Subsampling under distributional constraintsJournal articleFlorian Combes, Ricardo Fraiman and Badih Ghattas, Statistical Analysis and Data Mining: The ASA Data Science Journal, Volume 17, Issue 1, pp. e11661, 2024

Some complex models are frequently employed to describe physical and mechanical phenomena. In this setting, we have an input X\ X \ in a general space, and an output Y=f(X)\ Y=f(X) \ where f\ f \ is a very complicated function, whose computational cost for every new input is very high, and may be also very expensive. We are given two sets of observations of X\ X \, S1\ S_1 \ and S2\ S_2 \ of different sizes such that only fS1\ f\left(S_1\right) \ is available. We tackle the problem of selecting a subset S3⊂S2\ S_3\subset S_2 \ of smaller size on which to run the complex model f\ f \, and such that the empirical distribution of fS3\ f\left(S_3\right) \ is close to that of fS1\ f\left(S_1\right) \. We suggest three algorithms to solve this problem and show their efficiency using simulated datasets and the Airfoil self-noise data set.

Machine Learning Alternatives to Response Surface ModelsJournal articleBadih Ghattas and Diane Manzon, Mathematics, Volume 11, Issue 15, pp. 3406, 2023

In the Design of Experiments, we seek to relate response variables to explanatory factors. Response Surface methodology (RSM) approximates the relation between output variables and a polynomial transform of the explanatory variables using a linear model. Some researchers have tried to adjust other types of models, mainly nonlinear and nonparametric. We present a large panel of Machine Learning approaches that may be good alternatives to the classical RSM approximation. The state of the art of such approaches is given, including classification and regression trees, ensemble methods, support vector machines, neural networks and also direct multi-output approaches. We survey the subject and illustrate the use of ten such approaches using simulations and a real use case. In our simulations, the underlying model is linear in the explanatory factors for one response and nonlinear for the others. We focus on the advantages and disadvantages of the different approaches and show how their hyperparameters may be tuned. Our simulations show that even when the underlying relation between the response and the explanatory variables is linear, the RSM approach is outperformed by the direct neural network multivariate model, for any sample size (<50) and much more for very small samples (15 or 20). When the underlying relation is nonlinear, the RSM approach is outperformed by most of the machine learning approaches for small samples (n ≤ 30).

Looking for a hyper polyhedron within the multidimensional space of Design Space from the results of Designs of ExperimentsJournal articleDiane Manzon, Badih Ghattas, Magalie Claeys-Bruno, Sophie Declomesnil, Christophe Carité and Michelle Sergent, Chemometrics and Intelligent Laboratory Systems, Volume 232, pp. 104712, 2023

In pharmaceutical studies, the Quality by Design (QbD) approach is increasingly being implemented to improve product development. Product quality is tested at each step of the manufacturing process, allowing a better process understanding and a better risk management, thus avoiding manufacturing defects. A key element of QbD is the construction of a Design Space (DS), i.e., a region in which the specifications on the output parameters should be met. Among the various possible construction methods, Designs of Experiments (DoE), and more precisely Response Surface Methodology, represent a perfectly adapted tool. The DS obtained may have any geometrical shape; consequently, the acceptable variation range of an input may depend on the value of other inputs. However, the experimenters would like to directly know the variation range of each input so that their variation domains are independent. In this context, we developed a method to determine the “Proven Acceptable Independent Range” (PAIR). It consists of looking for all the hyper polyhedra included in the multidimensional DS and selecting a hyper polyhedron according to various strategies. We will illustrate the performance of our method on different DoE cases.

We introduce a new clustering procedure specialized for Big Data. It is inspired by the work of [1], and applies a MapReduce procedure for any base clustering algorithm, split-ting the data set at hand, clustering subsamples, and combining intermediate results. We use thus a high level parallelization running a base clustering approach on small samples. We analyse in detail our approach exploring various alternatives and showing its efficiency by simulations.

