A simulation study of maximum likelihood estimation in logistic regression with cured individuals

The logistic regression model is widely used to investigate the relationship between a binary outcome Y and a set of potential predictors X. Diop et al. (2011) present some conditions under which the maximum likelihood estimator is consistent and asymptotically normal in the logistic regression model with a cure fraction. So far, however, only limited simulation results are available to judge the quality of this estimator in finite samples. Therefore in this paper, we conduct a detailed simulation study of its numerical properties. We evaluate its accuracy and the quality of the normal approximation of its asymptotic distribution. We also study the quality of the approximation for constructing asymptotic Wald-type tests of hypothesis. Finally, we consider the problem of estimating the conditional probability of the outcome. Our results indicate that when the proportion of cured individuals is moderate to moderately large, and the sample size is large enough, reliable statistical inferences can be obtained for the regression effects and the probability of the outcome. Our results also indicate that the approximations can be problematic when the cure fraction is very large

Maximum likelihood estimation in the logistic regression model with a cure fraction

International audienceLogistic regression is widely used in medical studies to investigate the relationship between a binary response variable Y and a set of potential predictors X. The binary response may represent, for example, the occurrence of some outcome of interest (Y=1 if the outcome occurred and Y=0 otherwise). In this paper, we consider the problem of estimating the logistic regression model with a cure fraction. A sample of observations is said to contain a cure fraction when a proportion of the study subjects (the so-called cured individuals, as opposed to the susceptibles) cannot experience the outcome of interest. One problem arising then is that it is usually unknown who are the cured and the susceptible subjects, unless the outcome of interest has been observed. In this setting, a logistic regression analysis of the relationship between X and Y among the susceptibles is no more straightforward. We develop a maximum likelihood estimation procedure for this problem. We establish the consistency and asymptotic normality of the resulting estimator, and we conduct a simulation study to investigate its finite-sample behavior

Simultaneous confidence bands in a zero-inflated regression model for binary data

14 pagesInternational audienceThe logistic regression model has become a standard tool to investigate the relationship between a binary outcome and a set of potential predictors. When analyzing binary data, it often arises however that the observed proportion of zeros is greater than expected under the postulated logistic model. Zero-inflated binomial (ZIB) models have been developed to fit binary data that contain too many zeros, and maximum likelihood estimators in these models have been proposed and their asymptotic properties recently established. In this paper, we use these asymptotic properties to construct simultaneous confidence bands for the probability of a positive outcome in a ZIB regression model. Simultaneous confidence bands are especially attractive since they allow inference to be made over the whole predictor space. We construct two types of confidence bands, based on: i) the Scheffé method for the linear regression model, ii) Monte Carlo simulations to approximate the distribution of the supremum of a Gaussian field indexed by the regressor. The finite-samples properties of these two types of bands are investigated and compared in a simulation study

Clinical and Virological Study of Dengue Cases and the Members of Their Households: The Multinational DENFRAME Project

Dengue is the most important mosquito-borne viral disease in humans. This disease is now endemic in more than 100 countries and threatens more than 2.5 billion people living in tropical countries. It currently affects about 50 to 100 million people each year. It causes a wide range of symptoms, from an inapparent to mild dengue fever, to severe forms, including dengue hemorrhagic fever. Currently no specific vaccine or antiviral drugs are available. We carried out a prospective clinical study in South-East Asia and Latin America, of virologically confirmed dengue-infected patients attending the hospital, and members of their households. Among 215 febrile dengue subjects, 177 agreed to household investigation. Based on our data, we estimated the proportion of dengue-infected household members to be about 45%. At the time of the home visit, almost three quarters of (29/39) presented an inapparent dengue infection. The proportion of inapparent dengue infection was higher in South-East Asia than in Latin America. These findings confirm the complexity of dengue disease in humans and the need to strengthen multidisciplinary research efforts to improve our understanding of virus transmission and host responses to dengue virus in various human populations

Inférence statistique dans le modèle de régression logistique avec fraction immune

