Predicting Birth Weight with Conditionally Linear Transformation Models

Low and high birth weight (BW) are important risk factors for neonatal morbidity and mortality. Gynecologists must therefore accurately predict BW before delivery. Most prediction formulas for BW are based on prenatal ultrasound measurements carried out within one week prior to birth. Although successfully used in clinical practice, these formulas focus on point predictions of BW but do not systematically quantify uncertainty of the predictions, i.e. they result in estimates of the conditional mean of BW but do not deliver prediction intervals. To overcome this problem, we introduce conditionally linear transformation models (CLTMs) to predict BW. Instead of focusing only on the conditional mean, CLTMs model the whole conditional distribution function of BW given prenatal ultrasound parameters. Consequently, the CLTM approach delivers both point predictions of BW and fetus-specific prediction intervals. Prediction intervals constitute an easy-to-interpret measure of prediction accuracy and allow identification of fetuses subject to high prediction uncertainty. Using a data set of 8712 deliveries at the Perinatal Centre at the University Clinic Erlangen (Germany), we analyzed variants of CLTMs and compared them to standard linear regression estimation techniques used in the past and to quantile regression approaches. The best-performing CLTM variant was competitive with quantile regression and linear regression approaches in terms of conditional coverage and average length of the prediction intervals. We propose that CLTMs be used because they are able to account for possible heteroscedasticity, kurtosis, and skewness of the distribution of BWs

Most Likely Transformations

We propose and study properties of maximum likelihood estimators in the class of conditional transformation models. Based on a suitable explicit parameterisation of the unconditional or conditional transformation function, we establish a cascade of increasingly complex transformation models that can be estimated, compared and analysed in the maximum likelihood framework. Models for the unconditional or conditional distribution function of any univariate response variable can be set-up and estimated in the same theoretical and computational framework simply by choosing an appropriate transformation function and parameterisation thereof. The ability to evaluate the distribution function directly allows us to estimate models based on the exact likelihood, especially in the presence of random censoring or truncation. For discrete and continuous responses, we establish the asymptotic normality of the proposed estimators. A reference software implementation of maximum likelihood-based estimation for conditional transformation models allowing the same flexibility as the theory developed here was employed to illustrate the wide range of possible applications.Comment: Accepted for publication by the Scandinavian Journal of Statistics 2017-06-1

Conditional transformation models for survivor function estimation

In survival analysis, the estimation of patient-specific survivor functions that are conditional on a set of patient characteristics is of special interest. In general, knowledge of the conditional survival probabilities of a patient at all relevant time points allows better assessment of the patient’s risk than summary statistics, such as median survival time. Nevertheless, standard methods for analysing survival data seldom estimate the survivor function directly. Therefore, we propose the application of conditional transformation models (CTMs) for the estimation of the conditional distribution function of survival times given a set of patient characteristics. We used the inverse probability of censoring weighting approach to account for right-censored observations. Our proposed modelling approach allows the prediction of patient-specific survivor functions. In addition, CTMs constitute a flexible model class that is able to deal with proportional as well as non-proportional hazards. The well-known Cox model is included in the class of CTMs as a special case. We investigated the performance of CTMs in survival data analysis in a simulation that included proportional and non-proportional hazard settings and different scenarios of explanatory variables. Furthermore, we re-analysed the survival times of patients suffering from chronic myelogenous leukaemia and studied the impact of the proportional hazards assumption on previously published results

Creating a landscape of management: Unintended effects on the variation of browsing pressure in a national park

The principle objective of management in strictly protected areas, such as national parks, is to reduce human intervention as much as possible to secure natural assemblages and processes. As wildlife management in many national parks has to deal with increased ungulate populations and a broad lack of predators, park managers need to know how their wildlife management, including feeding and hunting, disturbs ungulate behaviour, which in turn might affect natural processes. One measure for this effect is the spatial distribution of browsing pressure in the landscape. Here we measured the browsing activity of ungulates on 5841 vegetation plots in the montane Bavarian Forest National Park to test the hypothesis that browsing in the landscape is mostly influenced by environmental covariables not related to park management. The survey revealed a browsing intensity that allows regrowth of tree species most palatable for ungulates. A comparison of different predictor sets in our spatial additive logistic regression models for silver fir, common rowan and European beech revealed that management activities and space are most important in explaining the variation in browsing level. These quantitative results underline that management activities are of major relevance for the variation of browsing intensity. Thereby, these activities shape a landscape of management that strongly contrasts the aims of the national park to reduce anthropogenic influence on natural processes. We therefore urge all park managers to carefully reconsider the necessity and effect of their management activities, especially of winter feeding, deer control areas and hiking trails

Toward a fundamental understanding of flow-based market coupling for cross-border electricity trading

Trading electricity across market zones furthers competitive power prices, security of supply and the integration of renewable energy. In the European Union, flow-based market coupling is the target model to compute correct trading capacities between markets, while approximating physical grid constraints. The methodology relies on predictive, carefully designed parameters to maximize trading opportunities, while keeping congestion management at acceptable levels. This paper explains the fundamentals of flow-based market coupling. It provides an open-access model based on a test network and its data. By providing a guide to the theory and conducting several case studies, the functioning and effects of the most influential parameters are demonstrated. Innovative aspects of this paper are its illustrative nature and its answer to the following research questions: (1) What is the effect of (a) generation shift keys and (b) threshold choice on the selection of critical network elements? (2) What is the effect of (a) generation shift keys, (b) selected critical network elements and (c) security margins on market coupling and congestion management results? It also addresses the effect of higher shares of renewable energy and minimum trading capacities on flow-based market coupling. This analysis shows that (1) the effects of flow reliability margins and selected critical network elements dominate the effect of generation shift keys on flow-based market coupling domains, (2) power systems with an increasing share of renewable energy may necessitate re-adjusted parameters and (3) minimum trading capacities can be guaranteed by redispatch or altering the base case