Dependence evolution in the Spanish disabled population: a functional data analysis approach Articles uri icon

publication date

  • February 2017

start page

  • 657

end page

  • 677


  • 2


  • 180

International Standard Serial Number (ISSN)

  • 0964-1998

Electronic International Standard Serial Number (EISSN)

  • 1467-985X


  • In a health context, dependence is defined as a lack of autonomy in performing the basic activities of daily living and requiring care giving or significant help from another person. However, this contingency, if present, changes over one's lifetime. Empirical evidence shows that, once this situation occurs, it is almost impossible to return to the previous state and in most cases increases in intensity. In the paper, the evolution of the intensity of this situation is studied for the Spanish population affected by this contingency. Evolution in dependence can be seen as sparsely observed functional data, where we obtain a curve for each individual that is observed at only those points where changes in his or her condition of dependence occur. We use functional data analysis techniques, such as curve registration, functional data depth and distance-based clustering, to analyse this type of data. This approach proves to be useful in this context because it considers the dynamics of the dependence process and provides more meaningful conclusions than simple pointwise ormultivariate analysis. We use the sample statistics obtained to predict the future evolution of dependence. The database analysed originates from the 'Survey on disability, personal autonomy and dependence situations' in Spain in 2008. The survey is the largest and most complete survey to be made available in Europe for the study of disability. In addition, the Spanish legislation is one of the most recent in Europe and provides a detailed quantitative scale to assess dependence. In the paper, the scale value according to this legislation has been calculated for each individual included in the survey. Differences between sex, age and the time of first appearance were considered, and a prediction of the future evolution of dependence is obtained.


  • chain ladder; dependence; disability; forecasting; functional data; time warping model; disability trends; curves; depth