Dynamic Models versus Frailty Models for Recurrent Event Data
Recurrent event data is a special type of multivariate
survival data. Dynamic and frailty models are one of the approaches
that dealt with this kind of data. A comparison between these two
models is studied using the empirical standard deviation of the
standardized martingale residual processes as a way of assessing the
fit of the two models based on the Aalen additive regression model.
Here we found both approaches took heterogeneity into account and
produce residual standard deviations close to each other both in the
simulation study and in the real data set.
[1] O. Aalen, J. Fosen, H. Wedon-Fekjaer, O. Borgan, and E. Husebye,
"Dynamic analysis of multivariate failure time data," Biometrics, vol.
60, pp. 764-773, 2004.
[2] J. Fosen, O. Borgan, H. Weedon-Fekjaer, and O. Aalen, "Dynamic
analysis of recurrent event data using the additive hazard model,"
Biometrical Journal, vol. 48, pp. 381-398, 2006.
[3] O. Borgan, R. L. Fiaccone, R. Henderson, M. L. Barreto, "Dynamic
analysis of recurrent event data with missing observations, with
application to infant diarrhoea in Brazil ," Scandinavian Journal of
Statistics , vol. 34, pp. 53-69, 2007.
[4] P. Andersen, R. Gill, "Cox-s regression model for counting processes: A
large sample study," The Annals of Statistics, vol. 10, pp. 1100-1120,
1982.
[5] O. Aalen, "A linear regression model for the analysis of life times,"
Statistics in Medicine, vol. 8, pp. 907-925, 1989.
[6] O. Aalen, "Further results on the non-parametric linear regression model
in survival analysis," Statistics in Medicine, vol. 12, pp. 1569-1588,
1993.
[7] J. Vaupel, K. Manton, E. Stallard, "The impact of heterogeneity in
individual frailty on the dynamics of mortality," Demography, vol. 16,
pp. 439-454, 1979.
[8] J. Vaupel, A. Yashin, "Heterogeneity-s ruses: some surprising effects of
selection on population dynamics," The American Statistician, vol. 39,
pp. 176-185, 1985.
[9] O. Aalen, "Effects of frailty in survival analysis," Statistical Methods in
Medical Research, vol. 3, pp. 227-243, 1994.
[10] P. Hougaard, "Analysis of multivariate survival data," Spring-
Verlag:New York, 2000.
[11] D. Clayton, "A model for association in bivariate life tables and its
application in epidemiological studies of familial tendency in chronic
disease incidence," Biometrika, vol. 65, pp.141-151, 1978.
[12] P. Hougaard, "Survival models for heterogeneous populations derived
from stable distributions," Biometrika, vol. 73, pp. 671-678, 1986a.
[13] P. Hougaard, "A class of multivariate failure time distributions,"
Biometrika, vol. 73, pp. 671-678, 1986b.
[14] C. McGilchrist, and C. Aisbett, "Regression with frailty in survival
analysis," Biometrics, vol. 47, pp. 461-466, 1991.
[15] O. Aalen, "Heterogeneity in survival analysis," Statistics in Medicine,
vol. 7, pp. 1121-1137, 1988.
[16] O. Aalen, "Modelling heterogeneity in survival analysis by the
compound poisson distribution," Annals of Applied Probability, vol. 4,
pp. 951-972, 1992.
[17] A. Yashin, J. Vaupel, and I. Iachine, "Correlated individual frailty: An
advantageous approach to survival analysis of bivariate data,"
Mathematical Population Studies, vol. 5, pp. 145-159, 1995.
[18] P. Andersen, O. Borgan, R. Gill, and N. Keiding, "Statistical Models
Based on Counting Processes," Spring-Verlag:New York, 1993.
[19] P. Andersen, O. Borgan, R. Gill, and N. Keiding, "Statistical Models
Based on Counting Processes," Spring-Verlag:New York, 1993.
[20] O. Aalen, O. Borgan, and H. Gjessing, "Survival and event history
analysis. A process point of view," Spring-Verlag:New York, 2008.
[21] E. Elgmati, R. Fiaccone, R. Hendersen, and M. Mohammadi, "Frailty
modeling for clustered recurrent incidence of diarrhoea," Statistics in
Medicine, vol. 27, pp. 6489-6504, 2008.
