Reconstruction automatique de formulaires d’enquête médicale sur la culture de sécurité des patients par une méthode de factorisation matricielle bayésienne

Diatta, B. Don Bosco; Ngom, Papa; Boussat, Bastien; François, Olivier

Journal de la société française de statistique, Tome 159 (2018) no. 2, pp. 111-127.

Certaines enquêtes de santé publique souffrent d’un problème d’acceptabilité auprès des personnes interrogées, en particulier à cause de la longueur des questionnaires. Pour aborder ce problème, nous proposons de réduire délibérément les questionnaires en les individualisant de manière randomisée. Afin de compléter automatiquement les questionnaires incomplets générés par cette procédure, nous considérons un modèle de factorisation matricielle bayésienne. Pour estimer les paramètres de ce modèle, nous proposons un algorithme combinant un échantillonneur de Gibbs et une approche variationnelle. En utilisant les résultats d’une enquête portant sur la culture de sécurité des patients réalisée au centre hospitalier universitaire de Grenoble auprès de 3888 travailleurs médicaux, nous comparons les performances de notre méthode à plusieurs approches classiques en santé publique, à la méthode des forêts aléatoires, ainsi qu’à trois autres méthodes de factorisation matricielle. L’erreur de reconstruction de notre algorithme est inférieure à celle des autres algorithmes lorsque la proportion d’items supprimés est supérieure à $40\%$. Lorsque la proportion d’items supprimés est moins élevée, les histogrammes des lois marginales sont reconstruits de manière satisfaisante. Pour ce second critère, la méthode des forêts aléatoires est la plus performante. En général, nos résultats suggèrent que des enquêtes médicales similaires à celle réalisée pour cet article pourraient réduire substantiellement le nombre de questions posées à chaque travailleur avec une perte d’information limitée pour l’interprétation des résultats.

Some public health surveys suffer from an issue of acceptability among respondents leading to a low response rate. To address this problem, we propose to reduce the length of individual questionnaires by randomly removing items. In order to impute the missing data, we introduce a Bayesian model for data imputation based on non-negative matrix factorization. We propose an inference algorithm combining a Gibbs sampler algorithm and a variational approach. Using the results of a survey on patient safety culture conducted at Grenoble University Hospital, we compare the performance of our new method with several classical approaches, with a random forest method, and with three additional matrix factorization methods. The average reconstruction error is lower than for other methods when the proportion of removed items is high (greater than $40\%$). With lower proportions of removed items (lower than $40\%$), the histograms of the marginal distributions are reconstructed satisfactorily. In this respect, the best performances were obtained with the random forest approach. Overall, our results suggest that similar surveys could be carried out by substantially reducing the number of questions asked to each worker with limited loss of information and interpretation.

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