The European Journal of Health Economics

, Volume 14, Issue 5, pp 715–723 | Cite as

Analysis of HIV/AIDS DRG in Portugal: a hierarchical finite mixture model

  • Sara Simões DiasEmail author
  • Valeska Andreozzi
  • Rosário O. Martins
Original Paper


Inpatient length of stay (LOS) is an important measure of hospital activity, but its empirical distribution is often positively skewed, representing a challenge for statistical analysis. Taking this feature into account, we seek to identify factors that are associated with HIV/AIDS through a hierarchical finite mixture model. A mixture of normal components is applied to adult HIV/AIDS diagnosis-related group data (DRG) from 2008. The model accounts for the demographic and clinical characteristics of the patients, as well the inherent correlation of patients clustered within hospitals. In the present research, a normal mixture distribution was fitted to the logarithm of LOS and it was found that a 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. Our findings provide important information for policy makers in terms of discharge planning and the efficient management of LOS. The presence of “atypical” hospitals also suggests that hospitals should not be viewed or treated as homogenous bodies.


Length of stay Diagnosis related group Mixture regression Hierarchical modelling 

JEL Classification

I18 I10 



This research is supported partially by the Portuguese agency Fundação para a Ciência e Tecnologia (FCT/OE PEst-OE/MAT/UI0006/2011), and partially by FCT providing a PhD scholarship to S.S.D. The authors would also like to thank Bettina Gruen for her endless support with the Flexmix library.


