Open Conference Systems, 50th Scientific meeting of the Italian Statistical Society

Font Size: 
Multi-State model with nonparametric discrete frailty
Francesca Gasperoni, Francesca Ieva, Anna Maria Paganoni, Chris Jackson, Linda Sharples

Last modified: 2018-04-26


In this work, we propose a novel semi-Markov multi-state model with a nonparametric discrete frailty and an application to an administrative clinical database about heart failure patients from a Northern Region of Italy. In particu- lar, we investigate a illness-death model with recovery in which the states space is composed by hospital admission, hospital discharge and death, as unique absorbing state. The available data are grouped longitudinal time-to-event data, indeed for each patient we know the times of admission and discharge of all hospitalizations (2005- 2012), the time of death (if it occurs) and the healthcare provider (grouping factor). Thanks to this model, we can investigate the effect of covariates, detect the presence and a pattern of latent populations of healthcare providers across transitions.


  1. Andersen, P. K., Keiding, N.: Multi-state models for event history analysis. Statistical methods in medical research, 11, 91–115. (2002)

  2. de Wreede,L.C.,Fiocco,M., Putter,H.: mstate:an R package for the analysis o fcompeting risks and multi-state models. Journal of Statistical Software, 38, 1–30. (2011)

  3. Foucher, Y., Saint-Pierre, P., Daures, J., Durand, J.: A semi-Markov frailty model for multi- state and clustered survival data. Far East Journal of Theoretical Statistics, 19, 185. (2006)

  4. Gasperoni,F.,Ieva,F.,Barbati,G.,Scagnetto,A.,Iorio,A.,Sinagra,G.,Di LenardaA.:Multi-state modelling of heart failure care path: A population-based investigation from Italy. PloSone. 12, e0179176. (2017)

  5. Gasperoni, F.; Ieva, F.; Paganoni, A.M.; Jackson C.H.; Sharples L.D.: Nonparametric frailty Cox models for hierarchical time-to-event data. MOX report. 45. (2017)

  6. Hougaard,P.:Multistate models:a review. Lifetime data analysis,5,239–264.(1999)

  7. Jackson, C. H.: Multi-state models for panel data: the msm package for R. Journal of Statistical Software, 38(8), 1–29. (2011)

  8. Kalbfleisch, J. D., Lawless, J. F.: Likelihood analysis of multistate models for disease incidence and mortality. Statistics in medicine, 7, 149–160.(1988)

  9. Laird, N.: Nonparametric maximum likelihood estimation of a mixing distribution. Journal of the American Statistical Association, 73, 805–811. (1978)

  10. Liquet, B., Timsit, J. F., Rondeau, V.: Investigating hospital heterogeneity with a multi-state frailty model: application to nosocomial pneumonia disease in intensive care units. BMC medical research methodology, 12, 79. (2012)

  11. Ma,T.Y.,Joly,I.,Raux,C.:A shared frailty semi-parametric markov renewal model for travel and activity time-use pattern analysis. (2010)

  12. McLachlan,G.,Peel,D.:Finite mixture models. JohnWiley&Sons.(2004)

  13. Putter,H.,Fiocco,M.,Geskus,R.B.:Tutorial in biostatistics: competing risks and multi-state models. Statistics in medicine. 26, 2389–2430. (2007)

  14. Ripatti,S.,Gatz,M.,Pedersen,N.L.,Palmgren,J.:Three-state frailty model for age at onset of dementia and death in Swedish twins. Genetic epidemiology, 24, 139–149. (2003)

  15. Yen, A. M., Chen, T. H., Duffy, S. W., Chen, C. D.: Incorporating frailty in a multi-state model: application to disease natural history modelling of adenoma-carcinoma in the large bowel. Statistical methods in medical research, 19, 529–546. (2010)

Full Text: PDF