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    2019-08-16

    r> Conflict of interest statement
    Funding This study was supported by a Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (NRF-2016R1C1B1013621).
    Authorship contribution statement
    Acknowledgments This study used data from the Korean Genome Analysis Project (4845-301), the Korean Genome and Epidemiology Study (4851-302), and the Korea Biobank Project (4851-307, KBP-2014-041), which were supported by the Korea Centers for Disease Control and Prevention, Republic of Korea.
    Introduction Flexible parametric survival models (FPMs), which were first introduced by Royston and Parmar, have been used in a range of settings [1,2]. The models have been used to estimate survival in epidemiological studies with applications involving international comparisons [3] and they have also been adapted to clinical trials settings [4]. The methodology has been extended to the relative survival framework in population-based data [5]. It has also been used to assess statistical cure [6] and to estimate the loss in life expectancy due to a cancer diagnosis [7]. Population-based studies that include all patients in a geographically-defined Acarbose provide a measure of the effectiveness of the healthcare system in diagnosing and treating the cancers that arise. A commonly reported measure of cancer survival is relative survival, which compares the all-cause survival for a group of cancer patients to the expected survival of a comparable group in the general population that is free of the cancer of interest [8]. An increasing number of population-based studies perform analysis by using FPMs rather than traditional methods [[9], [10], [11]]. The model is fitted on the log cumulative excess hazard scale and directly models the effect of time by using splines. Splines are flexible mathematical functions defined by piecewise polynomials, which under constraints, form a smooth function. The points at which the polynomials join are called knots. The number of knots, or degrees of freedom (df) that is equal to the number of knots minus 1, specified to create the splines determines the number of parameters to model the hazard function [12]. A small debate exists on the number of knots used for the splines. Sensitivity analyses are often conducted to ensure that the df does not influence the estimates. A simulation study, showed that the estimated relative effects are insensitive to the correct specification of the baseline hazard and that, provided enough knots are selected, complex hazard functions can be captured [13]. They also showed that absolute effects are well captured. Another simulation study showed that time-dependent effects can also be captured accurately [14].
    Methods
    Results Data includes a population of more than 1.2 million cancer patients. Patients with Hodgkin lymphoma are the youngest with the average age to be approximately 47 years (Table 1). The oldest are bladder cancer patients, at the mean age of 76 and 74 years for females and males respectively. Table 2A, Table 2B show the differences in the 1-year and 5-year relative survival estimates between the reference model and the model selected by the AIC or BIC criterion. For the age-standardised estimates, absolute differences remain lower than 0.5 percentage point. In specific, absolute differences between the reference model and the model chosen by the AIC criterion, for females, have a median value of 0.083 and a mean of 0.091 percentage points. Similarly, differences with the BIC model have a median and mean equal to 0.80 and 0.110 respectively and differences between the reference model and the Pohar Perme estimates have a median value of 0.182 and mean of 0.213. The age-standardised estimates for colon cancer female patients and prostate cancer patients can also be seen graphically in Fig. 1. The minor differences observed show that the standardised estimates do not depend heavily on the choice of df. The big size of the datasets results in narrow 95% confidence intervals. Detailed plots of standardised relative survival from 18 out of the 60 scenarios can be found in the interactive graphs.