R统计第14篇-以TCGA数据案例演示Cox回归分析！不存在学不会
今天是各类统计方法R语言实现的第14期，我们主要介绍Cox回归分析。
Cox回归分析
之前讲到生存分析可以通过K-M生存曲线、logrank检验以及的Cox回归分析实现，其中K-M生存曲线、logrank检验只能针对单个二分类变量进行研究，想要探索连续变量或者多个因素时，则可使用Cox回归分析。
得到的结果中β为回归系数，exp(β)为hazard ratio, 简称HR，含义类似于RR。
HR = 1，没有影响。
HR > 1，风险增加，该因素为危险因素。
HR < 1，风险降低，该因素为保护因素。
数据整理
Cox回归分析全称为cox等比例风险回归模型。
此处使用的是TCGA肝癌的数据，数据经下载整理，此处仍需再次整理。
# 载入数据
lihc<-read.table("tcga_lihc.tsv",header = T,row.names = 1,quote = "",sep = '\t')
summary(lihc)
## samples sample_type.samples
## TCGA-2V-A95S-01A: 1 Primary Tumor :377
## TCGA-2Y-A9GS-01A: 1 Recurrent Tumor : 3
## TCGA-2Y-A9GT-01A: 1 Solid Tissue Normal: 89
## TCGA-2Y-A9GU-01A: 1
## TCGA-2Y-A9GV-01A: 1
## TCGA-2Y-A9GW-01A: 1
## (Other) :463
## age_at_initial_pathologic_diagnosis tumor_stage.diagnoses
## Min. :16.00 stage i :212
## 1st Qu.:52.00 stage ii :107
## Median :62.00 stage iiia : 80
## Mean :60.26 not reported: 34
## 3rd Qu.:70.00 stage iiib : 12
## Max. :90.00 stage iiic : 11
## NA's :1 (Other) : 13
## neoplasm_histologic_grade OS OS.time
## : 8 Min. :0.000 Min. : 1.0
## G1: 68 1st Qu.:0.000 1st Qu.: 358.0
## G2:227 Median :0.000 Median : 636.0
## G3:153 Mean :0.406 Mean : 876.7
## G4: 13 3rd Qu.:1.000 3rd Qu.:1214.5
## Max. :1.000 Max. :3675.0
## NA's :6 NA's :6
## adjacent_hepatic_tissue_inflammation_extent_type PIK3CA
## :161 Min. :0.2124
## Mild :124 1st Qu.:0.9635
## None :162 Median :1.2005
## Severe: 22 Mean :1.2202
## 3rd Qu.:1.4643
## Max. :2.6090
## NA's :45
## AKT1 PTEN MYC TP53
## Min. :1.461 Min. :0.5392 Min. :0.3709 Min. :0.7284
## 1st Qu.:2.708 1st Qu.:2.4475 1st Qu.:2.7515 1st Qu.:2.3810
## Median :2.963 Median :2.7105 Median :3.9235 Median :2.9070
## Mean :2.976 Mean :2.7179 Mean :3.6971 Mean :2.8948
## 3rd Qu.:3.321 3rd Qu.:3.0350 3rd Qu.:4.7097 3rd Qu.:3.4730
## Max. :4.786 Max. :4.1610 Max. :7.0430 Max. :5.2620
## NA's :45 NA's :45 NA's :45 NA's :45
可以看到该数据包含样本名称，属于原发、复发还是癌旁，诊断年龄，分期，分级，OS状态，OS时间，癌旁炎症情况，还有几个癌基因/抑癌基因的log2(FPKM+1)
此处简单将有缺失值的样本删去，将癌旁和复发样本删去，将stage分为1、2、3、4，grade转化为1，2，3，4，癌旁炎症情况转换为1，2，3。当然也可考虑使用一些缺失值填充的方法，可以保留更多的样本。
lihc<-lihc[lihc$sample_type.samples=="Primary Tumor",]
lihc<-na.omit(lihc)
lihc<-lihc[,-c(1,2)]
lihc<-lihc[! lihc$tumor_stage.diagnoses =="not reported" & ! lihc$neoplasm_histologic_grade == "" &
! lihc$adjacent_hepatic_tissue_inflammation_extent_type == ""& !lihc$tumor_stage.diagnoses == "(Other)" ,]
summary(lihc)
