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 ? (site peak is the average diversity) is equipped during the a good Cox model and the concomitant Akaike Information Criterion (AIC) worthy of try calculated. The two of slashed-items that decrease AIC opinions is described as optimal clipped-points. Also, choosing reduce-items by the Bayesian advice requirement (BIC) has got the same show since the AIC (Extra file step 1: Dining tables S1, S2 countrymatch incelemesi and you may S3).
Implementation 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 simulator data
An effective Monte Carlo simulator research was utilized to test the brand new abilities of your own optimum equivalent-Time strategy or any other discretization methods for instance the average broke up (Median), the top minimizing quartiles viewpoints (Q1Q3), and minimal record-rank test p-worth method (minP). To research the latest overall performance ones steps, brand new predictive results out of Cox patterns fitting with assorted discretized variables try reviewed.
Form of the newest simulation studies
U(0, 1), ? try the size and style parameter off Weibull shipping, v is actually the shape factor away from Weibull distribution, x is actually a continuing covariate out of a basic regular shipment, and you will s(x) is actually the newest given function of appeal. So you’re able to replicate You-formed relationships between x and you will diary(?), the type of s(x) is actually set to end up being
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.