Abstract—Among the diseases with high treatment costs, oncologic and cardiovascular diseases are nowadays the main causes of death in Portugal as in many other high income per capita countries. This situation is a challenge for health insurance companies and financial institutions. Although there is currently some affordable health insurance in case of severe diseases, such as cardiovascular disorders or cancer, the available capital is easily depleted. The study of costs associated with many serious diseases shows that very often lognormal distribution fits well to the costs distribution. Therefore, a simulation study was made to compare different interval estimation methods of the average cost of a lognormal distribution. This work compares bootstrap parametric and non-parametric methodologies with Cox and large sample normal based methods and the results were applied to a breast cancer Portuguese dataset. Furthermore, for the lognormal distribution, a correction to the truncated values of costs following capital depletion is proposed, and the impact of this correction illustrated via its application to a heart failure dataset.

Index Terms—Bootstrap, confidence interval, costs distribution, heart and cancer diseases, lognormal distribution.

Marli Amorim is with Multicare - Health Insurer, Portugal, Lisbon (email: marli.amorim.ferreira@multicare.pt).
Joana Fernandes is with Faculty of Sciences at the University of Lisbon, Portugal, Lisbon. She is also with Multicare - Health Insurer, Portugal, Lisbon.
Teresa Alpuim is with Faculty of Sciences at the University of Lisbon, Portugal, Lisbon.

Cite: Marli Amorim, Joana Fernandes, Teresa Alpuim, "Lognormal Distribution in Health Insurance: Interval Estimation Methods for the Average Cost and Correction of Truncated Values," International Journal of Applied Physics and Mathematics vol. 9, no. 2, pp. 101-110, 2019.