Generalized linear models are a generalization of linear regression models, and are widely used in the field of life. The logistic regression model, one of this class of models, widely used in biomedical studies remains the most appropriate regression model when it comes to model discrete variable, binary in nature. In this thesis, we investigate the problem of statistical inference in the logistic regression model, in the presence of immune individuals in the study population.At first, we consider the problem of estimation in the logistic regression model in the presence of immune individuals that enters in the case of zero-inflated regression models. A subject is said to be immune if he cannot experience the outcome of interest. The immune status is unknown unless the event of interest has been observed. We develop a maximum like lihood estimation procedure for this problem, based on the joint modeling of the binary response of interest and the cure status. We investigate the identifiability of the resulting model. Then, we establish the existence, consistency and asymptotic normality of the proposed estimator, and we conduct a simulation study to investigate its finite-sample behavior. In a second time, we focus on the construction of simultaneous confidence bands for the probability of infection in the logistic regression model with immune fraction.We propose three methods of construction of confidence bands for the regression function. The first method (Scheffe's method) uses the asymptotic normality of the maximum like lihood estimator, and an approximation by the chi-squared distribution to approximate the necessary quantile for the construction of bands. The second method uses also the asymptotic normality of the maximum like lihood estimator and is based on a classical equality by (Landau & Sheep 1970). The third method (bootstrap method) is based on simulations, to estimate the appropriate quantile of the law of a supremum of a Gaussian process. Finally, we conduct a simulation study to investigate its finite-sample properties.Finally, we consider a study of dengue fever, which is a tropical mosquito-borneviral human disease, strictly inter-human. The results show that, the estimated probabilities of infection obtained from our approach are larger than the ones derived from a standard analysis that does not take account of the possible immunity. Inparticular, the estimates provided by our approach suggest that underweight constitutes a major risk factor for dengue infection, irrespectively of age.Les modèles linéaires généralisés sont une généralisation des modèles de régression linéaire, et sont très utilisés dans le domaine du vivant. Le modèle de régression logistique, l'un des modèles de cette classe, très souvent utilisé dans les études biomédicales demeure le modèle de régression le plus approprié quand il s'agit de modéliser une variable discrète de nature binaire. Dans cette thèse, nous nous intéressons au problème de l'inférence statistique dans le modèle de régression logistique, en présence d'individus immunes dans la population d'étude.Dans un premier temps, nous considérons le problème de l'estimation dans le modèle de régression logistique en présence d'individus immunes, qui entre dans le cadre des modèles de régression à excès de zéros (ou zéro-inflatés). Un individu est dit immune s'il n'est pas exposé à l'événement d'intérêt. Le statut d'immunité est inconnu sauf si l'événement d'intérêt a été observé. Nous développons une méthode d'estimation par maximum de vraisemblance en proposant une modélisation conjointe de l'immunité et des risques d'infection. Nous établissons d'abord l'identifiabilité du modèle proposé. Puis, nous montrons l'existence de l'estimateur du maximum de vraisemblance des paramètres de ce modèle. Nous montrons ensuite,la consistance de cet estimateur, et nous établissons sa normalité asymptotique. Enfin, nous étudions, au moyen de simulations, leur comportement sur des échantillons de taille finie.Dans un deuxième temps, nous nous intéressons à la construction de bandes de confiance simultanées pour la probabilité d'infection, dans le modèle de régression logistique avec fraction immune. Nous proposons trois méthodes de constructions de bandes de confiance pour la fonction de régression. La première méthode (méthodede Scheffé) utilise la propriété de normalité asymptotique de l'estimateur du maximum de vraisemblance, et une approximation par une loi du khi deux pour approcher le quantile nécessaire à la construction des bandes. La deuxième méthode utilise également la propriété de normalité asymptotique de l'estimateur du maximum de vraisemblance et est basée sur une égalité classique de (Landau & Sheep 1970). La troisième méthode (méthode bootstrap) repose sur des simulations, pour estimer le quantile approprié de la loi du supremum d'un processus gaussien. Enfin, nous évaluons, au moyen de simulations, leurs propriétés sur des échantillons de taille finie.Enfin, nous appliquons les résultats de modélisation à des données réelles surla dengue. Il s'agit d'une maladie vectorielle tropicale à transmission strictement inter-humaine. Les résultats montrent que les probabilités d'infection estimées à partir de notre approche de modélisation sont plus élevées que celles obtenues à partir d'un modèle de régression logistique standard qui ne tient pas compte d'une possible immunité. En particulier, les estimations fournies par notre approche suggèrent que le sous-poids constitue un facteur de risque majeur de l'infection par la dengue, indépendamment de l'âge