Modernizing quality of life assessment: development of a multidimensional computerized adaptive questionnaire for patients with schizophreniaJournal articlePierre Michel, Karine Baumstarck, Christophe Lançon, Badih Ghattas, Anderson Loundou, Pascal Auquier and Laurent Boyer, Quality of Life Research: An International Journal of Quality of Life Aspects of Treatment, Care and Rehabilitation, Volume 27, Issue 4, pp. 1041-1054, 2018

OBJECTIVE: Quality of life (QoL) is still assessed using paper-based and fixed-length questionnaires, which is one reason why QoL measurements have not been routinely implemented in clinical practice. Providing new QoL measures that combine computer technology with modern measurement theory may enhance their clinical use. The aim of this study was to develop a QoL multidimensional computerized adaptive test (MCAT), the SQoL-MCAT, from the fixed-length SQoL questionnaire for patients with schizophrenia.
METHODS: In this multicentre cross-sectional study, we collected sociodemographic information, clinical characteristics (i.e., duration of illness, the PANSS, and the Calgary Depression Scale), and quality of life (i.e., SQoL). The development of the SQoL-CAT was divided into three stages: (1) multidimensional item response theory (MIRT) analysis, (2) multidimensional computerized adaptive test (MCAT) simulations with analyses of accuracy and precision, and (3) external validity.
RESULTS: Five hundred and seventeen patients participated in this study. The MIRT analysis found that all items displayed good fit with the multidimensional graded response model, with satisfactory reliability for each dimension. The SQoL-MCAT was 39% shorter than the fixed-length SQoL questionnaire and had satisfactory accuracy (levels of correlation >0.9) and precision (standard error of measurement <0.55 and root mean square error <0.3). External validity was confirmed via correlations between the SQoL-MCAT dimension scores and symptomatology scores.
CONCLUSION: The SQoL-MCAT is the first computerized adaptive QoL questionnaire for patients with schizophrenia. Tailored for patient characteristics and significantly shorter than the paper-based version, the SQoL-MCAT may improve the feasibility of assessing QoL in clinical practice.

Clustering based on unsupervised binary trees to define subgroups of cancer patients according to symptom severity in cancerJournal articlePierre Michel, Zeinab Hamidou, Karine Baumstarck, Badih Ghattas, Noémie Resseguier, Olivier Chinot, Fabrice Barlesi, Sébastien Salas, Laurent Boyer and Pascal Auquier, Quality of Life Research: An International Journal of Quality of Life Aspects of Treatment, Care and Rehabilitation, Volume 27, Issue 2, pp. 555-565, 2018

Studies have suggested that clinicians do not feel comfortable with the interpretation of symptom severity, functional status, and quality of life (QoL). Implementation strategies of these types of measurements in clinical practice imply that consensual norms and guidelines regarding data interpretation are available. The aim of this study was to define subgroups of patients according to the levels of symptom severity using a method of interpretable clustering that uses unsupervised binary trees.

The patients were classified using a top-down hierarchical method: Clustering using Unsupervised Binary Trees (CUBT). We considered a three-group structure: "high", "moderate", and "low" level of symptom severity. The clustering tree was based on three stages using the 9-symptom scale scores of the EORTC QLQ-C30: a maximal tree was first developed by applying a recursive partitioning algorithm; the tree was then pruned using a criterion of minimal dissimilarity; finally, the most similar clusters were joined together. Inter-cluster comparisons were performed to test the sample partition and QoL data.

Two hundred thirty-five patients with different types of cancer were included. The three-cluster structure classified 143 patients with "low", 46 with "moderate", and 46 with "high" levels of symptom severity. This partition was explained by cut-off values on Fatigue and Appetite Loss scores. The three clusters consistently differentiated patients based on the clinical characteristics and QoL outcomes.

Our study suggests that CUBT is relevant to define the levels of symptom severity in cancer. This finding may have important implications for helping clinicians to interpret symptom profiles in clinical practice, to identify individuals at risk for poorer outcomes and implement targeted interventions.

