The continuous predictor X is discretized into a categorical covariate X ? with low range (X < Xstep step onek), median range (X1k < X < Xdosk), and high range (X > X2k) according to each pair of candidate cut-points.
Then the categorical covariate X ? (resource top is the average range) is fitted in an excellent Cox model and concomitant Akaike Advice Requirement (AIC) worth try computed. The pair of cut-items that minimizes AIC opinions is understood to be optimum reduce-products. More over, opting for cut-items from the Bayesian guidance traditional (BIC) has the same performance while the AIC (A lot more document 1: Tables S1, S2 and you may S3).
Implementation inside R
The optimal equal-HR method was implemented in the language R (version 3.3.3). The freely available R package ‘survival‘ was used to fit Cox models with P-splines. The R package ‘pec‘ was employed for computing the Integrated Brier Score (IBS). The R package ‘maxstat‘ was used to implement the minimum p-value method with log-rank statistics. And an R package named ‘CutpointsOEHR‘ was developed for the optimal equal-HR method. This package could be installed in R by coding devtools::install_github(“yimi-chen/CutpointsOEHR”). All tests were two-sided and considered statistically significant at P < 0.05.
Brand new simulator study
A great Monte Carlo simulator studies was utilized to test new results of the optimum equal-Hour means or any other discretization methods including the median split (Median), the upper minimizing quartiles opinions (Q1Q3), together www.datingranking.net/tr/chat-zozo-inceleme with minimal log-rank decide to try p-value means (minP). To investigate the latest performance of them tips, the brand new predictive overall performance away from Cox activities fitted with various discretized details are examined.
Design of the fresh simulator investigation
U(0, 1), ? are the size factor out-of Weibull shipments, v are the form parameter off Weibull distribution, x was a continuing covariate out-of a simple normal shipments, and you will s(x) is the latest considering function of attract. To imitate You-formed relationship between x and diary(?), the form of s(x) is set to become
where parameters k1, k2 and a were used to control the symmetric and asymmetric U-shaped relationships. When -k1 was equal to k2, the relationship was almost symmetric. For each subject, censoring time C was simulated by the uniform distribution with [0, r]. The final observed survival time was T = min(T0, C), and d was a censoring indicator of whether the event happened or not in the observed time T (d = 1 if T0 ? C, else d = 0). The parameter r was used to control the censoring proportion Pc.
One hundred independent datasets were simulated with n = 500 subjects per dataset for various combinations of parameters k1, k2, a, v and Pc. Moreover, the simulation results of different sample sizes were shown in the supplementary file, Additional file 1: Figures S1 and S2. The values of (k1, k2, a) were set to be (? 2, 2, 0), (? 8/3, 8/5, ? 1/2), (? 8/5, 8/3, 1/2), (? 4, 4/3, ? 1), and (? 4/3, 4, 1), which were intuitively presented in Fig. 2. Large absolute values of a meant that the U-shaped relationship was more asymmetric than that with small absolute values of a. Peak asymmetry factor of the above (k1, k2, a) values were 1, 5/3, 3/5, 3, 1/3, respectively. The survival times were Weibull distributed with the decreasing (v = 1/2), constant (v = 1) and increasing (v = 5) hazard rates. The scale parameter of Weibull distribution was set to be 1. The censoring proportion Pc was set to be 0, 20 and 50%. For each scenario, the median method, the Q1Q3 method, the minP method and the optimal equal-HR method were performed to find the optimal cut-points.