Feed forward neural networks for the analysis of censored survival data: a partial logistic regression approach

Flexible modelling in survival analysis can be useful both for exploratory and predictive purposes. Feed forward neural networks were recently considered for flexible non-linear modelling of censored survival data through the generalization of both discrete and continuous time models. We show that by treating the time interval as an input variable in a standard feed forward network with logistic activation and entropy error function, it is possible to estimate smoothed discrete hazards as conditional probabilities of failure. We considered an easily implementable approach with a fast selection criteria of the best configurations. Examples on data sets from two clinical trials are provided. The proposed artificial neural network (ANN) approach can be applied for the estimation of the functional relationships between covariates and time in survival data to improve model predictivity in the presence of complex prognostic relationships.     

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.     

Inference using conditional logistic regression with missing covariates

When there are many nuisance parameters in a logistic regression model, a popular method for eliminating these nuisance parameters is conditional logistic regression. Unfortunately, another common problem in a logistic regression analysis is missing covariate data. With many nuisance parameters to eliminate and missing covariates, many investigators exclude any subject with missing covariates and then use conditional logistic regression, often called a complete-case analysis. In this article, we derive a modified conditional logistic regression that is appropriate with covariates that are missing at random. Performing a conditional logistic regression with only the complete cases is convenient with existing statistical packages, but it may give bias if missingness is not completely at random.     

Random effects probit and logistic regression models for three-level data

In analysis of binary data from clustered and longitudinal studies, random effect models have been recently developed to accommodate two-level problems such as subjects nested within clusters or repeated classifications within subjects. Unfortunately, these models cannot be applied to three-level problems that occur frequently in practice. For example, multicenter longitudinal clinical trials involve repeated assessments within individuals and individuals are nested within study centers. This combination of clustered and longitudinal data represents the classic three-level problem in biometry. Similarly, in prevention studies, various educational programs designed to minimize risk taking behavior (e.g., smoking prevention and cessation) may be compared where randomization to various design conditions is at the level of the school and the intervention is performed at the level of the classroom. Previous statistical approaches to the three-level problem for binary response data have either ignored one level of nesting, treated it as a fixed effect, or used first- and second-order Taylor series expansions of the logarithm of the conditional likelihood to linearize these models and estimate model parameters using more conventional procedures for measurement data. Recent studies indicate that these approximate solutions exhibit considerable bias and provide little advantage over use of traditional logistic regression analysis ignoring the hierarchical structure. In this paper, we generalize earlier results for two-level random effects probit and logistic regression models to the three-level case. Parameter estimation is based on full-information maximum marginal likelihood estimation (MMLE) using numerical quadrature to approximate the multiple random effects. The model is illustrated using data from 135 classrooms from 28 schools on the effects of two smoking cessation interventions.     

Empirical comparisons of proportional hazards, poisson, and logistic regression modeling of occupational cohort data

Protein deprivation experienced in adult life leads to deficits in the number of hippocampal granule and CA3-CA1 pyramidal cells and to changes in the dendritic domain of granule cells and CA3 pyramids. To obtain a more complete insight into the effects of malnutrition on the limbic system of the adult rat we have analyzed the subiculum and the entorhinal cortex (neuronal layers II, III, and V-VI) in groups of 8-month-old rats fed with a low-protein diet (8% casein) since the age of 2 months and in age-matched control rats. Stereological methods were employed to estimate the total number of neurons in the subiculum and layers II, III, and V-VI of the entorhinal cortex and the volume of the respective cell layers. Moreover, to evaluate whether protein deprivation affects the dendritic domains of the neurons from these regions we have analyzed, in Golgi-impregnated material, the dendritic trees of the pyramidal cells of the subiculum and of the stellate neurons of the entorhinal cortex layer II applying quantitative and metric methods. The volume of the subiculum and the total number of its neurons were reduced in malnourished animals. In these animals we also found marked regressive changes in the apical and basal dendritic trees of the pyramidal subicular neurons. However, the spine density was increased in malnourished rats. No differences in the volume of the neuronal layers of the entorhinal cortex or in the total number of their neurons were found between protein-deprived and control rats, and no alterations were depicted in the dendritic trees of the stellate neurons of layer II. We can thus conclude that the effects of long-term protein deprivation are region specific and that the resulting structural alterations are confined to the three-layered components of the hippocampal region.     

