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PubMed1999

Marginally specified logistic-normal models for longitudinal binary data.

Likelihood-based inference for longitudinal binary data can be obtained using a generalized linear mixed model (Breslow, N. and Clayton, D. G., 1993, Journal of the American Statistical Association 88, 9-25; Wolfinger, R. and O'Connell, M., 1993, Journal of Statistical Computation and Simulation 48, 233-243), given the recent improvements in computational approaches. Alternatively, Fitzmaurice and Laird (1993, Biometrika 80, 141-151), Molenberghs and Lesaffre (1994, Journal of the American Statistical Association 89, 633-644), and Heagerty and Zeger (1996, Journal of the American Statistical Association 91, 1024-1036) have developed a likelihood-based inference that adopts a marginal mean regression parameter and completes full specification of the joint multivariate distribution through either canonical and/or marginal higher moment assumptions. Each of these marginal approaches is computationally intense and currently limited to small cluster sizes. In this manuscript, an alternative parameterization of the logistic-normal random effects model is adopted, and both likelihood and estimating equation approaches to parameter estimation are studied. A key feature of the proposed approach is that marginal regression parameters are adopted that still permit individual-level predictions or contrasts. An example is presented where scientific interest is in both the mean response and the covariance among repeated measurements.

Biometry↗

PubMed1998

A logistic regression model for analyzing the relation between dentists' attitudes, behavior, and knowledge in oral radiology.

The aim was to study the relation between risk attitude and knowledge in technical, patient-oriented, and organizationally related behavior within oral radiology. A questionnaire was mailed to 2000 randomly selected dentists listed in the register of the Swedish Dental Society, with a response rate of 69.3%. Regression analysis was used for analyzing the effects of the independent variables knowledge, risk attitude, continuing education in oral radiology, counties with specialists in oral radiology, type of practice, work experience, and sex on three categories of dependent variables: 1) technical behaviors: type of film, type of collimator, dose level, frequency of change of chemicals; 2) patient-oriented behaviors: use of patient protection barriers, strict indications for performing full-mouth X-ray examinations and bitewing radiography on new patients and recall patients; and 3) organizationally related behaviors: delegation of X-ray examinations to dental auxiliaries, influence on choice of collimator, influence on choice of film. Knowledge and education had strong direct effects for most of the dependent variables. The technical behaviors were mainly influenced by knowledge, education, and risk attitude, while organizationally related behaviors were influenced by type of practice and sex. The patient-oriented behaviors were influenced by a number of independent variables, such as education, type of practice, work experience, and sex. The present results indicate that both knowledge and the organizational context of dentists influence work.

Adult↗

PubMed1990

A model for prediction of failure in amputation of the lower limb.

A logistic regression analysis of eighteen variables in eighty-three lower limb amputations was performed in order to predict stump failure. Five variables were identified as having a significant effect on the logistic model: Age had an inverse relation to failure rate (p less than 0.005). This effect was mediated through a subgroup of 23 patients who had had a vascular operation (p less than 0.02), as this group had a higher failure rate and were younger than those without previous vascular surgery. Furthermore, the surgical experience (p less than 0.005) was of major importance for stump failure. Experienced surgeons had a failure rate of 2% while less experienced had a rate of 29% (p less than 0.001). In addition, it was confirmed that the higher the skin perfusion pressure (p less than 0.05) and the amputation level, (p less than 0.05) the better the healing. A model including "skin perfusion pressure," "previous vascular surgery," "amputation level" and "surgical experience" had a good predictive capability with a misclassification rate of 0.08-0.11. Therefore it is suggested that a logistic model including these variables could be a helpful tool to predict the risk of stump failure.

Adult↗

PubMed2006

[Development of a predictive program for microbial growth under various temperature conditions].

A predictive program for microbial growth under various temperature conditions was developed with a mathematical model. The model was a new logistic model recently developed by us. The program predicts Escherichia coli growth in broth, Staphylococcus aureus growth and its enterotoxin production in milk, and Vibrio parahaemolyticus growth in broth at various temperature patterns. The program, which was built with Microsoft Excel (Visual Basic Application), is user-friendly; users can easily input the temperature history of a test food and obtain the prediction instantly on the computer screen. The predicted growth and toxin production can be important indices to determine whether a food is microbiologically safe or not. This program should be a useful tool to confirm the microbial safety of commercial foods.

