Dependence Measures in Bivariate Gamma Frailty Models - Gerard J. van den Berg; Georgios Effraimidis (Institute for the Study of Labor (IZA), 2014)
Bivariate duration data frequently arise in economics, biostatistics and other areas. In bivariate frailty models, dependence between the frailties (i.e., unobserved determinants) induces dependence between the durations. Using notions of quadrant dependence, we study restrictions that this imposes on the implied dependence of the durations, if the frailty terms act multiplicatively on the corresponding hazard rates. Marginal frailty distributions are often taken to be gamma distributions. For such cases we calculate general bounds for two association measures, Pearson's correlation coefficient and Kendall's tau. The results are employed to compare the flexibility of specific families of bivariate gamma frailty distributions.
Keywords: C41; C51; C34; C33; C32; J64; 330; bivariate gamma distribution; duration models; competing risks; Kendall's tau; negative and positive quadrant dependence; Pearson's correlation coefficient; unobserved heterogeneity; survival analysis