[1] O. Aalen, J. Fosen, H. Wedon-Fekjaer, O. Borgan, and E. Husebye,
"Dynamic analysis of multivariate failure time data," Biometrics, vol.
60, pp. 764-773, 2004.
[2] J. Fosen, O. Borgan, H. Weedon-Fekjaer, and O. Aalen, "Dynamic
analysis of recurrent event data using the additive hazard model,"
Biometrical Journal, vol. 48, pp. 381-398, 2006.
[3] O. Borgan, R. L. Fiaccone, R. Henderson, M. L. Barreto, "Dynamic
analysis of recurrent event data with missing observations, with
application to infant diarrhoea in Brazil ," Scandinavian Journal of
Statistics , vol. 34, pp. 53-69, 2007.
[4] P. Andersen, R. Gill, "Cox-s regression model for counting processes: A
large sample study," The Annals of Statistics, vol. 10, pp. 1100-1120,
1982.
[5] O. Aalen, "A linear regression model for the analysis of life times,"
Statistics in Medicine, vol. 8, pp. 907-925, 1989.
[6] O. Aalen, "Further results on the non-parametric linear regression model
in survival analysis," Statistics in Medicine, vol. 12, pp. 1569-1588,
1993.
[7] J. Vaupel, K. Manton, E. Stallard, "The impact of heterogeneity in
individual frailty on the dynamics of mortality," Demography, vol. 16,
pp. 439-454, 1979.
[8] J. Vaupel, A. Yashin, "Heterogeneity-s ruses: some surprising effects of
selection on population dynamics," The American Statistician, vol. 39,
pp. 176-185, 1985.
[9] O. Aalen, "Effects of frailty in survival analysis," Statistical Methods in
Medical Research, vol. 3, pp. 227-243, 1994.
[10] P. Hougaard, "Analysis of multivariate survival data," Spring-
Verlag:New York, 2000.
[11] D. Clayton, "A model for association in bivariate life tables and its
application in epidemiological studies of familial tendency in chronic
disease incidence," Biometrika, vol. 65, pp.141-151, 1978.
[12] P. Hougaard, "Survival models for heterogeneous populations derived
from stable distributions," Biometrika, vol. 73, pp. 671-678, 1986a.
[13] P. Hougaard, "A class of multivariate failure time distributions,"
Biometrika, vol. 73, pp. 671-678, 1986b.
[14] C. McGilchrist, and C. Aisbett, "Regression with frailty in survival
analysis," Biometrics, vol. 47, pp. 461-466, 1991.
[15] O. Aalen, "Heterogeneity in survival analysis," Statistics in Medicine,
vol. 7, pp. 1121-1137, 1988.
[16] O. Aalen, "Modelling heterogeneity in survival analysis by the
compound poisson distribution," Annals of Applied Probability, vol. 4,
pp. 951-972, 1992.
[17] A. Yashin, J. Vaupel, and I. Iachine, "Correlated individual frailty: An
advantageous approach to survival analysis of bivariate data,"
Mathematical Population Studies, vol. 5, pp. 145-159, 1995.
[18] P. Andersen, O. Borgan, R. Gill, and N. Keiding, "Statistical Models
Based on Counting Processes," Spring-Verlag:New York, 1993.
[19] P. Andersen, O. Borgan, R. Gill, and N. Keiding, "Statistical Models
Based on Counting Processes," Spring-Verlag:New York, 1993.
[20] O. Aalen, O. Borgan, and H. Gjessing, "Survival and event history
analysis. A process point of view," Spring-Verlag:New York, 2008.
[21] E. Elgmati, R. Fiaccone, R. Hendersen, and M. Mohammadi, "Frailty
modeling for clustered recurrent incidence of diarrhoea," Statistics in
Medicine, vol. 27, pp. 6489-6504, 2008.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:49878", author = "Entisar A. Elgmati", title = "Dynamic Models versus Frailty Models for Recurrent Event Data", abstract = "Recurrent event data is a special type of multivariate
survival data. Dynamic and frailty models are one of the approaches
that dealt with this kind of data. A comparison between these two
models is studied using the empirical standard deviation of the
standardized martingale residual processes as a way of assessing the
fit of the two models based on the Aalen additive regression model.
Here we found both approaches took heterogeneity into account and
produce residual standard deviations close to each other both in the
simulation study and in the real data set.", keywords = "Dynamic, frailty, misspecification, recurrent events.", volume = "7", number = "4", pages = "570-5", }