Animals↗

PubMed2003

The clustering of neonatal deaths in triplet pregnancies: application of response conditional multivariate logistic regression models.

BACKGROUND/OBJECTIVES: A population-based retrospective cohort study of triplet pregnancies was conducted to estimate individual probabilities of neonatal mortality (death within 28 days of birth) conditional on the number of neonatal deaths experienced by other infants in the triplet set. METHODS: Data on 4,697 triplet sets (14,091 births) were derived from the U.S. 1995-1997 matched multiple birth file assembled by the National Center for Health Statistics. Response conditional multivariate logistic regression was used to model the association of neonatal mortality among cotriplets. To account for the correlation of the outcomes among cotriplets, regression parameters were estimated by the methodology of generalized estimating equations with robust variance estimates. RESULTS: Compared with a triplet where both cotriplets survived the neonatal period, the adjusted odds ratio and 95% confidence interval (CI) for a neonatal death associated with one and two cotriplet neonatal deaths were 1.80 (95% CI 1.06, 3.04), and 13.41 (95% CI 2.31, 77.7), respectively, after adjusting for birthweight and gestational age. CONCLUSIONS: These results show strong evidence of clustering of neonatal deaths in triplet pregnancies.

Humans↗

PubMed1999

A five-parameter logistic equation for investigating asymmetry of curvature in baroreflex studies.

Baroreceptor reflex curves are usually analyzed using a symmetric four-parameter function. We wished to ascertain the validity of assuming symmetry in the baroreflex curve and also of constraining the curves to pass through the resting blood pressure and heart rate (HR) values. Therefore, we have investigated the suitability of a new five-parameter asymmetric logistic model for analysis of baroreflex curves from rabbits and dogs. The five-parameter model is an extension of the usual four-parameter model and reduces to that model when the fitted data are symmetrical. Using 30 data sets of blood pressure versus renal sympathetic nerve activity (RSNA) and HR from six conscious rabbits, we compared the five-parameter curves with the four-parameter model. We also tested the effect of forcing these baroreflex curves through the resting point. We found that the five-parameter model reduced the unexplained variation and gave small but important improvements to the estimates of plateaus for RSNA and HR and the HR gain. Although forcing the HR curves through the resting values had little effect, this procedure, when applied to RSNA, produced a worse curve fit by increasing the unexplained variation with alteration to most of the estimated curve parameters. The mean arterial pressure-HR baroreflex relationship from six conscious dogs was also analyzed and showed clear evidence of systematic asymmetry. We conclude that the asymmetric model is a valuable extension to the symmetric logistic model when examining baroreceptor reflexes, giving improved estimates of the parameters and a new approach to examining the mechanisms contributing to baroreflex curve asymmetry. Furthermore, forcing the curves through the resting value is a statistically questionable practice when analyzing RSNA, because it affects the parameter estimates.

Animals↗

PubMed2000

Estimation and testing with overdispersed proportions using the beta-logistic regression model of Heckman and Willis.

Methods are presented for modeling dose-related effects in proportion data when extra-binomial variability is a concern. Motivation is taken from experiments in developmental toxicology, where similarity among conceptuses within a litter leads to intralitter correlations and to overdispersion in the observed proportions. Appeal is made to the well-known beta-binomial distribution to represent the overdispersion. From this, an exponential function of the linear predictor is used to model the dose-response relationship. The specification was introduced previously for econometric applications by Heckman and Willis; it induces a form of logistic regression for the mean response, together with a reciprocal biexponential model for the intralitter correlation. Large-sample, likelihood-based methods for estimating and testing the joint proportion-correlation response are studied. A developmental toxicity data set illustrates the methods.

Animals↗

PubMed2002

Color Doppler energy prediction of malignancy in adnexal masses using logistic regression models.

