The continuous predictor X is discretized into a categorical covariate X ? with low range (X < Xstep 1k), median range (X1k < X < Xdosk), and high range (X > X2k) according to each pair of candidate cut-points.
Then the categorical covariate X ? (source level is the average assortment) is equipped in good Cox design as well as the concomitant Akaike Advice Traditional (AIC) worth try determined. The pair regarding slashed-issues that decrease AIC viewpoints is understood to be optimal reduce-points. Furthermore, opting for slash-situations from the Bayesian guidance criterion (BIC) contains the exact same efficiency because the AIC (Even more document 1: Dining tables S1, S2 and you will S3).
Implementation from inside 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 new simulation study
A great Monte Carlo simulator study was utilized to check the fresh new efficiency of your max equal-Hour method or any other discretization procedures for instance the median broke up (Median), the top minimizing quartiles viewpoints (Q1Q3), as well as the minimum diary-review take to p-well worth means (minP). To research brand new results of these tips, new predictive show away from Cox models installing with different discretized parameters was examined.
Form of the simulator analysis
U(0, 1), ? is actually the dimensions parameter of Weibull delivery, v are the shape parameter off Weibull delivery, x is a continuous covariate out-of an elementary regular distribution, and s(x) is the offered function of appeal. To help you simulate U-formed dating ranging from x and you can log(?), the form of s(x) is actually 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 https://datingranking.net/tr/badoo-inceleme/ 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.