Probabilistic inconsistency correction for misclassification in statistical matching, with an example in health care

ABSTRACT

A recently proposed procedure for correcting inconsistent (i.e. incoherent) probability assessments is specifically tailored for the statistical matching problem with misclassification component. Such procedure is based on $L_1$ distance minimization encoded in mixed integer programming (MIP) problems and it results particularly apt to deal with assessments stemming from different sources of information. The statistical matching problem is one of those cases. The statistical matching problem has been recently studied also inside a misclassification setting. To proceed with a correction in such a framework, if marginal assessments on the conditioning event are wanted to remain fixed, the only possible solutions are the closest Fréchet–Hoeffding bounds for the misclassification probabilities. On the contrary, if also the marginal probabilities are allowed to be modified, the $L_1$-based procedure can be applied by a straightforward translation in an MIP problem. Such procedure is applied to a healthcare expenditures and health conditions data example.

KEYWORDS:

• Incoherence correction
• MIP programming
• statistical matching
• misclassification
• healthcare analysis

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Andrea Capotorti http://orcid.org/0000-0002-1337-8315

Additional information

Funding

This work was partially supported by the Universitá degli Studi di Perugia under grant “Operatori SMART per l'aggregazione fuzzy, anno finanziario 2015” and by Dipartimento di Matematica e Informatica – Universitá degli Studi di Perugia under grant “Fondo di funzionamento per la ricerca dipartimentale – Anno 2018”.

Notes on contributors

Andrea Capotorti

Andrea Capotorti received the M.Sc. degree in Mathematics (cum laude) and the Ph.D. degree in “Metodologia Statistica per la Ricerca Scientifica” (Statistics). He was Tenured Researcher in Probability and Mathematical Statistics from 2000 until 2016 and from 2017 he is Associate Professor in Mathematical Methods for Economy, Social and Actuarial Sciences at Università degli Studi di Perugia, Italy. Research interests are: Inference models based on partial conditional probability assessments; Coherence of probability assessments; Uncertainty measures; Qualitative uncertainty models. Since AY 1999/2000, teacher of several bachelor and master courses in Calculus, Probability and Statistics at the University of Perugia. He has job experience as software designer at SO.GE.I. spa (gruppo FINSIEL-STET).