• Asian Pacific Journal of Cancer Prevention
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• v.13 no.5
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• pp.1829-1831
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• 2012

Background: The generalized gamma distribution statistics constitute an extensive family that contains nearly all of the most commonly used distributions including the exponential, Weibull and log normal. A saturated version of the model allows covariates having effects through all the parameters of survival time distribution. Accelerated failure-time models assume that only one parameter of the distribution depends on the covariates. Methods: We fitted both the conventional GG model and the saturated form for each of its members including the Weibull and lognormal distribution; and compared them using likelihood ratios. To compare the selected parameter distribution with log logistic distribution which is a famous distribution in survival analysis that is not included in generalized gamma family, we used the Akaike information criterion (AIC; r=l(b)-2p). All models were fitted using data for 369 women age 50 years or more, diagnosed with stage IV breast cancer in BC during 1990-1999 and followed to 2010. Results: In both conventional and saturated parametric models, the lognormal was the best candidate among the GG family members; also, the lognormal fitted better than log-logistic distribution. By the conventional GG model, the variables "surgery", "radiotherapy", "hormone therapy", "erposneg" and interaction between "hormone therapy" and "erposneg" are significant. In the AFT model, we estimated the relative time for these variables. By the saturated GG model, similar significant variables are selected. Estimating the relative times in different percentiles of extended model illustrate the pattern in which the relative survival time change during the time. Conclusions: The advantage of using the generalized gamma distribution is that it facilitates estimating a model with improved fit over the standard Weibull or lognormal distributions. Alternatively, the generalized F family of distributions might be considered, of which the generalized gamma distribution is a member and also includes the commonly used log-logistic distribution.

• Korea journal of population studies
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• v.29 no.2
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• pp.53-88
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• 2006

The major aim of this paper is to develop a hypothetical set of age-specific fertility rates which are logically derived and reasonably accurate in the projection of future population. The first procedure is to select a generalized log-gamma distribution model, which includes Coale-McNeil nuptiality model, in order to estimate and project a set of age-specific fertility rates by birth cohort and birth order. The second is to apply the log-gamma model with an empirical adjustment to the actual data to estimate and project the future fertility rates for relatively young birth cohorts who did not complete their reproductive career. This study reconstructs or translates a set of cohort age-specific fertility rates into a set of period age-specific fertility rates which must be hypothesized in order to establish the broader framework of future population projection. For example, the fertility at age 20 in the year of 2020 is the fertility at age 20 for the cohort born in 1990, while the fertility at age 21 in the year of 2020 is the fertility at 21 for the cohort born in 1989. In turn, once a set of age-specific fertility rates for the cohorts who were born up to the year of 2010, it is possible for one to establish an hypothetical set of period age-specific fertility rates which will be needed to project the future population until the year of 2055. The difference in the hypothetical system of age-specific fertility rates between this study and the 2005 special population projection comes from the fact that the fertility estimation/projection model used in this study was skillfully exploited to reflect better actual trend of fertility decline caused by rise in marriage age and increasing proportion of those who remain single until their end of reproduction. In this regard, this paper argues that the set of age-specific fertility rates derived from this study is more logical and reasonably accurate than the set of those used for the 2005 special projection. In the population projection, however, the fundamental issue of the hypothetical setting of age-specific fertility rates in relation to the fertility estimation/projection model is about how skillfully one can handle the period effects. It is not easy for one to completely cope with the problem of period effects except for the a minor period adjustment based on recent actual data, along with the given framework of a cohort-based fertility estimation/projection model.