Biostatistik II - Day 4 - Survival
Carsten Simonsen
15 nov 2016
Indlæser pakker
Loading required package: HmiscLoading required package: latticeLoading required package: Formula
Attaching package: 'Hmisc'The following objects are masked from 'package:base':
format.pval, round.POSIXt, trunc.POSIXt, unitsLoading required package: SparseM
Attaching package: 'SparseM'The following object is masked from 'package:base':
backsolveData Management og overblik
#Variabelforklaring:
#osm = survival time
#survival = 1
#death = 0
data<- read.dta(file.path("C:/Users/Vision/Desktop/STATISTIK/BIOSTATISTIK2/Nodaold.dta"))
data <-data[,c(1,2,3)] # Sletter unødvendige kolonner
head(data, n=10) # viser første 10 rækker af det tilpassede datasæt survive trt_arm osm
1 1 1 13.568789
2 1 1 11.696099
3 1 1 12.517454
4 1 1 30.652977
5 1 1 2.726899
6 1 1 25.494867
7 1 1 13.305955
8 1 1 16.887064
9 1 1 10.940452
10 1 1 8.180698data$survive <- as.numeric(data$survive)
data$osm<- as.numeric(data$osm) OPG. 1-3) Kaplan Meier for each treatment with confidence intervals
# laver survival objekt:
survobj <- with(data, Surv(osm, survive == 0))
head(survobj)[1] 13.568789+ 11.696099+ 12.517454+ 30.652977+ 2.726899+ 25.494867+#survobj <- as.numeric(data$survobj)
survcompare<-survfit(Surv(data$osm, data$survive)~data$trt_arm, data=data)
summary(survcompare)Call: survfit(formula = Surv(data$osm, data$survive) ~ data$trt_arm,
data = data)
data$trt_arm=1
time n.risk n.event survival std.err lower 95% CI upper 95% CI
0.559 77 1 0.9870 0.0129 0.9620 1.000
2.136 76 1 0.9740 0.0181 0.9391 1.000
2.267 75 2 0.9481 0.0253 0.8998 0.999
2.727 73 1 0.9351 0.0281 0.8816 0.992
4.534 72 1 0.9221 0.0305 0.8641 0.984
4.862 71 1 0.9091 0.0328 0.8471 0.976
4.961 70 1 0.8961 0.0348 0.8305 0.967
5.092 69 1 0.8831 0.0366 0.8142 0.958
5.914 68 1 0.8701 0.0383 0.7982 0.949
6.538 67 1 0.8571 0.0399 0.7824 0.939
7.129 66 1 0.8442 0.0413 0.7669 0.929
7.852 65 1 0.8312 0.0427 0.7516 0.919
8.016 64 1 0.8182 0.0440 0.7364 0.909
8.181 63 1 0.8052 0.0451 0.7214 0.899
8.411 62 1 0.7922 0.0462 0.7066 0.888
8.444 61 1 0.7792 0.0473 0.6919 0.878
9.133 60 1 0.7662 0.0482 0.6773 0.867
9.199 59 1 0.7532 0.0491 0.6629 0.856
9.725 58 1 0.7403 0.0500 0.6485 0.845
9.758 57 1 0.7273 0.0508 0.6343 0.834
9.922 56 2 0.7013 0.0522 0.6062 0.811
10.021 54 1 0.6883 0.0528 0.5923 0.800
10.086 53 1 0.6753 0.0534 0.5784 0.788
10.119 52 1 0.6623 0.0539 0.5647 0.777
10.875 51 1 0.6494 0.0544 0.5511 0.765
10.940 50 1 0.6364 0.0548 0.5375 0.753
10.973 49 1 0.6234 0.0552 0.5240 0.742
11.400 48 1 0.6104 0.0556 0.5106 0.730
11.696 47 1 0.5974 0.0559 0.4973 0.718
