Modelling HIV/AIDS length of stay in Portugal

Tese apresentada como requisito parcial para obtenção do grau de Doutor em Estatística e Gestão de Informação pelo Instituto Superior de Estatística e Gestão de Informação da Universidade Nova de Lisboa

The introduction of highly active antiretroviral therapy (HAART) in late 1996 dramatically improved the prognosis of Human Immunodeficiency Virus (HIV) infected patients in most developed countries and also the number of newly infected adults and children. Despite declining mortality over the last years, adult HIV prevalence in 2007 ranges from 0.1% to 0.6% in Europe. Portugal is one of the European countries with the highest prevalence (0.5%), where 31,667 cases of HIV/AIDS were notified in 2007. HIV/AIDS was chosen as the focus of this Thesis, because the hospitalizations are one of the major financial burdens on healthcare systems worldwide. In Portugal, hospitalizations related to HIV infection are also some of the most expensive; in 2006, the average daily cost was around €825 and it was the second major diagnosis category (MDC) with the greatest average hospitalization time. In the same year, the average length of stay (LOS) in Portuguese hospitals of the National Health Service (NHS) was 23 days. With this Thesis I intend to contribute to a better understanding of the factors associated with HIV/AIDS LOS, taking into consideration that LOS data are usually right skewed and heterogeneous, representing a challenge for modelling and statistical analysis. The literature review reveals the need to analyse HIV/AIDS LOS through two different statistical points of view: survival analysis and mixture models. This Thesis is organised as follows: in the first chapter is an introduction, the literature review is presented in the second chapter, the third chapter presents the statistical methodologies developed during the Thesis, in the following three chapters I present the different studies regarding HIV/AIDS LOS and the last chapter presents a general conclusion. In three studies I analyse the Portuguese national database of all patient refined diagnosis related groups (DRG) that were provided by the Central Administration of Health Systems (ACSS). The data are anonymous and available for scientific research. In the DRG database each record corresponds to a discharge episode (hospitalization) and contains information collected while the patient was hospitalized. In the first study the population consists of 12,078 adult discharges of patients with HIV infection treated at Portuguese hospitals from 2005‐2007 that were registered on the DRG’s database. Discharge and hospital level variables were used to develop a hierarchical model. Kaplan‐Meier plots were used to examine differences in survival curves. Cox proportional hazard model and Cox proportional hazard model with frailty were applied to identify independent predictors of hospital mortality and to calculate hazard ratios (HR). The frailty model suggests that there are unmeasured factors affecting mortality in HIV associated hospitalizations. In the second study a hierarchical finite mixture model was developed to identify factors that are associated with HIV/AIDS. A mixture of normal components is applied to adult HIV/AIDS diagnosis‐related group data from 2008. The model accounts for demographic and clinical characteristics of the patients, as well as the inherent correlation of patients clustered within hospitals. A normal mixture distribution was fitted to the logarithm of LOS and it was found that the model with two‐components had the best fit, resulting in two subgroups of LOS: a short‐stay subgroup and a long‐stay subgroup. Associated risk factors for both groups were identified as well as some statistical differences in the hospitals. The third study presents a finite mixture Poisson regression model to analyse HIV/AIDS LOS. The statistical methodology proposed allows that different covariates explain different components (nested varying parameters), and those factors found to be significant may be compared and contrasted between subgroups. The model with three components was the one with the best fit, resulting in three subgroups of LOS: a short‐stay, a medium‐stay and a longstay subgroup. It was also found that gender and number of procedures are the only variables important to explain the three groups. With this Thesis I conclude that it is very important to have comprehensive and accurate information about LOS in order to develop strategic planning and to deploy financial, human, and physical resources of the hospitals. In addition, the determination of patient related characteristics affecting LOS can help physicians optimize care and rationalize their medical practice.