OBJECTIVE: The aim of this study was to assess the usefulness of color Doppler energy in the preoperative diagnosis of ovarian malignancy using multivariate logistic regression analysis. METHODS: One hundred and thirty adnexal masses were studied with transvaginal B-mode, color energy, and pulsed Doppler ultrasonography before surgery in order to develop a model that could be used to determine malignancy. Each ultrasonographic variable (tumor size, wall thickness, septal structure, echogenicity, papillary projection, density (solid or not)) was included individually or combined together as part of the Sassone ultrasound score. Intratumoral blood flow velocity waveforms were obtained to determine pulsatility index and resistance index and a more subjective parameter, location of tumor vascularity, was also assessed. Menopausal status and serum CA 125 levels were also entered as categorical variables. Sonographic parameters were entered alone, then associated with menopausal status and CA 125 serum levels, and finally with Doppler energy measurements. Our model was then validated in a group of 68 adnexal masses and compared to the model of Alcazar. RESULTS: Eighteen adnexal masses (13.8%) were malignant or of low malignant potential. Multivariate analysis showed that papillary projection of the tumor wall, cyst with solid parts, resistance index with a cut-off value of 0.53, CA 125, and central blood flow location, were the only factors to be independent predictors of malignancy. Menopausal status was not an independent factor. For the final model including the Doppler energy parameter the best sensitivity and specificity were 83% and 93%, respectively, at a cut-off value of 10% probability of malignancy compared to 83% and 87% for the morphological variables alone. Validation of the model showed its diagnostic performance to be as good as that reported in the original population and better than the model of Alcazar. CONCLUSION: Sonographic analysis of adnexal masses including color Doppler energy shows the best predictive properties according to histological diagnosis, and improves preoperative diagnosis of malignancy.

Adolescent↗

PubMed2001

Logistic regression model: an assessment of variability of predictions.

Risk prediction models available for cardiovascular prevention are statistical or based on machine learning methods. This paper investigates whether the logistic regression method can be considered as reference for validation of other methods. In order to test the stability of the predictions using this method, we performed two types of analyses on 50 random training and test samples drawn from the same database. In first analyses three models were obtained by forced entry of different sets of four variables. In second analyses, models were built with increasing number of predictive variables. The predictive performance was assessed by the area under the ROC curve. Although across-samples variability is low for a given model, it is large enough to lead to wrong conclusions when comparing different prediction methods. We also suggest that a low events-per-variable ratio alters the stability of a model's coefficients but does not affect the variability of prediction performance.

Area Under Curve↗

PubMed1987

Analysis of total mortality in the Rotterdam sample of the Kaunas-Rotterdam Intervention Study (KRIS).

In 3284 middle-aged Rotterdam men, the dependency of 9-year survival on a number of cardiovascular risk factors is analysed. The purpose of this analysis is twofold. First, there is interest in the relationship between total mortality and the continuous variables blood pressure and plasma cholesterol. In accordance with other studies, the results provide further evidence for a U-shaped relationship. The second purpose is to compare three models theoretically as well as empirically: a piecewise exponential distribution of survival time, Cox's proportional hazards model (both with a long-linear dependency specification of the mortality rate), and a logistic model. The disadvantage of a logistic model is that it is theoretically not appropriate in longitudinal (prospective) epidemiologic studies. The theoretical advantage of the piecewise exponential distribution to Cox's model is that longitudinal (time) effects on the mortality rate can be specified and estimated directly. Empirically, with 342 deaths all three methods yield quite similar estimates and therefore are almost equally capable of detecting relationships between mortality and the risk factors in the data set at hand.

Blood Pressure↗

PubMedDate not supplied

Logistic equations effectively model Mammalian cell batch and fed-batch kinetics by logically constraining the fit.

A four-parameter logistic equation was used to fit batch and fed-batch time profiles of viable cell density in order to estimate net growth rates from the inoculation through the cell death phase. Reduced three-parameter forms were used for nutrient uptake and metabolite/product formation rate calculations. These logistic equations constrained the fits to expected general concentration trends, either increasing followed by decreasing (four-parameter) or monotonic (three-parameter). The applicability of this approach was first verified for Chinese hamster ovary (CHO) cells cultivated in 15-L batch bioreactors. Cell density, metabolite, and nutrient concentrations were monitored over time and used to estimate the logistic parameters by nonlinear least squares. The logistic models fit the experimental data well, supporting the validity of this approach. Further evidence to this effect was obtained by applying the technique to three previously published batch studies for baby hamster kidney (BHK) and hybridoma cells in bioreactors ranging from 100 mL to 300 L. In 27 of the 30 batch data sets examined, the logistic models provided a statistically superior description of the experimental data than polynomial fitting. Two fed-batch experiments with hybridoma and CHO cells in benchtop bioreactors were also examined, and the logistic fits provided good representations of the experimental data in all 25 data sets. From a computational standpoint, this approach was simpler than classical approaches involving Monod-type kinetics. Since the logistic equations were analytically differentiable, specific rates could be readily estimated. Overall, the advantages of the logistic modeling approach should make it an attractive option for effectively estimating specific rates from batch and fed-batch cultures.

