We derive multiscale statistics for deconvolution in order to detect qualitative features of the ... more We derive multiscale statistics for deconvolution in order to detect qualitative features of the unknown density. An important example covered within this framework is to test for local monotonicity on all scales simultaneously. The errors in the deconvolution model are restricted to a certain class of distributions that include Laplace, Gamma and Exponential random variables. Our approach relies on inversion
Institute of Mathematical Statistics Lecture Notes - Monograph Series, 2007
lemma is an analytical result which implies √ n-consistency of the distribution function correspo... more lemma is an analytical result which implies √ n-consistency of the distribution function corresponding to the Grenander [Skand. Aktuarietidskr. 39 (1956) 125-153] estimator of a non-decreasing probability density. The present paper derives analogous results for the setting of convex densities on [0, ∞).
Many preschool children have wheeze or cough, but only some have asthma later. Existing predictio... more Many preschool children have wheeze or cough, but only some have asthma later. Existing prediction tools are difficult to apply in clinical practice or exhibit methodological weaknesses. We sought to develop a simple and robust tool for predicting asthma at school age in preschool children with wheeze or cough. From a population-based cohort in Leicestershire, United Kingdom, we included 1- to 3-year-old subjects seeing a doctor for wheeze or cough and assessed the prevalence of asthma 5 years later. We considered only noninvasive predictors that are easy to assess in primary care: demographic and perinatal data, eczema, upper and lower respiratory tract symptoms, and family history of atopy. We developed a model using logistic regression, avoided overfitting with the least absolute shrinkage and selection operator penalty, and then simplified it to a practical tool. We performed internal validation and assessed its predictive performance using the scaled Brier score and the area under the receiver operating characteristic curve. Of 1226 symptomatic children with follow-up information, 345 (28%) had asthma 5 years later. The tool consists of 10 predictors yielding a total score between 0 and 15: sex, age, wheeze without colds, wheeze frequency, activity disturbance, shortness of breath, exercise-related and aeroallergen-related wheeze/cough, eczema, and parental history of asthma/bronchitis. The scaled Brier scores for the internally validated model and tool were 0.20 and 0.16, and the areas under the receiver operating characteristic curves were 0.76 and 0.74, respectively. This tool represents a simple, low-cost, and noninvasive method to predict the risk of later asthma in symptomatic preschool children, which is ready to be tested in other populations.
Let (X, Y ) be a random variable consisting of an observed feature vector X ∈ X and an unobserved... more Let (X, Y ) be a random variable consisting of an observed feature vector X ∈ X and an unobserved class label Y ∈ {1, 2, . . . , L} with unknown joint distribution. In addition, let D be a training data set consisting of n completely observed independent copies of (X, Y ). Usual classification procedures provide point predictors (classifiers) Y (X, D) of Y or estimate the conditional distribution of Y given X. In order to quantify the certainty of classifying X we propose to construct for each θ = 1, 2, . . . , L a p-value π θ (X, D) for the null hypothesis that Y = θ, treating Y temporarily as a fixed parameter. In other words, the point predictor Y (X, D) is replaced with a prediction region for Y with a certain confidence. We argue that (i) this approach is advantageous over traditional approaches and (ii) any reasonable classifier can be modified to yield nonparametric p-values. We discuss issues such as optimality, single use and multiple use validity, as well as computational and graphical aspects.
The brain is capable of taking up monocarboxylates as energy substrates. Under physiological cond... more The brain is capable of taking up monocarboxylates as energy substrates. Under physiological conditions, plasma levels of monocarboxylates are very low and glucose is the primary energy substrate in brain metabolism. However, given conditions such as hyperglycemia and ketosis, levels of circulating monocarboxylates such as lactate and pyruvate are elevated. Previous studies reported an increased expression of monocarboxylate transporter MCT1 in brain following ketotic diet. The major aim of the present study was to answer the question whether chronic hyperglycemia is likewise sufficient to change local densities of MCT1 in the brain. Moreover, chronic hyperglycemia increases local cerebral glucose utilization (LCGU) in particular brain areas. Glucose hereby enters the brain parenchyma via glucose transporters and is partially metabolised by astrocytes, which then release lactate to meet the energetic demands of surrounding neurons. Streptozotocin was given intravenously to induce chronic hyperglycemia and local densities of MCT1 were measured by immunoautoradiographic methods in cryosections of rat brains. The density of monocarboxylate transporter MCT1 was significantly increased in 10 of 24 brain structures investigated (median increase 11.7 ± 3.4 %).
