The continuous predictor X is discretized into a categorical covariate X ? with low range (X < Xstep onek), median range (X1k < X < Xdosk), and high range (X > X2k) according to each pair of candidate cut-points.
Then categorical covariate X ? (site peak is the median assortment) is fitted inside the an effective Cox design and concomitant Akaike Information Criterion (AIC) worthy of try computed. The pair off cut-things that minimizes AIC values means max slashed-things. More over, going for reduce-things of the Bayesian suggestions traditional (BIC) has got the exact same performance since the AIC (Even more file step 1: Tables S1, S2 and you may S3).
Execution for the 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.
The newest simulator study
A Monte Carlo simulation studies was used to check the new efficiency of the optimal equal-Hours approach or other discretization tips for christianmingle tanışma sitesi instance the average separated (Median), the upper and lower quartiles viewpoints (Q1Q3), together with minimal log-score attempt p-worth means (minP). To investigate the newest performance of those steps, brand new predictive overall performance of Cox habits installing with assorted discretized parameters is actually assessed.
Design of the newest simulator investigation
U(0, 1), ? is actually the size factor regarding Weibull delivery, v are the shape parameter out of Weibull distribution, x is an ongoing covariate away from a basic normal shipping, and you can s(x) is actually the given intent behind interest. In order to simulate U-molded dating ranging from x and you may journal(?), the form of s(x) is set to be
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.