Computerized adaptive testing with decision regression trees: an alternative to item response theory for quality of life measurement in multiple sclerosisJournal articlePierre Michel, Karine Baumstarck, Anderson Loundou, Badih Ghattas, Pascal Auquier and Laurent Boyer, Patient Preference and Adherence, Volume 12, pp. 1043-1053, 2018

The aim of this study was to propose an alternative approach to item response theory (IRT) in the development of computerized adaptive testing (CAT) in quality of life (QoL) for patients with multiple sclerosis (MS). This approach relied on decision regression trees (DRTs). A comparison with IRT was undertaken based on precision and validity properties.

Materials and methods:
DRT- and IRT-based CATs were applied on items from a unidi-mensional item bank measuring QoL related to mental health in MS. The DRT-based approach consisted of CAT simulations based on a minsplit parameter that defines the minimal size of nodes in a tree. The IRT-based approach consisted of CAT simulations based on a specified level of measurement precision. The best CAT simulation showed the lowest number of items and the best levels of precision. Validity of the CAT was examined using sociodemographic, clinical and QoL data.

CAT simulations were performed using the responses of 1,992 MS patients. The DRT-based CAT algorithm with minsplit = 10 was the most satisfactory model, superior to the best IRT-based CAT algorithm. This CAT administered an average of nine items and showed satisfactory precision indicators (R = 0.98, root mean square error [RMSE] = 0.18). The DRT-based CAT showed convergent validity as its score correlated significantly with other QoL scores and showed satisfactory discriminant validity.
Conclusion: We presented a new adaptive testing algorithm based on DRT, which has equivalent level of performance to IRT-based approach. The use of DRT is a natural and intuitive way to develop CAT, and this approach may be an alternative to IRT.

Clustering nominal data using unsupervised binary decision trees: Comparisons with the state of the art methodsJournal articleBadih Ghattas, Pierre Michel and Laurent Boyer, Pattern Recognition, Volume 67, pp. 177-185, 2017

In this work, we propose an extension of CUBT (clustering using unsupervised binary trees) to nominal data. For this purpose, we primarily use heterogeneity criteria and dissimilarity measures based on mutual information, entropy and Hamming distance. We show that for this type of data, CUBT outperforms most of the existing methods. We also provide and justify some guidelines and heuristics to tune the parameters in CUBT. Extensive comparisons are done with other well known approaches using simulations, and two examples of real datasets applications are given.

Defining Quality of Life Levels to Enhance Clinical Interpretation in Multiple Sclerosis: Application of a Novel Clustering MethodJournal articlePierre Michel, Karine Baumstarck, Laurent Boyer, Oscar Fernandez, Peter Flachenecker, Jean Pelletier, Anderson Loundou, Badih Ghattas, Pascal Auquier and on behalf of Group, Medical Care, Volume 55, Issue 1, pp. e1, 2017

To enhance the use of quality of life (QoL) measures in clinical practice, it is pertinent to help clinicians interpret QoL scores.

The aim of this study was to define clusters of QoL levels from a specific questionnaire (MusiQoL) for multiple sclerosis (MS) patients using a new method of interpretable clustering based on unsupervised binary trees and to test the validity regarding clinical and functional outcomes.

In this international, multicenter, cross-sectional study, patients with MS were classified using a hierarchical top-down method of Clustering using Unsupervised Binary Trees. The clustering tree was built using the 9 dimension scores of the MusiQoL in 2 stages, growing and tree reduction (pruning and joining). A 3-group structure was considered, as follows: “high,” “moderate,” and “low” QoL levels. Clinical and QoL data were compared between the 3 clusters.

A total of 1361 patients were analyzed: 87 were classified with “low,” 1173 with “moderate,” and 101 with “high” QoL levels. The clustering showed satisfactory properties, including repeatability (using bootstrap) and discriminancy (using factor analysis). The 3 clusters consistently differentiated patients based on sociodemographic and clinical characteristics, and the QoL scores were assessed using a generic questionnaire, ensuring the clinical validity of the clustering.

