Christian Lavergne

Sensitivity analysis in presence of model uncertainty and correlated inputs

The first motivation of this work is to take into account model uncertainty in sensitivity analysis (SA). We present with some examples, a methodology to treat uncertainty due to a mutation of the studied model. Development of this methodology has highlighted an important problem, frequently encountered in SA: how to interpret sensitivity indices when random inputs are non-independent? This paper suggests a strategy for the problem of SA of models with non-independent random inputs. We propose a new application of the multidimensional generalization of classical sensitivity indices, resulting from group sensitivities (sensitivity of the output of the model to a group of inputs), and describe an estimation method based on Monte-Carlo simulations. Practical and theoretical applications illustrate the interest of this method.

Identifying ontogenetic, environmental and individual components of forest tree growth

BACKGROUND AND AIMS This study aimed to identify and characterize the ontogenetic, environmental and individual components of forest tree growth. In the proposed approach, the tree growth data typically correspond to the retrospective measurement of annual shoot characteristics (e.g. length) along the trunk. METHODS Dedicated statistical models (semi-Markov switching linear mixed models) were applied to data sets of Corsican pine and sessile oak. In the semi-Markov switching linear mixed models estimated from these data sets, the underlying semi-Markov chain represents both the succession of growth phases and their lengths, while the linear mixed models represent both the influence of climatic factors and the inter-individual heterogeneity within each growth phase. KEY RESULTS On the basis of these integrative statistical models, it is shown that growth phases are not only defined by average growth level but also by growth fluctuation amplitudes in response to climatic factors and inter-individual heterogeneity and that the individual tree status within the population may change between phases. Species plasticity affected the response to climatic factors while tree origin, sampling strategy and silvicultural interventions impacted inter-individual heterogeneity. CONCLUSIONS The transposition of the proposed integrative statistical modelling approach to cambial growth in relation to climatic factors and the study of the relationship between apical growth and cambial growth constitute the next steps in this research.

Multi-scale spatial sensitivity analysis of a model for economic appraisal of flood risk management policies

We demonstrate the use of sensitivity analysis to rank sources of uncertainty in models for economic appraisal of flood risk management policies, taking into account spatial scale issues. A methodology of multi-scale variance-based global sensitivity analysis is developed, and illustrated on the NOE model on the Orb River, France. The variability of the amount of expected annual flood avoided damages, and the associated sensitivity indices, are estimated over different spatial supports, ranging from small cells to the entire floodplain. Both uncertainty maps and sensitivity maps are produced to identify the key input variables in the NOE model at different spatial scales. Our results show that on small spatial supports, variance of the output indicator is mainly due to the water depth maps and the assets map (spatially distributed model inputs), while on large spatial supports, it is mainly due to the flood frequencies and depth-damage curves (non spatial inputs).

Markov and Semi-Markov Switching Linear Mixed Models Used to Identify Forest Tree Growth Components

Tree growth is assumed to be mainly the result of three components: (i) an endogenous component assumed to be structured as a succession of roughly stationary phases separated by marked change points that are asynchronous among individuals, (ii) a time-varying environmental component assumed to take the form of synchronous fluctuations among individuals, and (iii) an individual component corresponding mainly to the local environment of each tree. To identify and characterize these three components, we propose to use semi-Markov switching linear mixed models, i.e., models that combine linear mixed models in a semi-Markovian manner. The underlying semi-Markov chain represents the succession of growth phases and their lengths (endogenous component) whereas the linear mixed models attached to each state of the underlying semi-Markov chain represent-in the corresponding growth phase-both the influence of time-varying climatic covariates (environmental component) as fixed effects, and interindividual heterogeneity (individual component) as random effects. In this article, we address the estimation of Markov and semi-Markov switching linear mixed models in a general framework. We propose a Monte Carlo expectation-maximization like algorithm whose iterations decompose into three steps: (i) sampling of state sequences given random effects, (ii) prediction of random effects given state sequences, and (iii) maximization. The proposed statistical modeling approach is illustrated by the analysis of successive annual shoots along Corsican pine trunks influenced by climatic covariates.

What Patients Can Tell Us: Topic Analysis for Social Media on Breast Cancer

Background Social media dedicated to health are increasingly used by patients and health professionals. They are rich textual resources with content generated through free exchange between patients. We are proposing a method to tackle the problem of retrieving clinically relevant information from such social media in order to analyze the quality of life of patients with breast cancer. Objective Our aim was to detect the different topics discussed by patients on social media and to relate them to functional and symptomatic dimensions assessed in the internationally standardized self-administered questionnaires used in cancer clinical trials (European Organization for Research and Treatment of Cancer [EORTC] Quality of Life Questionnaire Core 30 [QLQ-C30] and breast cancer module [QLQ-BR23]). Methods First, we applied a classic text mining technique, latent Dirichlet allocation (LDA), to detect the different topics discussed on social media dealing with breast cancer. We applied the LDA model to 2 datasets composed of messages extracted from public Facebook groups and from a public health forum (cancerdusein.org, a French breast cancer forum) with relevant preprocessing. Second, we applied a customized Jaccard coefficient to automatically compute similarity distance between the topics detected with LDA and the questions in the self-administered questionnaires used to study quality of life. Results Among the 23 topics present in the self-administered questionnaires, 22 matched with the topics discussed by patients on social media. Interestingly, these topics corresponded to 95% (22/23) of the forum and 86% (20/23) of the Facebook group topics. These figures underline that topics related to quality of life are an important concern for patients. However, 5 social media topics had no corresponding topic in the questionnaires, which do not cover all of the patients’ concerns. Of these 5 topics, 2 could potentially be used in the questionnaires, and these 2 topics corresponded to a total of 3.10% (523/16,868) of topics in the cancerdusein.org corpus and 4.30% (3014/70,092) of the Facebook corpus. Conclusions We found a good correspondence between detected topics on social media and topics covered by the self-administered questionnaires, which substantiates the sound construction of such questionnaires. We detected new emerging topics from social media that can be used to complete current self-administered questionnaires. Moreover, we confirmed that social media mining is an important source of information for complementary analysis of quality of life.