. Whereas acute hyperglycemia has been shown to result in an unchanged local cerebral glucose uti... more . Whereas acute hyperglycemia has been shown to result in an unchanged local cerebral glucose utilization LCGU the changes of Ž . LCGU during chronic hyperglycemia are a matter of dispute. The present study had three aims: 1 To compare the effects of acute and Ž . chronic hyperglycemia on LCGU and to investigate in vivo the lactate level as a potential indicator of glycolytic flux. 2 To investigate Ž . local changes in brain Glut1 andror Glut3 glucose transporter densities during chronic hyperglycemia. 3 To analyze the relationship between LCGU and local Glut densities during chronic hyperglycemia. To induce chronic hyperglycemia in rats steptozotocin was given w 14 x i.p. and experiments were performed 3 weeks later. LCGU was measured by the 2 y C deoxyglucose method and intraparenchymal lactate concentration by MR-spectroscopy. Local densities of the glucose transport proteins were determined by immunoautoradiographic methods. During chronic hyperglycemia weighted average of LCGU increased by 13.9% whereas it remained unchanged during acute hyperglycemia. The cerebral lactatercholine ratio was increased by 143% during chronic hyperglycemia. The average density of glucose transporters Glut1 decreased by 7.5%. Local densities of Glut1 were decreased in 12 of 28 brain structures. Glut3 remained unchanged. Positive correlations were found between LCGU and local Glut densities during control conditions and during chronic hyperglycemia. It Ž . Ž . was concluded that 1 Chronic, but not acute hyperglycemia is followed by an increased LCGU. 2 The capacity to transport glucose is Ž . decreased during chronic hyperglycemia. 3 Increased LCGU and decreased densities of Glut1 are matched on a local level. q
The present study addresses the question whether a chronic decrease of plasma glucose concentrati... more The present study addresses the question whether a chronic decrease of plasma glucose concentration for 1 week induces a global or local increase in glucose transporter densities Glut1 and Glut3 in the brain. To induce chronic hypoglycemia insulin was infused into rats Ž by osmotic minipumps for 1 week resulting in a mean plasma glucose concentration of 3.1 " 0.5 mmolrl control group: 8.1 " 0.5 . mmolrl . Global and local densities of Glut1 and Glut3 glucose transporters were measured by immunoautoradiographic methods. The mean density of glucose transporters Glut1 remained unchanged, whereas the mean density of Glut3 increased slightly, although significantly. To determine whether the increased density of Glut3 is related to a change in glucose metabolism, the local cerebral Ž . metabolic rate of glucose lCMR was quantified by the 2-deoxyglucose method. Mean glucose utilization was decreased by 15%. glc Ž . Local analysis of transporter densities Glut1 and Glut3 and glucose utilization showed a significant correlation between local glucose Ž . transporter densities Glut1 and Glut3 and lCMR during hypoglycemia as already previously observed during normoglycemia. It is glc concluded that 1 week of hypoglycemia is a stimulus for the induction of additional glucose transporters Glut3 in the brain. These additional neuronal glucose transporters may support the maintenance of glucose utilization which is not completely maintained under these conditions. q
In the analysis of many medical studies variable selection methods are applied in order to select... more In the analysis of many medical studies variable selection methods are applied in order to select one final model, which includes only prognostic factors or covariates with an influence on the outcome. However, often several models fit the data equally well, but might lead to different predictions for individual patients. Furthermore, data-dependent modelling may lead to biased parameter estimates and can result in underestimating the length of confidence intervals. In the framework of the linear regression model we account for model selection uncertainty by averaging over a set of possible models using weights estimated from bootstrap resampling (Buckland et al, 1997 & Augustin et al, 2002. Results are compared to those obtained in the full model, by common backward selection strategies and bootstrap averaging (Breiman, 1996). For illustration we use an example from the literature (e.g. Hoeting et al., 1999) on the prediction of the percentage of body fat. The different approaches will be compared in a simulation study. We consider a model with 10 covariates (7 of them with an influence on the outcome), but will also present results from investigations with a larger number of noise variables (e.g. 25 covariates, 18 noise variables). Based on validation data we consider the bias, the mean squared error and the coverage in order to assess all approaches.
In this note we provide explicit expressions and expansions for a special function J which appear... more In this note we provide explicit expressions and expansions for a special function J which appears in nonparametric estimation of log-densities. This function returns the integral of a log-linear function on a simplex of arbitrary dimension. In particular it is used in the R-package ...