## age_at_initial_pathologic_diagnosis tumor_stage.diagnoses
## Min. :16.00 stage i :115
## 1st Qu.:51.00 stage ii : 58
## Median :61.00 stage iiia: 34
## Mean :59.29 stage iiib: 5
## 3rd Qu.:69.00 stage iiic: 4
## Max. :84.00 stage iii : 2
## (Other) : 3
## neoplasm_histologic_grade OS OS.time
## : 0 Min. :0.0000 Min. : 1.0
## G1: 24 1st Qu.:0.0000 1st Qu.: 409.0
## G2:115 Median :0.0000 Median : 662.0
## G3: 77 Mean :0.2805 Mean : 960.1
## G4: 5 3rd Qu.:1.0000 3rd Qu.:1386.0
## Max. :1.0000 Max. :3675.0
##
## adjacent_hepatic_tissue_inflammation_extent_type PIK3CA
## : 0 Min. :0.3078
## Mild : 93 1st Qu.:0.9649
## None :112 Median :1.2170
## Severe: 16 Mean :1.2237
## 3rd Qu.:1.5000
## Max. :2.3290
##
## AKT1 PTEN MYC TP53
## Min. :1.505 Min. :1.095 Min. :0.5372 Min. :0.7284
## 1st Qu.:2.663 1st Qu.:2.439 1st Qu.:2.6570 1st Qu.:2.4230
## Median :2.970 Median :2.704 Median :3.7650 Median :2.9220
## Mean :2.946 Mean :2.724 Mean :3.5609 Mean :2.8823
## 3rd Qu.:3.326 3rd Qu.:3.041 3rd Qu.:4.4950 3rd Qu.:3.5330
## Max. :4.786 Max. :4.161 Max. :7.0430 Max. :5.2620
##
##此处四期太少，归入三期
lihc$tumor_stage.diagnoses<- ifelse(lihc$tumor_stage.diagnoses == "stage i",1,
ifelse(lihc$tumor_stage.diagnoses == "stage ii"|lihc$tumor_stage.diagnoses == "stage iia"|lihc$tumor_stage.diagnoses == "stage iib"|
lihc$tumor_stage.diagnoses == "stage iic",2,3))
##G4太少，归入G3
lihc$neoplasm_histologic_grade<- ifelse(lihc$neoplasm_histologic_grade == "G1",1,
ifelse(lihc$neoplasm_histologic_grade == "G2",2,3))
lihc$adjacent_hepatic_tissue_inflammation_extent_type<-ifelse(lihc$adjacent_hepatic_tissue_inflammation_extent_type == "None",1,
ifelse(lihc$adjacent_hepatic_tissue_inflammation_extent_type == "Mild",2,3))
summary(lihc)
## age_at_initial_pathologic_diagnosis tumor_stage.diagnoses
## Min. :16.00 Min. :1.000
## 1st Qu.:51.00 1st Qu.:1.000
## Median :61.00 Median :1.000
## Mean :59.29 Mean :1.697
## 3rd Qu.:69.00 3rd Qu.:2.000
## Max. :84.00 Max. :3.000
## neoplasm_histologic_grade OS OS.time
## Min. :1.000 Min. :0.0000 Min. : 1.0
## 1st Qu.:2.000 1st Qu.:0.0000 1st Qu.: 409.0
## Median :2.000 Median :0.0000 Median : 662.0
## Mean :2.262 Mean :0.2805 Mean : 960.1
## 3rd Qu.:3.000 3rd Qu.:1.0000 3rd Qu.:1386.0
## Max. :3.000 Max. :1.0000 Max. :3675.0
## adjacent_hepatic_tissue_inflammation_extent_type PIK3CA
## Min. :1.000 Min. :0.3078
## 1st Qu.:1.000 1st Qu.:0.9649
## Median :1.000 Median :1.2170
## Mean :1.566 Mean :1.2237
## 3rd Qu.:2.000 3rd Qu.:1.5000
## Max. :3.000 Max. :2.3290
## AKT1 PTEN MYC TP53
## Min. :1.505 Min. :1.095 Min. :0.5372 Min. :0.7284
## 1st Qu.:2.663 1st Qu.:2.439 1st Qu.:2.6570 1st Qu.:2.4230
## Median :2.970 Median :2.704 Median :3.7650 Median :2.9220
## Mean :2.946 Mean :2.724 Mean :3.5609 Mean :2.8823
## 3rd Qu.:3.326 3rd Qu.:3.041 3rd Qu.:4.4950 3rd Qu.:3.5330
## Max. :4.786 Max. :4.161 Max. :7.0430 Max. :5.2620
str(lihc)
