0.86 (accuracy 84%). Logistic regressions including all these variables or those selected by backward elimination had AUC values of 0.91 and 0.92, respectively (accuracy 85% both). Eleven of 12 trained networks had better specificity than the backward elimination logistic regression, and the backward elimination logistic regression had a better sensitivity than 11 of the 12 networks. Both modeling approaches correctly identified all ears with sudden hearing loss, congenital hearing loss, head trauma, nuclear jaundice and ototoxicity, and 2-3 of 5 ears with acoustic trauma, but missed 1-3 of 3 ears with Ménière's disease and 4-6 of 8 ears with abnormal pure-tone thresholds on audiometry which had no accompanying findings. For SNHL exceeding 45 dB HL on a pure-tone threshold, sensitivity was 83% (15/18) by neural networks and 84 or 94% (16/18 or 17/18) by logistic regression. Both neural-network-based analysis and logistic regression modeling of the DPOAE pattern across a range of frequencies offer promising approaches for the objective diagnosis of moderate and severe SNHL.

Adult↗

Confidence interval estimates of an index of quality performance based on logistic regression models.

This paper considers an index of hospital quality performance defined as the ratio of the observed number deaths to the number predicted by a fitted logistic regression model. We study tests and confidence intervals under two different scenarios depending on the availability of an estimate of the covariance matrix of the coefficients from the fitted logistic regression model. We propose parametric as well as bootstrap-based confidence intervals. We apply the methods to an analysis of the performance of 27 intensive care units.

Aged↗

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

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

Humans↗