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I made best-censored success data which have known U-shaped visibility-response relationship

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 categorical covariate X ? (resource height ‘s the median assortment) is fitted during the a beneficial Cox model and concomitant Akaike Advice Standards (AIC) worth is actually determined. The pair out-of reduce-items that decrease AIC philosophy is defined as optimum cut-issues. Furthermore, opting for cut-situations of the Bayesian suggestions standards (BIC) has got the same show since the AIC (Most document step 1: Tables S1, S2 and S3).

Implementation during 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 simulation data

A great Monte Carlo simulation analysis was utilized to test the new overall performance of your optimal equivalent-Hr approach or any other discretization methods like the median split up (Median), the upper minimizing quartiles thinking (Q1Q3), and the minimal journal-score try p-value means (minP). To analyze the latest abilities of these actions, the fresh new predictive efficiency away from Cox designs fitting with assorted discretized variables try assessed.

Model of the new simulation studies

U(0, 1), ? try the size and style factor of Weibull shipments, v is the form parameter away from Weibull shipments, x was a continuous covariate away from a simple regular delivery, and you will s(x) try the brand new provided purpose of attract. To imitate U-shaped matchmaking between x and you can log(?), the form of s(x) is actually set to become

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.

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