11.795 46 1 0.5844 0.0562 0.4841 0.706
12.057 45 1 0.5714 0.0564 0.4709 0.693
12.452 44 1 0.5584 0.0566 0.4578 0.681
12.485 43 1 0.5455 0.0567 0.4448 0.669
12.517 42 2 0.5195 0.0569 0.4191 0.644
12.550 40 1 0.5065 0.0570 0.4063 0.631
12.813 39 1 0.4935 0.0570 0.3936 0.619
13.010 38 1 0.4805 0.0569 0.3809 0.606
13.306 37 1 0.4675 0.0569 0.3684 0.593
13.503 36 1 0.4545 0.0567 0.3559 0.581
13.536 35 1 0.4416 0.0566 0.3435 0.568
13.569 34 1 0.4286 0.0564 0.3311 0.555
13.700 33 1 0.4156 0.0562 0.3189 0.542
15.113 32 1 0.4026 0.0559 0.3067 0.528
15.244 31 1 0.3896 0.0556 0.2946 0.515
15.606 30 1 0.3766 0.0552 0.2826 0.502
15.639 29 1 0.3636 0.0548 0.2706 0.489
15.803 28 1 0.3506 0.0544 0.2587 0.475
16.526 27 1 0.3377 0.0539 0.2470 0.462
16.559 26 1 0.3247 0.0534 0.2353 0.448
16.887 25 1 0.3117 0.0528 0.2237 0.434
17.183 24 1 0.2987 0.0522 0.2121 0.421
17.281 23 1 0.2857 0.0515 0.2007 0.407
17.906 22 1 0.2727 0.0508 0.1894 0.393
18.366 21 1 0.2597 0.0500 0.1781 0.379
19.154 20 2 0.2338 0.0482 0.1560 0.350
19.680 18 1 0.2208 0.0473 0.1451 0.336
22.735 17 1 0.2078 0.0462 0.1343 0.321
23.589 16 1 0.1948 0.0451 0.1237 0.307
25.495 15 1 0.1818 0.0440 0.1132 0.292
26.283 14 1 0.1688 0.0427 0.1029 0.277
27.368 13 1 0.1558 0.0413 0.0927 0.262
29.996 12 1 0.1429 0.0399 0.0827 0.247
30.653 11 1 0.1299 0.0383 0.0728 0.232
34.201 8 1 0.1136 0.0368 0.0602 0.214
37.651 7 1 0.0974 0.0349 0.0482 0.197
56.378 1 1 0.0000 NaN NA NA
data$trt_arm=2
time n.risk n.event survival std.err lower 95% CI upper 95% CI
1.94 77 1 0.9870 0.0129 0.96205 1.000
2.30 76 1 0.9740 0.0181 0.93914 1.000
2.86 75 1 0.9610 0.0221 0.91878 1.000
3.75 74 1 0.9481 0.0253 0.89976 0.999
4.37 73 1 0.9351 0.0281 0.88162 0.992
4.86 72 1 0.9221 0.0305 0.86411 0.984
4.93 71 1 0.9091 0.0328 0.84710 0.976
5.13 70 1 0.8961 0.0348 0.83048 0.967
5.26 69 1 0.8831 0.0366 0.81419 0.958
5.36 68 2 0.8571 0.0399 0.78244 0.939
5.49 66 1 0.8442 0.0413 0.76691 0.929
5.52 65 1 0.8312 0.0427 0.75157 0.919
5.82 64 1 0.8182 0.0440 0.73641 0.909
5.88 63 1 0.8052 0.0451 0.72142 0.899
5.95 62 1 0.7922 0.0462 0.70658 0.888
5.98 61 1 0.7792 0.0473 0.69187 0.878
6.05 60 1 0.7662 0.0482 0.67730 0.867
6.18 59 1 0.7532 0.0491 0.66285 0.856
6.37 58 1 0.7403 0.0500 0.64852 0.845
6.47 57 1 0.7273 0.0508 0.63430 0.834
6.57 56 1 0.7143 0.0515 0.62019 0.823
6.67 55 1 0.7013 0.0522 0.60617 0.811
6.80 54 1 0.6883 0.0528 0.59226 0.800
7.10 53 1 0.6753 0.0534 0.57843 0.788
7.26 52 1 0.6623 0.0539 0.56470 0.777
7.56 51 1 0.6494 0.0544 0.55106 0.765
7.95 50 1 0.6364 0.0548 0.53750 0.753
8.02 49 1 0.6234 0.0552 0.52402 0.742