Artificial neural networks and logistic regression as tools for prediction of survival in patients with Stages I and II non-small cell lung cancer

BACKGROUND: This study examines the role of participation in psychosocial treatment as a mediator of the clinical effectiveness of clozapine. METHODS: Subjects participated in a 12-month double-blind random-assignment trial comparing clozapine and haloperidol in patients hospitalized 30 to 364 days for refractory schizophrenia at 15 Department of Veterans Affairs medical centers. A broker-advocate case management intervention was used to facilitate participation in psychosocial treatments and to document such participation. RESULTS: Between those who continued receiving clozapine (n=122) or a conventional antipsychotic drug (n=169) for 12 months, those receiving clozapine were more likely to participate in psychosocial rehabilitation treatment. Although they were no more likely to receive clinical recommendations for such treatments, they were more likely to both verbally accept recommendations and to act on them. Structural equation modeling shows that participation in psychosocial treatment did not play a mediating role in clozapine's effect on outcomes at 6 months, but was associated with both reduced symptoms and improved quality of life at 12 months. CONCLUSIONS: Clozapine facilitates participation in psychosocial treatment, and such enhanced participation is associated with improved quality-of-life and symptom outcomes. Psychosocial rehabilitation should be offered concomitantly with clozapine.     

Two-stage designs for the logistic regression model in single-agent bioassays

In this paper we focus on the use of a two-stage procedure for logistic regression that emphasizes predicting response through the use of the Q-optimality criterion. The use of D-optimality in the first stage is primarily to allow best possible parameter estimates as one enters the second stage. However, it is important to understand that there are many ways to formulate the two-stage procedure. It may involve any optimality criterion in either stage. In fact, theoretically, one need not stop at two stages. It was our intention in this paper to demonstrate the potential in the two-stage procedure in cases in which good initial parameter estimates are not available. Those investigators who are interested in the software for the two-stage procedure described here should contact Dr. William R. Myers.     

Dose-response relationship between total cadmium intake and metallothioneinuria using logistic regression analysis

The dose-response relationship for environmental cadmium exposure was assessed using logistic regression analysis. The prevalence of metallothioneinuria was employed as a response variable, while age and total cadmium intake, calculated from the average cadmium concentration in rice and duration of residence in the cadmium-polluted area, were used as explanatory variables. The target population comprised of 1843 cadmium-exposed and 240 non-exposed inhabitants of Ishikawa, Japan. The individuals were divided into 96 subgroups by sex, age (4 categories), cadmium concentrations in rice (3 categories) and length of residence in the polluted area (4 categories). Only total cadmium intake had a significant association with the prevalence of metallothioneinuria. In the non-exposed subjects total cadmium intakes corresponding to 2.5% prevalence of metallothioneinuria were calculated. Based on metallothionein levels expressed as either microgram/l urine or microgram/g creatinine, the total intakes were: 2.221 or 2.207 g in men and 2.365 or 0.319 g in women, respectively. Most of these values were similar to those reported by us previously, employing simple regression analysis. It is concluded, therefore, that a maximum allowable intake of about 2 g cadmium is a reasonable estimate for preventing the cadmium-induced renal dysfunction.     