Statistical inference in logistic regression model with immune fraction

Les modèles linéaires généralisés sont une généralisation des modèles de régression linéaire, et sont très utilisés dans le domaine du vivant. Le modèle de régression logistique, l'un des modèles de cette classe, très souvent utilisé dans les études biomédicales demeure le modèle de régression le plus approprié quand il s'agit de modéliser une variable discrète de nature binaire. Dans cette thèse, nous nous intéressons au problème de l'inférence statistique dans le modèle de régression logistique, en présence d'individus immunes dans la population d'étude.Dans un premier temps, nous considérons le problème de l'estimation dans le modèle de régression logistique en présence d'individus immunes, qui entre dans le cadre des modèles de régression à excès de zéros (ou zéro-inflatés). Un individu est dit immune s'il n'est pas exposé à l'événement d'intérêt. Le statut d'immunité est inconnu sauf si l'événement d'intérêt a été observé. Nous développons une méthode d'estimation par maximum de vraisemblance en proposant une modélisation conjointe de l'immunité et des risques d'infection. Nous établissons d'abord l'identifiabilité du modèle proposé. Puis, nous montrons l'existence de l'estimateur du maximum de vraisemblance des paramètres de ce modèle. Nous montrons ensuite,la consistance de cet estimateur, et nous établissons sa normalité asymptotique. Enfin, nous étudions, au moyen de simulations, leur comportement sur des échantillons de taille finie.Dans un deuxième temps, nous nous intéressons à la construction de bandes de confiance simultanées pour la probabilité d'infection, dans le modèle de régression logistique avec fraction immune. Nous proposons trois méthodes de constructions de bandes de confiance pour la fonction de régression. La première méthode (méthodede Scheffé) utilise la propriété de normalité asymptotique de l'estimateur du maximum de vraisemblance, et une approximation par une loi du khi deux pour approcher le quantile nécessaire à la construction des bandes. La deuxième méthode utilise également la propriété de normalité asymptotique de l'estimateur du maximum de vraisemblance et est basée sur une égalité classique de (Landau & Sheep 1970). La troisième méthode (méthode bootstrap) repose sur des simulations, pour estimer le quantile approprié de la loi du supremum d'un processus gaussien. Enfin, nous évaluons, au moyen de simulations, leurs propriétés sur des échantillons de taille finie.Enfin, nous appliquons les résultats de modélisation à des données réelles surla dengue. Il s'agit d'une maladie vectorielle tropicale à transmission strictement inter-humaine. Les résultats montrent que les probabilités d'infection estimées à partir de notre approche de modélisation sont plus élevées que celles obtenues à partir d'un modèle de régression logistique standard qui ne tient pas compte d'une possible immunité. En particulier, les estimations fournies par notre approche suggèrent que le sous-poids constitue un facteur de risque majeur de l'infection par la dengue, indépendamment de l'âge.Generalized linear models are a generalization of linear regression models, and are widely used in the field of life. The logistic regression model, one of this class of models, widely used in biomedical studies remains the most appropriate regression model when it comes to model discrete variable, binary in nature. In this thesis, we investigate the problem of statistical inference in the logistic regression model, in the presence of immune individuals in the study population.At first, we consider the problem of estimation in the logistic regression model in the presence of immune individuals that enters in the case of zero-inflated regression models. A subject is said to be immune if he cannot experience the outcome of interest. The immune status is unknown unless the event of interest has been observed. We develop a maximum like lihood estimation procedure for this problem, based on the joint modeling of the binary response of interest and the cure status. We investigate the identifiability of the resulting model. Then, we establish the existence, consistency and asymptotic normality of the proposed estimator, and we conduct a simulation study to investigate its finite-sample behavior. In a second time, we focus on the construction of simultaneous confidence bands for the probability of infection in the logistic regression model with immune fraction.We propose three methods of construction of confidence bands for the regression function. The first method (Scheffe's method) uses the asymptotic normality of the maximum like lihood estimator, and an approximation by the chi-squared distribution to approximate the necessary quantile for the construction of bands. The second method uses also the asymptotic normality of the maximum like lihood estimator and is based on a classical equality by (Landau & Sheep 1970). The third method (bootstrap method) is based on simulations, to estimate the appropriate quantile of the law of a supremum of a Gaussian process. Finally, we conduct a simulation study to investigate its finite-sample properties.Finally, we consider a study of dengue fever, which is a tropical mosquito-borneviral human disease, strictly inter-human. The results show that, the estimated probabilities of infection obtained from our approach are larger than the ones derived from a standard analysis that does not take account of the possible immunity. Inparticular, the estimates provided by our approach suggest that underweight constitutes a major risk factor for dengue infection, irrespectively of age