Animals↗

PubMed2002

Effects of linezolid on hospital length of stay compared with vancomycin in treatment of methicillin-resistant Staphylococcus infections. An application of multivariate survival analysis.

OBJECTIVES: This study was designed to estimate the effects of treatment with linezolid as compared with vancomycin, on the distribution of length of stay (LOS) for hospitalized patients with methicillin-resistant staphylococcal infections. Treatment with intravenous-oral linezolid may allow some patients to be discharged earlier than would treatment with intravenous vancomycin. METHODS: The analysis is based on the intention-to-treat sample from a randomized multinational phase 3 clinical trial of 460 patients showing that the treatments had equal efficacy. Given the nature of the LOS data, some censoring, and some imbalances between treatment groups, multivariate survival analysis was indicated. Cox proportional hazards assumptions were tested and failed, and accelerated failure time models were tested for best fit. The log-logistic model was selected and used as the basis for estimating the overall treatment effect on LOS. Two methods for multivariate corrections to the survivorship functions allowed more thorough description of the treatment effect on the distribution of LOS, including multivariate-adjusted Kaplan-Meier curves. RESULTS: The average reduction in LOS associated with linezolid treatment, based on the log-logistic model after correction for covariate effects, was 18.1% (p = .041) or 2.53 days at the median. This was consistent with differences at the medians of the adjusted survivorship functions, which were 2 or 3 days depending on the method used. Treatment-based differences exist at each decile of LOS and consistently favor linezolid. Estimated mean reduction in LOS due to linezolid was 1.62 days in both methods. CONCLUSIONS: In this study sample, linezolid treatment resulted in statistically significantly shorter hospital LOS as compared with vancomycin treatment. Appropriate use of multivariate survival analysis allows better examination of the nature of the treatment effect on LOS, which may be important for economic analysis.

Acetamides↗

PubMed2006

A stochastic metapopulation model accounting for habitat dynamics.

A stochastic metapopulation model accounting for habitat dynamics is presented. This is the stochastic SIS logistic model with the novel aspect that it incorporates varying carrying capacity. We present results of Kurtz and Barbour, that provide deterministic and diffusion approximations for a wide class of stochastic models, in a form that most easily allows their direct application to population models. These results are used to show that a suitably scaled version of the metapopulation model converges, uniformly in probability over finite time intervals, to a deterministic model previously studied in the ecological literature. Additionally, they allow us to establish a bivariate normal approximation to the quasi-stationary distribution of the process. This allows us to consider the effects of habitat dynamics on metapopulation modelling through a comparison with the stochastic SIS logistic model and provides an effective means for modelling metapopulations inhabiting dynamic landscapes.

Animals↗

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↗

PubMed2000

Diagnosis of small-for-gestational-age fetuses between 24 and 32 weeks, based on standard sonographic measurements.

OBJECTIVE: To create and validate a formula using sonographic biometry measurements for the optimal diagnosis of small-for-gestational-age (SGA) fetuses between 24 and 32 weeks of gestation. METHODS: A logistic model using gestational age, femur diaphysis length, abdominal and head circumferences to diagnose SGA was set up in a first group of 64 fetuses born between 24 and 32 weeks (group I). A Receiver Operating Characteristic (ROC) curve was drawn. Our model was compared with standard single ultrasound measurements or combined into an estimated fetal weight (EFW) formula. An external validation was carried out on a second group of 183 fetuses (group II) from another maternity unit (ROC curve and comparisons). RESULTS: The area under the ROC curve was 0.91 in group I and 0.93 in group II. Using a 0.5 cut off point for our model yielded a sensitivity of 76% and specificity of 91% for group I. This model is more specific than most other measurement methods with a similar sensitivity. Using the same cut off point (0.5) in Group II, our model was more specific (98%) but less sensitive (66%) when compared with single ultrasound measurements and EFW formulae. By varying the cut off point, we were able to demonstrate that, for a similar sensitivity, our model had a higher specificity than single ultrasound measurements and had similar specificity to EFW formulae. CONCLUSION: The logistic model we set up was able to calculate an SGA risk score between 24 and 32 weeks of gestation in a population at high risk for elective delivery. The cut off point with a view to diagnosis can vary and makes it possible to give greater importance to the sensitivity or specificity depending on the clinical context.

