The continuous predictor X is discretized into a categorical covariate X ? with low range (X < X1k), chatki ekÅŸi median range (X1k < X < Xdosk), and high range (X > X2k) according to each pair of candidate cut-points.
Then categorical covariate X ? (source top is the average range) is equipped inside a Cox design and the concomitant Akaike Suggestions Standard (AIC) really worth is actually determined. The two away from slashed-items that reduces AIC thinking means optimum slash-affairs. Furthermore, going for clipped-items because of the Bayesian guidance requirement (BIC) comes with the exact same results since the AIC (Extra document 1: Tables S1, S2 and S3).
Execution 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 fresh simulator studies
A good Monte Carlo simulation investigation was used to check on new abilities of one’s maximum equivalent-Hour means or other discretization tips like the median split (Median), the top minimizing quartiles values (Q1Q3), while the minimal journal-rating decide to try p-really worth means (minP). To investigate new results of those tips, the fresh new predictive results out of Cox models fitting with various discretized details was analyzed.
Form of the fresh simulator investigation
U(0, 1), ? are the scale factor away from Weibull shipping, v try the design factor out of Weibull delivery, x try an ongoing covariate from a simple typical shipments, and you will s(x) try this new given function of focus. In order to imitate You-shaped relationship anywhere between x and journal(?), the type of s(x) is actually 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 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.