On the shape of the cross-ratio function in bivariate survival models induced by truncated and folded normal frailty distributions. (English) Zbl 1396.62238
Summary: In shared frailty models for bivariate survival data the frailty is identifiable through the cross-ratio function (CRF), which provides a convenient measure of association for correlated survival variables. The CRF may be used to compare patterns of dependence across models and data sets. We explore the shape of the CRF for the families of one-sided truncated normal and folded normal frailty distributions.
MSC:
| 62N05 | Reliability and life testing |
| 62H12 | Estimation in multivariate analysis |
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
Keywords:
cross-ratio function; frailty; heterogeneity; Student-\(t\) distributions; survival data; truncationReferences:
| [1] | Aalen OO, Borgan Ø, Gjessing HK (2008) Survival and event history analysis: a process point of view. Springer, New York · Zbl 1204.62165 · doi:10.1007/978-0-387-68560-1 |
| [2] | Anderson JE, Louis TA, Holm NV, Harvald B (1992) Time-dependent association measures for bivariate survival distributions. J Am Stat Assoc 87:641-650 · Zbl 0781.62168 · doi:10.1080/01621459.1992.10475263 |
| [3] | Azzalini A, Capitanio A (2014) The skew-normal and related families. Cambridge University Press, Cambridge · Zbl 0924.62050 |
| [4] | Azzalini A, Kotz S (2003) Log-skew-normal and log-skew-\[t\] t distributions as models for family income data. J Income Distrib 11:12-20 |
| [5] | Callegaro A, Iacobelli S (2012) The cox shared frailty model with log-skew normal frailties. Stat Model 12:399-418 · Zbl 07257885 · doi:10.1177/1471082X12460146 |
| [6] | Clayton DG (1978) A model for association in bivariate life tables and its application in epidemiological studies of family tendency in chronic disease incidence. Biometrika 65:141-151 · Zbl 0394.92021 · doi:10.1093/biomet/65.1.141 |
| [7] | Clayton DG, Cuzick J (1985) Multivariate generalizations of the proportional hazards model. J R Stat Soci Ser A 148:82-117 · Zbl 0581.62086 · doi:10.2307/2981943 |
| [8] | Duchateau L, Janssen P (2008) The frailty model. Springer, New York · Zbl 1210.62153 |
| [9] | Farrington CP, Unkel S, Anaya-Izquierdo K (2012) The relative frailty variance and shared frailty models. J R Stat Soc Ser B 74:673-696 · Zbl 1411.62287 · doi:10.1111/j.1467-9868.2011.01021.x |
| [10] | Hougaard P (2000) Analysis of multivariate survival data. Springer, New York · Zbl 0962.62096 · doi:10.1007/978-1-4612-1304-8 |
| [11] | Hougaard, P.; Klein, JP (ed.); Houwelingen, HC (ed.); Ibrahim, JG (ed.); Scheike, TH (ed.), Frailty models, 457-474 (2014), London |
| [12] | Oakes D (1989) Bivariate survival models induced by frailities. J Am Stat Assoc 84:487-493 · Zbl 0677.62094 · doi:10.1080/01621459.1989.10478795 |
| [13] | Paik MC, Tsai W-Y, Ottman R (1994) Multivariate survival analysis using piecewise gamma frailty. Biometrics 50:975-988 · Zbl 0826.62085 · doi:10.2307/2533437 |
| [14] | R Core Team (2015) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna. https://www.R-project.org |
| [15] | Sahu, S. K.; Dey, D. K.; Genton, M. G (ed.), On a Bayesian multivariate survival model with a skewed frailty, 321-338 (2004), Boca Raton |
| [16] | Viswanathan B, Manatunga AK (2001) Diagnostic plots for assessing the frailty distribution in multivariate survival data. Lifetime Data Anal 7:143-155 · Zbl 0985.62084 · doi:10.1023/A:1011348823081 |
| [17] | Wienke A (2011) Frailty models in survival analysis. CRC Press, Boca Raton |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
