The continuous predictor X is discretized into a categorical covariate X ? with low range (X < X1k), median range (X1k < X < Xdosk), and high range (X > X2k) according to each pair of candidate cut-points.
Then categorical covariate X ? (reference peak is the median assortment) is equipped in good Cox model together with concomitant Akaike Suggestions Criterion (AIC) worth try determined. The two off reduce-points that decreases AIC thinking is defined as optimum cut-factors. Moreover, going for cut-products by the Bayesian pointers traditional (BIC) comes with the same overall performance once the blk sorun AIC (More file step 1: Tables S1, S2 and S3).
Implementation when you look at 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 newest simulation investigation
An effective Monte Carlo simulation investigation was applied to check this new overall performance of the maximum equivalent-Hours approach and other discretization procedures including the median separated (Median), the upper minimizing quartiles values (Q1Q3), in addition to minimum log-score attempt p-value strategy (minP). To research the brand new efficiency ones methods, the fresh new predictive abilities of Cox designs fitting with assorted discretized details are examined.
Form of the newest simulator study
U(0, 1), ? is actually the dimensions factor away from Weibull delivery, v is the design parameter off Weibull distribution, x are an ongoing covariate out-of a simple typical delivery, and s(x) is actually brand new given aim of appeal. So you can replicate U-designed relationship anywhere between x and you can 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 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.