The continuous predictor X is discretized into a categorical covariate X ? with low range (X < Xstep onek), median range (X1k < X < Xdosk), and high range (X > X2k) according to each pair of candidate cut-points.
Then the categorical covariate X ? (site peak is the average assortment) is fitted inside the an effective Cox model while the concomitant Akaike Pointers Criterion (AIC) well worth try computed. The pair regarding slashed-things that decrease AIC viewpoints is defined as optimum reduce-circumstances. Also, choosing cut-factors because of the Bayesian advice standards (BIC) gets the same abilities just like the AIC (Extra document 1: Dining tables S1, S2 and S3).
Execution in 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 new simulation studies
Good Monte Carlo simulation analysis was applied to test the brand new overall performance of your optimum equivalent-Hour approach or other discretization procedures such as the median separated (Median), the top of and lower quartiles viewpoints (Q1Q3), while the lowest record-review take to p-really worth method (minP). To investigate the newest efficiency of those tips, the predictive abilities out of Cox patterns suitable with assorted discretized variables try assessed.
Style of the new simulator study
U(0, 1), ? was the scale parameter off Weibull shipping, v are the shape factor out of Weibull delivery, x are a continuous covariate out-of a basic normal shipment, and you will s(x) was the newest offered function of attention. To help you simulate U-formed relationships anywhere between x and journal(?), the type of s(x) are 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 ethiopian personals reddit performed to find the optimal cut-points.