8.11 48 2 0.5974 0.0559 0.49732 0.718
8.34 46 1 0.5844 0.0562 0.48408 0.706
8.38 45 1 0.5714 0.0564 0.47093 0.693
8.71 44 1 0.5584 0.0566 0.45785 0.681
8.74 43 1 0.5455 0.0567 0.44484 0.669
9.26 42 1 0.5325 0.0569 0.43191 0.656
9.30 41 1 0.5195 0.0569 0.41906 0.644
9.40 40 1 0.5065 0.0570 0.40628 0.631
9.43 39 2 0.4805 0.0569 0.38094 0.606
9.49 37 1 0.4675 0.0569 0.36838 0.593
9.59 36 1 0.4545 0.0567 0.35589 0.581
9.69 35 1 0.4416 0.0566 0.34348 0.568
9.79 34 2 0.4156 0.0562 0.31888 0.542
10.51 32 1 0.4026 0.0559 0.30670 0.528
10.84 31 1 0.3896 0.0556 0.29459 0.515
11.76 30 1 0.3766 0.0552 0.28256 0.502
12.58 29 1 0.3636 0.0548 0.27061 0.489
12.81 28 1 0.3506 0.0544 0.25874 0.475
13.14 27 1 0.3377 0.0539 0.24696 0.462
13.27 26 1 0.3247 0.0534 0.23526 0.448
13.34 25 1 0.3117 0.0528 0.22365 0.434
13.54 24 1 0.2987 0.0522 0.21213 0.421
13.86 23 1 0.2857 0.0515 0.20070 0.407
14.03 22 1 0.2727 0.0508 0.18938 0.393
14.65 21 1 0.2597 0.0500 0.17815 0.379
14.69 20 1 0.2468 0.0491 0.16702 0.365
15.01 19 1 0.2338 0.0482 0.15601 0.350
15.28 18 1 0.2208 0.0473 0.14512 0.336
15.47 17 1 0.2078 0.0462 0.13435 0.321
15.54 16 1 0.1948 0.0451 0.12370 0.307
15.87 15 1 0.1818 0.0440 0.11320 0.292
16.26 14 1 0.1688 0.0427 0.10285 0.277
16.36 13 1 0.1558 0.0413 0.09267 0.262
16.46 12 2 0.1299 0.0383 0.07285 0.232
17.41 10 1 0.1169 0.0366 0.06326 0.216
17.61 9 1 0.1039 0.0348 0.05392 0.200
18.79 8 1 0.0909 0.0328 0.04486 0.184
18.99 7 1 0.0779 0.0305 0.03614 0.168
19.29 6 1 0.0649 0.0281 0.02782 0.152
21.75 5 1 0.0519 0.0253 0.02001 0.135
38.57 3 1 0.0346 0.0220 0.00997 0.120plot(survcompare, conf.int = TRUE, col=c("blue", "red"), xlab = "Survival (Months)", ylab="Survival (proportion)")
legend(30,1, c("treat_arm 1", "treat_arm 2"), col=c("blue","red"), lwd=0.5)
title("Survival by treatment with 95% conf.intervals")
Her ses at usikkerhedden bliver stor og overlappende efter 20 måneder.
OPG 4 - Er der forskel på de to behandlinger?
##7 sample test
survdiff(Surv(data$osm, data$survive)~data$trt_arm, data=data)Call:
survdiff(formula = Surv(data$osm, data$survive) ~ data$trt_arm,
data = data)
N Observed Expected (O-E)^2/E (O-E)^2/V
data$trt_arm=1 77 70 87.7 3.56 9.41
data$trt_arm=2 77 74 56.3 5.54 9.41
Chisq= 9.4 on 1 degrees of freedom, p= 0.00215 Der er altså forskel på de 2 behandlingsarme
Med COX
coxph<-(coxph(Surv(data$osm, data$survive)~data$trt_arm, data=data))
coxphCall:
coxph(formula = Surv(data$osm, data$survive) ~ data$trt_arm,
data = data)
coef exp(coef) se(coef) z p
data$trt_arm 0.516 1.675 0.170 3.04 0.0024
Likelihood ratio test=9.19 on 1 df, p=0.00244
n= 154, number of events= 144