Jointly conducted by UR and INSA Rennes, this research explores inference in zero-inflated count models.
Alpha Oumar Diallo, researcher at IRMAR (Université de Rennes).
Thesis defended in 2017 at the doctoral school École doctorale Mathématiques et sciences et technologies de l'information et de la communication (Rennes).
This research is the result of an international co-supervision between several partner institutions.
Referenced in the ABES/STAR network, this thesis meets the rigorous criteria of French higher education.
Zero-inflated regression models prove to be powerful and essential tools for analyzing count data, particularly in critical areas such as health economics. These models are specifically designed to handle situations where the data exhibit an excess of zeros, a situation frequently encountered in contexts such as the use of medical care. For example, in a study on access to care in certain regions of Benin, it was observed that many individuals do not utilize health services, resulting in a high number of zeros in the count data. This thesis, supported by the University of Rennes and INSA Rennes, addresses fundamental questions about inference in these models, focusing specifically on the zero-inflated binomial model.
The author, Alpha Oumar Diallo, rigorously demonstrates the existence of the maximum likelihood estimator in this model, as well as its consistency and asymptotic normality. These results are not only theoretical but are also validated by simulations on finite sample sizes, significantly enhancing the credibility of the adopted approach. Furthermore, an application to real data in health economics highlights practical aspects of this research. For instance, the analysis of data on medical consultations in public hospitals in Benin revealed interesting trends regarding the use of health services, underscoring the importance of these models in understanding health behaviors.
One of the strengths of this study is the development of a new model to analyze medical care consumption. This innovative model allows for the identification of the causes of non-utilization of care, a crucial issue for public health decision-makers. Indeed, understanding why certain populations do not access care can guide health policies and improve the efficiency of health systems. For example, factors such as geographical distance to health facilities, costs associated with care, or cultural beliefs can play a decisive role in access to care. By identifying these factors, decision-makers can implement targeted interventions to improve access to care.
The author also addresses the issue of missing data on covariates, a common problem in health studies. By proposing a weighting method based on the inverse of selection probabilities, he offers a relevant solution to ensure the robustness of the results. This approach is essential, especially in contexts where data are often incomplete, as is frequently the case in health surveys in West Africa. The numerical simulations conducted in this context demonstrate the effectiveness of this method, opening interesting perspectives for researchers and practitioners. For example, using this method, it would be possible to obtain more accurate estimates of health needs in vulnerable populations.
In summary, this research is not limited to a simple theoretical analysis. It proposes concrete tools and methods that can be applied in the health field, with direct implications for public policies. Decision-makers must take these results into account to improve access to care and optimize resources in the health sector. By integrating these models into health program evaluations, it would be possible to better target interventions and allocate resources more effectively. This could also contribute to reducing health inequalities, a major issue in many West African countries, including Benin. Ultimately, this thesis represents a significant advancement in the field of statistical inference applied to health economics, with implications that extend beyond the academic framework to directly impact the lives of populations.
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Sources and Access
Alpha Oumar Diallo. Inférence statistique dans des modèles de comptage à inflation de zéro. Applications en économie de la santé. Applications [stat.AP]. INSA de Rennes; Université de Saint-Louis (Sénégal), 2017. Français. ⟨NNT : 2017ISAR0027⟩. ⟨tel-01804894⟩