Indirect inference for survival data

• Autores: Wenxin Jiang, B.W. Turnbull
• Localización: Sort: Statistics and Operations Research Transactions, ISSN 1696-2281, Vol. 27, Nº. 1, 2003, págs. 79-94
• Idioma: inglés
• Títulos paralelos:
  • Inferencia indirecta para datos de supervivencia
• Enlaces
  • Texto completo (pdf)
• Resumen

  • In this paper we describe the so-called indirect method of inference, originally developed from the econometric literature, and apply it to survival analyses of two data sets with repeated events. This method is often more convenient computationally than maximum likelihood estimation when handling such model complexities as random effects and measurement error, for example; and it can also serve as a basis for robust inference with less stringent assumptions on the data generating mechanism. The first data set concerns recurrence times of mammary tumors in rats and is modeled using a Poisson process model with covariates and frailties. The second data set involves times of recurrences of skin tumors in individual patients in a clinical trial. The methodology is applied in both parametric and semi-parametric regression analyses to accommodate random effects and covariate measurement error.

• Referencias bibliográficas
  • Andersen, P.K., Borgan, O., Gill, R.D. and Keiding, N. (1993). Statistical Models Based on Counting Processes. New York: Springer-Verlag.
  • Berk, R.H. (1966). Limiting behavior of posterior distributions when the model is incorrect. Annals of Mathematical Statististics, 37, 51-58.
  • Bickel, P.J. and Doksum, K.A. (2001). Mathematical Statistics, 2nd Ed. Upper Saddle River, New Jersey: Prentice Hall.
  • Breslow, N. (1990). Tests of hypotheses in overdispersed Poisson regression and other quasi-likelihood models. Journal of American Statistical...
  • Carroll, R.J., Ruppert, D. and Stefanski, L.A. (1995). Measurement Error in Nonlinear Models. London: Chapman and Hall.
  • Chiang, C.L. (1956). On regular best asymptotically normal estimates. Annals of Mathematical Statististics, 27, 336-351.
  • Clark, L.C. , Combs, G.F., Turnbull, B.W., Slate, E.H., Chalker, D.K., Chow, J., Davis, L.S., Glover, R.A., Graham, G.F., Gross, E.G., Krongrad,...
  • Cox, D.R. (1962). Further results on tests of separate families of hypotheses. J. R. Statist. Soc. B, 24, 406- 424.
  • Cox, D.R. (1972). Regression models and life-tables (with discussion). J.R. Statist. Soc. B, 34, 187-207.
  • Cox D.R. (1983). Some remarks on overdispersion. Biometrika, 70, 269-274.
  • Ferguson, T.S. (1958). A method of generating best asymptotic normal estimates with application to the estimation of bacterial densities....
  • Gail, M.H., Santner, T.J. and Brown, C.C. (1980). An analysis of comparative carcinogenesis experiments based on multiple times to tumor....
  • Gallant, A.R. and Long, J.R. (1997). Estimating stochastic differential equations efficiently by minimum chi-squared. Biometrika, 84, 125-141.
  • Gallant, A.R. and Tauchen, G. (1996). Which moments to match? Econometric Theory, 12, 657-681.
  • Gallant, A.R. and Tauchen, G. (1999). The relative efficiency of method of moments estimators. Journal of Econometrics, 92, 149-172.
  • Gourieroux, C., Monfort, A. and Renault, E. (1993). Indirect inference. Journal of Applied Econometrics 8S, 85-118.
  • Hansen, L.P. (1982). Large sample properties of generalised method of moments estimators. Econometrica, 50, 1029-1054.
  • Huber, P.J. (1967). The behavior of maximum likelihood estimates under nonstandard conditions. In Procceedings of the Fifth Berkeley Symposium...
  • Insightful Corporation (2001). S-PLUS 6. Seattle, Washington.
  • Jiang, W. and Turnbull, B.W. (2001). The indirect method — robust inference based on intermediate statistics. Technical Report, Department...
  • Jiang, W., Turnbull, B.W. and Clark, L.C. (1999). Semiparametric Regression Models for Repeated Events with Random Effects and Measurement...
  • Kuk, A.Y.C. (1995). Asymptotically unbiased estimation in generalised linear models with random effects. Journal of Royal Statistical Association...
  • Lawless J.F. and Nadeau, C. (1995) Some simple robust methods for the analysis of recurrent events. Technometrics, 37, 158-168.
  • McCullagh, P. and Nelder, J.A. (1989). Generalized Linear Models. New York: Chapman and Hall.
  • McFadden, D. (1989). A method of simulated moments for estimation of discrete response models without numerical integration. Econometrica,...
  • Newey, W.K. and McFadden, D. (1994). Large sample estimation and hypothesis testing. in Handbook of Econometrics, edited by Engle, R.F. and...
  • Pakes, A. and Pollard, D. (1989). Simulation and the asymptotics of optimization estimators. Econometrica, 57, 1027-57.
  • Qin, J. and Lawless, J. (1994). Empirical likelihood and general estimating equations. Annals of Statistics, 22, 300-325.
  • Qu, A., Lindsay, B.G. and Li, B. (2000). Improving generalised estimating equations using quadratic inference functions. Biometrika, 87, 823-836.
  • StataCorp (1997). Stata Statistical Software, Release 5.0. Stata Corporation, College Station, Texas.
  • Thall, P.F. and Vail, S.C. (1990). Some covariance models for longitudinal count data with overdispersion. Biometrics, 46, 657-71.
  • Thompson, H.F., Grubbs, C.J., Moon, R.C. and Sporn, M.B. (1978). Continual requirement of retinoid for maintenance of mammary cancer inhibition....
  • Turnbull, B.W., Jiang, W. and Clark, L.C. (1997). Regression models for recurrent event data: parametric random effects models with measurement...
  • Wedderburn, R.W.M. (1974). Quasi-likelihood, generalized linear models and the Gauss-Newton method. Biometrika, 61, 439-447.
  • White, H. (1994). Estimation, Inference and Specification Analysis. Cambridge: Cambridge University Press.