## 'data.frame': 221 obs. of 11 variables:
## $ age_at_initial_pathologic_diagnosis : int 84 82 81 81 80 80 80 79 79 78 ...
## $ tumor_stage.diagnoses : num 1 2 1 1 3 1 1 2 2 1 ...
## $ neoplasm_histologic_grade : num 2 2 3 2 2 2 2 1 2 2 ...
## $ OS : int 0 1 1 0 1 1 0 0 0 1 ...
## $ OS.time : int 10 848 410 1168 1210 688 673 1241 387 1694 ...
## $ adjacent_hepatic_tissue_inflammation_extent_type: num 1 1 1 1 1 2 3 1 1 1 ...
## $ PIK3CA : num 1.03 1.61 1.94 1.04 1.22 ...
## $ AKT1 : num 4.79 3.88 3.02 2.7 3.59 ...
## $ PTEN : num 2.44 2.66 3.08 3.02 2.67 ...
## $ MYC : num 3.38 1.32 5.41 3.85 3.69 ...
## $ TP53 : num 0.882 2.604 5.262 3.719 2.878 ...
整理完毕。
首先查看分期
##此处查看分期是否是肝癌的危险因素
library("survival")
## Warning: package 'survival' was built under R version 3.6.3
library("survminer")
## Warning: package 'survminer' was built under R version 3.6.3
## Loading required package: ggplot2
## Warning: package 'ggplot2' was built under R version 3.6.3
## Loading required package: ggpubr
## Loading required package: magrittr
fit <- coxph(Surv(OS.time, OS) ~ tumor_stage.diagnoses, data = lihc)
print(fit)
## Call:
## coxph(formula = Surv(OS.time, OS) ~ tumor_stage.diagnoses, data = lihc)
##
## coef exp(coef) se(coef) z p
## tumor_stage.diagnoses 0.4904 1.6330 0.1485 3.303 0.000956
##
## Likelihood ratio test=10.66 on 1 df, p=0.001097
## n= 221, number of events= 62
res.sum <- summary(fit)
res.sum
## Call:
## coxph(formula = Surv(OS.time, OS) ~ tumor_stage.diagnoses, data = lihc)
##
## n= 221, number of events= 62
##
## coef exp(coef) se(coef) z Pr(>|z|)
## tumor_stage.diagnoses 0.4904 1.6330 0.1485 3.303 0.000956 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## tumor_stage.diagnoses 1.633 0.6124 1.221 2.185
##
## Concordance= 0.609 (se = 0.038 )
## Likelihood ratio test= 10.66 on 1 df, p=0.001
## Wald test = 10.91 on 1 df, p=0.001
## Score (logrank) test = 11.43 on 1 df, p=7e-04
此处p<0.05，exp(coef) = 1.6330，表明分期是肝癌的危险因素。
三个p值的含义：似然比检验，Wald检验和Score (logrank)检验 ，三者几乎等价。对于足够大的样本量，可得到的类似的结果。对于较小的样本量，它们可能有所不同。对于小样本量，似然比检通常优选。
再看分级
library("survival")
library("survminer")
fit <- coxph(Surv(OS.time, OS) ~ neoplasm_histologic_grade, data = lihc)
print(fit)
## Call:
## coxph(formula = Surv(OS.time, OS) ~ neoplasm_histologic_grade,
## data = lihc)
##
## coef exp(coef) se(coef) z p
## neoplasm_histologic_grade 0.4762 1.6100 0.2044 2.33 0.0198
##
## Likelihood ratio test=5.69 on 1 df, p=0.01704
## n= 221, number of events= 62
res.sum <- summary(fit)
res.sum
## Call:
## coxph(formula = Surv(OS.time, OS) ~ neoplasm_histologic_grade,
## data = lihc)
##
## n= 221, number of events= 62
##
## coef exp(coef) se(coef) z Pr(>|z|)
## neoplasm_histologic_grade 0.4762 1.6100 0.2044 2.33 0.0198 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## neoplasm_histologic_grade 1.61 0.6211 1.079 2.403
##
## Concordance= 0.618 (se = 0.033 )
## Likelihood ratio test= 5.69 on 1 df, p=0.02
## Wald test = 5.43 on 1 df, p=0.02
## Score (logrank) test = 5.51 on 1 df, p=0.02
此处p<0.05，exp(coef) = 1.6330，表明分级是肝癌的危险因素，