Change of Support in Spatial Variance-Based Sensitivity Analysis

Variance-based global sensitivity analysis (GSA) is used to study how the variance of the output of a model can be apportioned to different sources of uncertainty in its inputs. GSA is an essential component of model building as it helps to identify model inputs that account for most of the model output variance. However, this approach is seldom applied to spatial models because it cannot describe how uncertainty propagation interacts with another key issue in spatial modeling: the issue of model upscaling, that is, a change of spatial support of model output. In many environmental models, the end user is interested in the spatial average or the sum of the model output over a given spatial unit (for example, the average porosity of a geological block). Under a change of spatial support, the relative contribution of uncertain model inputs to the variance of aggregated model output may change. We propose a simple formalism to discuss this issue within a GSA framework by defining point and block sensitivity indices. We show that the relative contribution of an uncertain spatially distributed model input increases with its correlation length and decreases with the size of the spatial unit considered for model output aggregation. The results are briefly illustrated by a simple example.

A mixture model-based approach to the clustering of exponential repeated data

The analysis of finite mixture models for exponential repeated data is considered. The mixture components correspond to different unknown groups of the statistical units. Dependency and variability of repeated data are taken into account through random effects. For each component, an exponential mixed model is thus defined. When considering parameter estimation in this mixture of exponential mixed models, the EM-algorithm cannot be directly used since the marginal distribution of each mixture component cannot be analytically derived. In this paper, we propose two parameter estimation methods. The first one uses a linearisation specific to the exponential distribution hypothesis within each component. The second approach uses a Metropolis-Hastings algorithm as a building block of a general MCEM-algorithm.

Applying the Longitudinal Model from Item Response Theory to Assess Health-Related Quality of Life in the PRODIGE 4/ACCORD 11 Randomized Trial.

Introduction. A new longitudinal statistical approach was compared to the classical methods currently used to analyze health-related quality-of-life (HRQoL) data. The comparison was made using data in patients with metastatic pancreatic cancer. Methods. Three hundred forty-two patients from the PRODIGE4/ACCORD 11 study were randomly assigned to FOLFIRINOX versus gemcitabine regimens. HRQoL was evaluated using the European Organization for Research and Treatment of Cancer (EORTC) QLQ-C30. The classical analysis uses a linear mixed model (LMM), considering an HRQoL score as a good representation of the true value of the HRQoL, following EORTC recommendations. In contrast, built on the item response theory (IRT), our approach considered HRQoL as a latent variable directly estimated from the raw data. For polytomous items, we extended the partial credit model to a longitudinal analysis (longitudinal partial credit model [LPCM]), thereby modeling the latent trait as a function of time and other covariates. Results. Both models gave the same conclusions on 11 of 15 HRQoL dimensions. HRQoL evolution was similar between the 2 treatment arms, except for the symptoms of pain. Indeed, regarding the LPCM, pain perception was significantly less important in the FOLFIRINOX arm than in the gemcitabine arm. For most of the scales, HRQoL changes over time, and no difference was found between treatments in terms of HRQoL. Discussion. The use of LMM to study the HRQoL score does not seem appropriate. It is an easy-to-use model, but the basic statistical assumptions do not check. Our IRT model may be more complex but shows the same qualities and gives similar results. It has the additional advantage of being more precise and suitable because of its direct use of raw data.

Learning and inference in mixed-state conditionally heteroskedastic factor models using viterbi approximation

In this paper we develop a new approach within the framework of asset pricing models that incorporates two key features of the latent volatility: co-movement among conditionally heteroskedastic financial returns and switching between different unobservable regimes. By combining conditionally heteroskedastic factor models with hidden Markov chain models (HMM), we derive a dynamical local model for segmentation and prediction of multivariate conditionally heteroskedastic financial time series. The EM algorithm that we have developed for the maximum likelihood estimation, is based on a Viterbi approximation which yields inferences about the unobservable path of the common factors, their variances and the latent variable of the state process. Extensive Monte Carlo simulations and preliminary experiments obtained with a dataset on weekly average returns of closing spot prices for eight European currencies show promising results.

Item response models for the longitudinal analysis of health-related quality of life in cancer clinical trials

BackgroundThe use of health-related quality of life (HRQoL) as an endpoint in cancer clinical trials is growing rapidly. Hence, research into the statistical approaches used to analyze HRQoL data is of major importance, and could lead to a better understanding of the impact of treatments on the everyday life and care of patients. Amongst the models that are used for the longitudinal analysis of HRQoL, we focused on the mixed models from item response theory, to directly analyze raw data from questionnaires.MethodsWe reviewed the different item response models for ordinal responses, using a recent classification of generalized linear models for categorical data. Based on methodological and practical arguments, we then proposed a conceptual selection of these models for the longitudinal analysis of HRQoL in cancer clinical trials.ResultsTo complete comparison studies already present in the literature, we performed a simulation study based on random part of the mixed models, so to compare the linear mixed model classically used to the selected item response models. As expected, the sensitivity of the item response models to detect random effects with lower variance is better than that of the linear mixed model. We then used a cumulative item response model to perform a longitudinal analysis of HRQoL data from a cancer clinical trial.ConclusionsAdjacent and cumulative item response models seem particularly suitable for HRQoL analysis. In the specific context of cancer clinical trials and the comparison between two groups of HRQoL data over time, the cumulative model seems to be the most suitable, given that it is able to generate a more complete set of results and gives an intuitive illustration of the data.