R software version 4

SPSS 25.0 software (IBM Corp.) and R software version 4.1.1 were both used to update all statistical analyses. Continuous variables were presented as medians (ranges) and assessed through the Mann–Whitney U test. Categorical variables were expressed as percentages and applied for the chi‐squared test. Few PD‐L1‐negative patients are currently treated with immunotherapy, and to minimize the potential confounding effect and to derive well‐matched cohorts, a 1:2 propensity score matching (PSM) approach was used to match different patients who underwent chemotherapy combined with anti‐vascular therapy with patients who underwent chemotherapy combined with immunotherapy. A non‐replacement nearest neighbor matching algorithm was used to ensure a suitable match. Life curves were calculated by the Kaplan–Meier method and measured using the log‐rank test. A p‐value <0.05 in a two‐tailed test was considered a statistically notable difference.

Statistical analysis was performed by a biostatistician (K. H., with 16 years of experience) using SPSS software version 25.0 (IBM Corp., Armonk, NY, USA) and R software version 4.1.1 (https://www.R-project.org/, Vienna, Austria). The normal distribution of the data was confirmed by the Shapiro–Wilk test. To compare the clinical and radiologic features of the surgery and brace groups, the t-test was used for continuous variables, while the chi-square test was used for categorical variables. The linear mixed model was used to analyze the stiffness of the paraspinal muscles between the surgery and brace groups according to time. Using this model, we considered repeated measurements by incorporating patients as random effects. The fixed effects included treatment (bracing or surgery), time (0, 6, and 12 months), and measurement side (concave or convex). The model incorporated interactions between two factors and three-way interactions between three factors in terms of treatment, time, and measurement side. Means and 95% confidence intervals (CIs) were estimated based on the model with the least square method. P values less than 0.05 were considered statistically significant.

Means and standard deviations were used to describe continuous variables such as age. Chi-square or non-parametric U tests were used for comparison between groups. Other classifications were described by frequency (%), and the differences between the groups were compared using the chi-square test. The Cox regression model analyzed the patient prognostic factors, and the patient survival differences were analyzed by the log-rank test and the K-M curve. Statistical analyses were performed using the R software version 4.1.0 and SPSS26.0.The R package includes "survival,” “ggDCA,” “DynNom,” and “RMS” P values < 0.05 were considered statistically significant.

Mean and standard deviation were used to describe continuous variables (age), and frequency (%) was used to describe other categorical variables (race, marriage, tumor grade, TNM stage, PSA, GS, RT and chemotherapy).Differences between groups were compared using chi-square or non-parametric U-test. The patient prognostic factors were analyzed by the Cox regression model, and the patient survival differences were analyzed by the log-rank test and the K–M curve. Statistical analyses were performed using R software version 4.1.0 and SPSS26.0. The R package includes "survival", "matching", "ggDCA", "DynNom", and "RMS". P values less than 0.05 were considered statistically significant.

Continuous variables like age were described using the mean and the standard deviation. Group comparisons were made using the chi-square test or non-parametric U test. Categorical variables such as tumor size, stage, and surgical method were described by frequency and compared using the chi-square test. A Cox regression model analyzed prognostic influencing factors of the patients, and the log-rank test tested the patient survival differences. Statistical analysis was performed using the R software version 4.1.0 and SPSS 26.0. The R packages used included "DynNom", "RMS", "Survival", and "ggDCA". p values less than 0.05 were considered statistically significant.

Continuous variables(age) were tested for normal distribution and conform to the normal distribution, described by the mean ± standard deviation. Chi-square or non-parametric U tests were used for comparison between groups. Other categorical variables were described by frequency (%), and the groups were compared using the chi-square test. The Cox regression models analyzed patient prognostic factors, and the log-rank test and K-M curves analyzed the survival differences of patients. All statistical methods were performed using R software version 4.1.0 and SPSS26.0. The R packages including “DynNom”, “RMS”, “Survival”, and “ggDCA” were used. A P value less than 0.05 was considered statistically significant.