When the event of interest never occurs for
a proportion of subjects during the study period, survival models with a cure
fraction are more appropriate in analyzing this type of data. Considering the
non-linear relationship between response variable and covariates, we propose a
class of generalized transformation models motivated by Zeng et al. [1]
transformed proportional time cure model, in which fractional polynomials are
used instead of the simple linear combination of the covariates. Statistical
properties of the proposed models are investigated, including identifiability
of the parameters, asymptotic consistency, and asymptotic normality of the
estimated regression coefficients. A simulation study is carried out to examine
the performance of the power selection procedure. The generalized
transformation cure rate models are applied to the First National Health and
Nutrition Examination Survey Epidemiologic Follow-up Study (NHANES1) for the
purpose of examining the relationship between survival time of patients and
several risk factors.
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