Generalized log-gamma regression models with cure fraction

In this paper, the generalized log-gamma regression model is modified to allow the possibility that long-term survivors may be present in the data. This modification leads to a generalized log-gamma regression model with a cure rate, encompassing, as special cases, the log-exponential, log-Weibull and log-normal regression models with a cure rate typically used to model such data. The models attempt to simultaneously estimate the effects of explanatory variables on the timing acceleration/deceleration of a given event and the surviving fraction, that is, the proportion of the population for which the event never occurs. The normal curvatures of local influence are derived under some usual perturbation schemes and two martingale-type residuals are proposed to assess departures from the generalized log-gamma error assumption as well as to detect outlying observations. Finally, a data set from the medical area is analyzed.

[1]  K. Yamaguchi.  Accelerated Failure-Time Regression Models with a Regression Model of Surviving Fraction: An Application to the Analysis of “Permanent Employment” in Japan , 1992 .

[2]  E Lesaffre,et al.  Local influence in linear mixed models. , 1998, Biometrics.

[3]  Jim E. Griffin,et al.  A Bayesian Partition Model for Customer Attrition , 2001 .

[4]  R. Prentice.  A LOG GAMMA MODEL AND ITS MAXIMUM LIKELIHOOD ESTIMATION , 1974 .

[5]  A Yu Yakovlev,et al.  Stochastic Models of Tumor Latency and Their Biostatistical Applications , 1996 .

[6]  P. McCullagh,et al.  Generalized Linear Models , 1992 .

[7]  R. Cook.  Assessment of Local Influence , 1986 .

[8]  D. Harrington,et al.  Counting Processes and Survival Analysis , 1991 .

[9]  S. Weisberg,et al.  Residuals and Influence in Regression , 1982 .

[10]  Joseph G. Ibrahim,et al.  Bayesian Survival Analysis , 2004 .

[11]  J G Ibrahim,et al.  Estimating Cure Rates From Survival Data , 2003, Journal of the American Statistical Association.

[12]  Heleno Bolfarine,et al.  Influence diagnostics in exponentiated-Weibull regression models with censored data , 2006 .

[13]  P. McCullagh,et al.  Generalized Linear Models, 2nd Edn. , 1990 .

[14]  Joseph Berkson,et al.  Survival Curve for Cancer Patients Following Treatment , 1952 .

[15]  E. Stacy.  A Generalization of the Gamma Distribution , 1962 .

[16]  Jurgen A. Doornik,et al.  Ox: an Object-oriented Matrix Programming Language , 1996 .

[17]  Heleno Bolfarine,et al.  Deviance residuals in generalised log-gamma regression models with censored observations , 2008 .

[18]  J. Kalbfleisch,et al.  The Statistical Analysis of Failure Time Data , 1980 .

[19]  Bradley P Carlin,et al.  Flexible Cure Rate Modeling Under Latent Activation Schemes , 2007, Journal of the American Statistical Association.

[20]  P. Grambsch,et al.  Martingale-based residuals for survival models , 1990 .

[21]  Chin-Shang Li,et al.  Identifiability of cure models , 2001 .

[22]  Mauricio Lima Barreto,et al.  Log-Burr XII regression models with censored data , 2008, Comput. Stat. Data Anal..

[23]  R. Maller,et al.  Survival Analysis with Long-Term Survivors , 1996 .

[24]  José A. Díaz-García,et al.  Influence Diagnostics for Elliptical Multivariate Linear Regression Models , 2003 .

[25]  Joseph G. Ibrahim,et al.  A New Bayesian Model For Survival Data With a Surviving Fraction , 1999 .

[26]  Gilberto A. Paula,et al.  DIAGNOSTIC METHODS IN ELLIPTICAL LINEAR REGRESSION MODELS , 2000 .

[27]  Anthony N. Pettitt,et al.  Case-Weighted Measures of Influence for Proportional Hazards Regression , 1989 .

[28]  James O. Berger,et al.  Bayesian Analysis for the Poly-Weibull Distribution , 1993 .

[29]  Bin Lu,et al.  Assessing local influence for nonlinear structural equation models with ignorable missing data , 2006, Comput. Stat. Data Anal..

[30]  W. Barlow,et al.  Residuals for relative risk regression , 1988 .

[31]  J. Lawless.  Statistical Models and Methods for Lifetime Data , 2002 .

[32]  Heleno Bolfarine,et al.  Influence diagnostics in generalized log-gamma regression models , 2003, Comput. Stat. Data Anal..

[33]  Luis A. Escobar,et al.  Assessing influence in regression analysis with censored data. , 1992, Biometrics.