癌旁炎症情况
library("survival")
library("survminer")
fit <- coxph(Surv(OS.time, OS) ~ adjacent_hepatic_tissue_inflammation_extent_type, data = lihc)
print(fit)
## Call:
## coxph(formula = Surv(OS.time, OS) ~ adjacent_hepatic_tissue_inflammation_extent_type,
## data = lihc)
##
## coef exp(coef) se(coef)
## adjacent_hepatic_tissue_inflammation_extent_type 0.1032 1.1087 0.2006
## z p
## adjacent_hepatic_tissue_inflammation_extent_type 0.514 0.607
##
## Likelihood ratio test=0.26 on 1 df, p=0.6102
## n= 221, number of events= 62
res.sum <- summary(fit)
res.sum
## Call:
## coxph(formula = Surv(OS.time, OS) ~ adjacent_hepatic_tissue_inflammation_extent_type,
## data = lihc)
##
## n= 221, number of events= 62
##
## coef exp(coef) se(coef)
## adjacent_hepatic_tissue_inflammation_extent_type 0.1032 1.1087 0.2006
## z Pr(>|z|)
## adjacent_hepatic_tissue_inflammation_extent_type 0.514 0.607
##
## exp(coef) exp(-coef) lower .95
## adjacent_hepatic_tissue_inflammation_extent_type 1.109 0.902 0.7483
## upper .95
## adjacent_hepatic_tissue_inflammation_extent_type 1.643
##
## Concordance= 0.551 (se = 0.039 )
## Likelihood ratio test= 0.26 on 1 df, p=0.6
## Wald test = 0.26 on 1 df, p=0.6
## Score (logrank) test = 0.26 on 1 df, p=0.6
此处p>0.05，表明癌旁炎症浸润对肝癌患者生存没有影响。
年龄
library("survival")
library("survminer")
fit <- coxph(Surv(OS.time, OS) ~ age_at_initial_pathologic_diagnosis , data = lihc)
print(fit)
## Call:
## coxph(formula = Surv(OS.time, OS) ~ age_at_initial_pathologic_diagnosis,
## data = lihc)
##
## coef exp(coef) se(coef) z p
## age_at_initial_pathologic_diagnosis 0.02321 1.02349 0.01063 2.184 0.029
##
## Likelihood ratio test=5.19 on 1 df, p=0.02268
## n= 221, number of events= 62
res.sum <- summary(fit)
res.sum
## Call:
## coxph(formula = Surv(OS.time, OS) ~ age_at_initial_pathologic_diagnosis,
## data = lihc)
##
## n= 221, number of events= 62
##
## coef exp(coef) se(coef) z Pr(>|z|)
## age_at_initial_pathologic_diagnosis 0.02321 1.02349 0.01063 2.184 0.029 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## age_at_initial_pathologic_diagnosis 1.023 0.9771 1.002 1.045
##
## Concordance= 0.569 (se = 0.039 )
## Likelihood ratio test= 5.19 on 1 df, p=0.02
## Wald test = 4.77 on 1 df, p=0.03
## Score (logrank) test = 4.81 on 1 df, p=0.03
此处p<0.05，exp(coef) = 1.02349，表明年龄是肝癌的危险因素，但是影响较小。
PIK3CA、AKT1、PTEN、MYC、TP53
library("survival")
library("survminer")
fit <- coxph(Surv(OS.time, OS) ~ PIK3CA , data = lihc)
print(fit)
## Call:
## coxph(formula = Surv(OS.time, OS) ~ PIK3CA, data = lihc)
##
## coef exp(coef) se(coef) z p
## PIK3CA -0.1256 0.8819 0.3257 -0.386 0.7
##
## Likelihood ratio test=0.15 on 1 df, p=0.6992
## n= 221, number of events= 62
res.sum <- summary(fit)