  1. 1.
    Augusto, G.F.: Cuts in Portugal’s NHS could compromise care. Lancet 379(9814), 400 (2012)PubMedCrossRefGoogle Scholar
  2. 2.
    Martin, S., Smith, P.: Explaining variations in inpatient length of stay in the National Health Service. J. Health Econ. 15(3), 279–304 (1996). doi: 10.1016/0167-6296(96)00003-3 PubMedCrossRefGoogle Scholar
  3. 3.
    Xiao, J., Douglas, D., Lee, A.H.: A Delphi evaluation of the factors influencing length of stay in Australian hospitals. Int. J. Health Plan. Manag. 12, 207–218 (1997)CrossRefGoogle Scholar
  4. 4.
    Fetter, R.B., Youngsoo, S., Freeman, J.L., Averill, R.F., Thomson, J.D.: Case-mix: definition by diagnosis related groups. Med. Care 18, 1–53 (1980)Google Scholar
  5. 5.
    Averill, R.F., Goldfield, N., Hughes, J.S., Bonazelli, J., McCullough, E.C., Steinbeck, B.A., Mullin, R., Tang, A.M., Muldoon, J., Turner, L., Gay, J.: All patient refined diagnosis related groups (APR-DRGs) Version 20.0. Clinical Research and Documentation Departments of 3M Health Information Systems, Wallingford (2003)Google Scholar
  6. 6.
    ACSS: Sistema de Classificação de Doentes em Grupos de Diagnósticos Homogéneos (GDH). (2006)
  7. 7.
    Ministério, da, Saúde: Anexo I – Regulamento das Tabelas de Preços das Instituições e dos Serviços Integrados no Serviço Nacional de Saúde, Secção I, Artigo 3º - Definições. In, vol. Portaria nº 567/2006. pp. 4173-4267. Diário da República I—`série B, (2006)Google Scholar
  8. 8.
    Krentz, H.B., Dean, S., Gill, M.J.: Longitudinal assessment (1995–2003) of hospitalizations of HIV-infected patients within a geographical population in Canada. HIV Med. 7(7), 457–466 (2006)PubMedCrossRefGoogle Scholar
  9. 9.
    Barbour, K.E., Fabio, A., Pearlman, D.N.: Inpatient charges among HIV/AIDS patients in Rhode Island from 2000–2004. BMC Health Serv. Res. 9(1), 1–7 (2009)Google Scholar
  10. 10.
    Monitoring, F.H.: Diagnostic data of the hospitals starting from 2000 (cases/deaths, cases per 100,000 inhabitants, days of care, average length of stay). Classification: years, place of residence, age, sex, length of stay, ICD10. (2007)
  11. 11.
    Lee, A.H., Gracey, M., Wang, K., Kelvin, K.W.: A robustified modeling approach to analyze pediatric length of stay. Ann. Epidemiol. 15(9), 637–677 (2005)CrossRefGoogle Scholar
  12. 12.
    Atienza, N., Garcia-Heras, J., Munoz-Pichardo, J.M., Villa, R.: An application of mixture distributions in modelization of length of hospital stay. Stat. Med. 27(9):, 1403–1420 (2008)PubMedCrossRefGoogle Scholar
  13. 13.
    Dias, S.S., Andreozzi, V., Martins, M.O., Torgal, J.: Predictors of mortality in HIV-associated hospitalizations in Portugal: a hierarchical survival model. BMC Health Serv. Res. 9, 1–10 (2009)Google Scholar
  14. 14.
    Pérez-Hoyos, S., Ballester, F., Tenías, J.M., Marelles, A., Rivera, M.L.: Length of stay in a hospital emergency room due to asthma and chronic obstructive pulmonary disease: implications for air pollution studies. Eur. J. Epidemiol. 16, 455–463 (2000)PubMedCrossRefGoogle Scholar
  15. 15.
    Koton, S., Bornstein, N.M., Tsabari, R., Tanne, D., Investigators, N.: Derivation and validation of the prolonged length of stay score in acute stroke patients. Neurology 74(19), 1511–1516 (2010). doi: 10.1212/WNL.0b013e3181dd4dc5 PubMedCrossRefGoogle Scholar
  16. 16.
    Saez-Castillo, A.J., Olmo-Jimenez, M.J., Sanchez, J.M.P., Hernandez, M.A.N., Arcos-Navarro, A., Diaz-Oller, J.: Bayesian analysis of nosocomial infection risk and length of stay in a Department of General and Digestive Surgery. Value Health 13(4), 431–439 (2010). doi: 10.1111/j.1524-4733.2009.00680.x PubMedCrossRefGoogle Scholar
  17. 17.
    Singh, C.H., Ladusingh, L.: Inpatient length of stay: a finite mixture modeling analysis. Eur. J. Health Econ. 11(2), 119–126 (2010). doi: 10.1007/s10198-009-0153-6 PubMedCrossRefGoogle Scholar
  18. 18.
    Xiao, J., Lee, A.H., Vemurri, S.R.: Mixture distribution analysis of length of stay for efficient funding. Socio-Econ. Plan. Sci. 33, 39–59 (1999)CrossRefGoogle Scholar
  19. 19.
    Leyland, A.H., Boddy, F.A.: Measuring performance in hospital care—length of stay in gynaecology. Eur. J. Pub. Health 7(2), 136–143 (1997)CrossRefGoogle Scholar
  20. 20.
    Leung, K.M., Elashoff, R.M., Rees, K.S., Hasan, M.M., Legorreta, A.P.: Hospital- and patient-related characteristics determining maternity length of stay: a hierarchical linear model approach. Am. J. Public Health 88(3), 377–381 (1998)PubMedCrossRefGoogle Scholar
  21. 21.
    Downing, A., Lansdown, M., West, R.M., Thomas, J.D., Lawrence, G., Forman, D.: Changes in and predictors of length of stay in hospital after surgery for breast cancer between 1997/98 and 2004/05 in two regions of England: a population-based study. BMC Health Serv. Res. 9 (2009). doi: 10.1186/1472-6963-9-202
  22. 22.
