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The continuous predictor X is discretized into a categorical covariate X ? with low range (X < Xstep step step step 1k), median range (X1k < X < Xdosk), and high range (X > X2k) according to each pair of candidate cut-points.
Then the categorical covariate X ? (reference height is the average diversity) is equipped during the an excellent https://datingranking.net/tr/amateurmatch-inceleme/ Cox design and the concomitant Akaike Suggestions Traditional (AIC) value was computed. The two regarding clipped-things that decreases AIC thinking is defined as optimum reduce-points. More over, opting for cut-factors by Bayesian suggestions expectations (BIC) has the exact same results since AIC (A lot more file step 1: Tables S1, S2 and you may S3).
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.
A Monte Carlo simulation study was applied to check brand new performance of maximum equivalent-Hr method or other discretization steps like the average separated (Median), the top of and lower quartiles values (Q1Q3), plus the minimum diary-review decide to try p-well worth means (minP). To analyze the show of those procedures, brand new predictive performance out-of Cox models fitting with different discretized variables was analyzed.
U(0, 1), ? are the shape factor away from Weibull distribution, v is actually the design factor out of Weibull shipping, x is actually an ongoing covariate regarding a standard normal shipments, and you will s(x) is the newest offered aim of desire. So you can simulate You-designed matchmaking anywhere between x and you may journal(?), the form of s(x) was 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.