Neural networks and blood cell identification

The objective of this project is to propose a method of identifying cells found in human blood and to classify them based upon their morphological features using neural networks. The project focuses on three major blood cell types, namely, erythrocytes, leukocytes and platelets. The data are collected using peripheral blood smears from clinical patients. The image acquisition requires 100x magnification on all the blood smears, the preprocessing involves the use of median and edge enhance filters; the feature extraction is done by performing the wavelet transform on the images. Finally classification of the blood cell types is done using ALOPEX and Back Propagation trained neural networks. The efficacy of both networks is then compared by comparing their outputs and number of iterations required to reach the final result.     

Bayesian decision procedures based on logistic regression models for dose-finding studies

Early-phase clinical trials, conducted to determine the appropriate dose of an experimental drug to take forward to later trials, are considered. The objective is to find the dose associated with some low probability of an adverse event. A Bayesian model is presented, and a decision-theoretic procedure for finding the optimal doses for each of a series of cohorts of subjects is derived. The procedure is flexible and can easily be conducted using standard statistical software. The results of simulations investigating the properties of the procedure are presented.     

Conditional logistic regression with sandwich estimators: application to a meta-analysis

Motivated by a meta-analysis of animal experiments on the effect of dietary fat and total caloric intake on mammary tumorigenesis, we explore the use of sandwich estimators of variance with conditional logistic regression. Classical conditional logistic regression assumes that the parameters are fixed effects across all clusters, while the sandwich estimator gives appropriate inferences for either fixed effects or random effects. However, inference using the standard Wald test with the sandwich estimator requires that each parameter is estimated using information from a large number of clusters. Since our example violates this condition, we introduce two modifications to the standard Wald test. First, we reduce the bias of the empirical variance estimator (the middle of the sandwich) by using standardized residuals. Second, we approximately account for the variance of these estimators by using the t-distribution instead of the normal distribution, where the degrees of freedom are estimated using Satterthwaite's approximation. Through simulations, we show that these sandwich estimators perform almost as well as classical estimators when the true effects are fixed and much better than the classical estimators when the true effects are random. We achieve simulated nominal coverage for these sandwich estimators even when some parameters are estimated from a small number of clusters.     

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

The effects of exposure to an alcohol-related cue (drinking low-alcohol beer) and a musical depression/elation mood induction procedure, on craving, motivation and liking for alcohol, were studied in male and female recreational drinkers. Alcohol craving was assessed using the multidimensional desires for alcohol questionnaire (DAQ), motivation for alcohol was assessed by performance on a progressive ratio (PR) task reinforced with small volumes (25 ml) of low-alcohol beer, and liking for the reinforcers earned in the PR task was assessed using a visual analogue scale. Consumption of a half-pint of low-alcohol beer increased alcohol craving in male subjects but had no effect or decreased craving in female subjects. Subsequent induction of a depressed mood increased craving scores, relative to elated or neutral mood groups, but these effects were confined to abstinent (non-cued) subjects, both male and female. Performance on the PR task correlated significantly with one of the four factors of the DAQ, negative reinforcement, and was increased by induction of a depressed mood in abstinent female and cued male subjects. Reinforcer liking was unchanged following mood induction in male subjects, but decreased in both groups of female subjects. To summarize, the cue of drinking low-alcohol beer increased alcohol craving in men but not in women, and induction of a depressed mood increased alcohol craving and motivation, but also decreased alcohol liking. These effects were present to different extents in different cue/gender subgroups, and were partially independent.     

Focal calvarial bone lesions. Comparison of logistic regression and neural network models

RATIONALE AND OBJECTIVES: To assess the accuracy of logistic regression (LR) and artificial neural networks (NN) in the diagnosis of calvarial lesions using computed tomography (CT) and to establish the importance of the different features needed for the diagnosis. METHODS: One hundred sixty-seven patients with calvarial lesions as the only known disease were enrolled. The clinical and CT data were used for LR and NN models. Both models were tested with the leave-one-out method. The final results of each model were compared using the area under receiver operating characteristic curves (Az). RESULTS: Of the lesions, 73.1%, were benign and 26.9% were malignant. There was no statistically significant difference between LR and NN in differentiating malignancy. In characterizing the histologic diagnoses, NN was statistically superior to LR. Important NN features needed for malignancy classification were age and edge definition, and for the histologic diagnoses matrix, marginal sclerosis, and age. CONCLUSION: NNs offer wide possibilities over statistics for the study of calvarial lesions other than their superior diagnostic performance.     