We derive multiscale statistics for deconvolution in order to detect qualitative features of the ... more We derive multiscale statistics for deconvolution in order to detect qualitative features of the unknown density. An important example covered within this framework is to test for local monotonicity on all scales simultaneously. The errors in the deconvolution model are restricted to a certain class of distributions that include Laplace, Gamma and Exponential random variables. Our approach relies on inversion
Institute of Mathematical Statistics Lecture Notes - Monograph Series, 2007
lemma is an analytical result which implies √ n-consistency of the distribution function correspo... more lemma is an analytical result which implies √ n-consistency of the distribution function corresponding to the Grenander [Skand. Aktuarietidskr. 39 (1956) 125-153] estimator of a non-decreasing probability density. The present paper derives analogous results for the setting of convex densities on [0, ∞).
Many preschool children have wheeze or cough, but only some have asthma later. Existing predictio... more Many preschool children have wheeze or cough, but only some have asthma later. Existing prediction tools are difficult to apply in clinical practice or exhibit methodological weaknesses. We sought to develop a simple and robust tool for predicting asthma at school age in preschool children with wheeze or cough. From a population-based cohort in Leicestershire, United Kingdom, we included 1- to 3-year-old subjects seeing a doctor for wheeze or cough and assessed the prevalence of asthma 5 years later. We considered only noninvasive predictors that are easy to assess in primary care: demographic and perinatal data, eczema, upper and lower respiratory tract symptoms, and family history of atopy. We developed a model using logistic regression, avoided overfitting with the least absolute shrinkage and selection operator penalty, and then simplified it to a practical tool. We performed internal validation and assessed its predictive performance using the scaled Brier score and the area under the receiver operating characteristic curve. Of 1226 symptomatic children with follow-up information, 345 (28%) had asthma 5 years later. The tool consists of 10 predictors yielding a total score between 0 and 15: sex, age, wheeze without colds, wheeze frequency, activity disturbance, shortness of breath, exercise-related and aeroallergen-related wheeze/cough, eczema, and parental history of asthma/bronchitis. The scaled Brier scores for the internally validated model and tool were 0.20 and 0.16, and the areas under the receiver operating characteristic curves were 0.76 and 0.74, respectively. This tool represents a simple, low-cost, and noninvasive method to predict the risk of later asthma in symptomatic preschool children, which is ready to be tested in other populations.
Let (X, Y ) be a random variable consisting of an observed feature vector X ∈ X and an unobserved... more Let (X, Y ) be a random variable consisting of an observed feature vector X ∈ X and an unobserved class label Y ∈ {1, 2, . . . , L} with unknown joint distribution. In addition, let D be a training data set consisting of n completely observed independent copies of (X, Y ). Usual classification procedures provide point predictors (classifiers) Y (X, D) of Y or estimate the conditional distribution of Y given X. In order to quantify the certainty of classifying X we propose to construct for each θ = 1, 2, . . . , L a p-value π θ (X, D) for the null hypothesis that Y = θ, treating Y temporarily as a fixed parameter. In other words, the point predictor Y (X, D) is replaced with a prediction region for Y with a certain confidence. We argue that (i) this approach is advantageous over traditional approaches and (ii) any reasonable classifier can be modified to yield nonparametric p-values. We discuss issues such as optimality, single use and multiple use validity, as well as computational and graphical aspects.
The brain is capable of taking up monocarboxylates as energy substrates. Under physiological cond... more The brain is capable of taking up monocarboxylates as energy substrates. Under physiological conditions, plasma levels of monocarboxylates are very low and glucose is the primary energy substrate in brain metabolism. However, given conditions such as hyperglycemia and ketosis, levels of circulating monocarboxylates such as lactate and pyruvate are elevated. Previous studies reported an increased expression of monocarboxylate transporter MCT1 in brain following ketotic diet. The major aim of the present study was to answer the question whether chronic hyperglycemia is likewise sufficient to change local densities of MCT1 in the brain. Moreover, chronic hyperglycemia increases local cerebral glucose utilization (LCGU) in particular brain areas. Glucose hereby enters the brain parenchyma via glucose transporters and is partially metabolised by astrocytes, which then release lactate to meet the energetic demands of surrounding neurons. Streptozotocin was given intravenously to induce chronic hyperglycemia and local densities of MCT1 were measured by immunoautoradiographic methods in cryosections of rat brains. The density of monocarboxylate transporter MCT1 was significantly increased in 10 of 24 brain structures investigated (median increase 11.7 ± 3.4 %).