res.sum
## Call:
## coxph(formula = Surv(OS.time, OS) ~ PIK3CA, data = lihc)
##
## n= 221, number of events= 62
##
## coef exp(coef) se(coef) z Pr(>|z|)
## PIK3CA -0.1256 0.8819 0.3257 -0.386 0.7
##
## exp(coef) exp(-coef) lower .95 upper .95
## PIK3CA 0.8819 1.134 0.4658 1.67
##
## Concordance= 0.516 (se = 0.043 )
## Likelihood ratio test= 0.15 on 1 df, p=0.7
## Wald test = 0.15 on 1 df, p=0.7
## Score (logrank) test = 0.15 on 1 df, p=0.7
此处p>0.05，表明PIK2CA表达情况对肝癌患者生存没有影响。
library("survival")
library("survminer")
fit <- coxph(Surv(OS.time, OS) ~ AKT1 , data = lihc)
print(fit)
## Call:
## coxph(formula = Surv(OS.time, OS) ~ AKT1, data = lihc)
##
## coef exp(coef) se(coef) z p
## AKT1 0.006963 1.006987 0.245491 0.028 0.977
##
## Likelihood ratio test=0 on 1 df, p=0.9774
## n= 221, number of events= 62
res.sum <- summary(fit)
res.sum
## Call:
## coxph(formula = Surv(OS.time, OS) ~ AKT1, data = lihc)
##
## n= 221, number of events= 62
##
## coef exp(coef) se(coef) z Pr(>|z|)
## AKT1 0.006963 1.006987 0.245491 0.028 0.977
##
## exp(coef) exp(-coef) lower .95 upper .95
## AKT1 1.007 0.9931 0.6224 1.629
##
## Concordance= 0.473 (se = 0.042 )
## Likelihood ratio test= 0 on 1 df, p=1
## Wald test = 0 on 1 df, p=1
## Score (logrank) test = 0 on 1 df, p=1
此处p>0.05，表明AKT1表达情况对肝癌患者生存没有影响。
library("survival")
library("survminer")
fit <- coxph(Surv(OS.time, OS) ~ PTEN , data = lihc)
print(fit)
## Call:
## coxph(formula = Surv(OS.time, OS) ~ PTEN, data = lihc)
##
## coef exp(coef) se(coef) z p
## PTEN -0.09515 0.90923 0.28585 -0.333 0.739
##
## Likelihood ratio test=0.11 on 1 df, p=0.7398
## n= 221, number of events= 62
res.sum <- summary(fit)
res.sum
## Call:
## coxph(formula = Surv(OS.time, OS) ~ PTEN, data = lihc)
##
## n= 221, number of events= 62
##
## coef exp(coef) se(coef) z Pr(>|z|)
## PTEN -0.09515 0.90923 0.28585 -0.333 0.739
##
## exp(coef) exp(-coef) lower .95 upper .95
## PTEN 0.9092 1.1 0.5192 1.592
##
## Concordance= 0.507 (se = 0.041 )
## Likelihood ratio test= 0.11 on 1 df, p=0.7
## Wald test = 0.11 on 1 df, p=0.7
## Score (logrank) test = 0.11 on 1 df, p=0.7
此处p>0.05，表明PTEN表达情况对肝癌患者生存没有影响。
library("survival")
library("survminer")
fit <- coxph(Surv(OS.time, OS) ~ MYC , data = lihc)
print(fit)
## Call:
## coxph(formula = Surv(OS.time, OS) ~ MYC, data = lihc)
##
## coef exp(coef) se(coef) z p
## MYC 0.04345 1.04440 0.09827 0.442 0.658
##
## Likelihood ratio test=0.2 on 1 df, p=0.6577
## n= 221, number of events= 62
res.sum <- summary(fit)
res.sum
## Call:
## coxph(formula = Surv(OS.time, OS) ~ MYC, data = lihc)
##
## n= 221, number of events= 62
##
## coef exp(coef) se(coef) z Pr(>|z|)
## MYC 0.04345 1.04440 0.09827 0.442 0.658
##
## exp(coef) exp(-coef) lower .95 upper .95
## MYC 1.044 0.9575 0.8614 1.266
##
## Concordance= 0.531 (se = 0.043 )
## Likelihood ratio test= 0.2 on 1 df, p=0.7
## Wald test = 0.2 on 1 df, p=0.7
## Score (logrank) test = 0.2 on 1 df, p=0.7
此处p>0.05，表明MYC表达情况对肝癌患者生存没有影响。