    Lee, A.H., Ng, S.K., Yau, K.K.W.: Determinants of maternity length of stay: a gamma mixture risk-adjusted model. Health Care Manag. Sci. 4, 249–255 (2001)PubMedCrossRefGoogle Scholar
  23. 23.
    INE: Principais indicadores. (2008). Accessed June 2010
  24. 24.
    Ng, S.K., Yau, K.K.W., Lee, A.H.: Modelling inpatient length of stay by a hierarchical mixture regression via the EM algorithm. Math. Comput. Model. 37(3–4), 365–375 (2003)CrossRefGoogle Scholar
  25. 25.
    Everitt, B.S., Hand, D.J.: Finite mixture distribution. Monographs on applied probability and statistics. Chapman and Hall, London (1981)CrossRefGoogle Scholar
  26. 26.
    McLachlan, G.J., Basford, K.E.: Mixture models. Inference and applications to clustering. Dekker, New York (1988)Google Scholar
  27. 27.
    Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via EM algorithm. J. R. Stat. Soc. Ser. B Methodol. 39(1), 1–38 (1977)Google Scholar
  28. 28.
    Team, R.D.C.: R: A Language and Environment for Statistical Computing. In: The R Foundation for Statistical Computer, Vienna, Austria, (2008)Google Scholar
  29. 29.
    Leisch, F.: FlexMix: a general framework for finite mixture models and latent class regression. R. J. Stat. Softw. 11(8), 1–18Google Scholar
  30. 30.
    Grun, B., Leisch, F.: Fitting finite mixtures of generalized linear regressions in R. Comput. Stat. Data Anal. 51(11), 5247–5252 (2007). doi: 10.1016/j.csda.2006.08.014 CrossRefGoogle Scholar
  31. 31.
    Tribunal, de, Contas, Portugal: Auditoria ao sistema de pagamentos e de formação dos preços pagos às unidades hospitalares do Serviço Nacional de Saúde In. Lisboa, (2011)Google Scholar
  32. 32.
    Crystal, S., Lo Sasso, A.T., Sambamoorthi, U.: Incidence and duration of hospitalizations among persons with AIDS: an event history approach. Health Serv. Res. 33(6), 1611–1638 (1999)PubMedGoogle Scholar
  33. 33.
    Nunes, A.A., de Melo, I.M., da Silva, A.L.A., Rezende, L.D.D., Guimaraes, P.B., Silva-Vergara, M.L.: Hospitalizations for HIV/AIDS: differences between sexes. Gend. Med. 7(1), 28–38 (2010). doi: 10.1016/j.genm.2010.01.004 PubMedCrossRefGoogle Scholar
  34. 34.
    Mocroft, A., Monforte, A.D., Kirk, O., Johnson, M.A., Friis-Moller, N., Banhegyi, D., Blaxhult, A., Mulcahy, F., Gatell, J.M., Lundgren, J.D., Euro, S.S.G.: Changes in hospital admissions across Europe: 1995–2003. Results from the EuroSIDA study. HIV Med. 5(6), 437–447 (2004)PubMedCrossRefGoogle Scholar
  35. 35.
    Penniman, T.V., Taylor, S.L., Bird, C.E., Beckman, R., Collins, R.L., Cunningham, W.: The associations of gender, sexual identity and competing needs with healthcare utilization among people with HIV/AIDS. J. Natl Med. Assoc. 99(4), 419–427 (2007)PubMedGoogle Scholar
  36. 36.
    Wang, K., Yau, K.K.W., Lee, A.H.: A hierarchical Poisson mixture regression model to analyse maternity length of stay. Stat. Med. 21, 3639–3654 (2002)PubMedCrossRefGoogle Scholar
  37. 37.
    Eastaugh, S.R.: Organizational determinants of surgical lengths of stay. Inquiry 17(1), 85–96 (1980)PubMedGoogle Scholar
  38. 38.
    Aiken, L.H., Sloane, D.M., Lake, E.T., Sochalski, J., Weber, A.L.: Organization and outcomes of inpatient AIDS care. Med. Care 37(8), 760–772 (1999)PubMedCrossRefGoogle Scholar
  39. 39.
    Greenland, S.: Principles of multilevel modelling. Int. J. Epidemiol. 29, 158–167 (2000)PubMedCrossRefGoogle Scholar
  40. 40.
    Diez-Roux, A.V.: Multilevel analysis in public health research. Annu. Rev. Public Health 21, 171–192 (2000)PubMedCrossRefGoogle Scholar
  41. 41.
    Leyland, A., Goldstein, H.: Multilevel modelling of health statistics. Wiley series in probability and statistics—applied probability and statistics section. Wiley, New York (2001)Google Scholar
  42. 42.
    Bingenheimer, J.B., Raudenbush, S.W.: Statistical and substantive inferences in public health: issues in the application of multilevel models. Annu. Rev. Public Health 25, 53–77 (2004)PubMedCrossRefGoogle Scholar
  43. 43.
    Čačala, S., Mafana, E., Thomson, S., Smith, A.: Prevalence of HIV status and CD4 counts in a surgical cohort: their relationship to clinical outcome. Ann. R. Coll. Surg. Engl. 88(1), 46–51 (2006)PubMedCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Sara Simões Dias
    • 1
    • 2
    Email author
  • Valeska Andreozzi
    • 3
  • Rosário O. Martins
    • 2
    • 4
  1. 1.Departamento Universitário de Saúde Pública, Faculdade de Ciências MédicasUniversidade Nova de LisboaLisbonPortugal
  2. 2.Instituto Superior de Estatística e Gestão de InformaçãoUniversidade Nova de LisboaLisbonPortugal
  3. 3.Centro de Estatística e Aplicações da Universidade de LisboaFaculdade de Ciências da Universidade de LisboaLisbonPortugal
  4. 4.Instituto de Higiene e Medicina TropicalUniversidade Nova de LisboaLisbonPortugal

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