The continuous predictor X is discretized into a categorical covariate X ? with low range (X < Xstep step step 1k), median range (X1k < X < Xdosk), and high range (X > X2k) according to each pair of candidate cut-points.
Then your categorical covariate X ? (resource height ‘s the median assortment) is equipped during the a good Cox model and also the concomitant Akaike Information Requirement (AIC) worthy of try calculated. The pair of reduce-things that decreases AIC beliefs means optimal clipped-circumstances. Also, going for cut-affairs from the Bayesian recommendations requirement (BIC) has got the same show just like the AIC (Additional file 1: Tables S1, S2 and you may S3).
Execution inside 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 fresh new simulation studies
An effective Monte Carlo simulator study was used to evaluate brand new overall performance of the max equal-Hr approach or any other discretization tips like the median broke up (Median), top of the minimizing quartiles philosophy (Q1Q3), additionally the minimal journal-rank try p-well worth means (minP). To analyze the fresh new efficiency of those tips, the fresh new predictive results from Cox patterns installing with various discretized details was assessed.
Form of the latest simulation data
U(0, 1), ? is the dimensions factor from Weibull shipping, v is actually the proper execution factor out-of Weibull delivery, x is actually a continuous covariate of a basic normal shipments, and you will s(x) is the newest provided aim of attract. So you’re able to simulate U-designed matchmaking between x and record(?), the form of s(x) was set-to feel
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 Ã‘asualDates hesap silme 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.