The study suggests that Clustering using Unsupervised Binary Trees is an original, innovative, and relevant classification method to define clusters of QoL levels in MS patients.

A Multidimensional Computerized Adaptive Short-Form Quality of Life Questionnaire Developed and Validated for Multiple Sclerosis: The MusiQoL-MCATJournal articlePierre Michel, Karine Baumstarck, Badih Ghattas, Jean Pelletier, Anderson Loundou, Mohamed Boucekine, Pascal Auquier and Laurent Boyer, Medicine, Volume 95, Issue 14, pp. e3068, 2016

The aim was to develop a multidimensional computerized adaptive short-form questionnaire, the MusiQoL-MCAT, from a fixed-length QoL questionnaire for multiple sclerosis.A total of 1992 patients were enrolled in this international cross-sectional study. The development of the MusiQoL-MCAT was based on the assessment of between-items MIRT model fit followed by real-data simulations. The MCAT algorithm was based on Bayesian maximum a posteriori estimation of latent traits and Kullback-Leibler information item selection. We examined several simulations based on a fixed number of items. Accuracy was assessed using correlations (r) between initial IRT scores and MCAT scores. Precision was assessed using the standard error measurement (SEM) and the root mean square error (RMSE).The multidimensional graded response model was used to estimate item parameters and IRT scores. Among the MCAT simulations, the 16-item version of the MusiQoL-MCAT was selected because the accuracy and precision became stable with 16 items with satisfactory levels (r ≥ 0.9, SEM ≤ 0.55, and RMSE ≤ 0.3). External validity of the MusiQoL-MCAT was satisfactory.The MusiQoL-MCAT presents satisfactory properties and can individually tailor QoL assessment to each patient, making it less burdensome to patients and better adapted for use in clinical practice.

Finding the best trade-off between performance and interpretability in predicting hospital length of stay using structured and unstructured dataJournal articleFranck Jaotombo, Luca Adorni, Badih Ghattas and Laurent Boyer, PLoS ONE, Volume 18, Issue 11, pp. e0289795, Forthcoming

Objective This study aims to develop high-performing Machine Learning and Deep Learning models in predicting hospital length of stay (LOS) while enhancing interpretability. We compare performance and interpretability of models trained only on structured tabular data with models trained only on unstructured clinical text data, and on mixed data. Methods The structured data was used to train fourteen classical Machine Learning models including advanced ensemble trees, neural networks and k-nearest neighbors. The unstructured data was used to fine-tune a pre-trained Bio Clinical BERT Transformer Deep Learning model. The structured and unstructured data were then merged into a tabular dataset after vectorization of the clinical text and a dimensional reduction through Latent Dirichlet Allocation. The study used the free and publicly available Medical Information Mart for Intensive Care (MIMIC) III database, on the open AutoML Library AutoGluon. Performance is evaluated with respect to two types of random classifiers, used as baselines. Results The best model from structured data demonstrates high performance (ROC AUC = 0.944, PRC AUC = 0.655) with limited interpretability, where the most important predictors of prolonged LOS are the level of blood urea nitrogen and of platelets. The Transformer model displays a good but lower performance (ROC AUC = 0.842, PRC AUC = 0.375) with a richer array of interpretability by providing more specific in-hospital factors including procedures, conditions, and medical history. The best model trained on mixed data satisfies both a high level of performance (ROC AUC = 0.963, PRC AUC = 0.746) and a much larger scope in interpretability including pathologies of the intestine, the colon, and the blood; infectious diseases, respiratory problems, procedures involving sedation and intubation, and vascular surgery. Conclusions Our results outperform most of the state-of-the-art models in LOS prediction both in terms of performance and of interpretability. Data fusion between structured and unstructured text data may significantly improve performance and interpretability.