Multiple-trait mapping of quantitative trait loci after selective genotyping using logistic regression

Experiments to map QTL usually measure several traits, and not uncommonly genotype only those animals that are extreme for some trait(s). Analysis of selectively genotyped, multiple-trait data presents special problems, and most simple methods lead to biased estimates of the QTL effects. The use of logistic regression to estimate QTL effects is described, where the genotype is treated as the dependent variable and the phenotype as the independent variable. In this way selection on phenotype does not bias the results. If normally distributed errors are assumed, the logistic-regression analysis is almost equivalent to a maximum-likelihood analysis, but can be carried out with standard statistical packages. Analysis of a simulated half-sib experiment shows that logistic regression can estimate the effect and position of a QTL without bias and confirms the increased power achieved by multiple-trait analysis.     

Neural networks with dynamic synapses

Transmission across neocortical synapses depends on the frequency of presynaptic activity (Thomson & Deuchars, 1994). Interpyramidal synapses in layer V exhibit fast depression of synaptic transmission, while other types of synapses exhibit facilitation of transmission. To study the role of dynamic synapses in network computation, we propose a unified phenomenological model that allows computation of the postsynaptic current generated by both types of synapses when driven by an arbitrary pattern of action potential (AP) activity in a presynaptic population. Using this formalism, we analyze different regimes of synaptic transmission and demonstrate that dynamic synapses transmit different aspects of the presynaptic activity depending on the average presynaptic frequency. The model also allows for derivation of mean-field equations, which govern the activity of large, interconnected networks. We show that the dynamics of synaptic transmission results in complex sets of regular and irregular regimes of network activity.     

Dose-response relationship between total cadmium intake and beta 2-microglobulinuria using logistic regression analysis

Noradrenaline stimulates not only Ca2+ mobilization but also cAMP formation through activation of alpha 1-adrenoceptors in hepatocytes from mature male rats. We examined which subtype(s) of alpha 1-adrenoceptor mediate these signal transduction mechanisms. Treatment of hepatocytes with chloroethylclonidine produced a dose-dependent inhibition of noradrenaline-induced Ca2+ mobilization, involving both transient and sustained components. Chloroethylclonidine also blocked noradrenaline-induced cAMP accumulation. It was observed that prazosin was much more potent than WB4101 (2-(2,6-dimethoxy-phenoxyethyl)aminomethyl-1,4-benzodioxane) in antagonizing noradrenaline-induced Ca2+ mobilization. The same potency order was found in cAMP formation studies. Pretreatment of rats with pertussis toxin did not affect alpha 1-adrenergic responsiveness. Incubations of hepatocytes with tumor-promoting phorbol esters eliminated both Ca2+ mobilization and cAMP accumulation caused by noradrenaline. Our data suggest that in hepatocytes from mature male rats, single alpha 1B-adrenoceptors are linked to cAMP formation as well as Ca2+ mobilization.     

From multiple regression analysis to logistic model, proportional hazard model and log linear model. Its concept and application

Recently logistic model, proportional hazard model and log linear model have been used frequently in the medical literatures. Here, each model is reviewed briefly from basics to its application, pointing out pitfalls in its application, some of which are common to any regression analysis. The logistic model is especially useful for the analysis of retrospective data where odds ratio is utilized to evaluate the outcome probability. On the other hand, proportional hazard model is useful when we analyze censored data, utilizing hazard function. Log linear model has been used where contingency table has more than three independent variables, the situation where its applicability in clinical medicine is wide. Familiarity with these statistical methods would enable us to evaluate data more effectively and efficiently and ultimately to read literature more easily.     

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.