Simulation-based Inference in a Zero-inflated Bernoulli Regression Model

International audienc

Method development of extraction and identification of Nitidine, (Benzophenanthridine alkaloid) from the barks of Fagara chalybea

Objective: Fagara chalybea is an important medicinal plant belonging to the family Rutaceae. The plant is well known for its anti-malarial, anti-microbial and  anti-cancerous activity, which has been attributed to the presence of  benzophenanthridine alkaloid nitidine in the plants. The present work aims to develop a method of Nitidine extraction and Identification from the bark of Fagara chalybea Engl.Methodology and results: A simple, rapid and sensitive HPLC method has been developed for the qualitative determination of nitidine in the dried bark of Fagara chalybea after extraction. The calculated yield is 2.28%. The retention time of nitidine in the methanol was 27.639 min, and then this time was 27.393 nm in dichloromethane. The limit of detection and limit of quantization were found to be 2.18 and 7.29 Cg/mL respectively, the correlation coefficient was 0.998.Conclusion and application of results: The application of this method to the analyses of nitidine after extraction proved that the method is sensitive enough to detect low levels of analyses. To value traditional medicine, this method can be used as a tool for quality control of botanicals herbal formulations.Key words: Nitidine, HPLC, Fagara chalybea, Malaria

Study of the spatial variability of marine pollution around the peninsula of Cape Verde

International audienceMarine pollution, the scourge of modern times, is due to the runoff of domestic and industrial waters as well as to various anthropogenic activities, i.e. products and objects deliberately or accidentally discharged into the sea. The samples taken from 11 sites on the Cap-Vert peninsula in Senegal, indicate the presence of certain polluting substances in varying amounts. The objective of this work is to study the correlations between the physical, microbiological and chemical parameters in order to highlight the similarities between the sites and, if possible, to determine the most relevant parameter(s) to characterize the pollution. PCA results have shown that some sites appear to be less chemically polluted than others that are more polluted with eutrophication and chemicals (e.g., copper, mercury). From a physical point of view, for example, we observe that the characteristics of sediments (large silt, clays, fine silt) are related to certain chemical parameters.The AFC performed between the overall toxicity of the sediments and the microbiological quality of the water shows that the site of Ouakam has a medium toxicity and a good microbiological quality while that of Cambérène and the Vivier are characterized respectively by bad and good quality but also by low toxicity at both sites. The two sites of Hann (Hann1 and Hann2), Soumbédioune, Ngor, Yoff Tonghor and Dakar Le Dantec are characterized by high toxicity and poor microbiological quality. Those in the Madeleine Islands and the Port of Dakar are characterized by high toxicity and bad microbiological quality. Moreover, as expected Soumbédioune appears as the most polluted sites in terms of microbiological load. The interest of the multivariate approach (ACP and AFC) is then discussed in this type of analysis