Abdomen↗

PubMed1998

Diagnostic value of sural nerve biopsy in chronic inflammatory demyelinating polyneuropathy.

OBJECTIVE: To investigate the additional diagnostic value of sural nerve biopsy of 64 patients in whom chronic inflammatory demyelinating polyneuropathy (CIDP) was considered, as sural nerve biopsy is recommended in the research criteria of an ad hoc subcommittee to diagnose CIDP. METHODS: Firstly, the additional diagnostic value of sural nerve biopsy was analysed with multivariate logistic regression. Six clinical features (remitting course, symmetric sensorimotor neuropathy in arms and legs, areflexia, raised CSF protein concentration, nerve conduction studies consistent with demyelination, and absence of comorbidity or relevant laboratory abnormalities) were entered into a logistic model. Afterwards, all significant features identified from this model, as well as the results of sural nerve biopsy were forced into a second logistic model. Secondly, the diagnostic performance of a neurologist experienced in diagnosis of peripheral nerve disorders was studied by receiver operating characteristics (ROC) curve analysis. RESULTS: The results of the first logistic analysis showed that CSF protein concentration >1 g/l (odds ratio (OR)=38.5) and neurophysiological studies consistent with demyelination (OR=51.7) were strong predictors of CIDP. When forcing the significant features and the sural nerve biopsy data into the model, an independent predictive value of sural nerve biopsy could not be found. The neurologist was able to discriminate patients with and without CIDP (area under the curve (AUC)=0.95). His diagnostic performance did not improve significantly by offering him the results of sural nerve biopsy. CONCLUSION: Any additional diagnostic value of sural nerve biopsy in the diagnosis of CIDP could not be shown.

Adolescent↗

PubMed1999

Toward reconciling inferences concerning genetic variation in senescence in Drosophila melanogaster.

Standard models for senescence predict an increase in the additive genetic variance for log mortality rate late in the life cycle. Variance component analysis of age-specific mortality rates of related cohorts is problematic. The actual mortality rates are not observable and can be estimated only crudely at early ages when few individuals are dying and at late ages when most are dead. Therefore, standard quantitative genetic analysis techniques cannot be applied with confidence. We present a novel and rigorous analysis that treats the mortality rates as missing data following two different parametric senescence models. Two recent studies of Drosophila melanogaster, the original analyses of which reached different conclusions, are reanalyzed here. The two-parameter Gompertz model assumes that mortality rates increase exponentially with age. A related but more complex three-parameter logistic model allows for subsequent leveling off in mortality rates at late ages. We find that while additive variance for mortality rates increases for late ages under the Gompertz model, it declines under the logistic model. The results from the two studies are similar, with differences attributable to differences between the experiments.

Aging↗

PubMed1997

A logistic regression model for the decision to perform access surgery.

Access surgery may be recommended to about 80% of patients who present with advanced forms of periodontal disease. In this report, a multivariate logistic regression analysis which incorporated several clinical parameters for each tooth examined, i.e., tooth type, furcation involvement, bleeding on probing, attachment level, probing depth, mobility and BANA test score, was conducted using generalized estimating equations (GEE). This approach identified parameters that were significantly associated at p < 0.05 level with the need for access surgery or extraction for periodontal purposes. The estimated probabilities derived from the GEE model were plotted over the complete spectrum of operating conditions to obtain a receiver-operator characteristic (ROC) curve. At a probability cutpoint of 0.8, the decision threshold for surgery/extraction at the pretreatment examination would have a sensitivity of 76.1% and a specificity of 75.3%. We have taken this 0.8 cut point to look at specific clinical decisions made by our examiners after the patients had received scaling and root planing plus 2 weeks unsupervised usage of systemic antimicrobials. The clinicians' decision was taken as the primary reference standard. The model's estimated decision agreed with the clinicians' decision in 226 of the 284 teeth, for an accuracy of 80%. The specificity was 90% and the sensitivity was 43%.

Algorithms↗