The continuous predictor X is discretized into a categorical covariate X ? with low range (X < X_1k), median range (X_1k < X < X_dosk), and high range (X > X_2k) according to each pair of candidate cut-points.

Then categorical covariate X ? (resource top ‘s the average range) is equipped from inside the an excellent Cox design and the concomitant Akaike Suggestions Standards (AIC) worthy of are computed. The pair off cut-things that decreases AIC thinking is described as optimum clipped-affairs. Additionally, choosing slash-issues because of the Bayesian guidance standards (BIC) provides the same results as the AIC (Even more file step one: Dining tables S1, S2 and you may S3).

Execution inside 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 newest simulator analysis

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A good Monte Carlo simulation analysis was applied to check on the show of one’s max equivalent-Hr means and other discretization measures such as the median split up (Median), the top minimizing quartiles opinions (Q1Q3), while the minimum record-review try p-well worth method (minP). To analyze the fresh new overall performance of those tips, the newest predictive efficiency out-of Cox activities fitted with assorted discretized details are assessed.

Style of the new simulator study

U(0, 1), ? try the scale factor away from Weibull shipment, v is the design parameter regarding Weibull shipments, x was an ongoing covariate out of a standard typical distribution, and you can s(x) was the new given aim of appeal. In order to simulate U-formed matchmaking anywhere between x and you can record(?), the form of s(x) is set-to be

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 P_c.

One hundred independent datasets were simulated with n = 500 subjects per dataset for various combinations of parameters k₁, k₂, a, v and P_c. 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 P_c 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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