library("survival")
library("survminer")
fit <- coxph(Surv(OS.time, OS) ~ TP53 , data = lihc)
print(fit)
## Call:
## coxph(formula = Surv(OS.time, OS) ~ TP53, data = lihc)
##
## coef exp(coef) se(coef) z p
## TP53 -0.2363 0.7895 0.1616 -1.462 0.144
##
## Likelihood ratio test=2.1 on 1 df, p=0.1469
## n= 221, number of events= 62
res.sum <- summary(fit)
res.sum
## Call:
## coxph(formula = Surv(OS.time, OS) ~ TP53, data = lihc)
##
## n= 221, number of events= 62
##
## coef exp(coef) se(coef) z Pr(>|z|)
## TP53 -0.2363 0.7895 0.1616 -1.462 0.144
##
## exp(coef) exp(-coef) lower .95 upper .95
## TP53 0.7895 1.267 0.5752 1.084
##
## Concordance= 0.557 (se = 0.047 )
## Likelihood ratio test= 2.1 on 1 df, p=0.1
## Wald test = 2.14 on 1 df, p=0.1
## Score (logrank) test = 2.14 on 1 df, p=0.1
此处p>0.05，表明TP53表达情况对肝癌患者生存没有影响。
看来我对于肝癌的理解还不够深啊，挑选出来的基因表达均对肝癌患者生存没有影响，当然我挑出来的都是肿瘤中经常发生突变的基因，可能突变与否对于患者生存情况影响更大吧。
年龄、分期、分级纳入回归模型
library("survival")
library("survminer")
fit <- coxph(Surv(OS.time, OS) ~ age_at_initial_pathologic_diagnosis + tumor_stage.diagnoses + neoplasm_histologic_grade, data = lihc)
print(fit)
## Call:
## coxph(formula = Surv(OS.time, OS) ~ age_at_initial_pathologic_diagnosis +
## tumor_stage.diagnoses + neoplasm_histologic_grade, data = lihc)
##
## coef exp(coef) se(coef) z p
## age_at_initial_pathologic_diagnosis 0.02699 1.02735 0.01074 2.512 0.012012
## tumor_stage.diagnoses 0.55741 1.74614 0.15315 3.640 0.000273
## neoplasm_histologic_grade 0.56870 1.76596 0.20867 2.725 0.006424
##
## Likelihood ratio test=24.72 on 3 df, p=1.767e-05
## n= 221, number of events= 62
res.sum <- summary(fit)
res.sum
## Call:
## coxph(formula = Surv(OS.time, OS) ~ age_at_initial_pathologic_diagnosis +
## tumor_stage.diagnoses + neoplasm_histologic_grade, data = lihc)
##
## n= 221, number of events= 62
##
## coef exp(coef) se(coef) z Pr(>|z|)
## age_at_initial_pathologic_diagnosis 0.02699 1.02735 0.01074 2.512 0.012012
## tumor_stage.diagnoses 0.55741 1.74614 0.15315 3.640 0.000273
## neoplasm_histologic_grade 0.56870 1.76596 0.20867 2.725 0.006424
##
## age_at_initial_pathologic_diagnosis *
## tumor_stage.diagnoses ***
## neoplasm_histologic_grade **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## age_at_initial_pathologic_diagnosis 1.027 0.9734 1.006 1.049
## tumor_stage.diagnoses 1.746 0.5727 1.293 2.357
## neoplasm_histologic_grade 1.766 0.5663 1.173 2.658
##
## Concordance= 0.69 (se = 0.033 )
## Likelihood ratio test= 24.72 on 3 df, p=2e-05
## Wald test = 23.63 on 3 df, p=3e-05
## Score (logrank) test = 24.6 on 3 df, p=2e-05
可以看到三个p<0.05（似然比、Wald和Score (logrank)），表明模型是显著的。同时三个协变量均p<0.05，同时HR>1，表明三者均为独立危险因素。
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