Artículos de revistas
A Generalized Log-gamma Mixture Model For Cure Rate: Estimation And Sensitivity Analysis
Registro en:
Sankhya: The Indian Journal Of Statistics. , v. 71, n. 1 SERIES B, p. 1 - 29, 2009.
9727671
2-s2.0-76949105530
Autor
Ortega E.M.M.
Cancho V.G.
Lachos V.H.
Institución
Resumen
In a sample of censored survival times, the presence of an immune proportion of individuals who are not subject to death, failure or relapse may be indicated by a relatively high number of individuals with large censored survival times. In this paper, the generalized log-gamma model is modifed for the possible presence of long-term survivors in the data. The models attempt to simultaneously estimate the effects of covariates on the acceleration/deceleration of the timing of a given event and the surviving fraction, that is, the proportion of the population for which the event never occurs. The logistic function is used for the regression model of the surviving fraction. The generalized log-gamma mixture model is exible enough to include many commonly used failure time distributions as special cases. We consider maximum likelihood and Jackknife estimators for the parameters of the model. We derive the numerically matrices for assessing local Influence on the parameter estimates under di erent perturbation schemes and we also present some ways to perform global Influence. Finally, a data set from the medical area is analyzed under the log-gamma generalized mixture model. © 2009, Indian Statistical Institute. 71 1 SERIES B 1 29 Banerjee, S., Carlin, B.P., Parametric spatial cure rate models for interval-censored time-to-relapse data (2004) Biometrics, 60, pp. 268-275 Berkson, J., Gage, R.P., Survival curve for cancer patients following treatment (1952) J. Amer. Statist. Assoc, 88, pp. 1412-1418 Boag, J., Maximum likelihood estimates of the proportion of patients cured by cancer therapy (1949) J. Roy. Statist. Soc., Series B, 11, pp. 15-44 Carrasco, J.M.F., Ortega, E.M.M., Paula, G.A., Log-modi ed Weibull regression models with censored data: Sensitivity and residual analysis (2008) Computational Statistics and Data Analysis, 52, pp. 4021-4029 Cook, R.D., Assessment of local Influence (with discussion) (1986) J. Roy. Statist. Soc, 48, pp. 133-169 Cook, R.D., Weisberg, S., (1982) Residuals and Influence In Regression, , New York: Chapman and Hill Diaz-Garca, J.A., Galea, M., Leiva-Sánchez, V., Influence diagnostics for elliptical multivariate linear regression models (2004) Communications In Statistics - Theory and Methods, 32, pp. 625-641 Doornik, J., (2001) Ox: An Object-oriented Matrix Programming Language, , International Thomson Business Press Escobar, L.A., Meeker, W.Q., Assessing Influence in regression analysis with censored data (1992) Biometrics, 48, pp. 507-528 Farewell, V.T., The use of mixture models for tha analysis of survival data with long-term survivors (1982) Biometrics, 38, pp. 1041-1046 Galea, M., Riquelme, M., Paula, G.A., Diagnostics methods in elliptical linear regression models (2002) Brazilian Journal of Probability and Statistics, 14, pp. 167-184 Gomes, O., Combes, C., Dussauchoy, A., Parameter estimation of the generalized gamma distribution (2008) Mathematics and Computers In Simulation, 79, pp. 955-963 Ibrahim, J.G., Chen, M.H., Sinha, D., (2001) Bayesian Survival Analysis, , Springer-Verlag: New York Kalbfleisch, J.D., Prentice, R.L., (1980) The Statistical Analysis of Failure Time Data, , New York: John Wiley & Sons Lawless, J.F., (2003) Statistical Models and Methods For Lifetime Data, , Wiley: New York Lesaffre, E., Verbeke, G., Local Influence in linear mixed models (1998) Biometrics, 54, pp. 570-582 Li, C.-S., Taylor, J.M.G., Sy, J.P., Identifiability of cure models (2001) Statist. Probab. Lett, 54, pp. 389-395 Li, Y., Tiwari, R.C., Guha, S., Mixture cure survival models with dependent censoring (2005) Harvard University Biostatistics Working Paper Series, 41, pp. 211-224 Lipsitz, S.R., Laird, N.M., Harrington, D.P., Using the Jackknife to estimate the variance of regression estimators from repeated measures studies (1990) Communications In Statistics: Theory Methods, 19, pp. 821-845 Liu, S.Z., On local Influence for elliptical linear models (2000) Statist. Papers, 26, pp. 1-40 Longini, I.M., Halloran, M.E., A frailty mixture model for estimating vaccine e cacy (1996) Appl. Statist, 45, pp. 165-173 Maller, R., Zhou, X., (1996) Survival Analysis With Long-term Survivors, , New York:Wiley Manly, B.F.J., (1997) Randomization, Bootstrap and Monte Carlo Methods In Biology, , 2nd Edition. Chapman and Hall: London Mizoi, M.F., Bolfarine, H., Pedroso-De-Lima, A.C., Cure Rate Model with Measurement Error (2007) Communications In Statistics Simulation and Computation, 36, pp. 185-196 Ortega, E.M.M., Paula, G.A., Bolfarine, H., Deviance Residuals in Generalized Log-Gamma Regression Models with Censored Observations (2008) J. Statistical Computation and Simulation, 78, pp. 747-764 Ortega, E.M.M., Cancho, V.G., Bolfarine, H., Influence diagnostics in exponentiated-Weibull regression models with censored data (2006) Statistics and Operations Research Transactions, 30, pp. 171-192 Ortega, E.M.M., Bolfarine, H., Paula, G.A., Influence diagnostics in generalized log-gamma regression models (2003) Computational Statistics and Data Analysis, 42, pp. 165-186 Ortega, E.M.M., (2001) Influence Analysis and Residual In Generalized Log-gamma Regression Models, , Doctoral Thesis, Department of Statistics, University of São Paulo, Brazil (in Portuguese) Paula, G.A., Assessing local Influence in restricted regressions models (1993) Computational Statistics and Data Analysis, 16, pp. 63-79 Peng, Y., Dear, K., A nonparametric mixture model for cure rate estimation (2000) Biometrics, 56, pp. 237-243 Pettitt, A.N., Bin Daud, I., Case-weight measures of Influence for proportional hazards regression (1989) Applied Statistics, 38, pp. 51-67 Price, D.L., Manatunga, A.K., Modelling survival data with a cured fraction using frailty models (2001) Statistics In Medicine, 20, pp. 1515-1527 Silva, G.O., Ortega, E.M.M., Cancho, V.G., Barreto, M.L., Log- Burr XII Regression Models with Censored Data (2008) Computational Statistics and Data Analysis, 52, pp. 3820-3842 Stacy, E.W., A generalization of the gamma distribution (1962) Ann. Math. Stat, 33, pp. 1187-1192 Sy, J.P., Taylor, M.M.G., Estimation in a proportional hazards cure model (2000) Biometrics, 56, pp. 227-336 Wang, P., Puterman, M.L., Cockburn, I., Le, N., Mixed Poisson regression models with covariate dependent rates (1996) Biometrics, 52, pp. 381-400 Yu, B., Peng, Y., Mixture cure models for multivariate survival data (2008) Computational Statistics and Data Analysis, 52, pp. 1524-1532 Zen, D., Yin, G., Ibrahim, G.I., Semiparametric Transformation Models for Survival Data with a Cure Fraction data (2006) J. Amer. Statist. Assoc, 101, pp. 670-684