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 the categorical covariate X ? (site level ‘s the average variety) is fitted in the a great Cox design together with concomitant Akaike Suggestions Traditional (AIC) value try determined. The two regarding cut-things that minimizes AIC values is defined as optimal slash-issues. Furthermore, going for slashed-factors by the Bayesian information criterion (BIC) has got the same results since AIC (Additional file 1: Tables S1, S2 and you may S3).
Implementation in the Roentgen
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 brand new simulator studies
An effective Monte Carlo simulator study was used to check the latest show of optimum equivalent-Hr strategy or other discretization steps for instance the average separated (Median), top of the and lower quartiles beliefs (Q1Q3), and the lowest journal-score test p-really worth means (minP). To analyze the brand new performance of those strategies, new predictive results away from Cox activities fitting with different discretized variables are examined.
Type of the new simulation studies
U(0, 1), ? was the size and style parameter out-of Weibull shipping, v is the proper execution factor away from Weibull shipment, x was an ongoing covariate out-of an elementary regular shipment, and you can s(x) are the fresh considering aim of notice. To help you replicate U-designed matchmaking ranging from x and you will log(?), the type of s(x) are set to getting
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 chatango giriÅŸ 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.