. Whereas acute hyperglycemia has been shown to result in an unchanged local cerebral glucose uti... more . Whereas acute hyperglycemia has been shown to result in an unchanged local cerebral glucose utilization LCGU the changes of Ž . LCGU during chronic hyperglycemia are a matter of dispute. The present study had three aims: 1 To compare the effects of acute and Ž . chronic hyperglycemia on LCGU and to investigate in vivo the lactate level as a potential indicator of glycolytic flux. 2 To investigate Ž . local changes in brain Glut1 andror Glut3 glucose transporter densities during chronic hyperglycemia. 3 To analyze the relationship between LCGU and local Glut densities during chronic hyperglycemia. To induce chronic hyperglycemia in rats steptozotocin was given w 14 x i.p. and experiments were performed 3 weeks later. LCGU was measured by the 2 y C deoxyglucose method and intraparenchymal lactate concentration by MR-spectroscopy. Local densities of the glucose transport proteins were determined by immunoautoradiographic methods. During chronic hyperglycemia weighted average of LCGU increased by 13.9% whereas it remained unchanged during acute hyperglycemia. The cerebral lactatercholine ratio was increased by 143% during chronic hyperglycemia. The average density of glucose transporters Glut1 decreased by 7.5%. Local densities of Glut1 were decreased in 12 of 28 brain structures. Glut3 remained unchanged. Positive correlations were found between LCGU and local Glut densities during control conditions and during chronic hyperglycemia. It Ž . Ž . was concluded that 1 Chronic, but not acute hyperglycemia is followed by an increased LCGU. 2 The capacity to transport glucose is Ž . decreased during chronic hyperglycemia. 3 Increased LCGU and decreased densities of Glut1 are matched on a local level. q
The present study addresses the question whether a chronic decrease of plasma glucose concentrati... more The present study addresses the question whether a chronic decrease of plasma glucose concentration for 1 week induces a global or local increase in glucose transporter densities Glut1 and Glut3 in the brain. To induce chronic hypoglycemia insulin was infused into rats Ž by osmotic minipumps for 1 week resulting in a mean plasma glucose concentration of 3.1 " 0.5 mmolrl control group: 8.1 " 0.5 . mmolrl . Global and local densities of Glut1 and Glut3 glucose transporters were measured by immunoautoradiographic methods. The mean density of glucose transporters Glut1 remained unchanged, whereas the mean density of Glut3 increased slightly, although significantly. To determine whether the increased density of Glut3 is related to a change in glucose metabolism, the local cerebral Ž . metabolic rate of glucose lCMR was quantified by the 2-deoxyglucose method. Mean glucose utilization was decreased by 15%. glc Ž . Local analysis of transporter densities Glut1 and Glut3 and glucose utilization showed a significant correlation between local glucose Ž . transporter densities Glut1 and Glut3 and lCMR during hypoglycemia as already previously observed during normoglycemia. It is glc concluded that 1 week of hypoglycemia is a stimulus for the induction of additional glucose transporters Glut3 in the brain. These additional neuronal glucose transporters may support the maintenance of glucose utilization which is not completely maintained under these conditions. q
In the analysis of many medical studies variable selection methods are applied in order to select... more In the analysis of many medical studies variable selection methods are applied in order to select one final model, which includes only prognostic factors or covariates with an influence on the outcome. However, often several models fit the data equally well, but might lead to different predictions for individual patients. Furthermore, data-dependent modelling may lead to biased parameter estimates and can result in underestimating the length of confidence intervals. In the framework of the linear regression model we account for model selection uncertainty by averaging over a set of possible models using weights estimated from bootstrap resampling (Buckland et al, 1997 & Augustin et al, 2002. Results are compared to those obtained in the full model, by common backward selection strategies and bootstrap averaging (Breiman, 1996). For illustration we use an example from the literature (e.g. Hoeting et al., 1999) on the prediction of the percentage of body fat. The different approaches will be compared in a simulation study. We consider a model with 10 covariates (7 of them with an influence on the outcome), but will also present results from investigations with a larger number of noise variables (e.g. 25 covariates, 18 noise variables). Based on validation data we consider the bias, the mean squared error and the coverage in order to assess all approaches.
In this note we provide explicit expressions and expansions for a special function J which appear... more In this note we provide explicit expressions and expansions for a special function J which appears in nonparametric estimation of log-densities. This function returns the integral of a log-linear function on a simplex of arbitrary dimension. In particular it is used in the R-package ...
Uploads
Papers by Lutz Duembgen