The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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The Use of Generalized Gamma-Polynomial Approximation for Hazard Functions

  • Ha, Hyung-Tae (Department of Applied Statistics Kyungwon University)
  • Received : 20090800
  • Accepted : 20091000
  • Published : 2009.12.31
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Abstract

We introduce a simple methodology, so-called generalized gamma-polynomial approximation, based on moment-matching technique to approximate survival and hazard functions in the context of parametric survival analysis. We use the generalized gamma-polynomial approximation to approximate the density and distribution functions of convolutions and finite mixtures of random variables, from which the approximated survival and hazard functions are obtained. This technique provides very accurate approximation to the target functions, in addition to their being computationally efficient and easy to implement. In addition, the generalized gamma-polynomial approximations are very stable in middle range of the target distributions, whereas saddlepoint approximations are often unstable in a neighborhood of the mean.

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References

  1. Butler, R.W. (2000). Reliabilities for feedback systems and their saddlepoint approximation, Statistical Science, 15, 279–298 https://doi.org/10.1214/ss/1009212818
  2. Butler, R. W. and Huzurbazar, A. V. (1997). Stochastic network models for survival analysis, Journal of the American Statistical Association, 92, 246–257
  3. Butler, R. W. and Huzurbazar, A. V. (2000). Bayesian prediction of waiting times in stochastic models, The Canadian Journal of Statistics, 28, 311–325 https://doi.org/10.2307/3315981
  4. Daniels, H. E. (1954). Saddlepoint approximations in statistics, The Annals of Mathematical Statistics, 25, 631–650 https://doi.org/10.1214/aoms/1177728652
  5. Daniels, H. E. (1982). The saddlepoint approximation for a general birth process, Journal of Applied Probability, 19, 20–28
  6. Farewell, V. T. (1977). A model for a binary variable with time-censored observations, Biometrika, 64, 43–46 https://doi.org/10.1093/biomet/64.1.43
  7. Ha, H. T. and Provost, S. B. (2007). A viable alternative to resorting to statistical tables, Communication in Statistics: Simulation and Computation, 36, 1135–1151 https://doi.org/10.1080/03610910701569671
  8. Huzurbazar, S. and Huzurbazar, A. V. (1999). Survival and hazard functions for progressive diseases using saddlepoint approximations, Biometrics, 55, 198–203 https://doi.org/10.1111/j.0006-341X.1999.00198
  9. Keilson, J. (1978). Exponential spectra as a tool for the study of server-systems with several classes of customers, Journal of Applied Probability, 15, 162–170
  10. Langlands, A. O., Pocock, S. J., Kerr, G. R. and Gore, S. M. (1979). Long-term survival of patients with breast cancer: a study of the curability of the disease, British Medical Journal, 2, 1247–1251
  11. Pierce, D. A., Stewart, W. H. and Kopecky, K. J. (1979). Distribution-free regression analysis of grouped survival data, Biometrics, 35, 785–793
  12. Reid, N. (1996). Likelihood and higher order approximations to tail areas, The Canadian Journal of Statistics, 24, 141–165